Subject: The anticipation region
Date: Thu, 17 Mar 2005 22:35:04 +0200
From: Dimi Chakalov <>
To: Mark Hogarth <>
CC: Klaus Scharff <>,
     Michael L G Redhead <>,
     Nick Bostrom <>,
     Oliver Pooley <>,
     Rituparno Goswami <>,
     Pankaj S Joshi <>,
     Cenalo Vaz <>,

     Louis Witten <>,
     Roger Penrose <>

Dear Dr. Hogarth,

I very much like your idea that the possibility of prediction
*necessitates* the existence of singularities [Ref. 1]. However, given
the recent studies on naked singularities [Ref. 2], I think your
'anticipation region' [Ref. 1, Fig 2] should be interpreted as 'global
mode of spacetime',

I will appreciate your professional comments, as well as those from your colleagues.

Kindest regards,

Dimi Chakalov


[Ref. 1] Mark Hogarth, A Remark Concerning Prediction and Spacetime Singularities, Studies in History and Philosophy of Modern Physics, 28(1), 63-71 (March 1997).


"Intuitively, singularities may be thought to oppose prediction, but in
this paper it will be shown that in a sense the opposite is true: if the
universe admits at least one ‘predictable event’ (as precisely defined
by Geroch), then a singularity is expected to exist. The method of proof for this theorem is to show that every spacetime that admits at least one predictable event must also admit a so-called ‘trapped set’. A version of the Hawking-Penrose singularity theorem is then employed to show that this set signals geodesic incompleteness, i.e. a singularity. A further result shows that the singularity cannot reside within a well-defined region ‘between’ the event of prediction and the event predicted.

"Thirdly, not all singularities cause trouble for determinism: only
those that are ‘naked’ necessarily do (ibid.). And finally, although
singularities (particularly naked ones) can stand in the way of
prediction, it is wrong to think that in the absence of singularities
prediction is normally a viable option: for prediction is impossible
even in most non-singular environments (Hogarth, 1993).
Hogarth, M., 1993, ‘Predicting the Future in Relativistic Spacetimes’,
Studies in the History and Philosophy of Science (supplement on the
History and Philosophy of Modern Physics) 24: 721-740.

"Now Theorem 1 proves that LP universes are singular, but another result (Corollary 2 in Section 3) actually shows that in any LP spacetime there is a well-defined region ‘between’ the event at which the prediction occurs and the event being predicted which must be non-singular (non-singular in a sense made precise in Section 3). I call this the anticipation region (again, made precise in Section 3), so-called because an observer in this region is either anticipating, or can manoeuvre into a position and begin to anticipate, what will happen at the predicted event. See Figure 2. Theorem 1 and Corollary 2 combine to show that in LP universes the complement of the anticipation region must be singular.

"This, incidentally, does not imply the existence of unpredictable
events in the complement of the anticipation region. That would
necessarily follow only if the expected singularity was ‘naked’, and
there is nothing to suggest it is. In fact I have no information about
this singularity; and in particular, I do not know whether it resides in
the past (like the ‘big-bang’) or in the future (like the ‘big-crunch’).

"The obvious physical interpretation of Theorem 1 is that prediction
entails a singularity. However if one takes the view that closed
timelike curves are not physically impossible, then the theorem could be interpreted as saying that prediction entails either a singularity or a
closed timelike curve, or perhaps both. In any case, Corollaries 1 and 2 show that the anticipation region is free from such anomalies."

[Ref. 2] Rituparno Goswami, Pankaj S. Joshi, Cenalo Vaz, and Louis Witten, A Time-Like Naked Singularity, gr-qc/0410041 v1

"We have an example that shows that even in spherically symmetric
collapse, the naked singularity need not always be either point-like or
null, but can have an interesting causal structure, including being



Subject: How to dispense from world points
Date: Fri, 18 Mar 2005 03:00:05 +0200
From: Dimi Chakalov <>
To: Luca Lusanna <>,
     Massimo Pauri <>

Dear Luca and Massimo,

I'm reading your recent paper "General Covariance and the Objectivity of Space-Time Point-Events" [Ref. 1] with great interest. I believe the general conjecture of Bergmann and Komar [Ref. 2] and your concrete hypothesis about a canonical basis of scalars, which could render "physical individuation of point-events fully invariant and objective" [Ref. 1], tallies to my efforts to suggest a Global Mode (GM) of spacetime,

Namely, we think of the "points" in the GM as intrinsically individuated *potential* events, where 'intrinsic' means that their identity is independent of the metric tensor field and its derivatives - a conjecture that might be loosely associated with some kind of GM

More on Einstein's GR at

Best regards,



[Ref. 1] Luca Lusanna and Massimo Pauri, General Covariance and the Objectivity of Space-Time Point-Events. Invited Contribution to the ESF 2004 Oxford Conference on Space-Time. March 17, 2005, gr-qc/0503069 v1

"From the physicists' point of view, GR has indeed been immunized
against the Hole Argument - leaving aside any underlying philosophical issue - by simply embodying the Argument in the statement that mathematically different solutions of the Einstein equations related by passive - as well as active (see later) - diffeomorphisms are physically equivalent. Showing that this statement cannot be regarded as the last word on this matter even from the physical point of view, is the main scope of this paper.

"Let us point out that the explicit expression of the gauge variables
and the Dirac observables in terms of the metric tensor field and its
derivatives is not known. We know nevertheless that such variables are highly non-local functionals involving the whole E hypersurface.

"The main result of our analysis is given in Section V where we show how the ontic part of the metric (the intrinsic degrees of freedom of the gravitational field) may confer a physical individuation onto space-time points. Since - as mentioned before - such degrees of freedom depend in a highly non-local way upon the values of the metric and its derivatives over a whole space-like surface of distant simultaneity, point-events receive a peculiar sort of intrinsic properties that, nevertheless, are conferred on them holistically.

"Admittedly, the distinction between ontic and epistemic parts, as well as the form of the space-like surfaces of distant simultaneity, are gauge-dependent (non-invariant). Yet, according to a main conjecture we have advanced in Ref. [14], a canonical basis of scalars should exist, making the above distinction and, therefore, physical individuation of point-events fully invariant and objective."

[Ref. 2] Peter G. Bergmann and Arthur Komar, The Coordinate Group Symmetries of General Relativity, Int. J. Theor.Phys. 5, 15-28 (1972).

"In general relativity the identity of a world point is not preserved under the theory's widest invariance group. This assertion forms the basis for the conjecture that some physical theory of the future may teach us how to dispense with world points as the ultimate constituents of space-time altogether."