Dear Professor Horwitz,

I learned about your universal parameter [tau] from your hep-ph/9606330 v1, and read with great interest your quant-ph/0507044 v3, in which you elaborated on the recent demonstration of presence-and-absence of interference for the same electron at the same time, in F. Lindner et al., quant-ph/0503165 v2.

I believe there exist a Holon state of the whole universe, which I call 'potential reality'. It can keep cat states not just for attoseconds but for arbitrary large time interval from the cosmological time arrow. If you or some of your colleagues are interested, I'll be happy to elaborate, starting from the 1931 paper by Schrödinger,

http://www.God-does-not-play-dice.net/Kiefer.html#note_1931

Kindest regards,

Dimi Chakalov
--
http://www.God-does-not-play-dice.net
http://www.God-does-not-play-dice.net/download.html

====

Subject: Re: Quantum interference in the universal parameter [tau]
Date: Thu, 29 Sep 2005 12:54:11 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Larry Horwitz <larry@post.tau.ac.il>

Dear Larry,

Thank you for your interest. Your papers are brilliant, there is so much behind them. I learned a lot from you. Thank you.

My web site is a mess; sorry. I dump there everything that comes into my mind, and it's like my cellar, full of 'valuable stuff that might be useful some day'. I can't read it for more than 15 min, honestly.

The message I want to deliver at

http://www.God-does-not-play-dice.net/Kiefer.html#note_1931

is that we abuse QM by applying the parameter  t  from STR, which is known beforehand, like the state of the Sun 'out there'.

We should instead think about 'the quantum state out there' as
'potential reality',

http://www.God-does-not-play-dice.net/Landsman.html#note_last

The latter exists like a Platonic idea: it casts its localized explications, but does not "collapse",

http://www.God-does-not-play-dice.net/Vecchi.html

Now, the two hypothetical modes of spacetime are explained (I believe) at

http://www.God-does-not-play-dice.net/Szabados.html#note

http://www.God-does-not-play-dice.net/Price.html#note

Please tell me how you understand all this.

Sorry again for inviting you to my huge "cellar".

I'll keep your feedback strictly private.

Best regards,

Dimi

=====

Subject: QM & STR
Date: Thu, 27 Oct 2005 11:50:57 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Brian Allan Woodcock <bwoodcoc@uwo.ca>
CC: Jeff Barrett <jabarret@uci.edu>,
     Larry Horwitz <larry@post.tau.ac.il>

Dear Brian,

> Perhaps the statement of mine you quote should be footnoted to reflect
> the sense of compatibility that my project is aimed at.

Yes of course. I believe there are many ways in which incompatibility
arises. All I wanted to suggest was that there could be a general class
of such cases. Please see below.

> You seem to suggest that the point you bring up about time as a
> parameter is sufficient to conclude that any future (and yet unknown)
> version of quantum theory and special relativity will be incompatible.
> What is your justification for this?  Is this just a hunch?

It's just a hunch, yes. I suppose there are two intrinsic features of QM & STR, which would make *any* reconciliation impossible in principle. Please see below.

> The strongest justification would be if you have a no go proof that
> quantum theory under any way of trying to fix it up will remain
> incompatible with special relativity in the way you suggest.  If you know
> of such a thing, I would be interested in learning about it.

I don't have any no-go theorem, and I cannot cast my hunch in math either. I can only offer some informal reflections on the subject matter.

1. For QM, I take for granted that *any* non-contextual interpretation will violate KS theorem. If true, such non-contextual interpretation can be proven either wrong or marred with intractable metaphysical speculations. In the latter case, I'd put it aside as a typical statement about Father Christmas' beard (I suppose you've glanced at my essay on GW astronomy).

Thus, I take for granted that 'objective reality out there' cannot exist in the quantum realm.

2. For STR, I take for granted that  'time' , as a c-number, refers *only and exclusively only* to 'objective reality out there'. Its value is supposed to be exactly known *prior* to QM measurement, as it labels fixed classical states (no cat states of the measuring device prior measurement).

3. Taking the two considerations together, I wrote at

http://www.God-does-not-play-dice.net/Kiefer.html#note_1931

"Thus, we know since 1931 that we contradict the very foundations of QM by applying the value of the variable  t . The latter is taken from the 'objective reality out there' of the classical world of STR (...)."

