Casimir effect and vacuum energy and a bit of relativity....

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Discussion Overview

The discussion revolves around the Casimir effect, vacuum energy, and implications for Lorentz invariance in the context of spacetime and matter configurations. Participants explore theoretical aspects, conceptual clarifications, and the relationship between vacuum energy and the presence of matter, particularly in relation to the Casimir effect.

Discussion Character

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

Main Points Raised

  • One participant questions whether the vacuum energy density is constant throughout spacetime, suggesting that the presence of parallel plates alters the vacuum energy density between them.
  • Another participant asserts that there is no vacuum energy, claiming that the vacuum expectation of all fields is zero.
  • A different participant challenges this by asking what produces the Casimir force if there is no vacuum energy, referencing an article that states the energy in the vacuum between the plates is less than elsewhere.
  • One participant elaborates on the nature of the Casimir vacuum, discussing the role of different Hamiltonians and the implications for effective versus fundamental vacuums.
  • Another participant notes that the Casimir effect arises from van der Waals forces at a microscopic level, while effective theories simplify the description by treating only EM fields as dynamical.
  • Concerns are raised about the implications of varying vacuum energy densities for Lorentz invariance, with some participants suggesting that effective Hamiltonians may not maintain this invariance.
  • There is a discussion about the definition of vacuum energy and the concept of normal ordering, with some participants emphasizing that vacuum energy is defined as zero.

Areas of Agreement / Disagreement

Participants express differing views on the existence and implications of vacuum energy, with no consensus reached on whether vacuum energy is constant or how it relates to the Casimir effect and Lorentz invariance. Multiple competing perspectives remain on the nature of vacuum energy and its role in the Casimir effect.

Contextual Notes

The discussion highlights limitations in definitions and assumptions regarding vacuum energy and the Casimir effect, as well as the complexities introduced by different Hamiltonians. The relationship between effective and fundamental vacuums is also noted as a point of contention.

  • #31
Vanadium 50 said:
Why do you think they are completely different? In both cases, the force arises through the boundary conditions. The issue comes about when one tries to paint a mental picture of the results of this calculation.

If I understand what the two approaches to deriving the Casimir force are, they sure seem very different:
  1. Treat the electromagnetic field classically, but assume that the charges inside the metal plates are undergoing random internal motion. Then you get a Van der Waals type force between the plates.
  2. Treat the plates classically (as just boundary conditions for the electromagnetic field), and treat the field modes of the E&M field quantum mechanically.
The two approaches seem to be focusing on completely different subsystems, and are making completely different approximations about what to treat classically and what to treat quantum mechanically.
 
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  • #32
Vanadium 50 said:
Why do you think they are completely different? In both cases, the force arises through the boundary conditions. The issue comes about when one tries to paint a mental picture of the results of this calculation.
Well, I have to think about that, but the VdW-force I associate with dipole-interactions, giving a 1/r^6 law. For me that's really different from 'vacuum interactions' as described by Feynman diagrams.

-edit Steven's post above me states my issue a lot clearer, I guess.
 
  • #33
Just so people are clear, this business is deeply controversial in the literature and not settled. There are quite a few subtleties involved, and really requires going through the entire analysis with a scalpel.
 
  • #34
Just to make sure i get it: in Jaffe's paper fig.3, those external legs are the conducting charges of the plates, right?

What I still can't reconcile is the dependancy of the Casimir force on the distance between the plates, i.e. eqn.(3) v.s. the VdW expression between eqn.5 and 6 (top of page 5). Shouldn't one expect F~1/d^6? What am I missing?
 
  • #35
haushofer said:
Shouldn't one expect F~1/d^6? What am I missing?

The field from a charged plane is not the same as a field from a charged point.
 
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  • #36
Ok, that's something I definitely missed, thanks! :P
 
  • #37
haushofer said:
Just to make sure i get it: in Jaffe's paper fig.3, those external legs are the conducting charges of the plates, right?
No. Those are dielectric functions ##\epsilon## treated as a classical non-dynamic background field.
 
Last edited:
  • #38
stevendaryl said:
If I understand what the two approaches to deriving the Casimir force are, they sure seem very different:
  1. Treat the electromagnetic field classically, but assume that the charges inside the metal plates are undergoing random internal motion. Then you get a Van der Waals type force between the plates.
  2. Treat the plates classically (as just boundary conditions for the electromagnetic field), and treat the field modes of the E&M field quantum mechanically.
The two approaches seem to be focusing on completely different subsystems, and are making completely different approximations about what to treat classically and what to treat quantum mechanically.
Or
3. Treat both charges and EM field as quantum dynamical mutually correlated fields.
Eq. (14) in my https://arxiv.org/abs/1702.03291 explains the equivalence of the 3 pictures in a very simple way.
 
  • #39
Haelfix said:
Just so people are clear, this business is deeply controversial in the literature and not settled. There are quite a few subtleties involved, and really requires going through the entire analysis with a scalpel.
That's exactly why I have written
https://arxiv.org/abs/1702.03291
 
  • #40
haushofer said:
Is there any simple/intuitive way of seeing why these two seemingly completely different approaches lead to the same answer?
Yes. See Secs. IV.B and IV.C, as well as the discussions around Eqs. (14) and (78) in my https://arxiv.org/abs/1702.03291
 
  • #41
Vanadium 50 said:
The issue comes about when one tries to paint a mental picture of the results of this calculation.
I hope my https://arxiv.org/abs/1702.03291 helps to get a better mental picture.
 
  • #42
Sorry all for over-advertising my most recent paper, it's probably irritating. o0)
But I have written it precisely with intention to answer the kind of questions which are asked here, so I couldn't sleep well if I didn't point that out to you. :smile:
 
  • #43
Well, it's self-advertisement for something the readers can download for free. That's ok, I'd say :smile:
 
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  • #45
Congratulations! :partytime:
 
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  • #47
At a recent conference I have presented an invited talk entitled

The origin of Casimir effect: Vacuum energy or van der Waals force?

Abstract:
In the literature on Casimir effect there are two approaches that make the same measurable predictions but offer very different explanations on the conceptual level. According to one approach the effect has origin in vacuum energy, while according to another it has origin in van der Waals forces. To resolve the resulting conceptual confusion, I discuss the conceptual aspects of Casimir effect from several different points of view. This includes fundamental particle physics (general principles of quantum electrodynamics), condensed matter physics (electrodynamics in continuous media) and non-relativistic quantum mechanics (a toy model with only a few degrees of freedom). All points of view lead to the conclusion that, at the fundamental microscopic level, Casimir effect originates from van der Waals forces, while the vacuum energy approach is an effective theory valid only at the macroscopic level.

The pdf of the presentation is attached.
 

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