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.

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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.

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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 …..