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Status of relativistic 2body problem 
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#1
Feb1512, 07:09 PM

P: 17

I'd like to get back into theoretical physics as a retiree. I last worked on the relativistic 2body problem over 25 years ago. I've been reading Trump and Schieve's text on classical relativistic dynamics and I'm wondering has the classical 2body relativistic problem been solved. I realize the word "solved" has different meanings for different people. I'd like to hear your comments on the status of this problem. Perhaps you can suggest a more recent text than this one.
Thanks, Heavywater 


#2
Feb1512, 07:53 PM

P: 3,014

Please define what is the relativistic 2body problem. As you may know, the meaning of potential energy as a function of the positions of the particles is meaningless in SR, because the relative position of the particles is not Lorentz invariant.



#3
Feb1612, 08:52 AM

Sci Advisor
Thanks
P: 4,160

A CaltechCornell group led by Lee Lindblom and Saul Teukolsky have made excellent progress in the numerical simulation of black hole collisions. For a list of publications, see here.



#4
Feb1612, 11:06 AM

P: 1,555

Status of relativistic 2body problem



#5
Feb1612, 12:02 PM

Sci Advisor
PF Gold
P: 5,059

Adding to Bill_K's pointer, the following is a nice public website (that include the full paper list as well) for the collaboration he refers to:
http://www.blackholes.org/ Going from two body black holes to two bodies with equations of state, the best result I've been able to locate is the following: http://arxiv.org/abs/1103.3874 Going to the 3 body problem, I have not found any attempt to deal with this for bodies with equations of state, but there is progress for 3 black holes. Following is a sample of work: http://arxiv.org/abs/0711.1165 http://arxiv.org/abs/astroph/0509814 http://arxiv.org/abs/grqc/0702076 http://arxiv.org/abs/1012.4423 http://arxiv.org/abs/1108.4485 [EDIT: I guess I should add the general articles in the Numerical Relativity category of: http://relativity.livingreviews.org/...s/subject.html ] 


#6
Feb1612, 12:44 PM

P: 148

Skippy 


#7
Feb1612, 01:43 PM

P: 1,555

But any setup does not only require a position and momentum (which is already next to impossible to uniquely specify as we have no background) but also an infinite number of waves over the whole spacetime. 


#8
Feb1612, 03:01 PM

P: 476

Their extension of relativity to deal with manybody dynamics is the more popular in theoretical physics but still open to many objections. Even if were to ignore the objections, the generalized Hamiltonian equations that they work only deal with simplest case. 


#9
Feb1712, 04:30 PM

P: 17

Thank you for such a quick response. I'm sure a lot of theoretical physicists would like to see this problem(or should I say problems) resolved. Can you or anyone else point me to 1 or 2 current references. The latest text I have found is by Trump and Schieve and it is dated 1998. I am more interested in the relativistic classical mechanical problem than the relativistic quantum mechanical problembut any reference after 1999 will be helpful.
Heavywater 


#10
Feb1712, 04:45 PM

P: 17

Thank you Dickfore,
I am thinking about the Classical relativistic 2 body problem where both bodies are point particles AND I was only thinking about special relativity. I should have clarified my problem statement. I am aware of the famous Currie, Jordan, Sudharshan "No Interaction" or "No Go" theorem from around 1963. I am aware there were some issues associated with a world line being an invariant and/or observable. Also I'm aware of some uncertainties associated with whether their position variable was a canonical variable. Since I left the scene, 25+ years ago, I've found lots of interesting work was done in classical relativistic dynamics with the manybody problem. My trail of references seems to have stopped with Trump and Schieve's text. Are you aware of any references after Trump and Schieve's (1998) text? Thanks for your inputs and encouragement. HeavyWater 


#11
Feb1712, 04:48 PM

P: 17

Your references will definitely help me. I'll have to wait until Monday until I can get to a library. I am not interested in the problem as it relates to GR, only as it relates to SR. Feel free to make any other suggestion. I will definitely check out the work by Linblom and Teukolsky. Thanks, Heavywater 


#12
Feb1712, 04:51 PM

P: 17

Thanks, Heavywater 


#13
Feb1712, 04:56 PM

P: 17

Thank you for your insights and response. I was thinking of a much simpler problem, one that only deals with point particles, and only special relativity. In particular, I was thinking about the "No Go" or "No Interaction Theorem" of Currie, Jordan, and Sudharshan from way back in 1963. Thanks, Heavywater 


#14
Feb1712, 05:10 PM

P: 17

Thank you for letting me know about the references. I just spent an enjoyable 1/2 hour on the website. Let me clarify, I am working on a simpler problemthat being SR with the classical mechanics of 2 point particles. A frequently identified reference in this area is the "No Go" theorem by Currie, Jordan and Sudharshan. Thank you for you coments and references, HeavyWater 


#15
Feb1712, 05:20 PM

P: 1,555

If you are not talking about gravitation then what are you talking about? 


#16
Feb1712, 08:33 PM

P: 3,014

Regarding Currie, Jordan, Sudarshan's reference, here's a link:
http://dx.doi.org/10.1103/RevModPhys.35.350 


#17
Feb1712, 09:02 PM

P: 3,014

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 twobody problem turns into a problem in continuum mechanics. 


#18
Feb1812, 06:04 AM

P: 476

There is some interest in the application to manybody 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 SmirnovRueda 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 SmirnovRueda approach has been recently extended to manybody 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 


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