I Field fluctuations in the vacuum

[Jrs580]

How does relativistic qft predict quantum fluctuations in the vacuum? We see this in the experiment proving the Casimir Effect so we know it's physical, but why?

 

[malawi_glenn]

Vacuum fluctuation is not a good term, vacuum energy is better (zero point energy). Vaccum here means absence of particles.

Hard to understand your "why" question, do you want to see the casimir effect calculation or what else are you referring to?

 

[mfb]

We see this in the experiment proving the Casimir Effect so we know it's physical

We do not. The Casimir effect can be explained purely as electromagnetic force between the electric charges in the plates: The Casimir Effect and the Quantum Vacuum

 

[vanhees71]

Vacuum fluctuation is not a good term, vacuum energy is better (zero point energy). Vaccum here means absence of particles.

In SR there is no physics in the absolute value of the total energy, and thus it's convenient to associate the values 0 of the Poincare-invariant vacuum state for all additive conservation laws. Formally you can achieve this with introducing "normal ordering" in the Hamiltonian/Lagrangian.

The physics is in the energy differences rather than the absolute value of the energy. There are no fluctuations in the vacuum itself but rather it's a stationary state (eigenstate of the Hamiltonian).

Hard to understand your "why" question, do you want to see the casimir effect calculation or what else are you referring to?

The Casimir effect is due to fluctuations of charges and the em. field. The usual calculation you find in introductory chapters of some QFT books (e.g., in Itzykson, Zuber) is a limiting case for infinite (!) charges. For details see

https://arxiv.org/abs/hep-th/0503158
https://doi.org/10.1103/PhysRevD.72.021301