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

  • Context: Graduate 
  • Thread starter Thread starter Dmitry67
  • Start date Start date
  • Tags Tags
    Pressure Qm
Click For Summary

Discussion Overview

The discussion revolves around the concept of pressure in quantum mechanics, particularly in relation to the stress-energy tensor and its components, including energy density, momentum density, energy flux, and pressure. Participants explore the microscopic interpretation of pressure, especially in contexts like photon gas, and how it compares to classical definitions of pressure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion about the microscopic interpretation of pressure, particularly in a photon gas, questioning the existence of pressure when particles are simply moving in different directions.
  • Others argue that pressure in quantum mechanics should not differ from classical definitions, asserting that pressure is the force per unit area acting on an object within the gas.
  • One participant suggests that pressure can be understood as momentum flux, which is part of the energy-momentum tensor relevant in relativistic quantum field theory.
  • Another participant clarifies that while momentum flux relates to force, pressure is defined differently, being a tensor or scalar rather than a vector.
  • There is a discussion about the necessity of interaction for pressure to have meaning, with some asserting that pressure can be conceptualized without direct measurement, similar to temperature.
  • One participant emphasizes that the definition of pressure in quantum gases aligns with classical gases, reinforcing that the underlying principles remain consistent across both domains.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of pressure in quantum mechanics, particularly regarding its microscopic nature and relationship to classical concepts. No consensus is reached on these interpretations.

Contextual Notes

Participants highlight the complexity of defining pressure in quantum contexts, noting the dependence on interactions and measurement, as well as the distinction between tensor and scalar quantities in relation to pressure.

Dmitry67
Messages
2,564
Reaction score
1
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...
 
Physics news on Phys.org
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.
 
Dmitry67 said:
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.
 
Thank you!
I had a mental block thinking about pressure as 'Force' aapplied to some surface.
You had resolved it.
 
But momentum flux is the definition of 'Force', what's wrong with that picture?
 
JK423 said:
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.
 
I don't understand the assertion:
Dmitry67 said:
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?
 
JK423 said:
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.
 
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.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 15 ·
Replies
15
Views
3K
  • · Replies 232 ·
8
Replies
232
Views
22K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 44 ·
2
Replies
44
Views
6K