Dear Dr. Suneeta,

I'm reading your "Notes on Euclidean de Sitter space", hep-th/0209156 [Ref. 1], with great interest. I have a gut feeling that you're approaching something very important.

Please correct me if I'm wrong. The causality in STR is preserved iff no influence faster than the speed of light in vacuum is present, provided that the objects obtained their correlation at some common event in their joint past light cone.

I'm wondering, what if the correlation does not come/evolve from some common event in the joint past light cone nor from from the future light cone (as in Hellwig-Kraus reduction [Ref. 2]) but from a special holistic state which can not, even in principle, be located on the spacetime hypersurface.

What I mean is Reichenbach's Common Cause Principle: If two events  A  and  B  are correlated, then the correlation between  A  and  B  is either due to a direct causal influence connecting  A  and  B , or there is a third event  C  which is the common cause of the correlation.

Can you interpret your two-particle solution [Ref. 1] as the third event  C  in Reichenbach's Common Cause Principle? I believe the task is to reconstruct a classical spacetime from nonlocal diffeomorphism-invariant observables [Ref. 3]. Please see also Manfred Requardt's hep-th/0205168,

http://members.aon.at/chakalov/Tajmar.html#6

I will appreciate the opinion of your colleagues as well.

BTW I've compiled a CD ROM,

http://members.aon.at/chakalov/Brun.html#seminar_Imperial

If you agree for a brief and informal review, I will be happy to send it.

With kind regards,

Dimi Chakalov
http://members.aon.at/chakalov
--
Dead matter makes quantum jumps; the living-and-quantum matter is smarter.
 

References

[Ref. 1] V. Suneeta. Notes on Euclidean de Sitter space. Wed, 16 Oct 2002 13:31:30 GMT,
http://xxx.lanl.gov/abs/hep-th/0209156
Journal-ref: JHEP 0209 (2002) 040

"2) There is however no single point mass solution! This is in fact a two-particle solution. (...) Thus constant time slices are spheres with a wedge removed - corresponding to a point mass each at the north and south poles making this a two-particle solution.
...

"Now, looking at the analytic continuation of de Sitter from this perspective, we see that the de Sitter static patch is like 'the inside' of the black hole, i.e. the horizon is now the *outer*, rather than the *inner* boundary of the physically accessible spacetime."
 

[Ref. 2] R. Srikanth. Observables in Relativistic Quantum Mechanics.
http://xxx.lanl.gov/abs/quant-ph/0103070
 

[Ref. 3] S. Carlip. Quantum Gravity: A Progress Report.
http://xxx.lanl.gov/abs/gr-qc/0108040

"When we look more closely, however, it is not so clear that these two pillars are part of the same edifice. The foundations of general relativity -- a dynamical spacetime, with no preferred reference frame -- clash with the needs of quantum theory, which in its standard formulations requires a fixed background and a preferred splitting of spacetime into space and time. Despite some 70 years of active research, no one has yet formulated  a consistent and complete quantum theory of gravity.
...

"We must, for instance, understand how to approximately reconstruct a classical spacetime from nonlocal diffeomorphism-invariant observables."