July 19 12.00
How to think about ontology
Speaker: David Wallace
Commentator: Robert Geroch
Floor speakers (in order of appearance):
Valentini
Vaidman
Saunders
Hartle
Hemmo
Albert
Bacciagaluppi
Brown
Barbour
Lehner
4
Comment by Geroch
1. I don’t really have either the confidence nor the inclination to try to rebut these remarks, or even to argue them but I thought what I might do is just try to hit a few highlights to just give a few points that struck me. And I have two highlights I’d like to hit, at two and a half minutes per highlight. So the first one, it has to do with the word ‘is’. It seems to me the word is being used in two senses and I wanted to kind of push the idea of making a careful distinction between them. I’m sure there’s a philosophical word for all this but I’m not a philosopher. The first is as in the sentence ‘the cat is in a superposition of the dead state and the live state’. It seems to me that that’s a statement about the theory and so the question – there the statement is is the quantum description of the cat as a superposition? And the answer to that is yes. So that statement is true. A second kind of statement is ‘the cat is either dead or alive’ or, ‘the macro-variables have definite values’ or ‘the Everett branches are real’. Those statements, it seems to me, are not about the theory but they’re about the world. And we get our information about the world, not by osmosis but by doing experiments. So we might imagine that an experiment on the question that the cat is either in the dead state or the alive state. So the experiment might be to have another system, say a particle, turn on an interaction with the cat system through the projection operator onto the live cat state and then – so the result of the interaction is that the state of the particle here will move in one direction corresponding to liveness or deadness, and then we can have a second system that interacts with that and ask whether the wave packet ends up in the middle or ends up moved over to the live cat region or the dead cat region. And the result of that experiment will be that the last apparatus will indeed detect movement of the wave packet. In other words, if we conduct an experiment on the question ‘Is the cat either in a dead state or a live state?’ at least this particular experiment says that the answer is that the cat is indeed either in a dead state or an alive state. So from this point of view, keeping the distinction of the two meanings of the word ‘is’, there would seem to be no conflict between, on the one hand, the statement ‘The cat state is a superposition of live and dead’ and, on the other, the statement that the cat is either in a live state or a dead state, since they’re two different uses of the word ‘is’.
2. The second point I wanted to make is: where do these classical states come from? That’s an issue that we talk about and the answer is, of course, they come from the interactions. In this cat example its because the interaction is with the projection operator onto the live cat state that we get into a “live cat, dead cat” issue. More generally, when we turn on an interaction between a system that we’re interested in and some measuring system we do so through Hermitian operators on the two systems, we turn on the interaction, it gets in this superposition of states corresponding to values of this system and values for the measuring instrument and then we forget about this system and we look at the density operator and we look at the eigenvectors of the density operator and we indeed discover in the cat example that the eigenvectors of the density operator for the cat state that results from this interaction is indeed the live state eigenvector and the dead cat eigenvector. In other words, the classical states in this case, and in general, this is the decoherence argument, come from the interactions that are turned on. So we can now ask the question: how is it that the interactions seem to produce this classical occurrences, classical states, as coming out? So we can ask for example: is it true that all interactions in physics have the property that they single out in this manner the classical states? So if we take the example of a brick and a rabbit, we have a pretty good idea of what interactions take place between a brick and a rabbit and we can ask the question: is it true that brick-rabbit interactions are such that brick states, the density operator on a brick, ultimately has eigenvectors that correspond to classical brick states? And it seems to me that the answer is no. If you just take typical interactions from the physics we know, you do the calculation, you let the thing run for the age of the universe, it seems to me the brick will, quote, “not be in a classical state”. So from this point of view then we conclude that macro-systems would not be in classical states if we regard classical states as arising in this way from interactions.
3. So, we might ask, if macro-systems do not end up being in classical states where do the classical states come from at all and I presume that the place that they come from is people. That we believe - in the case of macro-systems interacting with each other, we pretty much know what the interactions are and we can compute whether the density operators are classical state density operators and the answer’s no. But the hope here is that people are so structured that the interactions that we have with macro-systems in fact are via operators that ultimately give a density operator on the system that indeed corresponds to the classical states. So the kind of mystery here is that our understanding of why systems are in classical states ultimately becomes trying to understand why people seem to manifest the interactions that they do.
Valentini
4. You talked about the quantum state and finding structure in the quantum state. When you say quantum state do you mean pure states?
Wallace
5. I don’t much mind. It seems to me, if I’m saying that the quantum state, we know very little about it other than structure then a corollary of that, I think, is that we don’t find it any more weird to understand the idea of a “mixed” state as a real and physical than a “pure” state. Whether the actual state of the universe is pure or mixed I haven’t a clue. It doesn’t seem to me to particularly matter here. Either way we’re looking for structure in that whole thing, although in practice, of course, we’re looking for structure inside sub-bits of that thing.
Valentini
6. The only reason I ask is that most models of decoherence, or many models of decoherence such as quantum Brownian motion, the sort of thing that Zurek writes about, they are…[noise]……the total state is mixed………..so that’s why……
Wallace
7. The position that says that mixed states are just as fine as pure states seems relatively unpopular amongst philosophers of physics for reasons I don’t understand, though they may be good reasons. My impression is that the use of mixed states in …the Zurek model is an inessential feature, that one could put rather complex stuff in instead but I could be wrong about that.
Vaidman
8. My question ……..you’re supposed to answer but really it’s also for Simon…….otherwise said. You say that we need this decoherence formalism to explain the separation of worlds. As I understand..very simple experiment of a photon, beam-splitter…..detector……Then many-worlds says there are two worlds and standard theory says there’s only one. The decoherence is obvious; there is not any interference whatsoever immediately, no preparation whatsoever you don’t have………..nothing. And if you consider other experiments like, you have a screen and you have diffraction then even in standard quantum mechanics one would start calculating when things are different or not exactly …..worlds?..are different. And when Simon brings this idea that…consistency condition, this is a kind of a consequence. When I have decoherence the probabilities work fine, why do………..these kinds of axioms…..and try to……in all normal cases it has to explain. It seems absolutely obvious; it’s necessary but it’s absolutely obvious.
Wallace
9. …multiple responses. Firstly, of course, what’s obvious to one person isn’t the same for another and not all of us share your genius Lev. Seriously, obviously it wasn’t that nobody had thought of decoherence before Zurek came along, I mean lots knew about decoherence. I think what decoherence brought us was a language and a sort of unified way of thinking, a way of asking questions like: why – sure, situation by situation it’s dead easy to model it, but what are the general features that lead to that sort of thing? And I that language is perspicuous to some, but I think the fact of the decoherence process, what’s driving it, is independent of whether one decides to call it decoherence and what is explained situation by situation. I find the language perspicuous and also very helpful as a way of getting at questions, or sort of seeing the structuralist aspect of this and getting at questions like: what about alternate ways of decomposing the wave function. Look, after all, as Tim Maudlin’s pointed out for instance, configuration space is not, or at least not guaranteed to be, a primary thing. Certainly not the classical configuration space that people talk about classically. So we need to ask something about why that particular decomposition is the thing to think about as special. I think there’s a sort of useful, unified way of thinking about it that makes the right answers to this, which are the answers to say I think, become a bit more obvious and a bit easier to talk about. So I don’t think it’s magic. It’s certainly not a new theory, it’s something that’s always in quantum mechanics.
Vaidman
10. …………………something which is not obvious, which is not obvious other ways? …..necessary to see. You say that the interference…you mentioned, it’s not complete?..there is some residual interference and then it’s a problem. Can you see something….
Wallace
11. I think there aren’t really examples and that’s kind of the point, it’s not a theory about – example by example one’s just doing the physics and if one wants to call it interference, go for it. I think the point is more to get a framework that reassures one in the fact that future examples will also work out that way. Look, the world’s not going to give us a once-and-for-all theorem that says, of course, all phenomenology of the classical world right up to Tony Blair’s resignation is indeed, yes, emergent from quantum mechanics. What one always finds in this situation is a sort of constellation of particular examples and thought experiments and computer simulations and bits of maths and actual experiments and theorems and folk-theorems and plausibility arguments and so on. That’s how we justify the emergence of zoology from molecular physics. That’s what’s going on here really. I think the claim that says one finds emergent quasi-classical structure in the quantum is very, very solidly supported through a range of things. Decoherence is a nice way of talking about a large chunk of that and furthermore a way of putting all of those arguments in place. If you want to be more general, we should expect this to be ubiquitous, here’s why.
Saunders
12. I’d just like to make a comment. Lev, what if some brilliant theorist comes along and finds a very alien……classical domain?..[background hum]….equations will seem to govern the independent autonomous behaviour of worlds, but worlds entirely different to our world. What would you say to that?
Vaidman
13. ..[continuing hum].. If the…worlds…physics is not local…interactions not as strong as here…no questions..Or maybe if the interactions are non-local..have non-local conscious?..objects
Saunders
14. It’s nothing to do with conscious beings, the point is is this or is this not interesting structure in the wave function? Clearly the answer is “yes”. Now, that would be an answer delivered through …direct?..analysis………..You, as an…….taking as….the sorts of experiences?.we have…. can identify very obvious………..decohering states of affairs…photon is registered here, registered there, clearly those are not going to interfere in….it’s obvious. But this alien set of entities, worlds, whatever, is at all obvious, because you don’t happen, as it were, to live in such a world……………
Wallace
15. Simon finds….world much more plausible than I do but-
Saunders
16. ..I agree. Jim I think you speculated on whether there …be……backwards in time relative to us
Hartle
17. Well, we speculated on all sorts of things……..Just to respond, I think what?..Lev is criticising in this approach is that he wants to restrict to?.a certain class of histories…….they’re described in quasiclassical terms, and he would agree that if we calculated…………….But we hope to start from some more general perspective in which all possible kinds of histories .. to be available to describe the world….which ones are more useful…..more reflective of this kind of goddamn?. structure. So, if we start from that perspective then the absence of interference…..necessary to get…probabilities. So it’s just a more general perspective, rather than jumping immediately to the idea that we already know what the top-down structure is – and if we confine ourselves to that we don’t have to worry about this problem?..because we can safely assume…but may be we should …here.
Vaidman
18. …we know the deconherence ..consistent history is zero. You ….be in your talk and say that many worlds [background hum starts again]..as it stands today. Because you spent……ten percent, twenty percent..time..so without this the many-worlds is deficient.
Saunders
19. I did want to remark on this, it’s a very remarkable thing. David Deutsch in his book ‘The Fabric of Reality’ mentions …….[background hum]…….You, Lev, in your Stanford Encyclopaedia article………………..So, it’s very that this way of explicating?..many-worlds………But I think to certain sorts of criticisms of many-worlds, for criticisms which say, look, I don’t even buy that the deterministic evolution can be taken as a given, where we know we’ll get the spin-up state and we measure that spin-up outcome….the criticism that says that is not consistent with unitary quantum mechanics as it stands, you can’t use that fact to leverage the interpretation. To?. that sort of line of criticism, the line of criticism that says: what tells me I’ve got a plurality at all, don’t put the plurality in by hand by talking about a preferred basis or something like that. What tells me there’s a plurality at all that decoheres……One needs……
[new question]
Hemmo
20. I just wanted to ask a quick question about the…..you mentioned of thinking about quantum mechanics……….of a single world………………..and I’m not saying it’s going to be easy to do that but one could see how it would go if we use decoherence as....fundamental?..way. Basically you just do whatever you guys are doing….Everett interpretation and just focus on one of these worlds as the actual one and I’m not saying ..[background hum again]…………..but the two problems you have…….and this is my question, don’t seem to be a problem for this particular……..If they are not a problem for …..[hum]……….
Wallace
21. I think the reasons why don’t think that’s viable are, if you like, quite locked up in some quite general philosophy of science. The reasons why I don’t think the one-world view works are because of two features of this approach which I wouldn’t claim originality for but of the approach I’m describing which work fine for the emerging structure story but not at all for the single world story; one of those is approximation and one of them is the top-down, in terms of higher-level stuff thing. I have nothing original to say as to why this is correct, but we do not think that it’s appropriate in our physics, in our micro-physics, to have fundamental axioms that make reference to all sorts of concepts which we have an irreducibly emergent description of, like structural claims or something like that. We’re fine with that if we can have a clean re-stated starting point but we’re not happy with the idea that you just put it in, if you like, by hand as an axiom. We could have solved the measurement problem like that a very long time ago. It wouldn’t have been, as you said, difficult. I don’t think it’s difficult at all. We could have done that long, long ago. We could have used higher-level terms like ‘conscious observer’ and that would’ve been just fine. We don’t really think that high-level way of talking ..[cross talk] ..it’s not deemed legitimate. For unoriginal reasons; I’ve got nothing new to add to it.
Saunders
22. I think that we can debate whether Copenhagen is acceptable or something but this isn’t what it’s?.about. We are interested in the question of whether Everett flies.
[new question]
Albert
23. This may be a little incoherent, I’m still trying to understand what you said and I think it’s really interesting. I want to point at what look like, at least superficially, fairly strong disanalogies with, say, the shadow matter case and so on and so forth. And I guess I just wanted to comment on these disanalogies. I don’t know if they’re ..[hum]..to the project or not but you didn’t seem to emphasise them in what you said. Look, take a simple branch post-measurement situation where I have branch A with a particle and a measuring device on it and I have branch B with a particle in a different state and maybe a measuring device in a different state on it. And I ask naively a question of the form: look at this quote ‘measuring device’ on branch A; does it have the functional and dispositional properties of the kind of thing we would usually call a measuring device? And somebody naively says, well, no, not at all, look, there’s a B particle right next to it and it’s not reacting to it at all. This seems to be a symptom of the following disanalogy between the examples you use and the kind of emergence that’s going on here. When we talk about the emergence of a tiger we still end up talking about the tiger as a collection of what the fundemental theory regards as fundamental ontological pieces of the world, particles or something like that. Something different seems to be going on here. That is, it looks like the right way to talk about emergence here is that the smallest unit that’s emerging is a world in its entirety rather that its pieces, okay.
24. Look at the shadow-matter case for example. In the shadow-matter case you can say there’s a measuring device here and there’s a shadow-matter measuring device right next to it and there’s a particle here and a shadow-matter particle right next to it. How can there be a measuring device which isn’t responding to the shadow particle in the way we expect measuring devices to react to particles? Answer: it’s not a particle, it’s a shadow-particle, it has quite different properties and there are different properties intrinsic to it which explain the dispositions of the measuring device to react or not to react to it. That’s apparently not going to be an available strategy in this case. In this case the overall structure of the wave function is determining which entire worlds emerge…and it doesn’t seem like we’re going to have the option to say about these worlds that emerge, oh, here’s how you make this world: you put in a tiger and you put in a lion and you put in a person and you put in a measuring device – something like that. If we just put those in we’re going to be missing, as it were, these world-membership relations among them that have to go along with it. So, that does seem like a disanalogy with the other cases of emergence. If we were committed to a claim of the form: worlds are the kinds of things that can be build up by putting in a lion and putting in a tiger and putting in a building and stuff like that then these aren’t going to count as worlds. Then we haven’t shown and emergence of worlds; this is a mysterious new kind of, on the emergent level, fundamental object. There’s a world, okay, and there’s some membership relation to a world that objects have or something like that. Rather than a world being a straightforward collection of these objects in the way that it is in these other emergence theories. I don’t have more to say than that and I don’t know how serious a worry this is, if at all, but it does seem disanalogous to the things that you were trying to draw an analogy to.
Wallace
25. Okay, great, there’s lots to respond to in that. The first point is, I don’t know how important it is, but I don’t find myself that the idea that fundamentally for?..things like cats and tigers the important thing is something like that they should fundamentally be thought of as a collection of stuff. I think the notion in which large things are collections of small things is derivative on the way in which they’re structured….small things rather than vice versa for reasons….
Albert
26. I just want to check one more thing, I’m sorry, but relevant to what you’re saying. Look at the simulation of a tiger on a computer. It’s easy to say why it’s not a tiger, it doesn’t have the functional properties of tigers, I can put a real mouse right in front of it and it won’t react at all.
Wallace
27. So, yes, I’m not sure how important it is. I think that sort of compositionality I’m not really happy with for reasons that James Ladyman’s done a lot more to spell out than I know what to say. I think that a lot of these analogies…..[hum]……these are not things in space. If we feel irreducibly committed to all of our relevant emergences being talked about in spatial terms then I think Everett has problems, I think that’s a profound mistake for general reasons I was trying to sketch out. What one’s got here, if you like, is a relation of dynamical distance such that if things are in this relation they can be dynamically isolated, which is not spatiotemporal..
Albert
28. ……It’s not like the shadow-matter
Wallace
29. ….So, in a sense it is interactional, that’s what the emergent interactions do, they don’t from this bit to that bit. Why is the particle detector on Earth wrong because it fails to detect a particle in the Andromeda galaxy? Answer: they’re spatially distant. Why is my detector bad because it doesn’t detect the particle which, assuming we can do spatial maps at all, is in a different world but in this spatial location? Answer: it’s distant in norm. The shadow matter thing…it doesn’t have that spatial thing and I that cashing that out in terms of intrinsic properties would quite surface. It would be dead easy to develop an example in a way that moves a bit away from the actual physics we have and say that essentially one has something at least relational?..here. We’re not generally inclined, at least I’m not generally inclined to say that the difference between positively and negatively charged things is that they have different intrinsic properties, one of positive charge and one of negative charge, it’s that they stand in the opposite-charge relation. So in the shadow matter case they stand in the different-in-shadowness relation and the reason I call the shadow ‘shadow’ is parochial.
30. And so, lastly, in terms of the tiger simulation, again, sure, you’re quite right, that’s one of the reasons we don’t call it a real tiger but that’s very much what I was calling….a ‘parochial’ problem with it. If we – okay, this is probably controversial and I don’t know if we have to accept it if we accept the Everett interpretation but I’ll run it anyway – If we lived in the Matrix then the tiger simulation, would we still call it a tiger? Our vocabulary might get terribly confused once we take the red pill and excape the Matrix but prior to that it seems the wrong way to think about the Matrix to say there are no cats, there are no tigers, there is this ….The right thing to say about the Matrix seems to be we’re wrong about the substratum which instantiates tigers, cats,….So it’s for parochial reasons there that we don’t call the computerised tiger a tiger, not fundamental reasons.
