The measurement problem and approaches to quantum gravity

[MaverickMenzies]

Hi, does anyone know whether any of the current approaches to Quantum Gravity shed any light on the measurement problem in quantum mechanics? Moreover have there been any attempts to consider the implications of the measurement problem from within either the string theory approach or the quantum geometry approach?

 

[Demystifier]

I have several my own results on the relation between quantum gravity/string theory and Bohmian interpretation of quantum mechanics.

First, in
http://xxx.lanl.gov/abs/hep-th/0407228
http://xxx.lanl.gov/abs/hep-th/0601027
I argue that the requirement of general covariance on the quantum level of bosonic fields naturally leads to a quantization method based on the de Donder-Weyl covariant canonical formalism, which, in turn, implies the (covariant) Bohmian equation of motion for fields.

Then, in
http://xxx.lanl.gov/abs/hep-th/0512186
I extend the idea above to show that the world-sheet covariant quantization of a bosonic string implies the (covariant) Bohmian equation of the string.

In
http://xxx.lanl.gov/abs/hep-th/0702060
I present further evidence for the relation between string theory and Bohmian mechanics. In particular, I find that string theory provides a simple solution of the problem of particle creation/destruction in Bohmian mechanics, as well as of the problem of fermions in Bohmian field theory.

Finally, in
http://xxx.lanl.gov/abs/0705.3542
I use the results of the previous paper to derive string theory from the requirement that Bohmian mechanics should be compatible with particle creation/destruction. In addition, I propose an experimental low energy test of this theory, which could test both Bohmian mechanics and superstring theory at once.

Needless to say, all these results are far from belonging to a part of the mainstream research.

 

[marcus]

Here's WikiP about the *measurement problem*
http://en.wikipedia.org/wiki/Measurement_problem
Do you have anything to add, just by way of defining the problem?

It strikes me as having to do less with Quantum Gravity and more with INTERPRETATIONS of QM and with FOUNDATIONS.

However, people who do QG have also considered foundations questions and have written papers that would have some bearing.

In this relational interpretation of QM by Rovelli there is, if I understand it correctly, no measurement problem. But there is no absolute wavefunction existing in nature. Each observer has a wavefunction describing what he knows about the system. QM is about the information that one system has about another.
http://arxiv.org/abs/quant-ph/0604064
Relational EPR
Authors: Matteo Smerlak, Carlo Rovelli
Found.Phys. 37 (2007) 427-445
(Submitted on 10 Apr 2006 (v1), last revised 4 Mar 2007 (this version, v3))

Abstract: We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of 'non-locality', when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.

In this proposed reformulation of QM by Smolin, if it could be carried out, there would be no measurement problem
http://arxiv.org/abs/quant-ph/0609109
Could quantum mechanics be an approximation to another theory?
Authors: Lee Smolin
(Submitted on 14 Sep 2006)

Abstract: We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by averaging over variables which are not internal to the subsystem, which may be considered non-local hidden variables. We find conditions for arriving at quantum mechanics through such a procedure...

 

[Demystifier]

It is also interesting to say that, although Rovelli and Smolin mentioned above are very famous physicists, their work above on foundations of quantum mechanics is also far from belonging to a part of the mainstream research.

 

[ccdantas]

Hi Demystifier,

What is the mainstream research on foundations of quantum mechanics?? Would you say this paper reflects the mainstream?

http://prola.aps.org/abstract/RMP/v64/i2/p339_1

Thanks

Christine

 

[marcus]

It is also interesting to say that, although Rovelli and Smolin mentioned above are very famous physicists, their work above on foundations of quantum mechanics is also far from belonging to a part of the mainstream research.

That is certainly true, Demy! Especially in the case of that particular paper by Smolin.
It is very far from central mainstream, which could be a good thing. Airing a radically new, very tentative idea.

what I would say about the Smolin paper is that it corresponds to what the O.P. was asking about in the sense that it has to do a type of quantum gravity which pictures the universe as an evolving network. Evolving according to QG rules, space expands but some residual non-local connections remain from the early universe.
These rare nonlocal connections are the source of uncertainty or indeterminacy observed at the quantum level. So they are "non-local hidden variables" which have arisen according to a quantum gravity model of an expanding universe.

This is a connection between QG and the foundations of QM. It is extremely speculative. Your calling it "not mainstream" is, I would say, a considerable understatement! But that is not necessarily bad and the paper, if I remember correctly, is quite frank about its speculative and tentative nature.

 

[Demystifier]

Would you say this paper reflects the mainstream?

http://prola.aps.org/abstract/RMP/v64/i2/p339_1

I would say it is a bit more mainstream, although not main-mainstream.

I would say that mainstream papers are those that adopt a version of the information-theoretic interpretation. E.g.
http://xxx.lanl.gov/abs/quant-ph/0212023

 

[marcus]

I would say that mainstream papers are those that adopt a version of the information-theoretic interpretation. E.g.
http://xxx.lanl.gov/abs/quant-ph/0212023

I am glad you think so! I have a high opinion of Asher Peres and his information-theoretic approach. BTW after Peres death, his co-author Danny Terno went to Perimeter. Probably still there. I'll copy part of the abstract
http://xxx.lanl.gov/abs/quant-ph/0212023
Quantum Information and Relativity Theory
Authors: Asher Peres, Daniel R. Terno
32 pages, Rev.Mod.Phys. 76 (2004) 93
(Submitted on 4 Dec 2002 (v1), last revised 7 Jul 2003 (this version, v2))

Abstract: Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. ... Special relativity imposes severe restrictions on the transfer of information between distant systems. Quantum entropy is not a Lorentz covariant concept. ...

A related 2004 Peres paper is one that Rovelli cited at the conclusion of *Relational EPR*. He found considerable overlap between his relational QM and Peres quantum information approach.

The last paragraph of the introduction to Rovelli's paper:

"Similar criticisms to the notion of 'quantum nonlocality'
have been recently expressed by a number of
authors [19, 20, 21, 22]. In particular, in a recent article
[23], Asher Peres concludes his analysis of the EPR
problem with a general statement, which, as we shall see
below, is precisely the ground assumption of RQM. Thus,
if we are inclined to accept RQM as a way to make sense of
quantum theory, the EPR correlations can be interpreted
as supporting this point of view."

The last paragraph in the conclusions section:

"...This recalls the conclusion that the late Prof. Peres
reached in his analysis of EPR in 2004: “The question
raised by EPR ‘Can the quantum–mechanical description
of physical reality be considered complete?’ has a positive
answer. However, reality may be different for different
observers” [23]. This is the idea at the basis of RQM."

Ref [23] A. Peres, “Einstein, Podolsky, Rosen, and Shannon”
Found. Phys. 35, 511-514 (2004)