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Status of relativistic 2-body problem

by HeavyWater
Tags: 2body, relativistic, status
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HeavyWater
#19
Feb19-12, 11:13 AM
P: 17
Quote Quote by Dickfore View Post
Regarding Currie, Jordan, Sudarshan's reference, here's a link:
http://dx.doi.org/10.1103/RevModPhys.35.350
Thank you Dickfore,
That article is a "classic". I've read it numerous times and I'm embarrassed to say that I still don't understand all of it. Now that I'm retiring, I'll have plenty of time to continue to study it.

Thanks for your suggestion,
HeavyWater
HeavyWater
#20
Feb19-12, 11:33 AM
P: 17
Quote Quote by Dickfore View Post
So, in the first paragraph of the Introduction it says:
"...But the combined requirements of relativistic symmetry and manifest invariance may restrict the theory so severly that it is capable only of describing non interacting particles. We will show that this is in fact the case in a Lorentz symmetric classical mechanical theory of the motion of a pair of particles..."

So, I guess this goes in favor of my first post in this thread. The point is that, due to the finite speed of propagation of interactions, one ought to consider a field as a physical object carrying the interaction. A field has (innumerably) infinitely many degrees of freedom, and the Lorentz invariant two-body problem turns into a problem in continuum mechanics.
Thank you for taking the time and for your thoughtful response. I am looking at a copy of the paper right now. Let me spend the rest of the day reviewing it and collecting my thoughts and questions and I will get back with you tomorrow.

Heavywater
HeavyWater
#21
Feb19-12, 11:40 AM
P: 17
Quote Quote by juanrga View Post
So far as I know that classical theory has not advanced since Trump and Schieve published their monograph and, as they admit in the monograph, the current theory only can solve some weak-field defects of general relativity.

There is some interest in the application to many-body quantum bound problems, where quantum field theory also fails, and some recent attempts to apply the new relativistic theory to an extension of string/brane theory (which inherits the defects of both quantum field theory and general relativity): The Landscape of Theoretical Physics, A Global View: From Point Particles to the Brane World and Beyond in Search of a Unifying Principle. But as said before the whole theory is still open to many technical objections.

Another attempt to solve the defects of field theory is by Chubykalo and Smirnov-Rueda

See specially the Physical Review E paper correcting the defects of Maxwell theory of electrodynamics and their experimental application in Journal of applied physics.

Chubykalo and Smirnov-Rueda approach has been recently extended to many-body gravitation, with the bonus that the new potentials solve the dark matter problem (dark matter is fictitious). See Modified Newtonian Dynamics and Dark Matter from a generalized gravitational theory
Thanks Juanrga,
I'll have to get copies of these papers on Tuesday, to give you an intelligent reply. Thanks for your inputs and I'll get back with you as soon as I can read these documents. I do appreciate your comments about the status of this "problem". It looks like I will have plenty of things to think about in retirement. You will hear from me in about a week.
Heavywater
HeavyWater
#22
Feb21-12, 06:32 PM
P: 17
Quote Quote by HeavyWater View Post
Thank you for taking the time and for your thoughtful response. I am looking at a copy of the paper right now. Let me spend the rest of the day reviewing it and collecting my thoughts and questions and I will get back with you tomorrow.

Heavywater
Dickfore,
I got out my re-read your quote above. Before I get into my questions, I have got to ask you what do CJS mean by "manifest invariance"? Why the word, "manifest". Does "manifest invariance" differ from "invariance" in some way? I note that CJS defines "manifest invariance" a sentence or two below your quote. They also define it on p351 of CJS, " ... property that the world line of a particle transforms as a sequence of space time events according to the usual Lorentz transofmation formula." And then below that (also on p351), " ... be formulated in terms of a set of equations involving these Lie brackets".

So, is Manifest invariance different than invariance? Is it a "stronger" form of invariance?

Thanks,
Heavywater


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