How Does Momentum in Special Relativity Connect with Quantum Mechanics?

[curiouser84]

Hi there!

Question on momentum in SR.
I'm trying to understand this holistically...

From what I understand... p=mv is an approximation.
when we look at the energy equation for a photon E = pc.
Since a photo is massless, this momentum p is an intrinsic feature of a particle apart from its mass...

So...

1. Why is it that we can use the mass of electrons/chairs/planets to calculate their momentum? Is there an a prior reason that the two are equivalent?

2. How does this momentum in SR relate to the operator momentum in QM?

Thank you!

 

[Simon Bridge]

Hi there!

Question on momentum in SR.
I'm trying to understand this holistically...

From what I understand... p=mv is an approximation.
when we look at the energy equation for a photon E = pc.
Since a photo is massless, this momentum p is an intrinsic feature of a particle apart from its mass...

So...

1. Why is it that we can use the mass of electrons/chairs/planets to calculate their momentum?

Because that makes the math easiest - these objects are not normally relativistic. Momentum is otherwise calculated from the total energy - $E^2 = m^2c^4 + p^2c^2$ which works for massive and massless particles.

Is there a prior reason that the two are equivalent?

No. Photon momentum was a later discovery. However, iirc, it turns out to be related to fundamental symmetries in space-time.

2. How does this momentum in SR relate to the operator momentum in QM?

The momentum in SR is the expectation value of the QM momentum just like normal.