Does Conservation of Momentum & Energy Hold in the C.O.M. Reference Frame?

[ruivocanadense]

TL;DR

Do classical conservation laws apply to center of mass frame at speeds close to the speed of light?

We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?

 

[Ibix]

The conservation laws work just fine (energy is neither created nor destroyed - tuis is true in relativity just as it is in Newtonian physics). It's the non-relativistic expressions for the energy and momentum that are not correct, and are not a good approximation at high speeds.

 

[Nugatory]

We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?

Yes, the classical formulas for momentum kinetic energy fail in the center of mass frame as well.

 

[pervect]

Summary:: Do classical conservation laws apply to center of mass frame at speeds close to the speed of light?

We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?

From context, I assume that you don't regard special relativity as a "classical theory". It seems that it's a bit ambiguous, I am used to regarding it as a classical theory (as it's not quantum), but after looking at the definition, I suspect the term may be ambiguous. In any event - if two relativistic particles collide, correct predictions of the energy require special relativity, not Newtonian physics. Which I believe would be a "yes", if we assume that by classical physics you mean only Newtonian physics.

 

[vanhees71]

In relativity it's more accurate to speak about a center-of-momentum frame rather than a center-of-mass frame. By definition the CM frame is defined such that the total three-momentum of the particles involved in the scattering vanishes.