Subject: The quantised deus ex machina
Date: Mon, 18 Feb 2002 15:07:48 +0200
From: "Dimiter G. Chakalov" <dchakalov@surfeu.at>
To: Gebhard Gruebl <gebhard.gruebl@uibk.ac.at>
CC: oldstein@math.rutgers.edu,
     duerr@rz.mathematik.uni-muenchen.de,
     tumulka@rz.mathematik.uni-muenchen.de, zanghi@ge.infn.it,
     kmb@amath.unizh.ch, teufel@ma.tum.de,
     martin.daumer@imse.med.tu-muenchen.de,
     bohmmech@rz.mathematik.uni-muenchen.de,
     b.hiley@physics.bbk.ac.uk, stachel@buphy.bu.edu,
     j.fearns@ic.ac.uk, smoller@math.lsa.umich.edu,
     marco.matone@pd.infn.it
BCC: [snip]


Dear Dr. Grübl,

I like very much your remarks on Gleason's theorem [A.M. Gleason, J. Math. Mech. 6, 885 (1957)] and the measurement problem [Ref. 1]. May I ask two questions.

If what reference frame, and with what physical clock would you measure the time evolution of Bohmian state: "It is assumed to be given by a Schrödinger equation for the wave function and by a time dependent tangent vector field  v  on the configuration space." [Ref. 1]?

How would you approach the task of Lorentz invariant nonlocality? It seems to me that you would have to consider an individual quantum system. As Shelly Goldstein put it, the issue if extremely subtle,

http://plato.stanford.edu/entries/qm-bohm/#li

Please also see [Refs. 2 and 3].

I hope to hear from you. I will also appreciate the feedback from all colleagues of yours reading these lines.

Thank you very much in advance.
 

Regards,

Dimiter G. Chakalov
http://members.aon.at/chakalov
http://members.aon.at/chakalov/dimi.html
(last update 17 February 2002)
 

References

[Ref. 1] Gebhard Grübl, Klaus Rheinberger. Time of Arrival from Bohmian Flow.
http://xxx.lanl.gov/abs/quant-ph/0202084

"The standard quantum physical interpretation of this body of mathematical facts leads to the following conclusion. It is inconsistent to suppose that the state of an individual quantum system is a deterministic state, i.e. determines values for all observables, and it is inconsistent to suppose that a density operator  p  only describes a mixture of such fictitious deterministic states. (It is generally held inconsistent to suppose that an individual particle has a specific position and a specific momentum and so on.)

"From this conclusion then the notorious quantum measurement problem follows: How can standard quantum theory represent within its formalism the mere fact that individual closed systems do have properties? (This surely is the case for systems comprising an observer and not being in need of any sort of external observation inducing a state reduction, the quantised deus ex machina.)
...
"In order to work out the dynamical program of reducing all state properties to position properties, the time evolution of Bohmian states is needed. It is assumed to be given by a Schrödinger equation for the wave function and by a time dependent tangent vector field  v  on the configuration space."
 

[Ref. 2] Joel Smoller. The Interaction of Gravity with Other Fields.
http://xxx.lanl.gov/abs/gr-qc/0202057

"It follows that the Dirac particle *must* eventually either disappear into the black hole, or escape to infinity; these are the only possibilities."
 

[Ref. 3] Marco Matone. Equivalence Postulate and Quantum Origin of Gravitation.
http://xxx.lanl.gov/abs/hep-th/0005274