[new question]
Bacciagaluppi
31. [background hum again] …..Simon..explain a bit more what you were saying about differences between relative states and many worlds and, David, I didn’t understand what the…..problem some philosophers have
Saunders
32. I think the short answer is more or less what I said: use local projections. And consider dynamical structure that can be defined in those terms. I think it’s very clear that one can do that over small macroscopic mixtures. I don’t think you can do that in general over small microscopic dimensions. So this would be a different take on how to see structure in the universal state. One builds up from localised…..One can, as it were, build up a universe around us, here, which will be distinguished, that …value-definite over distances…within……macroscopic superpositions. But this is not in contradiction to the picture of worlds, we do have a superposition of worlds. Consider those worlds that coincide on this local state of affairs, and consider the superposition of those, and you regain the localised approach. And what that localised approach does, well, you can do this in spacetime terms, one looks at relations between events and soforth, the difference in Everett is that those relations don’t close in an equivalence relation. You don’t get equivalence relations, you get something much more structured and elaborately structured in the ……universal state. To be quick, but it’s roughly how I see this relational-structural approach.
Wallace
33. The philosophy of physics measurement problem essentially is the view that there is something wrong with quantum mechanics as a physical theory over and above the fact that it fails approximately to reproduce something structurally isomorphic to the pre-quantum world. So, for instance, that there’s a conceptual problem with the GRW theory, leaving aside the structure of the tails, even if the tails were bare?..there would be a problem with the GRW theory and further interpretative work to do with the GRW theory….. not in itself a solution to the measurement problem….It may be a straw man but I think it’s a relevant?.thing…[background hum]..
[new question]
Brown
34. I think it might be useful for some related discussion, David, to say a little bit more…………aside?..which is decoherence evolution……classical…can you say a little more about that.
Wallace
35. Okay, if you take a non-chaotic system without decoherence a coherent state does a pretty good job of tracking the classical dynamics on pretty long timescales. Take a chaotic system without decoherence it doesn’t do that. The reason it doesn’t do that is that what the classical dynamics wants to do is become highly fribrelated and the quantum system can’t cope with that when the fibrelation is thin compared to h-bar so you start getting a violation of quasi-classicality in a certain sense. Throw the environment in and what you find those differences lead effectively to wave-function collapse and the sense in which you map the classical dynamics is that you kind of – effectively what you’re reproducing is a coarse-grainedness of the classical dynamics which means branch by branch what you’ve got is something like a stochastic dynamics. You’ve still got a branch structure, the environment is still recording the full history, you haven’t got a sort of merging together of branches but it’s no longer the case that each branch does something classical because it’s not….in those details. All the sort of examples that get used in chaos theory popularisations are things that lead, if you like, to indeterminacy and to a branching phenomenology. So I don’t regard it as importantly different……..
Valentini
36. Does this mean that – you said something about in a non-chaotic case, in phase space you have different blobs each evolving along approximately classical trajectories
Wallace
37. although not configuration-space isolated blobs, necessarily
Valentini
38. So now does this mean that in the chaotic case you do not get blobs individually tracing out approximately classical trajectories?
Wallace
39. The blob language is confusing because it implies that something ……separating them
Valentini
40. ….assumption……..spreads very quickly
Wallace
41. Yeah, well if you look at that, looking at the density operator you’re seeing it smoothed, if you include the environment what you find is that for each – take the relative state, if you like, to any given little blob in the space what you’ll find is an incoherent superposition of lots of histories describing lots of different ways?..[background hum]..-the environment recording in it lots of different histories describing lots of different ways that got the system fixed up in that place?..It’s still a history structure but you’ve got a dynamics that’s stochastic.
[new question]
Barbour
42. I totally agree that structure’s what counts. I would like to question…[background hum]..justify that you should be looking only at the structure of the universal wave function. I can’t believe really that….completely satisfactory that way because the wave function must have some basis. I personally suspect that it is the configuration basis and I came to this conclusion from supposing that there were super-mathematicians who were looking at our universal wave function and saying: where is the information encoded that we’re in an expanding rather than a contracting universe? And I don’t see that that information can be encoded in the structure of the wave function, I think it must be encoded in the structure of configurations which are favoured by the wave function. And this makes me convinced in a way that quantum mechanics is a dual theory as we have it at the moment, it’s about a wave function and things on which it’s defined and that the interpretation has got to take that into account much more. I think everything you’ve said about decoherence is fine and makes a lot of sense but it’s not going to be the complete story.
Wallace
43. Okay, good. So it’s mistaken to think of the quantum state – and you’re not doing this – as some sort of point in a featureless very high-dimensional complex space, just as it’s wrong to think about classical mechanics as a point in a featureless very high-dimensional ….space. In all these cases that space has to be highly non-isotropic, highly structured so as to make the quantum state a structured thing. There are basically two ways one introduces that sort of structure, one does it by picking out certain operators as preferred, or one picks them out as regarding certain tensor-product decompositions as preferred and of course those are more or less interchangeable. How one does that comes under…the nature of those structure questions I was raising. Of course, if one’s prepared to use a sufficiently cooked-up set of operators one can put structure into anything, that’s an old problem with functionalism, I’ve got nothing new to say to it. If one isn’t going to do that I don’t think there’s an important difference between, say, representing the quantum gravity wave function and …..added structure in terms of the configuration space and thinking of it just in terms of say finding configuration and conjugate…as preferred operators or maybe some other set of operators that’s simply defined in terms of them. Plainly this sort of structural game is very standard. If one does do it in configuration space terms then I think it’s only a semantic distinction to talk about a difference between the wave function and the configuration space on which it’s peaked. I’d say……….that it’s peaked in a certain place this highly……space. What I think is dangerous is to help oneself uncritically to the idea that the right way to think about that configuration is as n particles or whatever because of course that’s not true. I don’t think your making that move….
[new question]
Lehner
44. As a historian, a thing I’d like to point out about Everett himself is that the way he framed his theory was in this very simplistic definition of an observer as a recording device, right. And it seems like that’s all very badly out of fashion, nobody wants to talk about that any more, and I have a suspicion people think that decoherence is the appropriate modern substitute for this model of the observer that Everett used. And what I just would like to point out is two things. One: the two don’t conflict with each other. Zurek’s claim that recording devices are decoherence-inducing devices, so Everett’s observers is of course in itself a decoherence machine. And secondly, from the societal point of view I do think that Everett’s model is actually a very useful and helpful to discuss a lot of these philosophical, metaphysical point that come up, especially for David Albert’s metaphysical complaints about the Everett interpretation. More helpful, I would claim, than the fog about approximate decoherence which tries to absolutely avoid speaking of …observers. We can speak about …observers and be perfectly functionalistic about it. I totally subscribe to your ringing endorsement of functionalism and I think that’s exactly what Everett is doing; he’s being functionalistic about consciousness in this sense and it perfectly matches with decoherence but it might be actually a very useful way of talking ….
Wallace
45.I think it has fallen out of fashion, I think it’s good that it’s fallen out of fashion, the reason it’s good that it’s fallen out of fashion is, firstly, it avoids having to get entagled by the mind-body problem and it lets us leave the job of understanding conscious observers to the people that ought to, i.e. psychologists. And secondly I think talking that way makes the Everett interpretation sound “even” more weird than it actually is because, to me, leaving aside issues about possibly?.branching into multiple people synchronically, ….the only thing about the Everett universe is that it is much, much bigger than I thought it was. But, if one talks about consciousness one doesn’t mean ……have an actual recovery of quasi-classicality, we might have a recover of the appearance of quasi-classicality but it wouldn’t necessarily be quasi-classicality. One starts talking in I think a very unhelpful way about the fact that there isn’t really any definiteness at all, just an illusion of definiteness. I think those are traps which one is walking on the edge of when one talks about observers too much.
Saturday, September 15, 2007
Transcript discussion Maudlin
July 19 14.00
Can the world be only wave-function?
Speaker: Tim Maudlin
Commentator: Adrian Kent
Floor speakers (in order of appearance):
Albert
Pitowsky
Brown
Wallace
Greaves
Myrvold
Lehner
Barbour
Bacciagaluppi
Saunders
Valentini
16
Comment by Kent
1.I really just want to set out some possible lines of discussion following Tim’s paper rather than trying to supply any answers. So let’s go back to Tim’s starting point to quote: “A common understanding of both many-worlds and of the original version of GRW theory holds that they’re ontologically monistic, postulating only the existence of the wave function and nothing else”. I think, and I hope this is right, we can focus on non-relativistic quantum mechanics here, I think that gets to the heart of the question, without worrying about Minkowski space and quantum field theory let alone quantum gravity. So, it seems to me that there are two possible versions of the common understanding that Tim mentions and at the very least we should be careful to distinguish between them. One version is that these sole ingredients that we have when we’re building an interpretation, the only thing is a ray in an abstract Hilbert space and it’s a time-dependent ray and that’s the end of the story. And if that isn’t the end of the story then, as I think Tim persuasively argued, it does indeed seem very, very hard to see how we’re going to extract a picture of reality that allows us to derive a notion of configuration space and from that to derive a notion of quasi-classical physics taking place in four-dimensional spacetime and tigers roaming around and tigerish things and so on.
2. But another possibility, and it’s one that I think David [Wallace] and Julian already touched on in the discussion this morning, is when we say we wish to interpret the wave function and only the wave function we mean the wave function using all of the mathematical structure of the quantum formalism that defines the wave function. So we do have the abstract Hilbert space of course but we also have the Hamiltonian, we also have operators and, if we’re working with quantum mechanics then operators Xi, Pi where ‘i’ is some sort of abstract label, we have the Heisenberg algebra generated by each of those, and the Hilbert space is a representation of that algebra, we have the symmetry group interchanging the ‘i’s. We have a receipe that, at least formally, allows us to extend the Hilbert space so that we can justify writing down basis vectors X which are eigenvalues of one of the operators Xi, tensor products of such things which correspond to eigenvectors of tensor products of the X operators. And so on. And we could take the wave function representation of a state by taking the quantity psi, the abstract……..and taking it’s inner product with these basis vectors. It may be that I’m still missing a point but it seems to me at that point we have an explicit configuration space representation of the wave function available for interpretation and we can proceed from there.
3. Now certainly, if Everettians ………….do have this possibility in mind they should be explicit that that’s what they’re doing. And it is perhaps true that some authors haven’t always been as clear as they should have been on this point, but it does seem to me, and I’d be very interested to know if Tim and other people agree with this, that that’s a perfectly respectable position, that’s a perfectly respectable starting point for a discussion about ontology. And it seems to me further that probably the most interesting line of debate is between people who start from that point, and say that they can get a completely satisfactory ontology, and those who say, no, even if we are allowed all that ground it’s still going to be and inadequate interpretation in the absence of auxiliary be-ables; in the absence of Bohm particles or GRW flashes or something of the sort. Well, if we get into that debate then, as Tim has rightly stressed, at least one key question is the interpretation of mod. psi squared. We have a solution to the fundamental equations which, arguably at least, looks as though it includes a description of different quasi-classical systems corresponding to different cosmologies, different outcomes to the Big Bang, different measurement outcomes. We need, we know in our bones, we need to be able to treat some of them as negligible, as though they really correspond to nothing in reality; they’re there in the mathematics but they’re not in the physics. We need to do that in order to recover all the empirical successes of Copenhagen quantum theory. And we know we’ve got a procedure for doing that if we can pick out absolute classes of solutions that even in total correspond to very small mod. psi squared and just throw those away. And the interesting question is, at least one of the most interesting questions, I think, in this line of thought, is whether we can really justify that procedure from more fundamental physical principles. And there’ve been some brave, interesting and thoughtful attempts in that direction which I know we’re going to hear much more about later in the meeting.
Maudlin
4. Let me just say a couple of things. One issue when you were saying we have all this other structure, this operator structure. And this comes back to David’s point: what do we mean by structure? I was sort of pushing on the side of a certain ontological point of view that it wasn’t clear to me there was enough structure. When you start singling out mathematical structure, there’s lots of mathematical structure, the question is is there too much mathematical structure because there’s all kinds of operators, right, there’s all kinds of relations among the operators and so on, and it may be that if you focus on some of them you have something that you’re happy with, that someone can understand. If you focus on others of them, you know – the question is is mathematical structure the right kind of structure. I’m not saying I have the answer, I get puzzled about that.
5. There’s another question, this is a point which came up in David Albert’s discussion. It’s not of course just a matter of getting the position representation that you mentioned out, right. In a certain sense the same- I realise? .there’s a configuration space ….mathematically the same thing that corresponds to three particles in a four-dimensional space or four particles in a three-dimensional space or one particle in a twelve-dimensional space. And a lot of David Albert’s discussion is, well, what kind of dynamical considerations might make it plausible to think of this as one of these different things. Now, all of those are of course in position representation so I’m just not sure how much of your remarks – I didn’t want to separate the question of, as it were, picking out something special by say position representation which doesn’t, so far as I can tell, solve this other problem where I’m saying, fine, I’ll give you the position representation. So I’m not sure when you were saying if I have all these other things all that falls out as well
Kent
6. Well, you’re happy to grant choosing the position operator as special
Maudlin
7. The problem I understood I think is there even if I hand you that; I don’t make worries about that . I think I have still have some of the worries I was………..that’s all.
Albert
8. I think this is a really interesting talk and I have tons of questions that I guess I’ll pepper you with in private so let me just ask the most flat-footed one that occurs to me. It seems to me I agree completely that there’s got to be something fairly transparent or fairly perspicuous in the way that the ontology the physics causes? .describes which way the experiment came out or something like that, and that it’s obviously crazy to put ourselves in the position where, as it were, the rules of those links can be arbitrary. And I agree with this terminology of rules and links as ……..and misleading and probably best left behind but, look, take the case of the massy GRW. I’m not terribly sure if I’m joking here or…., okay. Do your game, do your honest flat-footed game with the massy GRW, just draw it in as simple a way as you can on a piece of paper, with the degree of shading proportional to the mass density. Just as with the Bohm case, it looks like we’re going to be able to say: you look at the picture, you ain’t?.going to have no trouble figuring out which way the experiment turned out. But presumably that slogan doesn’t carry the weight with you in this case that does in the Bohm case. Okay, talk a little about that.
Maudlin
9. The funny thing about this is of course I’m not going to be appealing to intuitions of the kind, I mean, much more specific, in other words DavidWallace talked about structure in what is to me a slightly too abstract way. But in this case we agree that in this ontology – let’s suppose we set up this thing originally so there’s a fifty percent chance that the pointer goes this way and a fifty percent chance that it goes that way. For the collapse your really have this. If I draw it and shade it by the density I have a double pointer that has two heads and so on and then you get a collapse and all of a sudden almost all of it’s here. There is this tiny bit there; you agree that no matter how I draw it, if I draw it accurately there’s that other bit there.
Albert
10. But if you draw it accurately and somebody goes and looks at the drawing…..
Maudlin
11. But what I said was we have to worry about when somebody goes to look, I made the assumption, I said I haven’t really solved the problem even in the Bohm case – if the particles were invisible and intangible, right, at some level the interaction with the observer
Albert
12. But Tim we can play that game here too
Maudlin
13. Yes, and you’ll have a high-density observer and a low-density observer. The credentials of the low-density observer, to be an observer, look pretty good to me. And then it’s the structural isomorphism between the low-density guy and the high-density guy is the same in all respects, except the density. And the high and low density parts become causally isolated from each other. My problem is that the low-density guy, his credentials are too good, I mean for me to understand the probabilities in the end, but surely that’s different in the case of Bohm’s theory where there just ain’t a low-density guy.
Pitowsky? –
14. The other observer is really killed. You have a GRW ghost here……..
Maudlin
15. I do have a footnote about this. This si something that David Wallace pointed out, it’s the first time I ever heard of it, about the effect of this exponential drop of the tails. David says he’ll be killed off solely by cancer; that’s what he said to me. But I guess, look, surely none of us thought that was part of our understanding of how GRW worked, right. None of us thought that the exact nature of the exponential drop-off of the tails was really important to the theory. I never thought – I thought it was enough to make it little. And if you made it go down and then had it go flat, or essentially so that it didn’t entirely disrupt the thing, I wouldn’t have thought that that made any conceptual difference with respect to what I thought I was doing. Now we’re going to have to worry about what’s the probability I’m going to die, because I’m the wrong guy, I get distorted and so on.
[new question]
Brown
16. Just a quick, minor question….In our paper David and I didn’t say that everyone agrees that there’s no measurement problem in the case of certain .[noise]….In fact we gave the example of Peter Holland who said very clearly that there is a measurement problem in the case of …………But it’s very curious how few people do say it. It’s almost a hundred percent clear in Bohm’s original writings that he did take the line that there was no measurement problem………[very faint]……….. But now to go on very quickly to the insufficiency of the wave function. Maybe the ‘configuration space’ is a misnomer. But I take it it’s not really a terminological issue and the problem isn’t solved by saying the wave function lives on in a mathematical space that’s called not configuration space. So I take it there’s a real conceptual issue here. But the conceptual issue raises the following question: Would you say that if you consider a world that had a free electromagnetic field defined on three-space, no test particles, no matter, that that theory would likewise be conceptually incoherent?
Maudlin
17. Conceptually incoherent?
Brown
18. Well, because there are no are no objects instantiated at points in? space. They simply have fields on them.
Maudlin
19. I’m not sure how – because it’s a little different from the theories we have. The sort of electromagnetic field that we’re aware of if there are any charged particles around is of course not anything we think we can make up localised objects that look like tables and chairs and so on. So, I mean, “conceptually incoherent”, I’m not sure how I would connect that to an account of our world, the physics of our world.
