How Does Momentum in Special Relativity Connect with Quantum Mechanics?

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In summary: So, there's no difference conceptually, it's just that SR is for a point particle and QM is for a wave function.In summary, momentum in special relativity can be calculated using the equation p=mv for non-relativistic objects, but for objects like photons, their momentum is an intrinsic feature apart from their mass. The mass of electrons, chairs, and planets can be used to calculate their momentum because it makes the calculations easier, but there is no a priori reason for their equivalence. In quantum mechanics, the momentum operator is related to the momentum in special relativity through the expectation value, but the conceptual difference lies in SR being for point particles and QM being for wave functions.
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curiouser84
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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!
 
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  • #2
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 - [itex]E^2 = m^2c^4 + p^2c^2[/itex] 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.
 

FAQ: How Does Momentum in Special Relativity Connect with Quantum Mechanics?

What is momentum?

Momentum is a measure of the quantity of motion an object has. It is a vector quantity, meaning it has both magnitude and direction.

How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

What is the difference between momentum and velocity?

Velocity is a measure of an object's speed and direction, while momentum also takes into account the object's mass. Two objects can have the same velocity but different momentum if they have different masses.

Why is momentum important?

Momentum is important because it is a fundamental concept in physics and is used to describe the motion of objects. It is also conserved in a closed system, meaning the total momentum of a system remains constant unless acted upon by an external force.

How is momentum related to Newton's laws of motion?

Momentum is related to Newton's laws of motion because it is a direct result of the second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In other words, a change in momentum is caused by a force acting on an object.

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