# Wave function collapse in curved spacetime

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1. Sep 3, 2013

### atyy

In flat spacetime, there isn't any problem with wave function collapse. I think that's the "textbook" position, although the only citation I have off the top of my head is the discussion in http://arxiv.org/abs/0706.1232 (section 1.1).

How about in curved spacetime (working in the regime where localized qubits are possible)? I found http://arxiv.org/abs/1108.3896 (section 8.2.2 and 9.2) which discusses the issue a little, and there seems to be no problem with wave function collapse. Is this a consensus position?

Last edited: Sep 3, 2013
2. Sep 3, 2013

### strangerep

Ballentine would probably disagree. At least, that's the impression I got from his textbook...

3. Sep 3, 2013

### atyy

What does he say?

4. Sep 4, 2013

### S.Daedalus

In which sense do you say there's 'no problem'? There's of course the usual problems with the notion of collapse, related to the more general cluster of issues subsumed under 'measurement problem', but I gather that's not your issue here.

However, your cite seems to point to a problem with collapse in flat spacetimes, i.e. that it's not possible to pinpoint who caused the collapse: in one frame, A may measure first, leading to a specific outcome for B; while in another, B may be taken to cause the 'collapse'.

Of course, this doesn't lead to any observably paradoxical consequences: all probabilities remain the same. Do you mean there's no problem in this sense? If so, then I think (but am not totally sure) that there's also no problem at least in the case where spacetime is curved, but nondynamical. Of course, what happens if there is nontrivial backreaction from the spacetime---if, for example, one has a superposition of matter that should yield a superposition of macroscopically different spacetimes---is anyone's guess.

5. Sep 4, 2013

### strangerep

Oh, you haven't read him? He says quite a bit in ch9, (and elsewhere, iirc), pointing out inconsistencies and other problems with the usual Copenhagen interpretation. It's far too much to summarize here in a few sentences, but I'm sure you'd find that investing in a copy of Ballentine would be money well spent...

6. Sep 4, 2013

### vanhees71

Wave-function (or better said state) collapse is the most problematic concept ever invented when it comes to the interpretation of quantum theory, as have pointed out famously Einstein, Podolsky, and Rosen in the 1930ies. Fortunately it's not needed at all. As already recommended, Ballentine is the perfect source to study these questions. In my opinion the minimal statistical interpretation is the least problematic of all interpretations of quantum theory, but that's an opinion, and many physicists will violently disagree :-)).

7. Sep 4, 2013

### atyy

Yes, that's what I mean - no logical contradiction and good experimental predictions. And only the nondynamical case.

Why do you think there's no problem in the curved spacetime case? That's what http://arxiv.org/abs/1108.3896 indicates, but I've never seen extensive discussion of this, whereas for flat spacetime I do believe it's essentially {textbook minus Ballentine} agreement - maybe not literally {textbook} but I can also point to http://arxiv.org/abs/quant-ph/9906023 and http://arxiv.org/abs/quant-ph/9906034. Is it because in curved spacetime one can still define spacelike separations objectively, and because spacelike local projections and local unitaries do commute? So the causal possibilities are essentially the same in flat and curved spacetime, and that's what really matters?

Last edited: Sep 4, 2013
8. Sep 4, 2013

### S.Daedalus

I don't believe Ballantine differs from the grain in that regard---of course, the collapse itself is a problematic notion, whether the space is flat, curved, or curled in on itself; but I'd say the prevailing viewpoint is that besides the impossibility to introduce a fixed order on the sequence of collapses---which doesn't correspond to anything measurable---there's no new difficulties introduced by special relativity.

Something like that. Basically, my reasoning was that all the field operators at spacelike separation commute, so you can't introduce anything like causal paradoxes and the like; it's simply the way the theory is constructed. But I'm entirely willing to be shown wrong by someone with more expertise in this area.

9. Sep 4, 2013

### S.Daedalus

Then again, there are various 'non-localizability' theorems, most famously due to Malarment, that essentially show (or purport to show; nothing's clear cut once you let a philosopher into the room) that you can't really talk about the concept of particles in the same way one does in ordinary QM (a often-used statement is that 'there is no consistent relativistic theory of a fixed number of particles', on pain of superluminal spreading of wave functions).

Now, why do I consider this as a potential problem with the notion of collapse? Well, a key assumption in these theorems is some form of localizability (hence the name), i.e. a sufficiently sharply peaked wave function. Maybe there is a sense in which one could then consider this as a problem of measurement, instead of as a problem for particles? I'm not sufficiently familiar with these issues and work done in that direction to raise this as more than a possibility, though.

However, this would be nothing new for curved spacetimes, as the theorem already holds in Minkowsky space.

10. Sep 4, 2013

### atyy

I used to naively assume that in the flat spacetime case that the wave function collapse is simultaneous, where I use the canonical notion of simultaneous for an inertial observer. In the curved spacetime case, there is no canonical notion of simultaneity, and according to Palmer it isn't needed, so I guess it's not needed in in the flat spacetime case either - just causal structure.

The Palmer paper does talk about this problem, and restricts itself to a limit in which one can talk about localized particles. I think the overall picture is this:) Copenhagen is not a problem, since it is justified by Bohmian mechanics which in turn emerges from something else (like Valentini's non-equilibrium Bohmian). Within Copenhagen, in a theory of quantum gravity, there are no local observables at all, and no notion of spacelike even, since the geometry is fluctuating. This is AdS/CFT and the only observer who has quantum mechanics holding is the guy on the boundary with his S matrix. Then in a limit in which there is a classical spacetime and quantum gravity as an effective field theory, the strict observables are still only nonlocal like the S-matrix http://arxiv.org/abs/1105.2036 . Then in the limit where there's no backreaction, we should get local observables in the lab, and these are approximate http://arxiv.org/abs/hep-th/0512200. Then in some further limit going from special relativistic to Galilean relativity, things like position emerge as observables. So most quantum mechanics is emergent anyway, it's just emergent from bigger quantum systems. Anyway, was it really Malament who introduced the locality problem - I usually associate it with Newton-Wigner?

The funny thing is why does unitarity get retained in these emergent theories? There was quite an interesting comment on this by Aydemir, Anber and Donoghue in http://arxiv.org/abs/1203.5153.

Last edited: Sep 4, 2013