Brown
20. So it’s not the wave function defined on configuration space results?in?.incoherence, it’s that lacking configurations we can’t account for the fact that we see objects around us that have macroscopic…
Maudlin
21. It would be too strong to say “lacking it”, again, I of course don’t want to foreclose the possibility of understanding things in a way very different than the one that naturally comes to this, and so on. The only point I was trying to make is: if it really is the configurations, and I guess we agree with this, I hope we agree with this, if I’m really entitled to call it configuration space……some object on it, the object somehow clumps up in or kicks out or…some particular point in that space. Because it’s a configuration space there’s also a lot of structure, as it were, to that particular point, right. And it would be very different if it had clumped up somewhere else; there’d be a different structure associated with that and it’s these structures that we can naturally interpret and connect, if it’s configuration space, to what we think is going on around us in the laboratory. And the question is if I don’t have anything that even vaguely looks like that, I’m not sure how I proceed. Now, there are things which are obviously look like that, which is the Bohmian case, and there’s things where it just seems I don’t see any connection at all, which would really be just a field on a very high-dimensional homogeneous space and then we have all kinds of intermediate, you know, we can have compactified dimensions and we can make strings and – there’s all kinds of intermediate steps between the extremes on either side. And I don’t have any pre-established notion about how far you can go along what’s probably a very long slippery slope before I all of a sudden wake up and say I don’t know what I’m doing any more. I don’t have anything very precise. I guess what I’m saying is that one of the things David Wallace characterises as the philosophers’ measurement problem I didn’t really recognise. It sounded like someone saying well …….particles, really particles and I don’t know what’s going on. There are lots of things I can imagine, I don’t have any trouble with compactified dimensions and strings and little foamy stuff. It’s a long way from there to the thing I’m worried about. Is that helpful?
[new question]
Wallace
22. I have a very yes or no quick question, and one longer one. The yes or no answer question is: I said I thought that if we lived in the Matrix, it would be wrong to say we’re not in a lecture room now, and it sounds like you wouldn’t agree with that.
Maudlin
23. Gosh, that question’s a question of philosophy of language, I would have to go into a causal theory of reference…..
Wallace
24. Okay then I’ll withdraw that question. The longer question is about going from a high dimensional space to a low one. I’m kind of uncertain about the rules here, I mean it seems to me a very unsatisfactory account of the way that physics is to be systematically related to our intuitions to say that somehow we can go a certain way away from the manifest image, if you like, but thus far and no further, and I’m a bit worried that if we do that philosophy of physics is in danger of becoming a debate about what my intuitions sets up, but not yours. I don’t have an intuition problem with that sort of higher dimension stuff……….if the higher-dimensional configuration space on which the wave-function lives were genuinely homogeneous possibly, but it’s not homogeneous at all, it’s got a very complicated spatio-temporal structure on it, but I mean…….do you feel you have something critical to say about where that cut is or is just going to be that this is where my intuitions take me?
Maudlin
25. I think that’s a very good question and that’s why I said I don’t have a philosophical analysis that…….my conceptual system baulks here. And that’s why I said at the end the best I can do is – I mean, I hope everyone appreciates the smoothness in the one case and the sort of lack of smoothness in the other case and I agree with you, I can imagine a series of steps and, who knows, maybe an……….psychology, maybe if I were slowly acclimatised, like the frog that boils to death, I could be slowly acclimatised so that in fifty years I became a many-worlds person without realising it. But all I’m doing is reporting the situation in my brain right now.
[new question]
Greaves
26. This is a question about the status of the supervenience rules that you briefly mentioned. An example would be the fuzzy-link semantic rule in GRW. You said: what’s the status of these things, is it okay, in addition to postulating a given fundamental ontology, to introduce a supervenience rule and how is this sort of thing empirically checked? So, I also wonder about the status of these rules but I wonder about that status doesn’t mean that status is obviously suspect so I want to try out on you an hypothesis about that status and see what you think. There seems to me to be self-locating hypotheses in the following sort of sense: so imagine, to make things simple, that we had a purely classical theory, so it’s all just point-particles, and that’s the fundamental ontology, there are ten to the power of ten point-particles and now we want to know what sort of emergent objects there might be in a world that was fundamentally just described by the classical particle theory and we can think of all sorts of composition rules, so maybe this set of 500 particles can be a higher-order object and that set of 264 particles can be a higher-order object. And then we might think that maybe composition doesn’t exhaust the space of possible supervenience rules and maybe we can find some ways of looking for emergent structure other than just this number of particles and that number of particles and by exploring the space of such options we could make a list of possible ways, let’s say, a room full of people with a few tables in it can supervene on the fundamental ontology and of course there are going to have to be some constraints because we don’t want to have to rely on gerrymandered rules so we have to have some naturalness criteria somewhere but it seems to me that the game we’re playing is – I’m just thinking out loud here really – the game is something like: we’re looking for some combination of a postulation of a fundamental ontology and a supervenience rule about how to locate ourselves and our surroundings in that ontology that in combination is empirically adequate.
Maudlin
27. What I’m going to say I don’t think is going to satisfy you but let me say what my problem is. I’m not sure I understand well enough the notion of emergence and supervenience here. Let’s go back to your classical world. You’ve got a certain number of particles, say, in this room and you say here’re all the different ways they can be configured – I have the configuration space and each point is a configuration. Now we have a worry about tables. And I’m not quite sure, when you say I need a rule , what it is – I mean, if I walked into the room and said, look, there’re five tables and the physics tells me here you are, in the configuration space here you are. And I walk into the room and I just look around and say, ah, five tables. We want it to be kind of obvious whether or not that particular configuration - if the configuration corresponded to a smooth distribution of dust we’d say no, no, something’s gone wrong here, you ain’t got five tables and we know that if we had sort of a fifth of it all more-or-less table-shaped and different things we’d be okay. So there’d be obviously good regions and obviously bad regions; are you worried about the edges between the good and bad regions? I’m just not sure where the worry comes in? I mean, did tables emerge in the account I just gave you? I’m really asking for information. Did I need a rule to say – if it’s dust, right, if your particles are evenly distributed, this is not a good candidate for a room with five tables in it. Do I need a rule to tell me that?
Greaves
28. Roughly what’s going on in the dust case is that there does not exist any reasonably natural supervenience rule on which tables can supervene. And what we need from………..fundamental ontology is the existence of some reasonably natural supervenience rule that recovers tables.
Maudlin
29. What you said was really fancy and what I said was really simple; that it was all kind of uniformly distributed then I guess we’d look at that and say you ain’t got five tables. Now, you redescribed what I just said in these very fancy terminology about supervenience rules and so on – What I was trying to say is I’m not aware I was using a supervenience rule. I was using some kind of what? Understanding..
[new question]
Myrvold
30. I’m glad you put the ……..thing up there because I was thinking along those lines and the way I think of that…..if I just give you a mathematical structure I don’t yet have a physical theory, I need what the logical positivists would call correspondence rules to tell me what bits of math map? Onto bits of the world. And it sounded to me like that’s what you were saying when you were saying just having the wave function, that’s not enough, we need some kind of correspondence rules. But then I don’t see why it’s more of a problem than ……..ontology to find out about ……. Take the example of four classical particles and you want to know if they’re in the shape of a tetrahedron. If I just give you a 12-dimentional space and say that’s configuration space for particles I need to tell you which three degrees of freedom belong to one particle and …….before I can give you the tetrahedron. And I think it’s implicit in the ………making a configuration space. Similarly when you’ve got a Hilbert space and you have to say which operators on that Hilbert space correspond to which observables in the world you also have to tell me something about what...........wave function and once you’ve done that it seems like you can do that in any of these theories just by adding correspondence rules…………..but it seems to me essentially the same problem in all of these theories.
Maudlin
31. Okay, yeah, that’s where I disagree and I think this talk about operators and observables is part of the reason which makes the situation so mirky. That is, there is no natural correspondence or relation between a Hermitian matrix, say, and anything that happens in the laboratory. If somebody says, oh, all the Hermitian matrices are observables and I hand you this math and say “go measure that”, right. Of course, you say, that’s not anything I can interpret in and of itself. Notice in the case of the Bohmian theory I didn’t talk about observables, I didn’t talk about matrices, I didn’t talk about…I talked about particles moving around in space; I gave you a world that you recognised without any help. It seems to me you recognised it without any help, as possibly the world you live in. So, I think you’re quite right, if you help yourself to any arbitrarily-definable rules you can solve any problem. What I was trying to point out is that some theories don’t seem to need to do that and in fact most of physics through history didn’t seem to need to do that, it seemed to be doing something else that seemed to be more comprehensible and there is a way to understand quantum mechanics that way, ther’re several ways to understand quantum mechanics that way and to me it’d be preferable if it were like that.
[new question]
Lehner
32. I’m very confused about your confusion so………….[difficult prelude]…….so I take it you would be just as unsatisfied by someone ……..field theory saying we have a quantum field theory with a …..ocentric model, right. That reconstructs any talk of particles as talk about field states. Is that in itself already a problem for you?
Maudlin
33. No
Lehner
34. How come that isn’t and
Maudlin
35. Well it depends what kind of field state. You’re asking two different questions. One is about really quantum field theory. Of course the interpretation of quantum field theory in general is going to inherit all the problems I’m worried about as a quantum theory. But if someone were to say, look, I don’t think there’re particles; I think there’s some kind of field and it lumps up in certain ways and the lumps mover around and – the sort of things we say, gee, so don’t ask yourself in a collision process whether this particle coming in is that one going out because really all you have is a kind of field state that is double-lumpy and goes in and you get a double-lumpy state out and there’s no fact about which one’s going in. I don’t have any problem with any of that. That seems to me in an obvious way – in the same way as if someone says the world is made of little tiny strings wiggling around, I can get my head around that. I can get my head around little compactified dimensions..
Lehner
36. Is the mass density in GRW with mass any different than these little lumps…
Maudlin
37. The problem with the GRW is exactly that you get, because of the decoherence problem, so this is very particular to quantum mechanics and to the decoherence, is that you get these low mass-density objects that become, as it were, causally screened off from the high-density stuff. See, that’s where the difference is. In classical physics, if you tell me (there’s a bit about this in the paper) – in classical physics you tell me, look, just pay attention to the high-density stuff, ignore the low-density stuff, for the purpose of, say, calculating the orbits of the planets. That’s the right thing to do. It’s the right thing to do because why? The high-density stuff pushes the low-density stuff out of the way. Now, you can’t calculate the dynamics of the low-density without taking into accout the high-density stuff. So if I want to know what happens to a single particle in the solar system I’d better know whether Jupiter just went by. So in classical physics there’s a real causal asymmetry. The high-density, as it were, has a very nearly autonomous dynamics in itself, the low-density stuff doesn’t. Because of the decoherence, these things each become autonomous from the other and it’s at that point that it seems much more difficult to understand, if the only difference is this, as it were, pure density, why that would make a difference.
[new question]
Barbour
38. First of all I totally agree with you on the desire for configuration space, following on from what I said before lunch. I couldn’t help feeling a lot of the time that actually you hadn’t got quite clear in your head what a configuration space is and what role it plays both in classical physics and in quantum physics. I was left uncertain about that, and heightened by this: I would say, if it weren’t GRW but it was any sort of many-worlds, any sort of interpretation of quantum mechanics, if you enlarge your system and have ultimately, say, the complete universe you get probabilities for configurations, so your probability will be for a high-density lump and a low-density lump together, all at once, and that’s exactly what we see when we open our eyes, we see a dark cloud and a light cloud in the sky at once, simultaneously. And I think that’s my way of thinking about quantum mechanics. Have I got this completely wrong?
Maudlin
39. I didn’t quite follow. Of course, on the picture I have, there would be a configuration space for the entire universe, we want this to be a universal theory and a single point in that space would specify the exact distribution of whatever the local stuff is everywhere all at once. So I entirely agree with that.
Barbour
40. And what is the problem then with – because this is surely only when GRW introduced the mass distribution …isn’t that the same thing that’s happening there, that they’re contemplating that the ontology is a distribution of mass…perfectly good configuration space. And you collapse to one of those so there wouldn’t be any problem with there being a ……high density somewhere else in space.
Maudlin
41. No, look, I don’t have any problem interpreting what’s going on in the space in the massy GRW case. There’s a perfectly definite distribution of mass-density that’s evolving, although stochastically, in a perfectly definite way. So it’s not that I have any difficulty understanding what the physical postulate is. If we look at the details of that we’ll find some very high-density obects that are living out lives, that look like people moving around and so on, and some very low-density objects that’re also living out lives that rather look like people moving around and so on. This is like the shadow-matter case with the high-density stuff and the low-density stuff not having any particular interesting influence on each other
Barbour
42. ….presumably because the theory’s stochastic, not because it’s not classically dynamic.
Maudlin
43. No, that’s because of the decoherence problem
[new question]
Bacciagaluppi
44. One thing on the decoherence and ………..stuck with that. It’s not clear to me that the low-density guys have the credential…..they’re supposed to have because decoherence only kills off exponentially ………..interference terms but …the repeated GRW hits are going to kill off the on -diagonal terms exponentially in time and so if there’s no discrepancy between the on- and off-diagonal terms for the low-density guys then I’m not sure they have any credentials to real existence.
Maudlin
45. There may be a technical question you’re asking, in which case I may not be competent – Here’s a way I was thinking about it, and maybe I’m just mathematically wrong. So, I was thinking that, look, the low-density guys - of course, with each successive hit they successively become lower and lower density and I’m going to leave aside the problem Lev was worried about, about distorting because the Gaussian drops off so it actually distorts – Suppose it doesn’t. Suppose that all that happens is that from time to time, as it were, in a certain region, the amplitude it taken uniformly down to a millionth of what it just was and so the GRW mass-density is taken down uniformly in this region a million. But the relative distribution of the mass-densities remain the same. So, you know, if this was half as much as that everything gets reduced a million but this is still half of that, everything gets reduced by a million again, half as much as that. So there’s clearly a sense in which there’s a level of structure. If we could find the structure; if we take the decoherence to give you as it were autonomous-looking pieces and we define the structure of the pieces by their relative amplitudes to each other, not their absolute amplitudes which are constantly shrinking, but their relative amplitudes. If I say that’s the relevant level of structure to make a person then the sort of absolute drops don’t seem to be affecting them. They don’t seem to be de-credentialling them. That was the worry. Now maybe I’m wrong at a technical level-
Bacciagaluppi
46. I haven’t done the calculation but …..just a point of intuition………….get from decoherence is not because there are no interference terms it’s because the interference terms are tying……here you have also the amplitude on these….which becomes tying? .both exponentially in time so –
Maudlin
47. I was just assuming and I maybe this is a technical error, I didn’t do any calculation …….go on.
Bacciagaluppi
48. Adrian was saying……..mathematical structure……think there are a set of arguments which have been around in the physics literature which would seem to go some way at least in addressing your problem, namely, say, symmetries, dynamical symmetries, Galilean symmetry in quantum mechanics…..from the abstract Hilbert space to recognisable spacetime descriptions of ……Galilei group is he symmetry group of non-relativistic quantum mechanics. Now, as in the case of Newtonian mechanics, the idea that spacetime just encodes the universal symmetries of the dynamics and seem to go through also in non-relativistic quantum mechanics. Or, look at the structure of the Hamiltonian, we’ve got two operators p and q …..is quadratic? in p there’s a ……..term which is a function of q. That introduces an asymmetry which is not in the……..relations, and so on. Again …..A-group rotations ..allow you to do a tensor decomposition of the Hilbert space into what …………and so on and so forth. Don’t all these results go a long way towards giving you what you want?
Maudlin
49. Let me make a very quick comment because this picks up with the discussion I had with David Albert. Look, there’s no doubt that the structure of the Hamiltonian – there’s a lot of structure in that. The natural way to understand it, and I would make exactly the same claim for the Galilean group and so on, is that the structure of the Hamiltonian is there because you already have a structure because you’re dealing with …….particles in a common space. And you know how to implement the Galilean transformation onto that, right. Now, you could try to go the other way round, I think this is sort of what David has been trying to do, and say no, no, let me just sort of add – there is no further explanation for this, all this interesting structure in the Hamiltonian, it’s just, you know, God decreed the Hamiltonian should have such and such a structure and then we have this discussion. Now, it’s not something I’ve talked about here but it does seem to me – suppose I had two programmes and one programme says, look, here’s a fairly simple, comprehensible, physical ontology. The postulation of that physical ontology implies that there’ll be these certain symmetries in the Hamiltonian, blah, blah, blah. Which you find. And the other one says, my theory says you’ve got a Hamiltonian, it’s got all these interesting symmetries – it becomes even more interesting if you’ve got identical particles because in a certain way the configuration space for identical particles has an interesting topological structure (I shouldn’t go into that). The configuration space has this very interesting structure, the Hamiltonian has this very interesting structure, there is no further story about why it has that structure; it doesn’t arrive from any other fundamental ontology. Interestingly enough it’s exactly the same structure that would arise if the other ontology had been this very simple ontology. At that point I would just say I just actually……….one more plausible theory than the other, as a piece of physics.
[new question]
Saunders
50. I think there’s a certain worry about the nature of the arguments you’ve presented; the target isn’t represented by anybody very well and I don’t know that it’s represented very well by me at any rate. It seems to me that the issue of the Everett interpretation of quantum mechanics isn’t so much “I swear by the wave function and nothing but”. The issue is do we need to change the equations. I sound like Dirac or someone, you know, saying the equations are what matters. Do we need to change the equations? So, I suppose the general point to make is: physicists extract structure from these equations in a very large variety of ways; the issue is can they extract structure from the wave-function. So whether you call that bare wave-functionalism, or not bare because you’ve got all these operators in it, I’m not sure if that’s a very interesting question.
