How Does Momentum in Special Relativity Connect with Quantum Mechanics?

  • Thread starter Thread starter curiouser84
  • Start date Start date
  • Tags Tags
    Momentum
curiouser84
Messages
1
Reaction score
0
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!
 
Physics news on Phys.org
curiouser84 said:
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.
 
OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
Back
Top