Editing Zero-point energy (section)

== History ==

=== Early aether theories ===
[[File:James Clerk Maxwell.png|thumb|upright|James Clerk Maxwell]]
Zero-point energy evolved from historical ideas about the [[vacuum]]. To [[Aristotle]] the vacuum was {{lang|grc|τὸ κενόν}}, "the empty"; i.e., space independent of body. He believed this concept violated basic physical principles and asserted that [[Classical element#Greece|the elements]] of [[Fire (classical element)|fire]], [[Air (classical element)|air]], [[Earth (classical element)|earth]], and [[Water (classical element)|water]] were not made of atoms, but were continuous. To the [[atomists]] the concept of emptiness had absolute character: it was the distinction between existence and nonexistence.{{sfnp|Saunders|Brown|1991|p=1}} Debate about the characteristics of the vacuum were largely confined to the realm of [[philosophy]], it was not until much later on with the beginning of [[Renaissance|the renaissance]], that [[Otto von Guericke]] invented the first vacuum pump and the first testable scientific ideas began to emerge. It was thought that a totally empty volume of space could be created by simply removing all gases. This was the first generally accepted concept of the vacuum.{{sfnp|Conlon|2011|p=225}}

Late in the 19th century, however, it became apparent that the evacuated region still contained [[thermal radiation]]. The existence of the [[Luminiferous aether|aether]] as a substitute for a true void was the most prevalent theory of the time. According to the successful [[Electromagnetism|electromagnetic]] aether theory based upon [[James Clerk Maxwell|Maxwell's]] [[electrodynamics]], this all-encompassing aether was endowed with energy and hence very different from nothingness. The fact that electromagnetic and gravitational phenomena were transmitted in empty space was considered evidence that their associated aethers were part of the fabric of space itself. However Maxwell noted that for the most part these aethers were ''ad hoc'':

{{Blockquote|To those who maintained the existence of a plenum as a philosophical principle, nature's abhorrence of a vacuum was a sufficient reason for imagining an all-surrounding aether&nbsp;... Aethers were invented for the planets to swim in, to constitute electric atmospheres and magnetic effluvia, to convey sensations from one part of our bodies to another, and so on, till a space had been filled three or four times with aethers.{{sfnp|Kragh|Overduin|2014|p=7}}}}

Moreever, the results of the [[Michelson–Morley experiment]] in 1887 were the first strong evidence that the then-prevalent aether theories were seriously flawed, and initiated a line of research that eventually led to [[special relativity]], which ruled out the idea of a stationary aether altogether. To scientists of the period, it seemed that a true vacuum in space might be created by cooling and thus eliminating all radiation or energy. From this idea evolved the second concept of achieving a real vacuum: cool a region of space down to absolute zero temperature after evacuation. Absolute zero was technically impossible to achieve in the 19th century, so the debate remained unsolved.

=== Second quantum theory ===
[[File:Max Planck Nobel 1918.jpg|thumb|upright|Planck in 1918, the year he received the [[Nobel Prize in Physics]] for his work on [[Quantum mechanics|quantum theory]]]]
In 1900, [[Max Planck]] derived the average energy {{mvar|ε}} of a single ''energy radiator'', e.g., a vibrating atomic unit, as a function of absolute temperature:{{sfnp|Planck|1900}}
<math display="block"> \varepsilon = \frac{h\nu}{ e^{h\nu/(kT)}-1} \,,</math>
where {{mvar|h}} is the [[Planck constant]], {{mvar|ν}} is the [[frequency]], {{mvar|k}} is the [[Boltzmann constant]], and {{mvar|T}} is the absolute [[temperature]]. The zero-point energy makes no contribution to Planck's original law, as its existence was unknown to Planck in 1900.{{sfnp|Loudon|2000|p=9}}

The concept of zero-point energy was developed by [[Max Planck]] in Germany in 1911 as a corrective term added to a zero-grounded formula developed in his original quantum theory in 1900.{{sfnp|Kragh|2012|p=7}}

