Field fluctuations in the vacuum

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SUMMARY

The forum discussion centers on the prediction of quantum fluctuations in the vacuum by relativistic quantum field theory (QFT), specifically illustrated by the Casimir Effect. Participants clarify that "vacuum fluctuation" is a misnomer, advocating for the term "vacuum energy" or "zero point energy" to describe the absence of particles. The Casimir Effect is attributed to electromagnetic forces between charged plates rather than fluctuations in the vacuum itself. The discussion emphasizes that energy differences, rather than absolute energy values, are crucial in understanding these phenomena.

PREREQUISITES
  • Relativistic Quantum Field Theory (QFT)
  • Understanding of the Casimir Effect
  • Concept of vacuum energy and zero point energy
  • Familiarity with Hamiltonian and Lagrangian mechanics
NEXT STEPS
  • Study the Casimir Effect calculation in QFT, referencing Itzykson and Zuber's texts
  • Explore the concept of normal ordering in Hamiltonians and Lagrangians
  • Research the implications of energy differences in quantum mechanics
  • Examine the electromagnetic forces involved in the Casimir Effect through academic papers
USEFUL FOR

Physicists, particularly those specializing in quantum mechanics and field theory, as well as students seeking to deepen their understanding of vacuum energy and the Casimir Effect.

Jrs580
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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?
 
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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?
 
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Jrs580 said:
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
 
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malawi_glenn said:
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).
malawi_glenn said:
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
 
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