Subject: "I only wish I could have acted on all suggestions!" (arXiv:0708.2192v1 [quant-ph])
Date: Fri, 17 Aug 2007 15:22:35 +0300
From: Dimi Chakalov <[email protected]>
To: Jeremy Nicholas Butterfield <[email protected]>

Dear Jeremy,

RE your arXiv:0708.2192v1 [quant-ph] and 'The moral in general
relativity', arXiv:0708.2189v1 [quant-ph], perhaps you may wish to

Since you endorse the "block-universe", I suppose you wouldn't like to comment on the ideas outlined above, as you haven't done it in the past seven years. It would be nice if you at least acknowledge the receipt of this email.

As ever,


Note: Regarding arXiv:0708.2192v1 [quant-ph], Sec. "Events and regions", and Reichenbach's Principle of the Common Cause (ibid., Eq. 39, p. 28), notice that the third event  C  in the “common past” of the two correlated events, “screens them off”, in the sense that their correlation disappears “once we conditionalize on C”.

But what is the dynamics of this Common Cause, or 'third event', C ? See a simple example with four dice here, from the second link above. If we place  C  in the “common past”, it cannot change in time, hence we again arrive at the "block universe". If we place  C  in the future, it will act backward in time (advanced causality). Hence the only option left is to place  C  in the global mode of spacetime.

Jeremy Nicholas Butterfield has never made any comment on the proposal that  C  should be placed in the putative global mode of spacetime, instead of placing it in the “common past” of the two correlated events. The immediate consequence from my proposal is that he should either refute it, or forget about the so-called "block universe" and re-write his papers.

D. Chakalov
August 17, 2007




Subject: From regions to points
Date: Fri, 14 Jun 2002 20:17:18 +0300
From: "Dimiter G. Chakalov" <[email protected]>
To: "Dr J.N. Butterfield" <[email protected]>
CC: [email protected], [email protected]

Hi Jeremy,

I spotted your name in Sec. Acknowledgments of Chris Isham's quant-ph/0206090 [Ref. 1].

Perhaps you or John could be so kind as to help me understand the basic premise in your approach. May I ask two questions.

In relative-frequency interpretation of probability, you can get "points"  IFF  you set N --> [infinity], "as is appropriate for a hypothetical 'infinite ensemble'" [Ref. 1].

1. Is there anything which you set to approach infinity? If yes, how does it 'get there' so that you can get "points"? These are very old questions,

2. How do you get points "determined in some way by the regions" [Ref. 1] while keeping the regions 'alive and kicking' for a finite time interval, as measured with your wristwatch? Regarding the latter, please see my recent email to Bob Wald,

I believe you know about my proposal,

I'm just trying to understand yours.

Best regards,


[Ref. 1] Chris Isham. Some Reflections on the Status of Conventional Quantum Theory when Applied to Quantum Gravity. Imperial/TP/01-02/20, 14 May 2002.
Thu, 13 Jun 2002 18:40:05 GMT,

"However, one of the key questions of interest in the present paper is not how the standard ideas of space and time (and probability) might *emerge* from a different formalism; but rather how one might proceed to construct a quantum theory *ab initio* in which whatever fundamental spatio-temporal concepts are present are definitely not the familiar continuum ones: for example, if one is given a finite causal set as a background structure. The first step, and the only one taken in the present paper, is to sound a cautionary note by emphasizing how strongly the continuum ideas of space and time are implicitly embedded in the standard formulation of quantum theory.

"My concern is that the use of these numbers may be problematic in the context of a quantum gravity theory whose underlying notion of space and time is different from that of a smooth manifold. The danger is that by imposing a continuum structure in the quantum theory *a priori*, one may be creating a theoretical system that is fundamentally unsuitable for the incorporation of spatio-temporal concepts of a non-continuum nature: this would be the theoretical-physics analogue of what a philosopher might call a 'category error'. For this reason, it is important to consider carefully the origin, and role, in standard quantum theory of this particular facet of the real (and complex) numbers.