In 1912, Max Planck published the first journal article to describe the discontinuous emission of radiation, based on the discrete quanta of energy.{{sfnp|Planck|1912a}} In Planck's "second quantum theory" resonators absorbed energy continuously, but emitted energy in discrete energy quanta only when they reached the boundaries of finite cells in phase space, where their energies became integer multiples of {{math|''hν''}}. This theory led Planck to his new radiation law, but in this version energy resonators possessed a zero-point energy, the smallest average energy a resonator could take on. Planck's radiation equation contained a residual energy factor, one {{math|{{sfrac|''hν''|2}}}}, as an additional term dependent on the frequency {{mvar|ν}}, which was greater than zero (where {{mvar|h}} is the Planck constant). It is therefore widely agreed that "Planck's equation marked the birth of the concept of zero-point energy."{{sfnp|Milonni|1994|p=10}} In a series of papers from 1911 to 1913,<ref>See {{harvs|last1=Planck|year1=1911|year2=1912a|year3=1912b|year4=1913}} and {{harvp|Planck|1958}} for reprints</ref> Planck found the average energy of an oscillator to be:{{sfnp|Kragh|2012|p=7}}{{sfnp|Kuhn|1978|p=235}}
<math display="block">\varepsilon =\frac{h\nu} 2 + \frac{h\nu}{e^{h\nu/(kT)}-1} ~.</math>

[[File:Albert Einstein (Nobel).png|thumb|upright|Einstein's official 1921 portrait after receiving the Nobel Prize in Physics]]
Soon, the idea of zero-point energy attracted the attention of Albert Einstein and his assistant [[Otto Stern]].<ref>{{cite journal|last1=Einstein|first1=Albert|last2=Stern|first2=Otto|title=Einige Argumente für die Annahme einer molekularen Agitation beim absoluten Nullpunkt|language=de|trans-title=Some arguments for the assumption of a molecular agitation at the absolute zero point|journal=Annalen der Physik|date=1913|volume=345|issue=3|pages=551–560|doi=10.1002/andp.19133450309|bibcode=1913AnP...345..551E|url=https://zenodo.org/record/1424262}}</ref> In 1913 they published a paper that attempted to prove the existence of zero-point energy by calculating the [[specific heat]] of hydrogen gas and compared it with the experimental data. However, after assuming they had succeeded, they retracted support for the idea shortly after publication because they found Planck's second theory may not apply to their example. In a letter to [[Paul Ehrenfest]] of the same year Einstein declared zero-point energy "dead as a doornail".{{sfnp|Einstein|1993|pp=563–565}} Zero-point energy was also invoked by [[Peter Debye]],<ref>{{cite journal|last1=Debye|first1=Peter|title=Interferenz von Röntgenstrahlen und Wärmebewegung|language=de|trans-title=Interference of X-rays and thermal motion|journal=Annalen der Physik|date=1913|volume=348|issue=1|pages=49–92|doi=10.1002/andp.19133480105|bibcode=1913AnP...348...49D|url=https://zenodo.org/record/1424272}}</ref> who noted that zero-point energy of the atoms of a [[crystal lattice]] would cause a reduction in the intensity of the diffracted radiation in [[X-ray diffraction]] even as the temperature approached absolute zero. In 1916 [[Walther Nernst]] proposed that empty space was filled with zero-point [[electromagnetic radiation]].<ref>{{cite journal|last1=Nernst|first1=Walther|title=Über einen Versuch, von quantentheoretischen Betrachtungen zur Annahme stetiger Energieänderungen zurückzukehren|language=de|trans-title=On an attempt to return from quantum-theoretical considerations to the assumption of constant energy changes|journal=Verhandlungen der Deutschen Physikalischen|date=1916|volume=18|pages=83–116}}</ref> With the development of general relativity Einstein found the energy density of the vacuum to contribute towards a cosmological constant in order to obtain static solutions to his field equations; the idea that empty space, or the vacuum, could have some intrinsic energy associated with it had returned, with Einstein stating in 1920:

{{blockquote|There is a weighty argument to be adduced in favour of the aether hypothesis. To deny the aether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view&nbsp;... according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an aether. According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.<ref>{{cite book|last1=Einstein|first1=Albert|title=Äther und Relativitäts-Theorie|language=de|trans-title=Aether and relativity theory|date=1920|publisher=Springer|location=Berlin}}</ref><ref>{{cite book|last1=Einstein|first1=Albert|editor1-last=Jeffery|editor1-first=G. B.|editor2-last=Perrett|editor2-first=W.|title=Sidelights on Relativity: Ether and the Theory of Relativity|url=https://archive.org/details/sidelightsonrela00einsuoft|date=1922|publisher=Methuen & Co|location=New York|pages=[https://archive.org/details/sidelightsonrela00einsuoft/page/n8 1]–24}}</ref>}}

