I do ask pardon if my question is stupid. I am but a mere graduate student.(adsbygoogle = window.adsbygoogle || []).push({});

How does the definition of momentum "hang together coherently" between the de Broglie wavelength definition and the SR definition?

My confusion comes as follows. p = (gamma) m v is one definition of momentum, where gamma is the 1 / root ( 1-(v/c)**2), m is mass, v is velocity in some reference frame. This is completely reasonable to me based on SR. It's also true that momentum can be described in terms of the de Broglie wavelength: lambda = h / p . This is satisfying in that it is consistent for both light and matter. How does the SR definition of momentum relate to the de Broglie theory?

It seems that SR has no statement about the momentum of mass-less particles. Is the de Broglie statement more general, since it applies to both light and matter?

Given this, what is momentum? A photon has zero mass and constant velocity; does momentum have any "meaning" in this realm? It seems like numerous experiments with regard to photons are explained in terms of photons "colliding" with different energies based different momentum, but this seems anthrapromorphic. It seems that the energy of a photon is 1-1 with momentum, such that any collision notion is silly.

And I have no idea how momentum hangs together with Noether's theorem now; momentum is a conserved quantity due to the symmetry of the system there. Is Noether's definition better than all of these?

What is momentum?

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# Confusion on Meaning of Momentum

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