Editing Zero-point energy (section)

== Experimental observations ==
Zero-point energy has many observed physical consequences.{{sfnp|Milonni|1994|p=111}} It is important to note that zero-point energy is not merely an artifact of mathematical formalism that can, for instance, be dropped from a Hamiltonian by redefining the zero of energy, or by arguing that it is a constant and therefore has no effect on Heisenberg equations of motion without latter consequence.{{sfnp|Milonni|1994|pp=42–43}} Indeed, such treatment could create a problem at a deeper, as of yet undiscovered, theory.{{sfnp|Peskin|Schroeder|1995|p=22}} For instance, in general relativity the zero of energy (i.e. the energy density of the vacuum) contributes to a cosmological constant of the type introduced by Einstein in order to obtain static solutions to his field equations.{{sfnp|Milonni|2009|p=865}} The zero-point energy density of the vacuum, due to all quantum fields, is extremely large, even when we cut off the largest allowable frequencies based on plausible physical arguments. It implies a cosmological constant larger than the limits imposed by observation by about 120 orders of magnitude. This "cosmological constant problem" remains one of the greatest unsolved mysteries of physics.<ref name=scientificamerican0588-106>{{cite journal|last1=Abbott|first1=Larry|title=The Mystery of the Cosmological Constant|journal=Scientific American|date=1988|volume=258|issue=5|pages=106–113|doi=10.1038/scientificamerican0588-106|url= http://pages.erau.edu/~reynodb2/blog/Abbott_CosmologicalConstant_SciAm.pdf|bibcode=1988SciAm.258e.106A}}</ref>

=== Casimir effect ===
{{Main|Casimir effect}}
[[File:Casimir plates.svg|thumb|Casimir forces on parallel plates]]

A phenomenon that is commonly presented as evidence for the existence of zero-point energy in vacuum is the Casimir effect, proposed in 1948 by [[Netherlands|Dutch]] [[physicist]] [[Hendrik Casimir]], who considered the quantized electromagnetic field between a pair of grounded, neutral metal plates. The vacuum energy contains contributions from all wavelengths, except those excluded by the spacing between plates. As the plates draw together, more wavelengths are excluded and the vacuum energy decreases. The decrease in energy means there must be a force doing work on the plates as they move.

Early experimental tests from the 1950s onwards gave positive results showing the force was real, but other external factors could not be ruled out as the primary cause, with the range of experimental error sometimes being nearly 100%.<ref>{{cite journal|last1=Derjaguin|first1=B. V.|last2=Abrikosova|first2=I. I.|last3=Lifshitz|first3=E. M.|title=Direct measurement of molecular attraction between solids separated by a narrow gap|journal=Quarterly Reviews, Chemical Society|date=1956|volume=10|issue=3|pages=295–329|doi=10.1039/QR9561000295}}</ref><ref>{{cite journal|last1=Sparnaay|first1=M. J.|title=Measurements of attractive forces between flat plates|journal=Physica|date=1958|volume=24|issue=6–10|pages=751–764|doi=10.1016/S0031-8914(58)80090-7|bibcode=1958Phy....24..751S}}</ref><ref>{{cite journal|last1=Tabor|first1=D.|last2=Winterton|first2=R. H. S.|title=Surface Forces: Direct Measurement of Normal and Retarded Van der Waals Forces|journal=Nature|date=1968|volume=219|issue=5159|pages=1120–1121|doi=10.1038/2191120a0|pmid=5675624|bibcode=1968Natur.219.1120T|s2cid=4258508}}</ref><ref>{{cite journal|last1=Hunklinger|first1=S.|last2=Geisselmann|first2=H.|last3=Arnold|first3=W.|title=A Dynamic Method for Measuring the Van der Waals Forces between Macroscopic Bodies|journal=Rev. Sci. Instrum.|date=1972|volume=43|issue=4|pages=584–587|doi=10.1063/1.1685696|bibcode=1972RScI...43..584H}}</ref><ref>{{cite journal|last1=Van Blokland|first1=Peter H. G. M.|last2=Overbeek|first2=J. Theodoor G.|title=Van der Waals forces between objects covered with a chromium layer|journal=J. Chem. Soc., Faraday Trans. 1|date=1978|volume=74|pages=2637–2651|doi=10.1039/F19787402637}}</ref> That changed in 1997 with Lamoreaux<ref>{{cite journal|last1=Lamoreaux|first1=S. K.|title=Demonstration of the Casimir Force in the 0.6 to 6&nbsp;μm Range|date=1997|journal=Physical Review Letters|volume=78|issue=1|pages=5–8|doi=10.1103/PhysRevLett.78.5|url=http://web.mit.edu/~kardar/www/research/seminars/Casimir/PRL-Lamoreaux.pdf|bibcode=1997PhRvL..78....5L}}</ref> conclusively showing that the Casimir force was real. Results have been repeatedly replicated since then.<ref>{{cite journal|last1=Mohideen|first1=Umar|last2=Roy|first2=Anushree|title=Precision Measurement of the Casimir Force from 0.1 to 0.9&nbsp;μm|journal=Physical Review Letters|year=1998|volume=81|issue=21|pages=4549–4552|doi=10.1103/PhysRevLett.81.4549|arxiv=physics/9805038|bibcode=1998PhRvL..81.4549M|s2cid=56132451}}</ref>{{sfnp|Chan et al.|2001}}{{sfnp|Bressi et al.|2002}}{{sfnp|Decca et al.|2003}}