[[File:Heisenberg,Werner 1924 Göttingen - adjusted.jpeg|thumb|upright|Heisenberg, 1924]]
{{ill|Kurt Bennewitz|de|Kurt Bennewitz (Chemiker)}} and [[Francis Simon]] (1923),<ref>{{cite journal|last1=Bennewitz|first1=Kurt|last2=Simon|first2=Franz|title=Zur Frage der Nullpunktsenergie|language=de|trans-title=On the question of zero-point energy|journal=Zeitschrift für Physik|date=1923|volume=16|issue=1|doi=10.1007/BF01327389|pages=183–199|bibcode=1923ZPhy...16..183B|s2cid=121049183}}</ref> who worked at [[Walther Nernst]]'s laboratory in Berlin, studied the melting process of chemicals at low temperatures. Their calculations of the melting points of [[hydrogen]], [[argon]] and [[Mercury (element)|mercury]] led them to conclude that the results provided evidence for a zero-point energy. Moreover, they suggested correctly, as was later verified by Simon (1934),<ref>{{cite journal|last1=Simon|first1=F.|title=Behaviour of Condensed Helium near Absolute Zero|journal=Nature|date=1934|volume=133|issue=3362|page=529|doi=10.1038/133529a0|bibcode=1934Natur.133Q.529S|s2cid=4130047|doi-access=free}}</ref><ref>{{cite journal|last1=Dugdale|first1=J. S.|last2=Simon|first2=F. E.|title=Thermodynamic Properties and Melting of Solid Helium|journal=Proceedings of the Royal Society|date=1953|volume=218|issue=1134|page=291|doi=10.1098/rspa.1953.0105|bibcode=1953RSPSA.218..291D|s2cid=98061516}}</ref> that this quantity was responsible for the difficulty in solidifying helium even at absolute zero. In 1924 [[Robert S. Mulliken|Robert Mulliken]]<ref>{{cite journal|last1=Mulliken|first1=Robert S.|title=The band spectrum of boron monoxide|journal=Nature|date=1924|volume=114|issue=2862|pages=349–350|doi=10.1038/114349a0|bibcode=1924Natur.114..349M|s2cid=4121118}}</ref> provided direct evidence for the zero-point energy of molecular vibrations by comparing the band spectrum of <sup>10</sup>BO and <sup>11</sup>BO: the isotopic difference in the transition frequencies between the ground vibrational states of two different electronic levels would vanish if there were no zero-point energy, in contrast to the observed spectra. Then just a year later in 1925,<ref>{{Cite book|last1=Heisenberg|first1=W.|chapter=Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen |language=de |trans-chapter=On quantum-theoretical reinterpretation of kinematic and mechanical relationships |editor-last=Blum|editor-first=Walter|editor-last2=Rechenberg|editor-first2=Helmut|editor-link2=Helmut Rechenberg |editor-last3=Dürr|editor-first3=Hans-Peter|trans-title=Original Scientific Papers |title=Wissenschaftliche Originalarbeiten|date=1925|pages=382–396|publication-date=1985|location=Berlin, Heidelberg|publisher=Springer|doi= 10.1007/978-3-642-61659-4_26|isbn=978-3-642-64900-4|oclc= 7331244990}}</ref> with the development of [[matrix mechanics]] in [[Werner Heisenberg]]'s article "[[Quantum theoretical re-interpretation of kinematic and mechanical relations]]" the zero-point energy was derived from quantum mechanics.{{sfnp|Kragh|2002|p=162}}