51. But I want to address something else you’ve been saying which I think is important, which is that the present situation is somehow unprecedented. I do wonder about this. The suggestion is that, your suggestion is that in the history of physics normally we haven’t had problems reading off, as it were, form the equations what they say about the world. But I find that, as a rather amateur historian of science, not terribly persuasive. Nor as an amateur historian of philosophy. And that most of the history of modern philosophy has been quite deeply engaged with puzzles about the corpuscularian philosophy as it was called in the seventeenth century and it seems that it’s only consistent? .development is essentially Boscovichian atomism. And it seems to me that Boscovichian atomism is just absolutely not transparent as a description of the world as we see it and I don’t think any philosopher ever found it so. This is a world without smells, without colours, without feels, without warmth. There was a huge project to try to extract an account of those sorts of things, secondary qualities and so on. And typically the business of extracting that account of those secondary qualities was broadly functionalist in many of the ways that David…….was saying…..Now, I agree with you Tim that in quantum mechanics it’s harder. Absolutely. And no one would suggest otherwise. But it doesn’t seem to me that we are in a dramatically different situation and it seems to me further that one would expect it to get harder, as it were, the further one goes into the microworld or very high energy regimes or the early universe……So in a sense I loose any real grip with that we are in some unusual situation.
Maudlin
52. I haven’t done any systematic or even unsystematic survey of how physicists – because the first point you made is, look, physicists are able to extract this structure from the wave-function – do this, but I think it’s pretty clear, and it’s just one guy but he’s an actual physicist…..an actual advocate of the theory, Demore, it’s easy to see how Demore. extracts the structure, he extracts it by taking the configuration space to be a configuration space; gives you a hell of a lot of structure. He doesn’t worry his head about it, and for all practical purposes, having done that, he doesn’t really have much problem. So the fact that physicists can get along and use quantum mechanics perfectly well, of course they can. As soon as you think you’ve got a configuration space – all my arguments are, if it really is a configuration space, if you pretend it is, you know what to do with it and as long as they’re pretending it is of course they’re not going to find they have any analytical difficulties, or practical difficulties.
53. The second point, look, as far as secondary qualities goes, of course, I don’t think physics has ever solved the mind-body problem; I don’t think any physics, Newtonian mechanics, ever told us how things were warm or anything like that. So, it’s not as if I thought earlier physics had solved that problem. What did Newtonian gravitational theory do? It gave us trajectories of planets and cannon balls and stuff like that and we came in thinking we knew a lot about the trajectories of planets and connon balls and stuff like that. In a way, the point that I’m making is: in philosophy there was a sidetrack during the logical empiricist period where the notion was, the evidence is sense data, the evidence is described in experiential terms. And so our job, to connect the physics up to the evidence has to bridge that gap somehow. Of course nobody knew how to do it analytically so what could you do except say, oh, there’s a bridge rule or I’m just going to tell you when such and such occurs then red spot for me here now. Now, that just seems to me to mischaracterise the nature of physics. The level of contact that is made typically, at least in a case like gravitational physics, isn’t at the level of anybody’s experience of anything. It’s at the level of motions of macroscopic objects which could on the one hand in a straightforward way be derived from the theory and on he other hand there’s something we thought that, through various means, we had a pretty good evidential handle on. It’s the absence of that that I think would be unprecedented. The absence of that meeting place between our pre-theoretical understanding of the world and the theoretical understanding.
Saunders
54. So you have no problem with that this table is mostly vacuum…
Maudlin
55. No, none whatsovever. Let me put it this way. If you thought I would have a problem with that you haven’t understood the problem I’ve presented because if you understood the problem you would see that it has nothing to do with – I’ve no problem whatsoever with any of those things. And I don’t think anybody ever did. So long as you say,yeah, the hand - maybe there’re point-like particles and there’s an electromagnetic force so when I try to do this [attempting to pass his hand through the table] I can’t do it. Because they get pushed back, not that they knock against each other – the force goes up, that’s all completely comprehensible. So if you thought I did have problems with that then I’ve really made a mess of trying to explain the problem.
[new question]
Valentini
56. Just a very short comment about history actually. So, you’ve talked about this point that if I don’t have an actual configuration in the theory then what does it mean to say there’s a configuration space? Interestingly enough, exactly the same point was made in 1927 by de Broglie, when he had is pilot-wave theory of an n-body system guided by a Schrodinger wave function. And Schrodinger had his rival theory where he said, no, every is just the wave function and de Broglie, in one of his papers and in his lecture at the fifth Solvay conference in 1927 says precisely this. He gives some criticisms of Schrodinger’s theory and one of them is: what does it mean to say you have this wave function on a configuration space when there’re no configurations. It’s interesting that this puzzle …..
Can the world be only wave-function?
Speaker: Tim Maudlin
Commentator: Adrian Kent
Floor speakers (in order of appearance):
Albert
Pitowsky
Brown
Wallace
Greaves
Myrvold
Lehner
Barbour
Bacciagaluppi
Saunders
Valentini
16
Comment by Kent
1.I really just want to set out some possible lines of discussion following Tim’s paper rather than trying to supply any answers. So let’s go back to Tim’s starting point to quote: “A common understanding of both many-worlds and of the original version of GRW theory holds that they’re ontologically monistic, postulating only the existence of the wave function and nothing else”. I think, and I hope this is right, we can focus on non-relativistic quantum mechanics here, I think that gets to the heart of the question, without worrying about Minkowski space and quantum field theory let alone quantum gravity. So, it seems to me that there are two possible versions of the common understanding that Tim mentions and at the very least we should be careful to distinguish between them. One version is that these sole ingredients that we have when we’re building an interpretation, the only thing is a ray in an abstract Hilbert space and it’s a time-dependent ray and that’s the end of the story. And if that isn’t the end of the story then, as I think Tim persuasively argued, it does indeed seem very, very hard to see how we’re going to extract a picture of reality that allows us to derive a notion of configuration space and from that to derive a notion of quasi-classical physics taking place in four-dimensional spacetime and tigers roaming around and tigerish things and so on.
2. But another possibility, and it’s one that I think David [Wallace] and Julian already touched on in the discussion this morning, is when we say we wish to interpret the wave function and only the wave function we mean the wave function using all of the mathematical structure of the quantum formalism that defines the wave function. So we do have the abstract Hilbert space of course but we also have the Hamiltonian, we also have operators and, if we’re working with quantum mechanics then operators Xi, Pi where ‘i’ is some sort of abstract label, we have the Heisenberg algebra generated by each of those, and the Hilbert space is a representation of that algebra, we have the symmetry group interchanging the ‘i’s. We have a receipe that, at least formally, allows us to extend the Hilbert space so that we can justify writing down basis vectors X which are eigenvalues of one of the operators Xi, tensor products of such things which correspond to eigenvectors of tensor products of the X operators. And so on. And we could take the wave function representation of a state by taking the quantity psi, the abstract……..and taking it’s inner product with these basis vectors. It may be that I’m still missing a point but it seems to me at that point we have an explicit configuration space representation of the wave function available for interpretation and we can proceed from there.
3. Now certainly, if Everettians ………….do have this possibility in mind they should be explicit that that’s what they’re doing. And it is perhaps true that some authors haven’t always been as clear as they should have been on this point, but it does seem to me, and I’d be very interested to know if Tim and other people agree with this, that that’s a perfectly respectable position, that’s a perfectly respectable starting point for a discussion about ontology. And it seems to me further that probably the most interesting line of debate is between people who start from that point, and say that they can get a completely satisfactory ontology, and those who say, no, even if we are allowed all that ground it’s still going to be and inadequate interpretation in the absence of auxiliary be-ables; in the absence of Bohm particles or GRW flashes or something of the sort. Well, if we get into that debate then, as Tim has rightly stressed, at least one key question is the interpretation of mod. psi squared. We have a solution to the fundamental equations which, arguably at least, looks as though it includes a description of different quasi-classical systems corresponding to different cosmologies, different outcomes to the Big Bang, different measurement outcomes. We need, we know in our bones, we need to be able to treat some of them as negligible, as though they really correspond to nothing in reality; they’re there in the mathematics but they’re not in the physics. We need to do that in order to recover all the empirical successes of Copenhagen quantum theory. And we know we’ve got a procedure for doing that if we can pick out absolute classes of solutions that even in total correspond to very small mod. psi squared and just throw those away. And the interesting question is, at least one of the most interesting questions, I think, in this line of thought, is whether we can really justify that procedure from more fundamental physical principles. And there’ve been some brave, interesting and thoughtful attempts in that direction which I know we’re going to hear much more about later in the meeting.
Maudlin
4. Let me just say a couple of things. One issue when you were saying we have all this other structure, this operator structure. And this comes back to David’s point: what do we mean by structure? I was sort of pushing on the side of a certain ontological point of view that it wasn’t clear to me there was enough structure. When you start singling out mathematical structure, there’s lots of mathematical structure, the question is is there too much mathematical structure because there’s all kinds of operators, right, there’s all kinds of relations among the operators and so on, and it may be that if you focus on some of them you have something that you’re happy with, that someone can understand. If you focus on others of them, you know – the question is is mathematical structure the right kind of structure. I’m not saying I have the answer, I get puzzled about that.
5. There’s another question, this is a point which came up in David Albert’s discussion. It’s not of course just a matter of getting the position representation that you mentioned out, right. In a certain sense the same- I realise? .there’s a configuration space ….mathematically the same thing that corresponds to three particles in a four-dimensional space or four particles in a three-dimensional space or one particle in a twelve-dimensional space. And a lot of David Albert’s discussion is, well, what kind of dynamical considerations might make it plausible to think of this as one of these different things. Now, all of those are of course in position representation so I’m just not sure how much of your remarks – I didn’t want to separate the question of, as it were, picking out something special by say position representation which doesn’t, so far as I can tell, solve this other problem where I’m saying, fine, I’ll give you the position representation. So I’m not sure when you were saying if I have all these other things all that falls out as well
Kent
6. Well, you’re happy to grant choosing the position operator as special
Maudlin
7. The problem I understood I think is there even if I hand you that; I don’t make worries about that . I think I have still have some of the worries I was………..that’s all.
Albert
8. I think this is a really interesting talk and I have tons of questions that I guess I’ll pepper you with in private so let me just ask the most flat-footed one that occurs to me. It seems to me I agree completely that there’s got to be something fairly transparent or fairly perspicuous in the way that the ontology the physics causes? .describes which way the experiment came out or something like that, and that it’s obviously crazy to put ourselves in the position where, as it were, the rules of those links can be arbitrary. And I agree with this terminology of rules and links as ……..and misleading and probably best left behind but, look, take the case of the massy GRW. I’m not terribly sure if I’m joking here or…., okay. Do your game, do your honest flat-footed game with the massy GRW, just draw it in as simple a way as you can on a piece of paper, with the degree of shading proportional to the mass density. Just as with the Bohm case, it looks like we’re going to be able to say: you look at the picture, you ain’t?.going to have no trouble figuring out which way the experiment turned out. But presumably that slogan doesn’t carry the weight with you in this case that does in the Bohm case. Okay, talk a little about that.
Maudlin
9. The funny thing about this is of course I’m not going to be appealing to intuitions of the kind, I mean, much more specific, in other words DavidWallace talked about structure in what is to me a slightly too abstract way. But in this case we agree that in this ontology – let’s suppose we set up this thing originally so there’s a fifty percent chance that the pointer goes this way and a fifty percent chance that it goes that way. For the collapse your really have this. If I draw it and shade it by the density I have a double pointer that has two heads and so on and then you get a collapse and all of a sudden almost all of it’s here. There is this tiny bit there; you agree that no matter how I draw it, if I draw it accurately there’s that other bit there.
Albert
10. But if you draw it accurately and somebody goes and looks at the drawing…..
Maudlin
11. But what I said was we have to worry about when somebody goes to look, I made the assumption, I said I haven’t really solved the problem even in the Bohm case – if the particles were invisible and intangible, right, at some level the interaction with the observer
Albert
12. But Tim we can play that game here too
Maudlin
13. Yes, and you’ll have a high-density observer and a low-density observer. The credentials of the low-density observer, to be an observer, look pretty good to me. And then it’s the structural isomorphism between the low-density guy and the high-density guy is the same in all respects, except the density. And the high and low density parts become causally isolated from each other. My problem is that the low-density guy, his credentials are too good, I mean for me to understand the probabilities in the end, but surely that’s different in the case of Bohm’s theory where there just ain’t a low-density guy.
Pitowsky? –
14. The other observer is really killed. You have a GRW ghost here……..
Maudlin
15. I do have a footnote about this. This si something that David Wallace pointed out, it’s the first time I ever heard of it, about the effect of this exponential drop of the tails. David says he’ll be killed off solely by cancer; that’s what he said to me. But I guess, look, surely none of us thought that was part of our understanding of how GRW worked, right. None of us thought that the exact nature of the exponential drop-off of the tails was really important to the theory. I never thought – I thought it was enough to make it little. And if you made it go down and then had it go flat, or essentially so that it didn’t entirely disrupt the thing, I wouldn’t have thought that that made any conceptual difference with respect to what I thought I was doing. Now we’re going to have to worry about what’s the probability I’m going to die, because I’m the wrong guy, I get distorted and so on.
[new question]
Brown
16. Just a quick, minor question….In our paper David and I didn’t say that everyone agrees that there’s no measurement problem in the case of certain .[noise]….In fact we gave the example of Peter Holland who said very clearly that there is a measurement problem in the case of …………But it’s very curious how few people do say it. It’s almost a hundred percent clear in Bohm’s original writings that he did take the line that there was no measurement problem………[very faint]……….. But now to go on very quickly to the insufficiency of the wave function. Maybe the ‘configuration space’ is a misnomer. But I take it it’s not really a terminological issue and the problem isn’t solved by saying the wave function lives on in a mathematical space that’s called not configuration space. So I take it there’s a real conceptual issue here. But the conceptual issue raises the following question: Would you say that if you consider a world that had a free electromagnetic field defined on three-space, no test particles, no matter, that that theory would likewise be conceptually incoherent?
Maudlin
17. Conceptually incoherent?
Brown
18. Well, because there are no are no objects instantiated at points in? space. They simply have fields on them.
Maudlin
19. I’m not sure how – because it’s a little different from the theories we have. The sort of electromagnetic field that we’re aware of if there are any charged particles around is of course not anything we think we can make up localised objects that look like tables and chairs and so on. So, I mean, “conceptually incoherent”, I’m not sure how I would connect that to an account of our world, the physics of our world.
Brown
20. So it’s not the wave function defined on configuration space results?in?.incoherence, it’s that lacking configurations we can’t account for the fact that we see objects around us that have macroscopic…
Maudlin
21. It would be too strong to say “lacking it”, again, I of course don’t want to foreclose the possibility of understanding things in a way very different than the one that naturally comes to this, and so on. The only point I was trying to make is: if it really is the configurations, and I guess we agree with this, I hope we agree with this, if I’m really entitled to call it configuration space……some object on it, the object somehow clumps up in or kicks out or…some particular point in that space. Because it’s a configuration space there’s also a lot of structure, as it were, to that particular point, right. And it would be very different if it had clumped up somewhere else; there’d be a different structure associated with that and it’s these structures that we can naturally interpret and connect, if it’s configuration space, to what we think is going on around us in the laboratory. And the question is if I don’t have anything that even vaguely looks like that, I’m not sure how I proceed. Now, there are things which are obviously look like that, which is the Bohmian case, and there’s things where it just seems I don’t see any connection at all, which would really be just a field on a very high-dimensional homogeneous space and then we have all kinds of intermediate, you know, we can have compactified dimensions and we can make strings and – there’s all kinds of intermediate steps between the extremes on either side. And I don’t have any pre-established notion about how far you can go along what’s probably a very long slippery slope before I all of a sudden wake up and say I don’t know what I’m doing any more. I don’t have anything very precise. I guess what I’m saying is that one of the things David Wallace characterises as the philosophers’ measurement problem I didn’t really recognise. It sounded like someone saying well …….particles, really particles and I don’t know what’s going on. There are lots of things I can imagine, I don’t have any trouble with compactified dimensions and strings and little foamy stuff. It’s a long way from there to the thing I’m worried about. Is that helpful?
[new question]
Wallace
22. I have a very yes or no quick question, and one longer one. The yes or no answer question is: I said I thought that if we lived in the Matrix, it would be wrong to say we’re not in a lecture room now, and it sounds like you wouldn’t agree with that.
Maudlin
23. Gosh, that question’s a question of philosophy of language, I would have to go into a causal theory of reference…..
Wallace
24. Okay then I’ll withdraw that question. The longer question is about going from a high dimensional space to a low one. I’m kind of uncertain about the rules here, I mean it seems to me a very unsatisfactory account of the way that physics is to be systematically related to our intuitions to say that somehow we can go a certain way away from the manifest image, if you like, but thus far and no further, and I’m a bit worried that if we do that philosophy of physics is in danger of becoming a debate about what my intuitions sets up, but not yours. I don’t have an intuition problem with that sort of higher dimension stuff……….if the higher-dimensional configuration space on which the wave-function lives were genuinely homogeneous possibly, but it’s not homogeneous at all, it’s got a very complicated spatio-temporal structure on it, but I mean…….do you feel you have something critical to say about where that cut is or is just going to be that this is where my intuitions take me?
Maudlin
25. I think that’s a very good question and that’s why I said I don’t have a philosophical analysis that…….my conceptual system baulks here. And that’s why I said at the end the best I can do is – I mean, I hope everyone appreciates the smoothness in the one case and the sort of lack of smoothness in the other case and I agree with you, I can imagine a series of steps and, who knows, maybe an……….psychology, maybe if I were slowly acclimatised, like the frog that boils to death, I could be slowly acclimatised so that in fifty years I became a many-worlds person without realising it. But all I’m doing is reporting the situation in my brain right now.