3.1. The well-known phrase 'immediately prior the collapse the quantum system was in state [X]' is wrong, because if it were true, we would be able to trace back the state [X] in our back light cone, and MERGE the time parameter from STR with something which does not exist: time operators in QM.

3.2. If we were able to merge the time parameter from STR with the "dynamics" of the collapse, we would establish/discover an absolute reference frame and 'absolute timeline', because the "dynamics" of the collapse is "instantaneous" in all frames.

3.3. The history of 'quantum system was in state [X]' cannot be traced back to the ENTRY POINT in our back (or forward, if you prefer) light cone. We can trace it to 'immediately prior the entry point'. Can't go further.

3.4. My speculation is that the 'entry point' can only be the apex of the cone, in line with the Ansatz about 'potential reality', as explained in my essay on GW astronomy (now 16 pages),

http://www.God-does-not-play-dice.net/gw.pdf

Put it differently, I suggest that the proper notion of time for QM & STR is the "time" of 'potential reality'. It includes the time in STR as a limiting case (the pocket of 'propensity states' being vanishing small; cf. p. 7 from gw.pdf). If I'm on the right track, I can suggest a notion of 'quantum reality', in line with my thesis 'dead matter makes quantum jumps; the living-and-quantum matter is smarter'. More at

http://www.God-does-not-play-dice.net/Kiefer.html#Isham

Best regards,

Dimi

==========

From: Dimi Chakalov <dimi@chakalov.net>
To: Larry Horwitz <larry@post.tau.ac.il>
Cc: Stan Brodsky <sjbth@slac.stanford.edu>,
Chris Isham <c.isham@imperial.ac.uk>,
Erasmo Recami <Erasmo.Recami@mi.infn.it>
Subject: Re: QM & STR
Date: Fri, 28 Oct 2005 21:58:13 +0300

Dear Larry,

Thank you very much for your prompt reply. I'm very impressed by your
publication list. If possible, may I ask you for a copy from

L.P. Horwitz, R.I. Arshansky and A. Elitzur, On the two aspects of time: The distinction and its implications, Foundations of Physics 18 (1988) 1159-1193.

You wrote:

> However, we know that the axiomatic basis for the NR quantum theory
> calls for a set of measurements to be made at a given time t (see Piron's
> book, Foundations of Quantum Physics). The corresponding axiomatic
> basis for the relativistic theory would correspond to a set of
> measurement made at a given \tau, but since we only observe x,t
> directly, it is difficult to know at which \tau a given measurement is
> made. This problem is still open.

Let me share my thoughts on this problem. I believe Erwin Schrödinger pointed out the acute problem of the "sharp time" of STR in 1935 [Ref. 1], and it seems to me that the question 'at which \tau a given measurement is made' may never be resolved: we need both the sharp time and the extended domain of \tau.

You suggest to treat t as a dynamical variable, rather than a c-number, and suggest adding \tau as an additional coordinate in configuration space [Ref. 2], while I think the universal time \tau (I call it 'global mode of
spacetime') refers to 'potential reality', in the sense that two or more
(infinitely many) *potential events* may overlap in the local mode of
spacetime.

How do they "overlap"? If you look at Stan Brodsky's web site, you will see a surface crossing the cone at the apex,

http://www.slac.stanford.edu/grp/th/Brodsky/BrodskyHome.html

http://God-does-not-play-dice.net/Brodsky.html#1

I suggest to place all *potential events* on a null-plane; that's how the
global mode of spacetime should "look" from the local mode. Please see also

Spacetime Mediation of Quantum Interactions
http://www.mathpages.com/rr/s9-11/9-11.htm

Quantum Interactions on Null Surfaces
http://www.mathpages.com/home/kmath238.htm

http://www.God-does-not-play-dice.net/Brown.html#Erasmo

The sharp time of STR [Ref. 1] can filter one-event-at-a-time through the
apex, while the rest of potential events may stay on the null-plane, ready to 'jump inside' the cone, if needed. See the interpretation of 'quantum jump' on p. 16 in

