Casimir effect and the quantum vacuum
Though the author refutes the validity of Casimir Force he states that answering the question of whether or not zero point fluctuations of the vacuum are real is beyond the scope of his paper. Yet, he presents interesting arguments that the Casimir force could be trace fluctuations ("over spin") in the background of the field "of interest" since "the fields penetrate further than the nominal separation of the plates". That is very interesting.
It's also interesting that he accredits the Casimir force as possibly being "... simply the (relativistic, retarded) van der Waals force between the metal plates." Let alone the "boundary conditions" applied to an ideal conductor in such experiements. He also considers that "the Casimir force originates in the forces between charged particles in the metal plates."
Another interesting thing is that though the author can give account of the Casimir force by other means indicating that it does not stem form "vacuum fluctuations" he notes "Even if one could argue away quantum zero-point contributions to the vacuum energy, the problem of spontaneous symmetry breaking remains: condensates that carry energy appear at many energy scales in the standard model. So there is good reason to be skeptical of attempts to avoid the standard formulation of quantum field theory and the zero-point energies it brings with it. Still, no known phenomenon, including the Casimir effect, demonstrates that zero-point energies are real."
Why bother writting a paper citing cases that refute the interpretation of an affect when, in the end, one notes that there is good reason to be skeptical of attempts to avoid the interpretation of that which you seem to have just refuted? This paper has the character of an escape clause in some legal contract. If you don't want to use the theoretical trappings of QED's "zero-point" vacuum fields; other means of a way out are provided yet, one is advised to be "skeptical" of them?In quantum field theory as usually formulated, the zero point fluctuations of the fields contribute to the energy of the vacuum. However this energy does not seem to be observable in any laboratory experiment...
Caution is appropriate when an effect, for which there is no direct experimental evidence, is the source of a huge discrepancy between theory and experiment. As evidence of the ‘‘reality’’ of the quantum fluctuations of fields in the vacuum, theorists often point to the Casimir effect...
Casimir physics has become an active area of nanoscopic physics in its own right [12]. Not surprisingly, every review and text on the subject highlights the supposed special connection between the Casimir effect and the vacuum fluctuations of
the electromagnetic field...
The object of this paper is to point out that the Casimir effect gives no more (or less) support for the reality of the vacuum energy of fluctuating quantum fields than any other one-loop effect in quantum electrodynamics...
The Casimir force can be calculated without reference to vacuum fluctuations, and like all other observable effects in QED, it vanishes as the fine structure constant, goes to zero.
There is a long history and large literature surrounding the question whether the zero-point fluctuations of quantized fields are ‘‘real’’...
The question of whether zero-point fluctuations of the vacuum are or are not real is beyond the scope of this paper. Instead I address only the narrower question of whether the Casimir effect can be considered evidence in their favor...
In the standard approach [13], the Casimir force is calculated by computing the change in the zero-point energy of the electromagnetic field when the separation between parallel perfectly conducting plates is changed. The result, Eq. (3), seems universal, independent of everything except @, c, and the separation, inviting one to regard it as a property of the vacuum. This, however, is an illusion. When the plates were idealized as perfect conductors, assumptions were made about the properties of the materials and the strength of the QED coupling , that obscure the fact that the Casimir force originates in the forces between charged particles in the metal plates. More specifically,
(i) The Casimir effect is a function of the fine structure
constant and vanishes as ! 0. Explicit dependence
on is absent from Eq. (3) because it is an
asymptotic form, exact in the !1 limit. The
Casimir force is simply the (relativistic, retarded)
van der Waals force between the metal plates....
...a moment’s thought reveals that interactions entered when one idealized the metallic plates as perfect conductors that
impose boundary conditions on the electromagnetic fields....
A conductor is characterized by a plasma frequency, !pl, and a skin depth,...
...the separation, d, becomes ill defined since the fields penetrate further than the nominal separation of the plates....
...Casimir’s original goal was to compute the van der Waal’s force between polarizable molecules at separations so large that relativistic (retardation) effects are essential....
...Despite the simplicity of Casimir’s derivation based on zero-point energies, it is nevertheless possible to derive his result without any reference to zero-point fluctuations or even to the vacuum. Such a derivation was first given by Schwinger [27] for a scalar field, and then generalized to the electromagnetic case by Schwinger, DeRaad, and Milton [28]. Reviewing their derivation, one can see why the zero-point fluctuation approach won out. It is far simpler.
In more modern language the Casimir energy can be expressed in terms of the trace of the Green’s function for the fluctuating field in the background of interest (e.g. conducting plates),...
G is the full Green’s function for the fluctuating field, G0 is the free Green’s function, and the trace is over spin...
The deeper question remains: Do the zero-point energies of quantum fields contribute to the energy density of the
vacuum and, mutatis mutandis, to the cosmological constant? Certainly there is no experimental evidence for the reality of zero-point energies in quantum field theory (without gravity). Perhaps there is a consistent formulation of relativistic quantum mechanics in which zero-point energies never appear. I doubt it. Schwinger intended
source theory to provide such a formulation. However, to my knowledge no one has shown that source theory or another S-matrix based approach can provide a complete description of QED to all orders. In QCD confinement would seem to present an insuperable challenge to an S-matrix based approach, since quarks and gluons do not appear in the physical S matrix. Even if one could argue away quantum zero-point contributions to the vacuum energy, the problem of spontaneous symmetry breaking remains: condensates that carry energy appear at many energy scales in the standard model. So there is good reason to be skeptical of attempts to avoid the standard formulation of quantum field theory and the zero-point energies it brings with it. Still, no known phenomenon, including the Casimir effect, demonstrates that zero-point energies are real.
When considering the aggregate of "the forces between charged particles in the metal plates" is it possible that a region of space around those plates would be electromagnetically affected to such extent that bringing them into close micrometer proximity would result in the detection of a force of attraction between the plates that would be greater than the force measured on the inside of the plates? That seems to be true.