[new question]
Greaves
26. This is a question about the status of the supervenience rules that you briefly mentioned. An example would be the fuzzy-link semantic rule in GRW. You said: what’s the status of these things, is it okay, in addition to postulating a given fundamental ontology, to introduce a supervenience rule and how is this sort of thing empirically checked? So, I also wonder about the status of these rules but I wonder about that status doesn’t mean that status is obviously suspect so I want to try out on you an hypothesis about that status and see what you think. There seems to me to be self-locating hypotheses in the following sort of sense: so imagine, to make things simple, that we had a purely classical theory, so it’s all just point-particles, and that’s the fundamental ontology, there are ten to the power of ten point-particles and now we want to know what sort of emergent objects there might be in a world that was fundamentally just described by the classical particle theory and we can think of all sorts of composition rules, so maybe this set of 500 particles can be a higher-order object and that set of 264 particles can be a higher-order object. And then we might think that maybe composition doesn’t exhaust the space of possible supervenience rules and maybe we can find some ways of looking for emergent structure other than just this number of particles and that number of particles and by exploring the space of such options we could make a list of possible ways, let’s say, a room full of people with a few tables in it can supervene on the fundamental ontology and of course there are going to have to be some constraints because we don’t want to have to rely on gerrymandered rules so we have to have some naturalness criteria somewhere but it seems to me that the game we’re playing is – I’m just thinking out loud here really – the game is something like: we’re looking for some combination of a postulation of a fundamental ontology and a supervenience rule about how to locate ourselves and our surroundings in that ontology that in combination is empirically adequate.
Maudlin
27. What I’m going to say I don’t think is going to satisfy you but let me say what my problem is. I’m not sure I understand well enough the notion of emergence and supervenience here. Let’s go back to your classical world. You’ve got a certain number of particles, say, in this room and you say here’re all the different ways they can be configured – I have the configuration space and each point is a configuration. Now we have a worry about tables. And I’m not quite sure, when you say I need a rule , what it is – I mean, if I walked into the room and said, look, there’re five tables and the physics tells me here you are, in the configuration space here you are. And I walk into the room and I just look around and say, ah, five tables. We want it to be kind of obvious whether or not that particular configuration - if the configuration corresponded to a smooth distribution of dust we’d say no, no, something’s gone wrong here, you ain’t got five tables and we know that if we had sort of a fifth of it all more-or-less table-shaped and different things we’d be okay. So there’d be obviously good regions and obviously bad regions; are you worried about the edges between the good and bad regions? I’m just not sure where the worry comes in? I mean, did tables emerge in the account I just gave you? I’m really asking for information. Did I need a rule to say – if it’s dust, right, if your particles are evenly distributed, this is not a good candidate for a room with five tables in it. Do I need a rule to tell me that?
Greaves
28. Roughly what’s going on in the dust case is that there does not exist any reasonably natural supervenience rule on which tables can supervene. And what we need from………..fundamental ontology is the existence of some reasonably natural supervenience rule that recovers tables.
Maudlin
29. What you said was really fancy and what I said was really simple; that it was all kind of uniformly distributed then I guess we’d look at that and say you ain’t got five tables. Now, you redescribed what I just said in these very fancy terminology about supervenience rules and so on – What I was trying to say is I’m not aware I was using a supervenience rule. I was using some kind of what? Understanding..
[new question]
Myrvold
30. I’m glad you put the ……..thing up there because I was thinking along those lines and the way I think of that…..if I just give you a mathematical structure I don’t yet have a physical theory, I need what the logical positivists would call correspondence rules to tell me what bits of math map? Onto bits of the world. And it sounded to me like that’s what you were saying when you were saying just having the wave function, that’s not enough, we need some kind of correspondence rules. But then I don’t see why it’s more of a problem than ……..ontology to find out about ……. Take the example of four classical particles and you want to know if they’re in the shape of a tetrahedron. If I just give you a 12-dimentional space and say that’s configuration space for particles I need to tell you which three degrees of freedom belong to one particle and …….before I can give you the tetrahedron. And I think it’s implicit in the ………making a configuration space. Similarly when you’ve got a Hilbert space and you have to say which operators on that Hilbert space correspond to which observables in the world you also have to tell me something about what...........wave function and once you’ve done that it seems like you can do that in any of these theories just by adding correspondence rules…………..but it seems to me essentially the same problem in all of these theories.
Maudlin
31. Okay, yeah, that’s where I disagree and I think this talk about operators and observables is part of the reason which makes the situation so mirky. That is, there is no natural correspondence or relation between a Hermitian matrix, say, and anything that happens in the laboratory. If somebody says, oh, all the Hermitian matrices are observables and I hand you this math and say “go measure that”, right. Of course, you say, that’s not anything I can interpret in and of itself. Notice in the case of the Bohmian theory I didn’t talk about observables, I didn’t talk about matrices, I didn’t talk about…I talked about particles moving around in space; I gave you a world that you recognised without any help. It seems to me you recognised it without any help, as possibly the world you live in. So, I think you’re quite right, if you help yourself to any arbitrarily-definable rules you can solve any problem. What I was trying to point out is that some theories don’t seem to need to do that and in fact most of physics through history didn’t seem to need to do that, it seemed to be doing something else that seemed to be more comprehensible and there is a way to understand quantum mechanics that way, ther’re several ways to understand quantum mechanics that way and to me it’d be preferable if it were like that.
[new question]
Lehner
32. I’m very confused about your confusion so………….[difficult prelude]…….so I take it you would be just as unsatisfied by someone ……..field theory saying we have a quantum field theory with a …..ocentric model, right. That reconstructs any talk of particles as talk about field states. Is that in itself already a problem for you?
Maudlin
33. No
Lehner
34. How come that isn’t and
Maudlin
35. Well it depends what kind of field state. You’re asking two different questions. One is about really quantum field theory. Of course the interpretation of quantum field theory in general is going to inherit all the problems I’m worried about as a quantum theory. But if someone were to say, look, I don’t think there’re particles; I think there’s some kind of field and it lumps up in certain ways and the lumps mover around and – the sort of things we say, gee, so don’t ask yourself in a collision process whether this particle coming in is that one going out because really all you have is a kind of field state that is double-lumpy and goes in and you get a double-lumpy state out and there’s no fact about which one’s going in. I don’t have any problem with any of that. That seems to me in an obvious way – in the same way as if someone says the world is made of little tiny strings wiggling around, I can get my head around that. I can get my head around little compactified dimensions..
Lehner
36. Is the mass density in GRW with mass any different than these little lumps…
Maudlin
37. The problem with the GRW is exactly that you get, because of the decoherence problem, so this is very particular to quantum mechanics and to the decoherence, is that you get these low mass-density objects that become, as it were, causally screened off from the high-density stuff. See, that’s where the difference is. In classical physics, if you tell me (there’s a bit about this in the paper) – in classical physics you tell me, look, just pay attention to the high-density stuff, ignore the low-density stuff, for the purpose of, say, calculating the orbits of the planets. That’s the right thing to do. It’s the right thing to do because why? The high-density stuff pushes the low-density stuff out of the way. Now, you can’t calculate the dynamics of the low-density without taking into accout the high-density stuff. So if I want to know what happens to a single particle in the solar system I’d better know whether Jupiter just went by. So in classical physics there’s a real causal asymmetry. The high-density, as it were, has a very nearly autonomous dynamics in itself, the low-density stuff doesn’t. Because of the decoherence, these things each become autonomous from the other and it’s at that point that it seems much more difficult to understand, if the only difference is this, as it were, pure density, why that would make a difference.
[new question]
Barbour
38. First of all I totally agree with you on the desire for configuration space, following on from what I said before lunch. I couldn’t help feeling a lot of the time that actually you hadn’t got quite clear in your head what a configuration space is and what role it plays both in classical physics and in quantum physics. I was left uncertain about that, and heightened by this: I would say, if it weren’t GRW but it was any sort of many-worlds, any sort of interpretation of quantum mechanics, if you enlarge your system and have ultimately, say, the complete universe you get probabilities for configurations, so your probability will be for a high-density lump and a low-density lump together, all at once, and that’s exactly what we see when we open our eyes, we see a dark cloud and a light cloud in the sky at once, simultaneously. And I think that’s my way of thinking about quantum mechanics. Have I got this completely wrong?
Maudlin
39. I didn’t quite follow. Of course, on the picture I have, there would be a configuration space for the entire universe, we want this to be a universal theory and a single point in that space would specify the exact distribution of whatever the local stuff is everywhere all at once. So I entirely agree with that.
Barbour
40. And what is the problem then with – because this is surely only when GRW introduced the mass distribution …isn’t that the same thing that’s happening there, that they’re contemplating that the ontology is a distribution of mass…perfectly good configuration space. And you collapse to one of those so there wouldn’t be any problem with there being a ……high density somewhere else in space.
Maudlin
41. No, look, I don’t have any problem interpreting what’s going on in the space in the massy GRW case. There’s a perfectly definite distribution of mass-density that’s evolving, although stochastically, in a perfectly definite way. So it’s not that I have any difficulty understanding what the physical postulate is. If we look at the details of that we’ll find some very high-density obects that are living out lives, that look like people moving around and so on, and some very low-density objects that’re also living out lives that rather look like people moving around and so on. This is like the shadow-matter case with the high-density stuff and the low-density stuff not having any particular interesting influence on each other
Barbour
42. ….presumably because the theory’s stochastic, not because it’s not classically dynamic.
Maudlin
43. No, that’s because of the decoherence problem
[new question]
Bacciagaluppi
44. One thing on the decoherence and ………..stuck with that. It’s not clear to me that the low-density guys have the credential…..they’re supposed to have because decoherence only kills off exponentially ………..interference terms but …the repeated GRW hits are going to kill off the on -diagonal terms exponentially in time and so if there’s no discrepancy between the on- and off-diagonal terms for the low-density guys then I’m not sure they have any credentials to real existence.
Maudlin
45. There may be a technical question you’re asking, in which case I may not be competent – Here’s a way I was thinking about it, and maybe I’m just mathematically wrong. So, I was thinking that, look, the low-density guys - of course, with each successive hit they successively become lower and lower density and I’m going to leave aside the problem Lev was worried about, about distorting because the Gaussian drops off so it actually distorts – Suppose it doesn’t. Suppose that all that happens is that from time to time, as it were, in a certain region, the amplitude it taken uniformly down to a millionth of what it just was and so the GRW mass-density is taken down uniformly in this region a million. But the relative distribution of the mass-densities remain the same. So, you know, if this was half as much as that everything gets reduced a million but this is still half of that, everything gets reduced by a million again, half as much as that. So there’s clearly a sense in which there’s a level of structure. If we could find the structure; if we take the decoherence to give you as it were autonomous-looking pieces and we define the structure of the pieces by their relative amplitudes to each other, not their absolute amplitudes which are constantly shrinking, but their relative amplitudes. If I say that’s the relevant level of structure to make a person then the sort of absolute drops don’t seem to be affecting them. They don’t seem to be de-credentialling them. That was the worry. Now maybe I’m wrong at a technical level-
Bacciagaluppi
46. I haven’t done the calculation but …..just a point of intuition………….get from decoherence is not because there are no interference terms it’s because the interference terms are tying……here you have also the amplitude on these….which becomes tying? .both exponentially in time so –
Maudlin
47. I was just assuming and I maybe this is a technical error, I didn’t do any calculation …….go on.
Bacciagaluppi
48. Adrian was saying……..mathematical structure……think there are a set of arguments which have been around in the physics literature which would seem to go some way at least in addressing your problem, namely, say, symmetries, dynamical symmetries, Galilean symmetry in quantum mechanics…..from the abstract Hilbert space to recognisable spacetime descriptions of ……Galilei group is he symmetry group of non-relativistic quantum mechanics. Now, as in the case of Newtonian mechanics, the idea that spacetime just encodes the universal symmetries of the dynamics and seem to go through also in non-relativistic quantum mechanics. Or, look at the structure of the Hamiltonian, we’ve got two operators p and q …..is quadratic? in p there’s a ……..term which is a function of q. That introduces an asymmetry which is not in the……..relations, and so on. Again …..A-group rotations ..allow you to do a tensor decomposition of the Hilbert space into what …………and so on and so forth. Don’t all these results go a long way towards giving you what you want?
Maudlin
49. Let me make a very quick comment because this picks up with the discussion I had with David Albert. Look, there’s no doubt that the structure of the Hamiltonian – there’s a lot of structure in that. The natural way to understand it, and I would make exactly the same claim for the Galilean group and so on, is that the structure of the Hamiltonian is there because you already have a structure because you’re dealing with …….particles in a common space. And you know how to implement the Galilean transformation onto that, right. Now, you could try to go the other way round, I think this is sort of what David has been trying to do, and say no, no, let me just sort of add – there is no further explanation for this, all this interesting structure in the Hamiltonian, it’s just, you know, God decreed the Hamiltonian should have such and such a structure and then we have this discussion. Now, it’s not something I’ve talked about here but it does seem to me – suppose I had two programmes and one programme says, look, here’s a fairly simple, comprehensible, physical ontology. The postulation of that physical ontology implies that there’ll be these certain symmetries in the Hamiltonian, blah, blah, blah. Which you find. And the other one says, my theory says you’ve got a Hamiltonian, it’s got all these interesting symmetries – it becomes even more interesting if you’ve got identical particles because in a certain way the configuration space for identical particles has an interesting topological structure (I shouldn’t go into that). The configuration space has this very interesting structure, the Hamiltonian has this very interesting structure, there is no further story about why it has that structure; it doesn’t arrive from any other fundamental ontology. Interestingly enough it’s exactly the same structure that would arise if the other ontology had been this very simple ontology. At that point I would just say I just actually……….one more plausible theory than the other, as a piece of physics.
[new question]
Saunders
50. I think there’s a certain worry about the nature of the arguments you’ve presented; the target isn’t represented by anybody very well and I don’t know that it’s represented very well by me at any rate. It seems to me that the issue of the Everett interpretation of quantum mechanics isn’t so much “I swear by the wave function and nothing but”. The issue is do we need to change the equations. I sound like Dirac or someone, you know, saying the equations are what matters. Do we need to change the equations? So, I suppose the general point to make is: physicists extract structure from these equations in a very large variety of ways; the issue is can they extract structure from the wave-function. So whether you call that bare wave-functionalism, or not bare because you’ve got all these operators in it, I’m not sure if that’s a very interesting question.
51. But I want to address something else you’ve been saying which I think is important, which is that the present situation is somehow unprecedented. I do wonder about this. The suggestion is that, your suggestion is that in the history of physics normally we haven’t had problems reading off, as it were, form the equations what they say about the world. But I find that, as a rather amateur historian of science, not terribly persuasive. Nor as an amateur historian of philosophy. And that most of the history of modern philosophy has been quite deeply engaged with puzzles about the corpuscularian philosophy as it was called in the seventeenth century and it seems that it’s only consistent? .development is essentially Boscovichian atomism. And it seems to me that Boscovichian atomism is just absolutely not transparent as a description of the world as we see it and I don’t think any philosopher ever found it so. This is a world without smells, without colours, without feels, without warmth. There was a huge project to try to extract an account of those sorts of things, secondary qualities and so on. And typically the business of extracting that account of those secondary qualities was broadly functionalist in many of the ways that David…….was saying…..Now, I agree with you Tim that in quantum mechanics it’s harder. Absolutely. And no one would suggest otherwise. But it doesn’t seem to me that we are in a dramatically different situation and it seems to me further that one would expect it to get harder, as it were, the further one goes into the microworld or very high energy regimes or the early universe……So in a sense I loose any real grip with that we are in some unusual situation.
Maudlin
52. I haven’t done any systematic or even unsystematic survey of how physicists – because the first point you made is, look, physicists are able to extract this structure from the wave-function – do this, but I think it’s pretty clear, and it’s just one guy but he’s an actual physicist…..an actual advocate of the theory, Demore, it’s easy to see how Demore. extracts the structure, he extracts it by taking the configuration space to be a configuration space; gives you a hell of a lot of structure. He doesn’t worry his head about it, and for all practical purposes, having done that, he doesn’t really have much problem. So the fact that physicists can get along and use quantum mechanics perfectly well, of course they can. As soon as you think you’ve got a configuration space – all my arguments are, if it really is a configuration space, if you pretend it is, you know what to do with it and as long as they’re pretending it is of course they’re not going to find they have any analytical difficulties, or practical difficulties.
53. The second point, look, as far as secondary qualities goes, of course, I don’t think physics has ever solved the mind-body problem; I don’t think any physics, Newtonian mechanics, ever told us how things were warm or anything like that. So, it’s not as if I thought earlier physics had solved that problem. What did Newtonian gravitational theory do? It gave us trajectories of planets and cannon balls and stuff like that and we came in thinking we knew a lot about the trajectories of planets and connon balls and stuff like that. In a way, the point that I’m making is: in philosophy there was a sidetrack during the logical empiricist period where the notion was, the evidence is sense data, the evidence is described in experiential terms. And so our job, to connect the physics up to the evidence has to bridge that gap somehow. Of course nobody knew how to do it analytically so what could you do except say, oh, there’s a bridge rule or I’m just going to tell you when such and such occurs then red spot for me here now. Now, that just seems to me to mischaracterise the nature of physics. The level of contact that is made typically, at least in a case like gravitational physics, isn’t at the level of anybody’s experience of anything. It’s at the level of motions of macroscopic objects which could on the one hand in a straightforward way be derived from the theory and on he other hand there’s something we thought that, through various means, we had a pretty good evidential handle on. It’s the absence of that that I think would be unprecedented. The absence of that meeting place between our pre-theoretical understanding of the world and the theoretical understanding.
Saunders
54. So you have no problem with that this table is mostly vacuum…
Maudlin
55. No, none whatsovever. Let me put it this way. If you thought I would have a problem with that you haven’t understood the problem I’ve presented because if you understood the problem you would see that it has nothing to do with – I’ve no problem whatsoever with any of those things. And I don’t think anybody ever did. So long as you say,yeah, the hand - maybe there’re point-like particles and there’s an electromagnetic force so when I try to do this [attempting to pass his hand through the table] I can’t do it. Because they get pushed back, not that they knock against each other – the force goes up, that’s all completely comprehensible. So if you thought I did have problems with that then I’ve really made a mess of trying to explain the problem.