http://www.God-does-not-play-dice.net/gw.pdf

Another reason for my efforts to 'have my cake and eat it' (keep the sharp
time of the local mode and the extended "time" of the global mode) is the
normalization procedure: we need a sharp, fixed instant w.r.t.w. we impose the rule. Can't normalize probabilities over an extended time interval, which is, I believe, the problem encountered by Chris Isham in his recent neo-realist paper, quant-ph/0508225. If we don't include the act of measurement that will kill the wave function, but instead operate with counterfactuals, they will spread over a finite time interval from the *global mode* of spacetime. But we need the sharp time to solve the normalization problem, namely, we have to pinpoint an instant of time (local mode) at which the probabilities for an exhaustive set of mutually exclusive alternatives would add up to one. Hence solving the normalization problem without the global mode (null-plane) may be
impossible,

http://www.God-does-not-play-dice.net/Kiefer.html#Isham

Anyway, I will be very happy to read your 1998 paper on the two aspects of time, requested above. Also, if you have some ideas on the dark energy in 5-D inflationary cosmology [Ref. 2], please let me know.

Best regards,

Dimi
--
D. Chakalov
Box 13, Dragalevtsy
BG-1415 Sofia, Bulgaria


References

[Ref. 1] Erwin Schrödinger, "Die gegenwärtige Situation in der
Quantenmechanik", Naturwissenschaften 23, pp. 807-812; 823-828; 844-849 (1935). Translated by John D. Trimmer, Sec. 15, Natural Law or Calculating Device?
http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html#sect15

"That "sharp time" is an anomaly in Q.M. and that besides, more or less
independent of that, the special treatment of time forms a serious hindrance to adapting Q.M. to the relativity principle, is something that in recent years I have brought up again and again, unfortunately without being able to make the shadow of a useful counterproposal."


[Ref. 2] Time and the Evolution of States in Relativistic Classical and
Quantum Mechanics. Presented at the conference on Physical Interpretations of Relativity Theory, Imperial College, 6-9 September, 1996. hep-ph/9606330 v1.

"Nonrelativistic quantum mechanics, making explicit use of the Newtonian
notion of a universal, absolute time, provides a description of such a state
in terms of a square integrable function over spatial variables at a given
moment of time. This function is supposed to develop dynamically, from one moment of time to another, according to Schrödinger's equation, with some model Hamiltonian operator for the system."
...
"To understand the role of t as a dynamical variable, rather than a c-number parameter, we must examine carefully the Einstein notion of time.
...
p. 6: "What we explicitly assume, as a postulate, is that *there exists a
universal time by means of which dynamical interactions are correlated*.

"We are, however, free to postulate that two events which overlap in
spacetime, but have different values of the universal time \tau , are not
identically the same physical objects. The separation can be easily seen
graphically by adding \tau as an additional coordinate in configuration
space."
...
p. 16: "(S)ubstituting this formula into the expression for the invariant
interval leads to a *five*-dimensional metric tensor, somewhat similar in form to that of Kaluza-Klein. The energy momentum tensor, before integration over its world history, would then form the source term for this (pre-)Einstein theory. Some preliminary investigations have been made of this structure [33]."

=====

Note: In Non-Relativistic (NR) quantum mechanics, the Schrödinger equation "governs" the evolution of the state "in between" measurements, which refers to the universal time \tau (global mode of spacetime). We add by hand a simple "collapse" rule, after von Neumann and Born, to produce the local mode of spacetime: the projection on the outcome of the measurement. Jim Hartle explains (gr-qc/0510126 v1):

"Both of these laws of evolution assume a fixed background spacetime. A fixed geometry of spacetime is needed to define both the t in the Schrödinger equation and the spacelike surface on which the state
vector is reduced.

"But, in quantum gravity, the geometry of spacetime is not fixed. Rather geometry is a quantum variable, fluctuating and generally without a definite value. There is no fixed t. Quantum mechanics must therefore be generalized to deal with quantum spacetime."

Welcome aboard! See paragraph 8 in my note from July 16, 1997. I referred to the seminal paper by Jim Hartle "Quantum Cosmology: Problems for the 21st Century?",  gr-qc/9701022, but never heard from him. As if Jim Hartle was collecting bottle labels, while I was suggesting to switch to paper napkins. He wouldn't droop his favorite hobby. More at his dedicated web page here.
 

D. Chakalov
November 1, 2005
--

Sage, was du willst, solange dich das nicht verhindert, zu sehen, wie es sich verhält. (Und wenn du das siehst, wirst du Manches nicht sagen.)

Ludwig Wittgenstein