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

[sHimprinten]

TL;DR Summary: about the Special Relativity

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

 

[PeroK]

Is this homework? If so, what do you think about it?

 

[PeterDonis]

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.

 

[sHimprinten]

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.

 

[sHimprinten]

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
And in fact, what I need is not the answer but your thinking which can help me to think throughly about the question.

 

[PeterDonis]

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?

 

[PeterDonis]

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.

 

[Orodruin]

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?