In 2009, Munday et al.<ref>{{cite journal|last1=Munday|first1=J. N.|last2=Capasso|first2=Federico|last3=Parsegian|first3=V. Adrian|title=Measured long-range repulsive Casimir–Lifshitz forces|date=2009|volume=457|issue=7226|pages=170–173|doi=10.1038/nature07610|url=http://nanoqed.synthasite.com/resources/nature07610.pdf|pmid=19129843|pmc=4169270|journal=Nature|bibcode=2009Natur.457..170M}}</ref> published experimental proof that (as predicted in 1961<ref>{{cite journal|last1=Dzyaloshinskii|first1=I. E.|last2=Lifshitz|first2=E. M.|last3=Pitaevskii|first3=Lev P.|title=General Theory of Van der Waals' Forces|journal=Soviet Physics Uspekhi|date=1961|volume=4|issue=2|page=154|doi=10.1070/PU1961v004n02ABEH003330|bibcode=1961SvPhU...4..153D}}</ref>) the Casimir force could also be repulsive as well as being attractive. Repulsive Casimir forces could allow quantum levitation of objects in a fluid and lead to a new class of switchable nanoscale devices with ultra-low static friction.{{sfnp|Capasso et al.|2007}}

An interesting hypothetical side effect of the Casimir effect is the [[Scharnhorst effect]], a hypothetical phenomenon in which light signals travel slightly [[Faster-than-light|faster than {{mvar|c}}]] between two closely spaced conducting plates.<ref name="Scharnhorst 1993">See {{harvp|Barton|Scharnhorst|1993}} and {{harvp|Chown|1990}}.</ref>

=== Lamb shift ===
{{Main|Lamb shift}}
[[File:Hydrogen fine structure.svg|thumb|[[Fine structure]] of energy levels in hydrogen – relativistic corrections to the [[Bohr model]]]]

The quantum fluctuations of the electromagnetic field have important physical consequences. In addition to the Casimir effect, they also lead to a splitting between the two [[energy level]]s {{math|<sup>2</sup>''S''<sub>{{sfrac|1|2}}</sub>}} and {{math|<sup>2</sup>''P''<sub>{{sfrac|1|2}}</sub>}} (in [[term symbol]] notation) of the [[hydrogen atom]] which was not predicted by the [[Dirac equation]], according to which these states should have the same energy. Charged particles can interact with the fluctuations of the quantized vacuum field, leading to slight shifts in energy;{{sfnp|Itzykson|Zuber|1980|p=80}} this effect is called the Lamb shift.<ref>
{{cite journal
 |last=Hawton |first=M.
 |year=1993
 |title=Self-consistent frequencies of the electron–photon system
 |journal=[[Physical Review A]]
 |volume=48 |issue=3 |pages=1824–1831
 |bibcode=1993PhRvA..48.1824H
 |doi=10.1103/PhysRevA.48.1824
 |pmid=9909797
}}</ref> The shift of about {{val|4.38|e=-6|u=eV}} is roughly {{val|e=-7}} of the difference between the energies of the 1s and 2s levels, and amounts to 1,058&nbsp;MHz in frequency units. A small part of this shift (27&nbsp;MHz ≈ 3%) arises not from fluctuations of the electromagnetic field, but from fluctuations of the electron–positron field. The creation of (virtual) electron–positron pairs has the effect of screening the Coulomb field and acts as a vacuum dielectric constant. This effect is much more important in muonic atoms.{{sfnp|Le Bellac|2006|p=381}}

