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Dear Dr. Weinstein,
I read your essay on 'Non-local Constraints' with great interest. What you mention in your opening passage is certainly something that has been overlooked in the current theories and it is a Fundamental Problem that we definitely need to address:
You wrote: "non-relativistic and relativistic, classical and quantum - share one assumption: the features of the world at distinct points in space are understood to be independent. Particles may exist anywhere, independent of the location or velocity of other particles".
However, I feel that the present fashion and fascination with 'large-scale structure physics' i.e. cosmological theories (rather hypotheses), is distracting our attention from making the required connections between micro and macro physics in regard to such concepts as 'non-local constraints'. I think it would be more fruitful to look at things more closer to home, on geodynamics and planetary physics for which we have a lot of verifiable data already available.
For instance, when another planet changes its position with respect to the earth, earth's rotation changes (this is most pronounced with the position of Jupiter). On the other hand present theories cannot account for earth's rotation. Rather it says that earth's rotation is the remnant of angular momentum from condensation, after losing most of it in the intervening period due to tidal friction. This draws a picture of a continuous decline of earth's rotation due to tidal friction. Then if there are no non-local couplings with earth's rotation, then how can it be that it fluctuates periodically with the distance and relative velocity of the sun, moon and the planets?
Earth's lunar and solar tides are 'explained' by gravitational attraction. However, Sun's gravitational attraction of the earth is as many times (100 times?) as great as that of the moon. There are two unanswered questions here. How come that the Lunar tide is twice as great as the solar tide (and not 100 times less)? Secondly, when the attraction is on one side, and water is attracted to that side as expected, but how can a bulge also appear on the other side? (Ofcourse, there are concocted explanations like the earth's centre shifting while the water on the other side remaining still in absolute space!!)
Connected to the tidal theory is the theory of precession of the earth's axis. This is a complete sham. It is fabricated by contriving the required answers by pe-fixing the value of the constant called "mechanical ellipcity". All the above problems can be solved, by non-local actions occurring due to the impact of the velocity of a body in one location, on another body in another location. (Unfortunately the sad story is, I have not been able to have these papers published for whatever reasons, except in some conference proceedings).
You wrote:
"I would conclude by reminding the reader that the sort of nonlocality under discussion in no way violates either the letter or the spirit of relativity".
We must remember that Einstein himself did not consider his theories as final.
"No influences travel faster than light".
I would leave this question open in regard to non-local signals - Alain Aspects experiment. However, with the Algorithm of Motion of matter particles, I have developed on the basis of energy-momentum equation, it can be proved that matter particles cannot travel even at c ("the speed of light").
"The idea is simply that there are correlations between spatially separate degrees of freedom, and thus that the fabric of nature is a more richly structured tapestry than we have heretofore believed".
I totally agree with this statement.
Now it is obvious that Non-Local constraints have to a) act through the field and b) the action has to take the form of induction. Although I have not covered non-local action per se in my essay, I have covered a whole bunch of interconnected fundamental problems in it : The open system I have developed, with in flow and outflow from and to the field, accounts how induction works.
If you can find the time, I request you to please have a look at my essay - "A Treatise on Fundamental Problems of Physics" posted on Sep 06 on FQXi.
I quote the list of problems:
"We may note that among the problematic foundational concepts created by Newton that have congenitally infected RT and QM are a) the primacy of the concepts of space and time, b) representation of bodies as mass-points without internal structure, c) consideration of centrifugal force as a pseudo-force, d) the closed system with the consequent inability to account for inflow and outflow of energy between the system and the field etc. e) Not recognizing that it is by the two quantities of energy (Mc2 and pc) fusing together to form a system that motion occurs. f) the omission of the fact that a fraction of the applied energy of motion pc gets usurped for the co-movement with the location. g) Not developing the theory with state changes of energy as the basis of its physical geometry. With these congenital foundational problems being inherent in these two progeny theories as well, it should be obvious that revamping of physics must begin from where the problems originated".
Best regards,
Viraj.
PS. By the way, I live in Toronto, and have been very much impressed with the policies of the Perimeter Institute. I have wanted to take a drive to Waterloo to meet the natural philosophers (academics) there for some time. But I did not know whom to contact. So it never happened. - VF