In general terms, the real numbers arise in three ways in physical theories: (i) as the values of physical quantities; (ii) to model space and time; and (iii) as the values of probabilities. Our present task is to consider more precisely the use real numbers in quantum theory in these terms.

"It is thus pertinent to ask *why* physical quantities -- classical or quantum -- are taken to be real-valued. Many will doubtless say that the answer is obvious, or that it is even part of the definition of a physical quantity, but I would challenge these assertions as being over-hasty.

One reason why the values of physical quantities are assumed to be real numbers is undoubtedly the operational one that -- at least, in the pre-digital age -- physical quantities are ultimately measured with rulers and pointers, and so it is the assumed continuum nature of physical space that comes into play.

However, it is by no means obvious that physical quantities should necessarily be real-valued in, for example, a quantum gravity theory in which it is not appropriate to think of space as a smooth manifold, and where, therefore, there is no place for operational considerations that presuppose a continuum nature for space and/or time.

Of course, it is a totally open question as to what should replace  R  as the value space of a physical quantity in these circumstances -- it could be something as obvious as a finite number field, but it could also be something far more radical. In any event, a key role in deciding this issue should be played by any underlying spatio-temporal concepts (albeit, non-standard) that are present.

"In the context of standard physics, it is clear why probabilities are required to lie in the interval [0,1]. As physicists, we most commonly employ a relative-frequency interpretation of probability in which an experiment is repeated a large number, say N, times, and the probability associated with a particular result is then defined to be the ratio N_i/N, where N_i is the number of experiments in which that result was obtained. The rational numbers N_i/N necessarily lie between 0 and 1, and if we take the limit as  N --> [infinity] , as is appropriate for a hypothetical 'infinite ensemble', we get real numbers in the closed interval [0, 1].

p. 9: "Under such circumstances it might be more natural to follow Aristotle, Heisenberg and Popper in adopting a *propensity* interpretation of probability, perhaps within the context of a 'post-Everett' form of quantum theory, such as consistent-histories theory.

"However, if probability is viewed in this more realist way, there is no overwhelming reason for assigning its values to be real numbers lying in the interval [0, 1]. The minimal requirement is presumably only that the value space should be a partially ordered set (V,<_and_=) so that it makes sense to say that certain events are more, or less, probable (in the sense of the partial-ordering operation <_and_=) than others.

"3.1.1 From points to regions

"In standard general relativity -- and, indeed, in all classical physics -- space (and similarly time) is modelled by a set, and the elements of that set correspond to points in space. However, it is often claimed that the notion of a spatial (or temporal) point has no real physical meaning, and this motivates trying to construct a theory in which 'regions' are the primary concept. In such a theory, 'points' -- if they exist at all -- would play a secondary role in which they are determined in some way by the regions (rather than regions being collections of points, as in standard set theory).

"This could give valuable insight into what is perhaps the hardest task of all: to construct a quantum formalism for use in situations where there are no prima facie spatio-temporal concepts at all -- a situation that could well arise in a quantum gravity theory in which all of what we might want to call "spatio-temporal concepts" emerge from the basic formalism only in some limiting sense.


"Some of the material presented here is a development of earlier work [1] with Jeremy Butterfield. I am grateful to him for permission to include this material."


Subject: Panta rei conditio sine qua non est
Date: Tue, 19 Oct 2004 16:58:41 +0300
From: Dimi Chakalov <[email protected]>
To: Jeremy Nicholas Butterfield <[email protected]>
CC: Chris Isham <[email protected]>,
     Karel Kuchar <[email protected]>

Dear Jeremy,

I read last night some of the papers you sent me three years ago, and, as it always happens with reading papers from you, Chris, and Karel, I found some new ideas, which I typed a few minutes ago and posted at

Thank you all very much!

No need to reply, please, I know you're very busy.

Best regards,