[new question]
Valentini
56. Just a very short comment about history actually. So, you’ve talked about this point that if I don’t have an actual configuration in the theory then what does it mean to say there’s a configuration space? Interestingly enough, exactly the same point was made in 1927 by de Broglie, when he had is pilot-wave theory of an n-body system guided by a Schrodinger wave function. And Schrodinger had his rival theory where he said, no, every is just the wave function and de Broglie, in one of his papers and in his lecture at the fifth Solvay conference in 1927 says precisely this. He gives some criticisms of Schrodinger’s theory and one of them is: what does it mean to say you have this wave function on a configuration space when there’re no configurations. It’s interesting that this puzzle …..
Transcript discussion Bub and Pitowsky
July 19 16.00
Two dogmas about quantum mechanics
Speakers: Jeff Bub & Itamar Pitowsky
Commentators: Chris Timpson
Floor speakers (in order of appearance):
Ladyman
Valentini
Wallace
Maudlin
Lehner
Rae
31
Comment by Timpson
1. Some quick comments. The comments I’m afraid are going to be somewhat polemical so forgive me in advance. There are a bunch of quibbles I could raise, particularly with that last claim that we were hearing, particularly that one can de-clone in Everett, that’s a suprising kind of claim given that it’s a theorem of quantum mechanics that one can’t clone in Everett which is just straight-out quantum mechanics so clearly there’s some jiggery-pokery about what one means by whether or not one can clone. Whether de facto it turns out in advance that people don’t clone … whether it’s ruled out as a matter of law. I think it’s that latter one which people understandably take the claim to be. That’s a quibble; I want to focus on the big picture. So, the big picture here is that Jeff and Itamar .. are interested in this question of .. locating in quantum mechanics in the space of possible theories that allow … information theories of various kinds, and they’re interested in what kinds of information-theoretic constraints can narrow down … quantum mechanics uniquely as the one correct theory. Now, I think that’s and extremely interesting project to be engaged in but I don’t see it as a project which actually tells us anything about the ontology of the world, or which is a candidate for telling us anything about the ontology of the world ….. It is not an approach which is going to tell us which interpretation of quantum mechanics is .. a candidate which we should adopt, be it Bhorian instrumentalist, Bohmian or what not. Why not? Because it’s about .. pictures of the theory as a theory, not about pictures of what the theory says about the world. So, in providing their argument that Everett and Bohm are ruled out by focussing on the no-cloning theorem in this kind of approach I think really there isn’t – the argument here isn’t a logical one … logical principles, it’s really a kind of rhetorical positioning. Okay, that’s my claim. And what I want to do is to redress the rhetorical balance here. So, basically the rhetorical position is that we line up the Bohmian and Everettian .. with a bunch of well-known loosers, so we have Carnap versus Quine and .. the Everettians and Bohmians with Carnap and the other loosers, poor old Lorenz and .. Einstein is on the side of the angels. Lorenz was a looser, oh dear, Everett and Bohm are like Lorenz. This is what the rhetoric is. I just ... both sections.
2. Regarding the two dogmas, my immediate response is that, well, as Carnap might well have said to Quine, one man’s dogma is another man’s axiom. The dogmas here are supposed to be: no dynamical
.. theory?of measurement is possible and that quantum states aren’t ontologically significant. So .. want to line themselves up with bold, bright young Quine. Who’s the Carnap figure here? Well, I think the natural candidate is Bell. Now, what would Bell have made of the proposal that we have been presented with today? I think he would think it’s rather peculiar to be told that it follows as a theorem from the theoretical structure that we’re commited to (that we subscribe to) that we can’t have what indeed we demonstrably do have. I think he’d think that’s a peculiar kind of argument. We demonstrably do have adequate dynamical analyses of measurement in quantum mechanics; they’re called Everett and Bohm. Okay, granted, measurement when we use the phrase ‘quantum measurement’ doesn’t mean measurement when we’re talking about classical measurement. Okay, fine, intuitively we know that. There are Kosher?-Speker?kinds of results of course which tell us that, and Jeff and Itamar’s use of the no-cloning theorem is just another example of that. Measurement means something different in quantum mechanics; that’s not a good reason to reject the Everett and Bohm .. it’s not a good reason to say that what they do when they look at interactions of a particular kind doesn’t make any sense. Of course it makes sense and it is extremely valuable to go through those processes. So, to close off this section, basically no difference in focussing on the no-cloning theorem from the kind of conclusion which can be drawn from the Bell-Kosher-Speker results. Those things don’t tell us that we can’t have a complete dynamical account of measurement.
3. Okay, so on to Lorenz as a looser. As Harvey Brown and I have argued in print, we think of drawing this analogy with what went on with relativity in order to motivate .. the doing-down of Everett and Bohm kind of backfires in a big way because Einstein himself came to realise that the original way in which he’d formulated theory in 1905, the principle.. theory approach, was the wrong way of formulating relativity. He himself came to realise that actually something more along the lines of what Lorenz was doing was the right thing to do. Because he realised and is quoted himself as saying that he’d commited a great sin in 1905 in treating measuring rods and clocks as unanalysed .. just primitives and really .. atomic configurations subject to dynamical laws .. and if we want to know why ..the Lorenz.. contract and time-dilate we’d better see what those laws tell you about the behaviour of those things. Now, people couldn’t do that in 1905, obviously, because they didn’t have the ground-level theory.. constructive theory to build up from so Einstien .. stroke genius went to .. I can sidestep for the momen pro tem? .. constructive theory in order to draw some conclusions about what any .. this kind of constructive theory should look like, but that’s not to reject the thought that … constructive theory … postulate the laws .. you see it going to follow … and see what rods and clocks .. behave isn’t actually what we want to end up doing. So, Einstein himself would want to … against the principle theory kinds of approach which he first had and which Jeff and Itamar are suggesting we ought to have towards quantum mechanics. So, when we’re looking at constructive theories underlying the principle-theory version of special relativity there are two kinds of ways of going about this as Harvey and Oliver .. have argued. On the one hand there is the kind of standard view which is that we postulate Minkowsky spacetime as an ontological structure which explains Lorenz contraction and time dilation, I think Michel likes that way of doing it, alternatively, the way that Harvey and Oliver prefer, is to say that actually it’s just a fact that the dynamical laws have certain symmetries associated with them .. entails that Lorenz contraction and time dilation will indeed occur. So those are the two kinds of constructive ways of doing special relativity. So rather than lumping Everett and Bohm with the ‘Lorenz as a looser’ kind of tag we should really be seeing putting Everett and Bohm together with what Minkowsky was doing, and I don’t think anybody thinks Minkowsky was looser.
4. So, to conclude, I don’t think there are any troubles raised for adopting enthusiastically the Everett interpretation that come from reflecting on the no-cloning theorem.
Bub
5. A quick minute reply.. If one at least entertains the possibility that it makes sense to consider a universe in which no-cloning is in principle impossible, that we really discovered in the case of quantum mechanics is that .. there are information are information sources which can’t be cloned, that in principle can’t be cloned, then, in this might be false, but let’s say that we entertain this possibility. If we entertain this possibility then there is I think .. two questions. First of all, one can consider: well, if you say that how do you make sense of quantum mechanics in the sense of is there some remaining problem and what we take to ourselves to have done is show look, you can make sense of probabilities that way and so there isn’t any further conceptual problem. Now, you might accept that and say okay (you might not accept that but if you do accept that), yea, but I still would like to understand why can’t we clone.
6. Now, that I think is an interesting question which might have an interesting answer but I don’t think the question just as posed that way, why can’t we clone, can be answered now. I mean it might be that in terms of some future physics there will be an interesting answer to that which is different from . sorry .. I don’t think that the question is just silly, or uninteresting. But I do think it’s an uninteresting answer to say that I’ll tell you why we can’t clone, let’s suppose that we can clone and now there some sort of .. it’s not that we can’t clone in principle and then give some sort of dynamical story about why as a contingent matter of fact we can’t clone right now. We could if things were a little different, if the decoherence process was different or something like that. That’s in effect denying the claim here to start off with that .. this is the import of quantum mechanics that we’re looking at a world in which cloning is in principle impossible, so
Timpson
7. It’s a corollary of quantum mechanics
Bub
8. Well the claim here is, look, there is no conceptual problem if we take that as the message of quantum mechanics, so to speak. And I guess we .. Itamar suggested this morning that the situation would be as if we have .. thermodynamics with a law like ‘no perpetual motion machines’, and someone came up with an explanation of why there can be no perpetual motion machines in terms of statistical-mechanical analysis, but that statistical-mechanical analysis was idle in terms of machinery .. I mean it isn’t today, you get new results out of it ...but if it was sort of completely idle and simply gave you a kind of comfortable story about why one couldn’t have a perpetual motion machine, I think that would be more analogous to the situation that you have with, say, Bohm’s theory or many-worlds. They don’t do anything more than provide a dynamical explanation of no-cloning within a framework in which cloning is possible.
Timpson
9. .. that’s at this point the quibble I had at the beginning about exactly what one means by no-cloning, kind of does get important
Pitowsky
10. .. you know, the one thing I opened with was, I think it’s really a place to take off and I think in many of the approaches this is not ……. This is the fact that you have a structure here, you have the structure which is a realistic structure and this is what you should follow. I mean it’s not as if there’s no alternative, our point is not a polemic point and it’s probably .. this is the question that Simon had, is it a realistic interpretation .. it’s a realistic interpretation in the following sense: you have events and you have measurement results .. nothing to do with whether human beings are there or not , because measurements are not privileged in the theory, so you’re not told an event is a .. of probability theory.. there’s no analysis of what an event is in probability theory . You have a whole set of those that are actually occurring or ostensibly occurring, and you have a whole lot of very interesting structure on that and this is the structure of the Hilbert space. So this is realism about the structure of the Hilbert space. It’s realism about operators, not realism about a wave function, and in that respect it’s completely orthogonal to the. It’s realism about events and operators, projection operators.
Ladyman
11. Well, I had ... when you were talking about cloning theory because it’s obvious that the uncertainty relation implies the no-cloning theorem. If we could clone, the we could make lots of copies of the same state and measure different observables again … violations of the uncertainty relation. So then it just seems like what’s at issue between the Bohmian take on things and your take on it is just like with the uncertaintly relation, you think it’s in principle a fact about the world and they think it’s a contingent epistemic limitation on what we can practically do and so I’m not really sure how much progress we’ve made by thinking about things in terms of no-cloning rather than the uncertainty relation. But the question I had was: do you think that, granted the uncertainty relation implies no-cloning, do you think that no-cloning implies the uncertainty relation.
Pitowsky.
12. Yes, this is it, so it implies many other things so that’s why it’s stronger. You mean just uncertainty.. ?
Ladyman.
13. Well, I mean..
Pitowsky
14. But you have non-commuting operators. No-cloning implies that, in particular
Bub
15. Yea, or rather there is …. If you consider a large class of theories and just impose a no-cloning constraint, these theories would be a class of theories which are no-signalling theories and in terms of the definition of no-signalling they would also be theories where … there is a set of informationally incomplete observables with respect to which you can reconstruct the state, so there are certain features of this class of theories … this describes a very large class of theories which includes quantum mechanics and classical mechanics and the claim here is that the principle that demarcates classical from non-classical theories is the no-cloning principle or really the no-broadcasting principle and so it’s really a general result which has nothing specific to do with quantum mechanics.
I mean no-cloning basically demarcates classical from a whole class of non-classical theories
Sudbery
16. ….comment on behalf of another looser…. If non-cloning does turn out to be a fundamental principle it seems a shame that Giancarlo Ghirardi should have his name associated with it because the excuse … and Zurek to publish their paper was a paper by…..
Bub
17. Oh, that’s right, yeah
Sudbery
18. ….pointed out that there were funamental principles which showed that this couldn’t happen. Now that paper by Hewet? .. followed by Giancarlo Ghirardi ….pointed out that there was a fundamental principle which showed that therefore .. leading to rejection .. he was overruled and therefore wasn’t listened to by any of his associates … and therefore…
Bub
19. Oh yeah, I think that we did ….isn’t that right?
Timpson
20. Well actually this is no-broadcast which is Fooks, Barnham and that lot, so, and what we have here is different and was only proven in, when, 1996?
Bub?
21. What we
Timpson
22. No-broadcasting was only proven …
Pitowsky
23. No-broadcasting is a bit more complicated
Timpson
24. And that’s the crucial one, no-broadcasting
Pitowsky
25. Yeah, because ….
Timpson
26. Yeah
Valentini
27. Yes, so I agree with Chris on this analogy with Lorenz is bad …..this whole issue of Einstein and Minkowski nevertheless rejected this objective account of the world, but what seems to me a better analogy in many respects is with the approach called energetics in the late nineteenth century when people, there was a whole group people, Oswald, Mach and various other people saying, look, these people with their models and generic? theory and these billiard balls bouncing in a container; we don’t need that, just focus on general principles to do with energy. Energy-theoretic principles like, conservation of energy, no perpetual motion … what we now call thermodynamic principles. Now, there was an argument back then saying, look, I can explain everything about gases in thermal equilibrium from these principles, why do I need this complicated mechanism underlying it. And at that time the kinetic theory of gasses was what Jeff called a sort of idle theory. People were saying things like, look, if you take a box of gas and you say it’s made of N molecules of a certain mass and so on, I can take another box of gas made of 2N molecules of half that mass and I still get the same picture. It’s a bit like a de Broglie-Bohm, you could say well I could have different trajectories and I’d get the same thing. Further, you could have argued … saying something like, look, de Broglie-Bohm says that in principle you could have non-equilibrium and you could clone and that violates our principles … you may have said back then, well, if there really are these molecules then there is perpetual motion. And in fact in 190? … under the microscope and you see pollen grains jiggling you see perpetual motion, and you may have said ……violate the principle…….. and finally of course on this analogy, another reason why it’s a good one, particularly from the point of view of hidden variables and de Broglie-Bohm is that you can show that in terms of .. hidden variables theory , no signalling is a specific contingency on equilibrium, simply cloning has been discussed in de Broglie-Bohm.. . So, there’s an alternative analogy which points in a very different direction, and again, too, I think there’s a question about what one might call an analogue of the big measurement problem. Someone back then who was saying just concentrate on macroscopic experiments and worry about what we can do with the energy .. would .. defend .. Boltzman who would have and did say but look if you’re just talking about this macroscopic world, what happens when you chop things up into little bits and at the very small scale what’s going to happen, how can you.? So … in a sense this is a reality problem, what are the things really made of, what happens when you probe things more precisely . This is why we’re not comfortable with an operational macroscopic approach. So that is how I your approach, that’s my analogy, which again puts you as Chris was saying ..in the looser ..
Bub
28. I have something to say quickly on that. Just on the issue of Einstein’s realisation that .. his rejection of his own approach and the thought that there should be a dynamical account which applies to rods and clocks and so on, I think the analogy of that in quantum mechanics as we see it as a no-cloning theory, is the whole dynamical analysis of decoherence of the quantum dynamical analysis of decoherence, so its not as if this position, once one starts .. no-cloning is just to say well, this is some sort of abstract principle, we don’t talk dynamics. I mean the solution to the small measurement problem is the quantum dynamical solution it’s the the whole story about decoherence which is a complicated story in itself .. which we have alluded to .. so that, I think, could be analogous to the dynamical story about rods and clocks in relativity theory because it’s not the same as Lorenz’s dynamical story which involves a presupposition about Newtonian spacetime structure, rather it’s a relativistic dynamical analysis and I think that’s just analogous to the decoherence dynamics. Anyway
Pitowsky
29. I want to say something about thermodynamics; it’s a very good analogy and I’ll tell you why. In the case of thermodynamics and statistical mechanics very quickly, with van der Waals? you’ve got results which you couldn’t get from thermodynamics or, at least, people did not get only ad hoc … so this is exactly the point. The point is the following: suppose that you’re right and people will probe the state in such a way as to get non-equilibrium states , so you’re going to get a Nobel prize, okay, now I’m going to adopt the theory, okay, but ….. this didn’t happen yet, I don’t see, after how many years, since 1925 or so, anyone who …… nothing like that happened at the mico-level, there’s no new phenomena, so what I’m saying is, okay, if the analogy goes, we stick with thermodynamics, we don’t stick with statistical mechanics because statistical mechanics doesn’t give us anything but a kind of pillow to … you know.
?
30. It’s a rhetoric
Valentini
31. ….I think it took longer than you’re saying, there was a period of several decades where statistical mechanics was .. seen as this idle theory but, okay, let’s say this period is not as long as it has … but even so there’s still the question of what ….. people like Boltzman who spent years developing statistical mechanics, it wasn’t just because, ah, we’re doing this because we’re getting results, new physics … There was a concern about a real description of things which went beyond just crude sensations in the lab of a macroscopic box of gas, there’s no .. why can I not? .. let’s say I’m given a description of what I’m doing in a lab with a box of gas and a pump and so on. Now, why can’t I extend that description down to smaller and smaller scales? What happens? There’s no divide, no boundary
Pitowsky
32. We don’t have any boundaries
Valentini
33. ..so, the motivation, I think, reading Boltzman’s writings … is a sense that the world is built out of some smaller constituents and it’s just not good enough to have a picture of the world that is based just on crude approximately-defined macroscopic things, and these are exactly the same concerns that a lot of people have today, that when you’re talking about doing a measurement (this is why Bell didn’t like measurement as a primitive) because it’s just a fuzzy concept based on: you’ve got this piece of equipment which is just a fuzzily-defined thing
Pitowsky
34. If no-cloning is a valid principle then it must be fuzzy, that’s the theorem here
Valentini
35. ..so, well I would interpret that as: if it is a valid principle and if you take your point of view then your view is simply incapable, you have proven that your point is incapable, of solving the big measurement problem , which, you know, that’s interesting, but now we want to solve the big measurement problem.
