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.
 

Thread 'Describing the Big Bang'

I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
View full post »
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
View full post »

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »

Similar threads

I How is photon momentum compatible with special relativity?
Replies
19
Views
2K
A How to show spin ##= \pm 2/\omega## for a circ-polarized gravity wave
Replies
0
Views
1K
I Understanding the Relationship Between Energy and Momentum in Special Relativity
Replies
11
Views
3K
I Does p=mc Apply To Photons? | A.P. French's Special Relativity
Replies
15
Views
2K
I Different methods of deriving the energy-momentum equation
Replies
28
Views
4K
I Getting Invariant Curvature from Momentum & Energy
Replies
9
Views
2K
I Relativistic Energy Dispersion Relation: Explained
Replies
10
Views
3K
I General physics question -- How can massless photons have momentum?
Replies
9
Views
1K
A The Lagrangian of a free particle ##L=-m \, ds/dt##
Replies
3
Views
430
I Zeroth component of 4-momentum & energy-momentum relation
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top