Homework: Can a rest frame be chosen for the center of momentum for a system of two photons?

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SUMMARY

The discussion centers on the feasibility of selecting a rest frame for the center of momentum (CoM) of a system comprising two photons. It is established that a CoM frame can be determined when the photons travel in opposite directions, resulting in a total momentum of zero. However, when photons travel in the same direction, a CoM frame cannot be defined due to the nature of their velocities. Participants emphasize the importance of both quantitative and qualitative interpretations in understanding this phenomenon, particularly through the lens of vector analysis and the total 4-momentum of the system.

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  • Knowledge of vector analysis in physics
  • Basic concepts of 4-momentum in relativistic physics
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  • Explore the mathematical construction of the center of momentum frame in relativistic systems
  • Study the implications of 4-momentum conservation in photon interactions
  • Investigate the conditions under which a CoM frame exists for multiple particles
  • Learn about qualitative versus quantitative analysis in physics problem-solving
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sHimprinten
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TL;DR Summary: about the Special Relativity

Can a rest frame be chosen for the center of momentum for a system of two photos?
 
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:welcome:

Is this homework? If so, what do you think about it?
 
PeroK said:
Is this homework?
Based on the thread title, I have moved this thread to the appropriate homework forum.

@sHimprinten please be aware that for homework, you must show your own efforts at a solution. We do not give out answers to homework problems; we only provide help in approaching them.
 
PeroK said:
:welcome:

Is this homework? If so, what do you think about it?
In my opinion, I think it depends. It could be correct in some situations, like the two photons travel in the opposite direction, it is possible to find a point where the total momentum equals zero, and I think if they travek in other different directions, it also makes sense.
While if they travel in the same direction, I think the answer is not. However, I meet some problems when tring to elaborate this situation. You know, the center of momentum must be between the two photons, but what will I-standing in the center- see if I turn my head back? The behind phonton is approaching me or escaping me in the velocity of c?
Actually I find some quantitative interpretations, and they do support my idea, but I'd like to do a qualitative interpretation.
 
PeterDonis said:
Based on the thread title, I have moved this thread to the appropriate homework forum.

@sHimprinten please be aware that for homework, you must show your own efforts at a solution. We do not give out answers to homework problems; we only provide help in approaching them.
Sorry for that, I'm new to PF:bow:
And in fact, what I need is not the answer but your thinking which can help me to think throughly about the question.:kiss:
 
sHimprinten said:
I find some quantitative interpretations, and they do support my idea, but I'd like to do a qualitative interpretation.
I'm not sure what you mean by "quantitative interpretations". If it is possible to find the frame you're looking for, a quantitative answer would mean actually finding it--giving an explicit mathematical construction. If it's not possible, a quantitative answer would mean finding a mathematical proof that it's not possible.

In either case, if you have that, why would you care about a merely qualitative answer?
 
sHimprinten said:
the center of momentum must be between the two photons
With an appropriate meaning for the term "between", yes. Can you think of what such a meaning might be? Try thinking in terms of vectors.

Also, an appropriate meaning for "between" might help you to analyze the case of two photons moving in the same direction.
 
What is the condition of a CoM frame existing? (You have already hinted at it)
What does this imply for the total 4-momentum?
Does the total 4-momentum of the two-photon system satisfy this?
 

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