36. Pitowski - ..I think ..did solve, by putting that as primitive
[new question]
Wallace
37. Okay, one person’s dogma is another person’s axiom is another person’s empirical datum. I can imagine living in a world where measurement was a primitive. In this world there are indestructible black boxes dotted over the landscape; they have a knob on and a button and a dial. The world’s not like that. The measurement devices we actually see in the world do not seem to be primitive, they seem to be built by very clever people, from principles that we basically think we can understand. One can look at them and deduce rather than postulate how they work, and I think in that context it’s worth remembering the real reason why we adopt statistical mechanics rather than thermodynamics or why we continue to use a form of modern thermocy.. as primitive I think is not really about fluctuations it’s about the equation of statae, it doesn’t require us to postulate as primitive . it allows us to derive it from the mathematics. So it’s not … I mean that objection is utterly unoriginal, but if there is something to be said about it I’m very interested to hear what that thing is.
Bub
38. Well, in principle the claim is simply not that the no-cloning principle entails that .. the are measuring instruments around which are just black boxes which copy …. The claim is that it follows from the principle that a quantum-mechanical analysis can be given at any level so if somebody builds a black box you can proceed to analyse any aspect of it down to its smallest microscopic constituents and keep going as much as you want with a quantum-mechanical analysis but at the end of the day there will always be some aspect of the analysis, there will always be some aspect of the physical system, which is treated simply as a classical information source. If you want to analyse that quantum mechanically then you can, you .. look at .some further bit of the apparatus which is functioning in the analysis purely as a classical information source. And the claim is that that’s a consequence of the no-cloning principle. But I find it a bit surprising that there’s all this charge of : well, if you say this then you’re sort of giving up on physics or something. It seems to me that, I’m sure nobody here believes, well maybe there are one or two people, but I doubt that anybody here really believes that real physics will be done using, well Anthony does, but to me it seems really bizarre to try and perform some quantum-mechanical calculation from the point of view of the Bohm theory in order to get some new insight about ….(I’m not only talking about new prediction, I just mean that there …..equilibrium distribution) but some new insights and new way of looking at things which is suggestive of something which quantum mechanics might be able to produce too. But this is really getting at the roots of the way the world is put together so if we look at it this way then we see things which the quantum-mechanical view would just clumsily try to reproduce.
Valentini
39. The discovery of Bell’s theorem is a case where this actually happened … de Broglie-Bohm helped Bell discover non-locality .
Timpson
40. and non-contextuality.
Bub
41. ..well he knows that Bohm’s theory is non-local and he asked the question must any hidden-variable theory have to be like Bohm’s theory. But that seems to be something … different
Valentini
42. ..it is an example would be .. . insight … not just looking at quantum mechanics
Pitowsky
43. .. it wasn’t developed on the basis of Bohm’s theory, it was derived from Hilbert space. This is the point,
Valentini?
44. ..there was the question of whether .. lead to
Pitowsky
45. oh, lead to in the sense of inspiring , yes .. that I don’t contend? With
Maudlin
46. I don’t know what to say except that I don’t understand how anything about
Bub
47. I knew you’d begin with that
Maudlin
48. …..could become associated in anyone’s mind with the measurement problem. Decades and decades of talk about there being a problem, something that was identified as the measurement problem, people thought about it ……. Behaving or not behaving ….. Whatever problem that is it ain’t the measurement problem and people thought that …
Now, let me say something about making measurement primitive. From a normal information-theoretic point of view I would have thought that any interaction between two systems provides some information. I take system A and I throw it at system B what happens is that ….the actual state system B has to be in, and I can figure out what happened to system A then I would ….some information about the state of system B. From that point of view any interaction is something measurement-like and we heard early on that one of the dogmas that you said you got … I didn’t quite understand you can’t have a dynamical explanation of measurement since any interaction is sort of measurement-like and provides information, that seems to say you can’t have a dynamical explanation of anything … we have lots of dynamical explanations .. of lots of things, so
Bub
49. We can’t have a complete dynamical explanation of … there’s always going to have to be some system which is functioning as a classical information source that’s really what ..
Maudlin
50. Maybe I can just re-ask Chris’s question how can you claim that you can’t have something that exist? I mean, you say you can’t have it and I say well here’s a theory that has it …
Pitowsky
51. Again, a theory that has it, with certain dynamical conditions put from the outside .. such as equilibrium in Bohmian theory
Maudlin?
52. … deny the premis?
Pitowsky
53. Yes, you deny the premis
Maudlin
54. … the second law of thermodynamics really exactly .. classical explanation of the fact that we can’t extract mechanical energy from a heat reservoir … is somehow bad or insufficient because after all in principle you can, if you’re lucky, it just turns out that in equilibrium the chances are so small that in the history of the universe it probably never happened. Do you consider that to be an inadequacy?
Pitowsky
55. It’s an inadequacy, I think, just in one respect. If we didn’t have evidence that- . Suppose we stay with the second law of thermodynamics, the original formulation say, no … and then .. the only purpose of the atomic story would be to say, look, this is highly unlikely
Maudlin
56. Anything else that you get from the theory?
Pitowsky
57. No, just that this is highly unlikely . I think that this would not be an interesting physical theory, it would be an uninteresting physical that is just doing a simple thing in a very complicated form.
Maudlin
58. That … the only purpose of the atomic theory? ..
Pitowsky
59. No, I don’t think it was the only purpose of the atomic theory
[new question]
Lehner
60. I just wanted to sharpen Antony’s point about ….ther is exactly a parallel to .. .that’s supposed.. ……… tried to argue against Bolzman’s statistical mechanics … exactly that argument that the second law of thermodynamics comes out only as a statistical law, right, … and who was the looser? … but I mean what I want to substantially argue about your approach is that, just as Tim says, you can only claim that no-cloning implies dynamic description of measurement because you assume that measuremant has to be non-destructive, so let’s assume that measurement changes or destroys the state of the object and immediately your argument doesn’t go through at all any more, right. I mean, nobody says .. that we still have the measurement problem, it hasn’t changed a whit about the measurement problem if we assume that measurement changes the state of the measured object
Bub
61. Well, no, we’re talking about changing irreversibly?
Lehner
62. Yes
Pitowsky
63. Right, so we didn’t talk about GRW for example. GRW is an extension of quantum mechanics. It’s an extension of quantum mechanics about which we didn’t talk. We were talking about deterministic theory
Lehner
64. Look, let me put it another way no-cloning is a consequence of unitarity right?
Pitowsky
65. We are reversing that .. Suppose that, assuming no-cloning, then you get that certain processes could not be unitary. This is the inverse theorem. The inverse theorem says if you assume no-cloning then certain processes cannot be unitary
Lehner
66. …..perfectly equivalent but that for example Everett, the core of Everett’s claim is that unitarity is universal. So how can no-cloning be in conflict with that? If the unitary evolution is all we have then of course we’ll have no-cloning in that sense
Timpson
67. I think the issue here is that Itamar and Jeff have in mind something different in no-cloning than what the standard view is. …. I think you’re dead right that given the dynamics .. subsystem …even in the most general case linear … complete positive map … the no-cloning theorem follows. But they’re interested in basically .. de facto non-happening of cloning in some abnormal branches
Maudlin
68. ..exactly the parallel with ..
Timpson
69. Yeah, because of the particular meaning they put in their …not cloning, not happening ..
Pitowsky
70. Okay, the claim is just that you need a very complicated dynamical explanation of why people don’t see cloning, a very complicated dynamical explanation for that
Lehner
71. ….was personally offended that Boltzman marred the beauty of the second law of thermodynamics ..
Pitowsky
72. But I think you all ignore the fact that there was the black body radiation and here we don’t have a black body radiation. Here you don’t have evidence
Lehner
73. This was the 1890s, right, Boltzman died without any good evidence for the atomic hypothesis … this went on for just as long as ..
Pitowsky
74. The black body radiation was there and was not explained by Boltzman’s statistics. This is something that you don’t have here. There is not a parallel
Lehner
75. This all happened long before black body radiation was even discussed
[new question]
Rae
76. ...somewhat naively and at the beginning of the talk … I understand, I think ..does not mean to claim …. At the beginning of the talk it seemed to me you were saying that information theory plus no-cloning theorm .. was all we needed to deduce the von Neuman axioms of quantum mechanics including all …if that were true that would be a huge claim. I’m sorry, it did sound like that at the beginning, so could you between you just summarise just how far down that road you actually have gone
Bub
77. Well we don’t derive quantum mechanics …. All that we did today was to produce a principle which demarcates classical from non-classical theories; it’s still an open question what other principle or principles you need to actually demarcate quantum mechanics from (which is just one of a large group of non-classical theories) from the other, let’s say ‘super quantum theories’ . Or even, for that matter, sort of sub-quantum but non-classical theories. I mean there are some theories .. at some point I mean the correlations are not as strong as the Bell correlations but they’re still not classical. You see there’s a whole range of theories … actually picking out quantum mechanics would require more than just no-cloning, and nobody knows what that is ..
Pitowsky
78. There are some counter-examples on that, but they’re perhaps, less simple than just not ..
Rae
79. ..you say that we’ve got quantum mechanics … von Neuman postulates or something like them, and then you put on, you add no-cloning to it, this sounds like an extra postulate
Pitowsky
80. No, what you’re doing is something else .. .we’re taking very general information-theoretic accounts which have no-signalling, and you add no-cloning and you see that many of the features of the measurement problem arise already. And you don’t need quantum mechanics for that.
Rae
81. Why do you need no-cloning? I mean, what’s it telling you? … ruling out that sensible people don’t believe in it anyway …
Bub
82. It gives you non-classicality. The claim is that that is the essential principle which divides classical from non-classical theories and all these non-classical theories are similar in respect to the measurement problem
Two dogmas about quantum mechanics
Speakers: Jeff Bub & Itamar Pitowsky
Commentators: Chris Timpson
Floor speakers (in order of appearance):
Ladyman
Valentini
Wallace
Maudlin
Lehner
Rae
31
Comment by Timpson
1. Some quick comments. The comments I’m afraid are going to be somewhat polemical so forgive me in advance. There are a bunch of quibbles I could raise, particularly with that last claim that we were hearing, particularly that one can de-clone in Everett, that’s a suprising kind of claim given that it’s a theorem of quantum mechanics that one can’t clone in Everett which is just straight-out quantum mechanics so clearly there’s some jiggery-pokery about what one means by whether or not one can clone. Whether de facto it turns out in advance that people don’t clone … whether it’s ruled out as a matter of law. I think it’s that latter one which people understandably take the claim to be. That’s a quibble; I want to focus on the big picture. So, the big picture here is that Jeff and Itamar .. are interested in this question of .. locating in quantum mechanics in the space of possible theories that allow … information theories of various kinds, and they’re interested in what kinds of information-theoretic constraints can narrow down … quantum mechanics uniquely as the one correct theory. Now, I think that’s and extremely interesting project to be engaged in but I don’t see it as a project which actually tells us anything about the ontology of the world, or which is a candidate for telling us anything about the ontology of the world ….. It is not an approach which is going to tell us which interpretation of quantum mechanics is .. a candidate which we should adopt, be it Bhorian instrumentalist, Bohmian or what not. Why not? Because it’s about .. pictures of the theory as a theory, not about pictures of what the theory says about the world. So, in providing their argument that Everett and Bohm are ruled out by focussing on the no-cloning theorem in this kind of approach I think really there isn’t – the argument here isn’t a logical one … logical principles, it’s really a kind of rhetorical positioning. Okay, that’s my claim. And what I want to do is to redress the rhetorical balance here. So, basically the rhetorical position is that we line up the Bohmian and Everettian .. with a bunch of well-known loosers, so we have Carnap versus Quine and .. the Everettians and Bohmians with Carnap and the other loosers, poor old Lorenz and .. Einstein is on the side of the angels. Lorenz was a looser, oh dear, Everett and Bohm are like Lorenz. This is what the rhetoric is. I just ... both sections.
2. Regarding the two dogmas, my immediate response is that, well, as Carnap might well have said to Quine, one man’s dogma is another man’s axiom. The dogmas here are supposed to be: no dynamical
.. theory?of measurement is possible and that quantum states aren’t ontologically significant. So .. want to line themselves up with bold, bright young Quine. Who’s the Carnap figure here? Well, I think the natural candidate is Bell. Now, what would Bell have made of the proposal that we have been presented with today? I think he would think it’s rather peculiar to be told that it follows as a theorem from the theoretical structure that we’re commited to (that we subscribe to) that we can’t have what indeed we demonstrably do have. I think he’d think that’s a peculiar kind of argument. We demonstrably do have adequate dynamical analyses of measurement in quantum mechanics; they’re called Everett and Bohm. Okay, granted, measurement when we use the phrase ‘quantum measurement’ doesn’t mean measurement when we’re talking about classical measurement. Okay, fine, intuitively we know that. There are Kosher?-Speker?kinds of results of course which tell us that, and Jeff and Itamar’s use of the no-cloning theorem is just another example of that. Measurement means something different in quantum mechanics; that’s not a good reason to reject the Everett and Bohm .. it’s not a good reason to say that what they do when they look at interactions of a particular kind doesn’t make any sense. Of course it makes sense and it is extremely valuable to go through those processes. So, to close off this section, basically no difference in focussing on the no-cloning theorem from the kind of conclusion which can be drawn from the Bell-Kosher-Speker results. Those things don’t tell us that we can’t have a complete dynamical account of measurement.
3. Okay, so on to Lorenz as a looser. As Harvey Brown and I have argued in print, we think of drawing this analogy with what went on with relativity in order to motivate .. the doing-down of Everett and Bohm kind of backfires in a big way because Einstein himself came to realise that the original way in which he’d formulated theory in 1905, the principle.. theory approach, was the wrong way of formulating relativity. He himself came to realise that actually something more along the lines of what Lorenz was doing was the right thing to do. Because he realised and is quoted himself as saying that he’d commited a great sin in 1905 in treating measuring rods and clocks as unanalysed .. just primitives and really .. atomic configurations subject to dynamical laws .. and if we want to know why ..the Lorenz.. contract and time-dilate we’d better see what those laws tell you about the behaviour of those things. Now, people couldn’t do that in 1905, obviously, because they didn’t have the ground-level theory.. constructive theory to build up from so Einstien .. stroke genius went to .. I can sidestep for the momen pro tem? .. constructive theory in order to draw some conclusions about what any .. this kind of constructive theory should look like, but that’s not to reject the thought that … constructive theory … postulate the laws .. you see it going to follow … and see what rods and clocks .. behave isn’t actually what we want to end up doing. So, Einstein himself would want to … against the principle theory kinds of approach which he first had and which Jeff and Itamar are suggesting we ought to have towards quantum mechanics. So, when we’re looking at constructive theories underlying the principle-theory version of special relativity there are two kinds of ways of going about this as Harvey and Oliver .. have argued. On the one hand there is the kind of standard view which is that we postulate Minkowsky spacetime as an ontological structure which explains Lorenz contraction and time dilation, I think Michel likes that way of doing it, alternatively, the way that Harvey and Oliver prefer, is to say that actually it’s just a fact that the dynamical laws have certain symmetries associated with them .. entails that Lorenz contraction and time dilation will indeed occur. So those are the two kinds of constructive ways of doing special relativity. So rather than lumping Everett and Bohm with the ‘Lorenz as a looser’ kind of tag we should really be seeing putting Everett and Bohm together with what Minkowsky was doing, and I don’t think anybody thinks Minkowsky was looser.
4. So, to conclude, I don’t think there are any troubles raised for adopting enthusiastically the Everett interpretation that come from reflecting on the no-cloning theorem.
Bub
5. A quick minute reply.. If one at least entertains the possibility that it makes sense to consider a universe in which no-cloning is in principle impossible, that we really discovered in the case of quantum mechanics is that .. there are information are information sources which can’t be cloned, that in principle can’t be cloned, then, in this might be false, but let’s say that we entertain this possibility. If we entertain this possibility then there is I think .. two questions. First of all, one can consider: well, if you say that how do you make sense of quantum mechanics in the sense of is there some remaining problem and what we take to ourselves to have done is show look, you can make sense of probabilities that way and so there isn’t any further conceptual problem. Now, you might accept that and say okay (you might not accept that but if you do accept that), yea, but I still would like to understand why can’t we clone.
6. Now, that I think is an interesting question which might have an interesting answer but I don’t think the question just as posed that way, why can’t we clone, can be answered now. I mean it might be that in terms of some future physics there will be an interesting answer to that which is different from . sorry .. I don’t think that the question is just silly, or uninteresting. But I do think it’s an uninteresting answer to say that I’ll tell you why we can’t clone, let’s suppose that we can clone and now there some sort of .. it’s not that we can’t clone in principle and then give some sort of dynamical story about why as a contingent matter of fact we can’t clone right now. We could if things were a little different, if the decoherence process was different or something like that. That’s in effect denying the claim here to start off with that .. this is the import of quantum mechanics that we’re looking at a world in which cloning is in principle impossible, so
Timpson
7. It’s a corollary of quantum mechanics
Bub
8. Well the claim here is, look, there is no conceptual problem if we take that as the message of quantum mechanics, so to speak. And I guess we .. Itamar suggested this morning that the situation would be as if we have .. thermodynamics with a law like ‘no perpetual motion machines’, and someone came up with an explanation of why there can be no perpetual motion machines in terms of statistical-mechanical analysis, but that statistical-mechanical analysis was idle in terms of machinery .. I mean it isn’t today, you get new results out of it ...but if it was sort of completely idle and simply gave you a kind of comfortable story about why one couldn’t have a perpetual motion machine, I think that would be more analogous to the situation that you have with, say, Bohm’s theory or many-worlds. They don’t do anything more than provide a dynamical explanation of no-cloning within a framework in which cloning is possible.
Timpson
9. .. that’s at this point the quibble I had at the beginning about exactly what one means by no-cloning, kind of does get important
Pitowsky
10. .. you know, the one thing I opened with was, I think it’s really a place to take off and I think in many of the approaches this is not ……. This is the fact that you have a structure here, you have the structure which is a realistic structure and this is what you should follow. I mean it’s not as if there’s no alternative, our point is not a polemic point and it’s probably .. this is the question that Simon had, is it a realistic interpretation .. it’s a realistic interpretation in the following sense: you have events and you have measurement results .. nothing to do with whether human beings are there or not , because measurements are not privileged in the theory, so you’re not told an event is a .. of probability theory.. there’s no analysis of what an event is in probability theory . You have a whole set of those that are actually occurring or ostensibly occurring, and you have a whole lot of very interesting structure on that and this is the structure of the Hilbert space. So this is realism about the structure of the Hilbert space. It’s realism about operators, not realism about a wave function, and in that respect it’s completely orthogonal to the. It’s realism about events and operators, projection operators.
