Subject: Too much freedom in QM and GR
Date: Wed, 23 Jan 2002 18:56:24 +0200
From: "Dimiter G. Chakalov" <dchakalov@surfeu.at>
To: shimony@bu.edu
CC: stachel@buphy.bu.edu, ashtekar@gravity.phys.psu.edu
BCC: [snip]

Dear Professor Shimony:

Thank you, once more, for your kind reply from Tue, 22 Jan 2002 13:14:05 -0600.

I just thought about an issue which I'm sure is in the realm of your expertise [Ref. 1]. May I ask for your opinion on the "too much freedom" in QM and in GR, as explained below.

Regarding the non-covariance of the state reduction process, Bloch [Ref. 2] argued that the hypersurface on which the state reduction may be taken to occur can be chosen arbitrarily, since that choice will not affect the probability distribution of all local observables. This prescription is not only non-covariant, but also shows that there is *too much freedom* in choosing a "preferred" hypersurface. In fact, there is no such thing, whichis one of the reasons why we haven't developed a theory of Lorentz invariantnonlocality, as well as a general solution to the basis problem in QM.

Similarly, in GR there is too much freedom in choosing some "preferred" spacetime foliation [Ref. 3], but there is no such thing, again.

It seems to me that in both cases there is (unlimited?) freedom of choice, but the 'choser' (Pearle) is not there,

http://members.aon.at/chakalov/Matone.html

I believe we can attribute these peculiar facts to the putative global time mode. It does not exist in the local time mode, as read with any physical clock,

http://members.aon.at/chakalov/Stachel.html#PS

and can be operationally defined as "the phenomenon which does not allow things to go into zero dimensions, such as a mathematical point",

http://members.aon.at/chakalov/PHI.html#point  ,

as implied by many paradoxes due to Zeno, Lucretius, and Thompson,

http://members.aon.at/chakalov/Giovanni.html

This is the only way I can envisage the solution to the problem of time in quantum gravity: in the global time mode, you have the 'chooser' of *one* propensity (potentiality). It acts dynamically, one selection at a time, along the putative universal time arrow. In each selection 'now' you have a set of *already* normalized physical stuff, as seen in your past light cone only.

Otherwise you're felt with the problem of Ashtekar [Ref. 4],

http://members.aon.at/chakalov/Ashtekar.html

which neither he nor anyone else has solved so far.

Please correct me if I'm wrong.

Looking forward to hearing from you and from Professor John Stachel,

Best regards,

Dimi

P.S. You can read this email also at my web site,

http://members.aon.at/chakalov/Shimony.html
 
 

References

[Ref. 1] A. Shimony (1997). On Mentality, Quantum Mechanics and the Actualization of Potentialities. In: R. Penrose. The Large, the Small and the Human Mind. Cambridge: Cambridge University Press, pp. 144-160.
 

[Ref. 2] I. Bloch (1967). Some relativistic oddities in the quantum theory of observation. Physical Review 156, 1377-1384. (Quoted after: Federico Laudisa, Non-Locality and Theories of Causation, quant-ph/0111028.)
 

[Ref. 3] J. Butterfield and C.J. Isham (1999). Spacetime and the Philosophical Challenge of Quantum Gravity.
http://xxx.lanl.gov/abs/gr-qc/9903072

[Section Time in General Relativity]:

"When we turn to classical general relativity, the treatment of time is very different. Time is not treated as a background parameter, even in the liberal sense used in special relativity, viz. as an aspect of a fixed, background spacetime structure. Rather, what counts as a choice of a time (i.e. of a timelike direction) is influenced by what matter is present; (as is, of course, the spatial metrical structure). The existence of many such times is reflected in the fact that if the spacetime manifold has a topology that enables it to be foliated as a one-parameter family of spacelike surfaces,this can generally be done in many ways -- without any subset of foliations being singled out in the way families of inertial reference frames are singled out in special relativity. From one perspective, each such parameter might be regarded as a legitimate definition of (global) time. However, in general, there is no way of selecting a particular foliation, or a special family of such, that is 'natural' within the context of the theory alone. In particular, these definitions of time are in general unphysical, in that they provide no hint as to how their time might be measured or registered."
 

[Ref. 4] A. Ashtekar. Mathematical Problems of Non-perturbative QuantumGeneral Relativity.

http://xxx.lanl.gov/abs/gr-qc/9302024

"At a fundamental level, since there is no background metric, there is no a priori notion of time either. What does dynamics and evolution even mean if there is no background space-time? How is time born in the framework?
...
"The probabilities for an exhaustive set of mutually exclusive alternatives should add up to one. In quantum mechanics, this is generally ensured by using an instant of time to specify such alternatives. What is one to do when there is no time and no instants? These are fascinating issues."