Understanding Pressure in Quantum Mechanics: Energy, Momentum, and Flux

[Dmitry67]

In Stress Energy Tensor the following components make sense to me:

Energy density,
Momentum Density,
Energy flux

because they are based on the 'observables'

Whats about the Pressure? What is it (microscopically)?
On the microscopic level there are 'particles' flying in different directions.
Take one example: photon gas. I don't see any 'pressure'. I just see photons flying around...

 

[JK423]

Why should it be any different than the classical case?
In the classical case, you still have particles flying around, and pressure is the force per unit surface that acts on an 'item' that you put in the gas.
Same should be in the quantum case, its just that now the interactions between the gas and the 'item' will be of quantum nature.

 

[A. Neumaier]

In Stress Energy Tensor the following components make sense to me:

Energy density,
Momentum Density,
Energy flux

Whats about the Pressure? What is it (microscopically)?

Pressure = momentum flux

All the stuff you mention is part of the energy-momentum tensor, which figures in every relativistic quantum field theory.

 

[Dmitry67]

Thank you!
I had a mental block thinking about pressure as 'Force' aapplied to some surface.
You had resolved it.

 

[JK423]

But momentum flux is the definition of 'Force', what's wrong with that picture?

 

[A. Neumaier]

But momentum flux is the definition of 'Force', what's wrong with that picture?

Not quite. Force is usually considered to be a vector, while momentum flux is a tensor. And pressure is either identified with the momentum flux tensor, or with 1/3 of its trace. Thus it is a tensor or a scalar, but not a vector.

 

[JK423]

I don't understand the assertion:

Whats about the Pressure? What is it (microscopically)?
On the microscopic level there are 'particles' flying in different directions.
Take one example: photon gas. I don't see any 'pressure'. I just see photons flying around...

Even in the classical case the gas particles are free and just flying around. In my understanding, pressure has a meaning only if you have the gas interacting with something else. This view is wrong?

 

[A. Neumaier]

Even in the classical case the gas particles are free and just flying around. In my understanding, pressure has a meaning only if you have the gas interacting with something else. This view is wrong?

Pressure is what you _would_ measure if you would put an obstacle in the way. Just as temperature is what you would measure if you would put a thermometer in the way.

You don't need to _actually_ measure to talk about pressure or temperature.

 

[JK423]

Yes ok i got it, i mean the same thing. I just wanted to show that a quantum gas doesn't differ from a classical one when you're trying to define the notion of pressure.