Ladyman
11. Well, I had ... when you were talking about cloning theory because it’s obvious that the uncertainty relation implies the no-cloning theorem. If we could clone, the we could make lots of copies of the same state and measure different observables again … violations of the uncertainty relation. So then it just seems like what’s at issue between the Bohmian take on things and your take on it is just like with the uncertaintly relation, you think it’s in principle a fact about the world and they think it’s a contingent epistemic limitation on what we can practically do and so I’m not really sure how much progress we’ve made by thinking about things in terms of no-cloning rather than the uncertainty relation. But the question I had was: do you think that, granted the uncertainty relation implies no-cloning, do you think that no-cloning implies the uncertainty relation.
Pitowsky.
12. Yes, this is it, so it implies many other things so that’s why it’s stronger. You mean just uncertainty.. ?
Ladyman.
13. Well, I mean..
Pitowsky
14. But you have non-commuting operators. No-cloning implies that, in particular
Bub
15. Yea, or rather there is …. If you consider a large class of theories and just impose a no-cloning constraint, these theories would be a class of theories which are no-signalling theories and in terms of the definition of no-signalling they would also be theories where … there is a set of informationally incomplete observables with respect to which you can reconstruct the state, so there are certain features of this class of theories … this describes a very large class of theories which includes quantum mechanics and classical mechanics and the claim here is that the principle that demarcates classical from non-classical theories is the no-cloning principle or really the no-broadcasting principle and so it’s really a general result which has nothing specific to do with quantum mechanics.
I mean no-cloning basically demarcates classical from a whole class of non-classical theories
Sudbery
16. ….comment on behalf of another looser…. If non-cloning does turn out to be a fundamental principle it seems a shame that Giancarlo Ghirardi should have his name associated with it because the excuse … and Zurek to publish their paper was a paper by…..
Bub
17. Oh, that’s right, yeah
Sudbery
18. ….pointed out that there were funamental principles which showed that this couldn’t happen. Now that paper by Hewet? .. followed by Giancarlo Ghirardi ….pointed out that there was a fundamental principle which showed that therefore .. leading to rejection .. he was overruled and therefore wasn’t listened to by any of his associates … and therefore…
Bub
19. Oh yeah, I think that we did ….isn’t that right?
Timpson
20. Well actually this is no-broadcast which is Fooks, Barnham and that lot, so, and what we have here is different and was only proven in, when, 1996?
Bub?
21. What we
Timpson
22. No-broadcasting was only proven …
Pitowsky
23. No-broadcasting is a bit more complicated
Timpson
24. And that’s the crucial one, no-broadcasting
Pitowsky
25. Yeah, because ….
Timpson
26. Yeah
Valentini
27. Yes, so I agree with Chris on this analogy with Lorenz is bad …..this whole issue of Einstein and Minkowski nevertheless rejected this objective account of the world, but what seems to me a better analogy in many respects is with the approach called energetics in the late nineteenth century when people, there was a whole group people, Oswald, Mach and various other people saying, look, these people with their models and generic? theory and these billiard balls bouncing in a container; we don’t need that, just focus on general principles to do with energy. Energy-theoretic principles like, conservation of energy, no perpetual motion … what we now call thermodynamic principles. Now, there was an argument back then saying, look, I can explain everything about gases in thermal equilibrium from these principles, why do I need this complicated mechanism underlying it. And at that time the kinetic theory of gasses was what Jeff called a sort of idle theory. People were saying things like, look, if you take a box of gas and you say it’s made of N molecules of a certain mass and so on, I can take another box of gas made of 2N molecules of half that mass and I still get the same picture. It’s a bit like a de Broglie-Bohm, you could say well I could have different trajectories and I’d get the same thing. Further, you could have argued … saying something like, look, de Broglie-Bohm says that in principle you could have non-equilibrium and you could clone and that violates our principles … you may have said back then, well, if there really are these molecules then there is perpetual motion. And in fact in 190? … under the microscope and you see pollen grains jiggling you see perpetual motion, and you may have said ……violate the principle…….. and finally of course on this analogy, another reason why it’s a good one, particularly from the point of view of hidden variables and de Broglie-Bohm is that you can show that in terms of .. hidden variables theory , no signalling is a specific contingency on equilibrium, simply cloning has been discussed in de Broglie-Bohm.. . So, there’s an alternative analogy which points in a very different direction, and again, too, I think there’s a question about what one might call an analogue of the big measurement problem. Someone back then who was saying just concentrate on macroscopic experiments and worry about what we can do with the energy .. would .. defend .. Boltzman who would have and did say but look if you’re just talking about this macroscopic world, what happens when you chop things up into little bits and at the very small scale what’s going to happen, how can you.? So … in a sense this is a reality problem, what are the things really made of, what happens when you probe things more precisely . This is why we’re not comfortable with an operational macroscopic approach. So that is how I your approach, that’s my analogy, which again puts you as Chris was saying ..in the looser ..
Bub
28. I have something to say quickly on that. Just on the issue of Einstein’s realisation that .. his rejection of his own approach and the thought that there should be a dynamical account which applies to rods and clocks and so on, I think the analogy of that in quantum mechanics as we see it as a no-cloning theory, is the whole dynamical analysis of decoherence of the quantum dynamical analysis of decoherence, so its not as if this position, once one starts .. no-cloning is just to say well, this is some sort of abstract principle, we don’t talk dynamics. I mean the solution to the small measurement problem is the quantum dynamical solution it’s the the whole story about decoherence which is a complicated story in itself .. which we have alluded to .. so that, I think, could be analogous to the dynamical story about rods and clocks in relativity theory because it’s not the same as Lorenz’s dynamical story which involves a presupposition about Newtonian spacetime structure, rather it’s a relativistic dynamical analysis and I think that’s just analogous to the decoherence dynamics. Anyway
Pitowsky
29. I want to say something about thermodynamics; it’s a very good analogy and I’ll tell you why. In the case of thermodynamics and statistical mechanics very quickly, with van der Waals? you’ve got results which you couldn’t get from thermodynamics or, at least, people did not get only ad hoc … so this is exactly the point. The point is the following: suppose that you’re right and people will probe the state in such a way as to get non-equilibrium states , so you’re going to get a Nobel prize, okay, now I’m going to adopt the theory, okay, but ….. this didn’t happen yet, I don’t see, after how many years, since 1925 or so, anyone who …… nothing like that happened at the mico-level, there’s no new phenomena, so what I’m saying is, okay, if the analogy goes, we stick with thermodynamics, we don’t stick with statistical mechanics because statistical mechanics doesn’t give us anything but a kind of pillow to … you know.
?
30. It’s a rhetoric
Valentini
31. ….I think it took longer than you’re saying, there was a period of several decades where statistical mechanics was .. seen as this idle theory but, okay, let’s say this period is not as long as it has … but even so there’s still the question of what ….. people like Boltzman who spent years developing statistical mechanics, it wasn’t just because, ah, we’re doing this because we’re getting results, new physics … There was a concern about a real description of things which went beyond just crude sensations in the lab of a macroscopic box of gas, there’s no .. why can I not? .. let’s say I’m given a description of what I’m doing in a lab with a box of gas and a pump and so on. Now, why can’t I extend that description down to smaller and smaller scales? What happens? There’s no divide, no boundary
Pitowsky
32. We don’t have any boundaries
Valentini
33. ..so, the motivation, I think, reading Boltzman’s writings … is a sense that the world is built out of some smaller constituents and it’s just not good enough to have a picture of the world that is based just on crude approximately-defined macroscopic things, and these are exactly the same concerns that a lot of people have today, that when you’re talking about doing a measurement (this is why Bell didn’t like measurement as a primitive) because it’s just a fuzzy concept based on: you’ve got this piece of equipment which is just a fuzzily-defined thing
Pitowsky
34. If no-cloning is a valid principle then it must be fuzzy, that’s the theorem here
Valentini
35. ..so, well I would interpret that as: if it is a valid principle and if you take your point of view then your view is simply incapable, you have proven that your point is incapable, of solving the big measurement problem , which, you know, that’s interesting, but now we want to solve the big measurement problem.
36. Pitowski - ..I think ..did solve, by putting that as primitive
[new question]
Wallace
37. Okay, one person’s dogma is another person’s axiom is another person’s empirical datum. I can imagine living in a world where measurement was a primitive. In this world there are indestructible black boxes dotted over the landscape; they have a knob on and a button and a dial. The world’s not like that. The measurement devices we actually see in the world do not seem to be primitive, they seem to be built by very clever people, from principles that we basically think we can understand. One can look at them and deduce rather than postulate how they work, and I think in that context it’s worth remembering the real reason why we adopt statistical mechanics rather than thermodynamics or why we continue to use a form of modern thermocy.. as primitive I think is not really about fluctuations it’s about the equation of statae, it doesn’t require us to postulate as primitive . it allows us to derive it from the mathematics. So it’s not … I mean that objection is utterly unoriginal, but if there is something to be said about it I’m very interested to hear what that thing is.
Bub
38. Well, in principle the claim is simply not that the no-cloning principle entails that .. the are measuring instruments around which are just black boxes which copy …. The claim is that it follows from the principle that a quantum-mechanical analysis can be given at any level so if somebody builds a black box you can proceed to analyse any aspect of it down to its smallest microscopic constituents and keep going as much as you want with a quantum-mechanical analysis but at the end of the day there will always be some aspect of the analysis, there will always be some aspect of the physical system, which is treated simply as a classical information source. If you want to analyse that quantum mechanically then you can, you .. look at .some further bit of the apparatus which is functioning in the analysis purely as a classical information source. And the claim is that that’s a consequence of the no-cloning principle. But I find it a bit surprising that there’s all this charge of : well, if you say this then you’re sort of giving up on physics or something. It seems to me that, I’m sure nobody here believes, well maybe there are one or two people, but I doubt that anybody here really believes that real physics will be done using, well Anthony does, but to me it seems really bizarre to try and perform some quantum-mechanical calculation from the point of view of the Bohm theory in order to get some new insight about ….(I’m not only talking about new prediction, I just mean that there …..equilibrium distribution) but some new insights and new way of looking at things which is suggestive of something which quantum mechanics might be able to produce too. But this is really getting at the roots of the way the world is put together so if we look at it this way then we see things which the quantum-mechanical view would just clumsily try to reproduce.
Valentini
39. The discovery of Bell’s theorem is a case where this actually happened … de Broglie-Bohm helped Bell discover non-locality .
Timpson
40. and non-contextuality.
Bub
41. ..well he knows that Bohm’s theory is non-local and he asked the question must any hidden-variable theory have to be like Bohm’s theory. But that seems to be something … different
Valentini
42. ..it is an example would be .. . insight … not just looking at quantum mechanics
Pitowsky
43. .. it wasn’t developed on the basis of Bohm’s theory, it was derived from Hilbert space. This is the point,
Valentini?
44. ..there was the question of whether .. lead to
Pitowsky
45. oh, lead to in the sense of inspiring , yes .. that I don’t contend? With
Maudlin
46. I don’t know what to say except that I don’t understand how anything about
Bub
47. I knew you’d begin with that
Maudlin
48. …..could become associated in anyone’s mind with the measurement problem. Decades and decades of talk about there being a problem, something that was identified as the measurement problem, people thought about it ……. Behaving or not behaving ….. Whatever problem that is it ain’t the measurement problem and people thought that …
Now, let me say something about making measurement primitive. From a normal information-theoretic point of view I would have thought that any interaction between two systems provides some information. I take system A and I throw it at system B what happens is that ….the actual state system B has to be in, and I can figure out what happened to system A then I would ….some information about the state of system B. From that point of view any interaction is something measurement-like and we heard early on that one of the dogmas that you said you got … I didn’t quite understand you can’t have a dynamical explanation of measurement since any interaction is sort of measurement-like and provides information, that seems to say you can’t have a dynamical explanation of anything … we have lots of dynamical explanations .. of lots of things, so
Bub
49. We can’t have a complete dynamical explanation of … there’s always going to have to be some system which is functioning as a classical information source that’s really what ..
Maudlin
50. Maybe I can just re-ask Chris’s question how can you claim that you can’t have something that exist? I mean, you say you can’t have it and I say well here’s a theory that has it …
Pitowsky
51. Again, a theory that has it, with certain dynamical conditions put from the outside .. such as equilibrium in Bohmian theory
Maudlin?
52. … deny the premis?
Pitowsky
53. Yes, you deny the premis
Maudlin
54. … the second law of thermodynamics really exactly .. classical explanation of the fact that we can’t extract mechanical energy from a heat reservoir … is somehow bad or insufficient because after all in principle you can, if you’re lucky, it just turns out that in equilibrium the chances are so small that in the history of the universe it probably never happened. Do you consider that to be an inadequacy?
Pitowsky
55. It’s an inadequacy, I think, just in one respect. If we didn’t have evidence that- . Suppose we stay with the second law of thermodynamics, the original formulation say, no … and then .. the only purpose of the atomic story would be to say, look, this is highly unlikely
Maudlin
56. Anything else that you get from the theory?
Pitowsky
57. No, just that this is highly unlikely . I think that this would not be an interesting physical theory, it would be an uninteresting physical that is just doing a simple thing in a very complicated form.
Maudlin
58. That … the only purpose of the atomic theory? ..
Pitowsky
59. No, I don’t think it was the only purpose of the atomic theory
[new question]
Lehner
60. I just wanted to sharpen Antony’s point about ….ther is exactly a parallel to .. .that’s supposed.. ……… tried to argue against Bolzman’s statistical mechanics … exactly that argument that the second law of thermodynamics comes out only as a statistical law, right, … and who was the looser? … but I mean what I want to substantially argue about your approach is that, just as Tim says, you can only claim that no-cloning implies dynamic description of measurement because you assume that measuremant has to be non-destructive, so let’s assume that measurement changes or destroys the state of the object and immediately your argument doesn’t go through at all any more, right. I mean, nobody says .. that we still have the measurement problem, it hasn’t changed a whit about the measurement problem if we assume that measurement changes the state of the measured object
Bub
61. Well, no, we’re talking about changing irreversibly?
Lehner
62. Yes
Pitowsky
63. Right, so we didn’t talk about GRW for example. GRW is an extension of quantum mechanics. It’s an extension of quantum mechanics about which we didn’t talk. We were talking about deterministic theory
Lehner
64. Look, let me put it another way no-cloning is a consequence of unitarity right?
Pitowsky
65. We are reversing that .. Suppose that, assuming no-cloning, then you get that certain processes could not be unitary. This is the inverse theorem. The inverse theorem says if you assume no-cloning then certain processes cannot be unitary
Lehner
66. …..perfectly equivalent but that for example Everett, the core of Everett’s claim is that unitarity is universal. So how can no-cloning be in conflict with that? If the unitary evolution is all we have then of course we’ll have no-cloning in that sense
Timpson
67. I think the issue here is that Itamar and Jeff have in mind something different in no-cloning than what the standard view is. …. I think you’re dead right that given the dynamics .. subsystem …even in the most general case linear … complete positive map … the no-cloning theorem follows. But they’re interested in basically .. de facto non-happening of cloning in some abnormal branches
Maudlin
68. ..exactly the parallel with ..
Timpson
69. Yeah, because of the particular meaning they put in their …not cloning, not happening ..
Pitowsky
70. Okay, the claim is just that you need a very complicated dynamical explanation of why people don’t see cloning, a very complicated dynamical explanation for that
Lehner
71. ….was personally offended that Boltzman marred the beauty of the second law of thermodynamics ..
Pitowsky
72. But I think you all ignore the fact that there was the black body radiation and here we don’t have a black body radiation. Here you don’t have evidence
Lehner
73. This was the 1890s, right, Boltzman died without any good evidence for the atomic hypothesis … this went on for just as long as ..
Pitowsky
74. The black body radiation was there and was not explained by Boltzman’s statistics. This is something that you don’t have here. There is not a parallel
Lehner
75. This all happened long before black body radiation was even discussed
[new question]
Rae
76. ...somewhat naively and at the beginning of the talk … I understand, I think ..does not mean to claim …. At the beginning of the talk it seemed to me you were saying that information theory plus no-cloning theorm .. was all we needed to deduce the von Neuman axioms of quantum mechanics including all …if that were true that would be a huge claim. I’m sorry, it did sound like that at the beginning, so could you between you just summarise just how far down that road you actually have gone
Bub
77. Well we don’t derive quantum mechanics …. All that we did today was to produce a principle which demarcates classical from non-classical theories; it’s still an open question what other principle or principles you need to actually demarcate quantum mechanics from (which is just one of a large group of non-classical theories) from the other, let’s say ‘super quantum theories’ . Or even, for that matter, sort of sub-quantum but non-classical theories. I mean there are some theories .. at some point I mean the correlations are not as strong as the Bell correlations but they’re still not classical. You see there’s a whole range of theories … actually picking out quantum mechanics would require more than just no-cloning, and nobody knows what that is ..
Pitowsky
78. There are some counter-examples on that, but they’re perhaps, less simple than just not ..
Rae
79. ..you say that we’ve got quantum mechanics … von Neuman postulates or something like them, and then you put on, you add no-cloning to it, this sounds like an extra postulate
Pitowsky
80. No, what you’re doing is something else .. .we’re taking very general information-theoretic accounts which have no-signalling, and you add no-cloning and you see that many of the features of the measurement problem arise already. And you don’t need quantum mechanics for that.
Rae
81. Why do you need no-cloning? I mean, what’s it telling you? … ruling out that sensible people don’t believe in it anyway …
Bub
82. It gives you non-classicality. The claim is that that is the essential principle which divides classical from non-classical theories and all these non-classical theories are similar in respect to the measurement problem
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