Editing Casimir effect (section)

===Vacuum energy===<!-- This section is linked from [[Faster-than-light]] -->
{{Quantum field theory}}
{{Main|Vacuum energy}}
The causes of the Casimir effect are described by quantum field theory, which states that all of the various fundamental [[field (physics)|fields]], such as the [[electromagnetic field]], must be quantized at each and every point in space. In a simplified view, a "field" in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field can be visualized as the displacement of a ball from its rest position. Vibrations in this field propagate and are governed by the appropriate [[wave equation]] for the particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength of the field be quantized at each point in space. At the most basic level, the field at each point in space is a [[Harmonic oscillator|simple harmonic oscillator]], and its quantization places a [[quantum harmonic oscillator]] at each point. Excitations of the field correspond to the [[elementary particle]]s of [[particle physics]]. However, even the vacuum has a vastly complex structure, so all calculations of quantum field theory must be made in relation to this model of the vacuum.

The vacuum has, implicitly, all of the properties that a particle may have: [[Spin (physics)|spin]],<ref>{{Cite journal|last1=Du|first1=Z. Z.|last2=Liu|first2=H. M.|last3=Xie|first3=Y. L.|last4=Wang|first4=Q. H.|last5=Liu|first5=J.-M.|date=2015-12-07|title=Spin Casimir effect in noncollinear quantum antiferromagnets: Torque equilibrium spin wave approach|journal=Physical Review B|volume=92|issue=21|pages=214409|doi=10.1103/PhysRevB.92.214409|issn=1098-0121|arxiv=1506.05211|bibcode=2015arXiv150605211D|s2cid=118348464 }}</ref> [[polarization (waves)|polarization]] in the case of [[light]], [[energy]], and so on. On average, most of these properties cancel out: the vacuum is, after all, "empty" in this sense. One important exception is the [[vacuum energy]] or the [[vacuum expectation value]] of the energy. The quantization of a simple harmonic oscillator states that the lowest possible energy or zero-point energy that such an oscillator may have is

<math display="block">{E}=\tfrac12 \hbar \omega \, .</math>

Summing over all possible oscillators at all points in space gives an infinite quantity. Since only ''differences'' in energy are physically measurable (with the notable exception of gravitation, which remains [[Quantum gravity#Nonrenormalizability of gravity|beyond the scope of quantum field theory]]), this infinity may be considered a feature of the mathematics rather than of the physics. This argument is the underpinning of the theory of [[renormalization]]. Dealing with infinite quantities in this way was a [[Renormalization#Attitudes and interpretation|cause of widespread unease among quantum field theorists]] before the development in the 1970s of the [[renormalization group]], a mathematical formalism for scale transformations that provides a natural basis for the process.

When the scope of the physics is widened to include gravity, the interpretation of this formally infinite quantity remains problematic. There is currently [[Cosmological constant problem|no compelling explanation]] as to why it should not result in a [[cosmological constant]] that is many orders of magnitude larger than observed.<ref name=Rugh>{{cite journal
 |author=SE Rugh, H Zinkernagel
 |year=2002
 |title=The quantum vacuum and the cosmological constant problem
 |url=http://philsci-archive.pitt.edu/398/
 |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
 |volume=33 |pages=663–705
 |doi=10.1016/S1355-2198(02)00033-3
 |issue=4
 |last2=Zinkernagel
 |arxiv=hep-th/0012253|bibcode = 2002SHPMP..33..663R |s2cid=9007190
 }}</ref> However, since we do not yet have any fully coherent [[quantum gravity|quantum theory of gravity]], there is likewise no compelling reason as to why it should instead actually result in the value of the cosmological constant that we observe.<ref name=Bianchi>{{cite arXiv |eprint=1002.3966
 |last1=Bianchi
 |first1=Eugenio
 |title=Why all these prejudices against a constant?
 |last2=Rovelli
 |first2=Carlo
 |class=astro-ph.CO
 |year=2010
}}</ref>

The Casimir effect for [[fermion]]s can be understood as the [[spectral asymmetry]] of the [[(−1)F|fermion operator {{math|(−1)<sup>''F''</sup>}}]], where it is known as the [[Witten index]].