=== Fine-structure constant ===
{{Main|Fine-structure constant}}

Taking {{mvar|ħ}} (the [[Planck constant]] divided by {{math|2π}}), {{mvar|c}} (the [[speed of light]]), and {{math|''e''<sup>2</sup> {{=}} {{sfrac|''q''{{su|b=''e''|p=2}}|4π''ε''<sub>0</sub>}}}} (the electromagnetic [[coupling constant]] i.e. a measure of the strength of the [[electromagnetic force]] (where {{math|''q<sub>e</sub>''}} is the absolute value of the [[Electron charge|electronic charge]] and <math>\varepsilon_0</math> is the [[vacuum permittivity]])) we can form a dimensionless quantity called the [[fine-structure constant]]:
<math display="block">\alpha = \frac{e^2}{\hbar c} = \frac{q_e^2}{4\pi\varepsilon_0\hbar c} \approx \frac{1}{137}</math>

The fine-structure constant is the coupling constant of quantum electrodynamics (QED) determining the strength of the interaction between electrons and photons. It turns out that the fine-structure constant is not really a constant at all owing to the zero-point energy fluctuations of the electron-positron field.{{sfnp|Le Bellac|2006|p=33}} The quantum fluctuations caused by zero-point energy have the effect of screening electric charges: owing to (virtual) electron-positron pair production, the charge of the particle measured far from the particle is far smaller than the charge measured when close to it.

The Heisenberg inequality where {{math|''ħ'' {{=}} {{sfrac|''h''|2π}}}}, and {{math|Δ<sub>''x''</sub>}}, {{math|Δ<sub>''p''</sub>}} are the standard deviations of position and momentum states that:
<math display="block">\Delta_x\Delta_p\ge\frac{1}{2}\hbar</math>

It means that a short distance implies large momentum and therefore high energy i.e. particles of high energy must be used to explore short distances. QED concludes that the fine-structure constant is an increasing function of energy. It has been shown that at energies of the order of the [[Z boson|Z<sup>0</sup> boson]] rest energy, {{math|''m<sub>z</sub>c''<sup>2</sup> ≈}} 90&nbsp;GeV, that:
<math display="block">\alpha\approx\frac{1}{129}</math>
rather than the low-energy {{math|''α'' ≈ {{sfrac|1|137}}}}.<ref>{{cite book|last1=Aitchison|first1=Ian|last2=Hey|first2=Anthony|title=Gauge Theories in Particle Physics: A Practical Introduction: Volume 1: From Relativistic Quantum Mechanics to QED|date=2012|publisher=CRC Press|isbn=9781466512993|page=343|edition=4th}}</ref><ref>{{cite book|last1=Quigg|first1=C|editor1-last=Espriu|editor1-first=D|editor2-last=Pich|editor2-first=A|title=Advanced School on Electroweak Theory: Hadron Colliders, the Top Quark, and the Higgs Sector|date=1998|publisher=World Scientific|isbn=9789814545143|page=143}}</ref> The renormalization procedure of eliminating zero-point energy infinities allows the choice of an arbitrary energy (or distance) scale for defining {{mvar|α}}. All in all, {{mvar|α}} depends on the energy scale characteristic of the process under study, and also on details of the renormalization procedure. The energy dependence of {{mvar|α}} has been observed for several years now in precision experiment in high-energy physics.

=== Vacuum birefringence ===
{{Main|Lorentz-violating electrodynamics|Euler–Heisenberg Lagrangian}}
[[File:Eso1641a.ogg|thumb|Light coming from the surface of a strongly magnetic [[neutron star]] (left) becomes linearly polarised as it travels through the vacuum.]]
In the presence of strong electrostatic fields it is predicted that virtual particles become separated from the vacuum state and form real matter.{{Citation needed|date=May 2019}} The fact that electromagnetic radiation can be transformed into matter and vice versa leads to fundamentally new features in quantum electrodynamics. One of the most important consequences is that, even in the vacuum, the Maxwell equations have to be exchanged by more complicated formulas. In general, it will be not possible to separate processes in the vacuum from the processes involving matter since electromagnetic fields can create matter if the field fluctuations are strong enough. This leads to highly complex nonlinear interaction – gravity will have an effect on the light at the same time the light has an effect on gravity. These effects were first predicted by Werner Heisenberg and [[Hans Heinrich Euler]] in 1936{{sfnp|Heisenberg|Euler|1936}} and independently the same year by Victor Weisskopf who stated: "The physical properties of the vacuum originate in the "zero-point energy" of matter, which also depends on absent particles through the external field strengths and therefore contributes an additional term to the purely Maxwellian field energy".{{sfnp|Weisskopf|1936|p=3}}{{sfnp|Greiner|Müller|Rafelski|2012|p=278}} Thus strong magnetic fields vary the energy contained in the vacuum. The scale above which the electromagnetic field is expected to become nonlinear is known as the [[Schwinger limit]]. At this point the vacuum has all the properties of a [[Birefringence|birefringent medium]], thus in principle a rotation of the polarization frame (the [[Faraday effect]]) can be observed in empty space.{{sfnp|Greiner|Müller|Rafelski|2012|p=291}}<ref>See {{harvp|Dunne|2012}} for a historical review of the subject.</ref>

[[File:Wide field view of the sky around the very faint neutron star RX J1856.5-3754.jpg|thumb|left|Wide field view of the neutron star [[RX J1856.5-3754]]]]
Both Einstein's theory of special and general relativity state that light should pass freely through a vacuum without being altered, a principle known as [[Lorentz invariance]]. Yet, in theory, large nonlinear self-interaction of light due to quantum fluctuations should lead to this principle being measurably violated if the interactions are strong enough. Nearly all theories of [[quantum gravity]] predict that Lorentz invariance is not an exact symmetry of nature. It is predicted the speed at which light travels through the vacuum depends on its direction, polarization and the local strength of the magnetic field.{{sfnp|Heyl|Shaviv|2000|p=1}} There have been a number of inconclusive results which claim to show evidence of a [[Modern searches for Lorentz violation|Lorentz violation]] by finding a rotation of the polarization plane of light coming from distant galaxies.<ref>See {{harvp|Carroll|Field|1997}} and {{harvs|txt|last1=Kostelecký|last2=Mewes|year1=2009|year2=2013}} for an overview of this area.</ref> The first concrete evidence for vacuum birefringence was published in 2017 when a team of [[astronomers]] looked at the light coming from the star [[RX J1856.5-3754]],<ref>See {{harvp|Mignani et al.|2017}} for experiment and {{harvp|Cho|2016}}, {{harvp|Crane|2016}} and {{harvp|Bennett|2016}} for comment.</ref> the closest discovered [[neutron star]] to [[Earth]].{{sfnp|Rees|2012|p=528}}

Roberto Mignani at the [[National Institute for Astrophysics]] in [[Milan]] who led the team of [[astronomers]] has commented that "When Einstein came up with the theory of general relativity 100 years ago, he had no idea that it would be used for navigational systems. The consequences of this discovery probably will also have to be realised on a longer timescale."{{sfnp|Crane|2016}} The team found that visible light from the star had undergone linear polarisation{{clarify|date=May 2018}} of around 16%. If the birefringence had been caused by light passing through [[interstellar gas]] or plasma, the effect should have been no more than 1%. Definitive proof would require repeating the observation at other wavelengths and on other neutron stars. At [[X-ray]] wavelengths the polarization from the quantum fluctuations should be near 100%.{{sfnp|Cho|2016}} Although no [[telescope]] currently exists that can make such measurements, there are several proposed X-ray telescopes that may soon be able to verify the result conclusively such as China's [[Hard X-ray Modulation Telescope]] (HXMT) and NASA's Imaging X-ray Polarimetry Explorer (IXPE).