In 1913 [[Niels Bohr]] had proposed what is now called the [[Bohr model]] of the atom,<ref>{{cite journal | first=Niels |last=Bohr | title=On the Constitution of Atoms and Molecules, Part I | journal=Philosophical Magazine | year=1913 | volume=26 | pages=1–24 | doi= 10.1080/14786441308634955| url=http://web.ihep.su/dbserv/compas/src/bohr13/eng.pdf | issue=151 | bibcode=1913PMag...26....1B}}</ref><ref>{{cite journal | first=Niels |last=Bohr | title=On the Constitution of Atoms and Molecules, Part II Systems Containing Only a Single Nucleus | journal=Philosophical Magazine | year=1913 | volume=26 | pages=476–502 | url=http://web.ihep.su/dbserv/compas/src/bohr13b/eng.pdf | doi=10.1080/14786441308634993 | issue=153 | bibcode=1913PMag...26..476B}}</ref><ref>{{cite journal | first=Niels |last=Bohr | title=On the Constitution of Atoms and Molecules, Part III Systems containing several nuclei| journal=Philosophical Magazine | year=1913 | volume=26 | issue=155| pages=857–875 | doi=10.1080/14786441308635031| url=https://zenodo.org/record/1430922 | bibcode=1913PMag...26..857B}}</ref> but despite this it remained a mystery as to why electrons do not fall into their nuclei. According to classical ideas, the fact that an accelerating charge loses energy by radiating implied that an electron should spiral into the nucleus and that atoms should not be stable. This problem of classical mechanics was nicely summarized by [[James Hopwood Jeans]] in 1915: "There would be a very real difficulty in supposing that the (force) law {{math|{{sfrac|1|''r''<sup>2</sup>}}}} held down to the zero values of {{mvar|r}}. For the force between two charges at zero distance would be infinite; we should have charges of opposite sign continually rushing together and, when once together, no force would be adequate to separate them. [...] Thus the matter in the universe would tend to shrink into nothing or to diminish indefinitely in size."<ref>{{cite book|last1=Jeans|first1=James Hopwood|title=The mathematical theory of electricity and magnetism|url=https://archive.org/details/cu31924012330589|date=1915|publisher=Cambridge University Press|location=Cambridge|page=[https://archive.org/details/cu31924012330589/page/n179 168]|edition=3rd}}</ref> The resolution to this puzzle came in 1926 when [[Erwin Schrödinger]] introduced the [[Schrödinger equation]].<ref>{{cite journal|last1=Schrödinger|first1=Erwin|title=Quantisierung als Eigenwertproblem|language=de|trans-title=Quantization as an eigenvalue problem|journal=Annalen der Physik|date=1926|volume=79|issue=13|pages=361–376|doi=10.1002/andp.19263851302|bibcode=1926AnP...385..437S}}</ref> This equation explained the new, non-classical fact that an electron confined to be close to a nucleus would necessarily have a large kinetic energy so that the minimum total energy (kinetic plus potential) actually occurs at some positive separation rather than at zero separation; in other words, zero-point energy is essential for atomic stability.<ref>{{cite book|last1=Lieb|first1=E. H.|last2=Seiringer|first2=R.|title=The Stability of Matter in Quantum Mechanics|url=https://archive.org/details/stabilitymatterq00hlie|url-access=limited|date=2009|publisher=Cambridge University Press|location=Cambridge|isbn=978-0-521-19118-0|pages=[https://archive.org/details/stabilitymatterq00hlie/page/n19 2]–3|oclc=638472161}}</ref>

=== Quantum field theory and beyond ===

In 1926, [[Pascual Jordan]]<ref>{{cite journal|last1=Born|first1=M.|last2=Heisenberg|first2=W.|last3=Jordan|first3=P.|title=Zur Quantenmechanik. II|language=de|trans-title=On quantum mechanics II|journal=Zeitschrift für Physik|date=1926|volume=35|issue=8|pages=557–615|doi=10.1007/BF01379806|bibcode=1926ZPhy...35..557B|s2cid=186237037}}</ref> published the first attempt to quantize the electromagnetic field. In a joint paper with [[Max Born]] and [[Werner Heisenberg]] he considered the field inside a cavity as a superposition of quantum harmonic oscillators. In his calculation he found that in addition to the "thermal energy" of the oscillators there also had to exist an infinite zero-point energy term. He was able to obtain the same fluctuation formula that Einstein had obtained in 1909.<ref>{{cite journal|last1=Einstein|first1=Albert|title=Zum gegenwärtigen Stand des Strahlungsproblems|journal=Physikalische Zeitschrift|date=1909|volume=10|pages=185–193|bibcode= 1909PhyZ...10..185E}}</ref> However, Jordan did not think that his infinite zero-point energy term was "real", writing to Einstein that "it is just a quantity of the calculation having no direct physical meaning".<ref>{{cite book|last1=Mehra|first1=J.|last2=Rechenberg|first2=H.|author-link1=Jagdish Mehra |author-link2=Helmut Rechenberg |title=The Historical Development of Quantum Theory |volume=6|date=2002|publisher=Springer|isbn=978-0-387-95262-8|page=57|oclc= 722601833}}</ref> Jordan found a way to get rid of the infinite term, publishing a joint work with Pauli in 1928,<ref>{{cite journal|last1=Jordan|first1=P.|last2=Pauli|first2=W.|title=Zur Quantenelektrodynamik ladungsfreier Felder|language=de|trans-title=On the quantum electrodynamics of charge-free fields|journal=Zeitschrift für Physik|date=1928|volume=47|issue=3|pages=151–173|doi= 10.1007/BF02055793|bibcode= 1928ZPhy...47..151J|s2cid=120536476}}</ref> performing what has been called "the first infinite subtraction, or renormalisation, in quantum field theory".<ref>{{cite book|last1=Schweber|first1=Silvan S.|title=QED and the Men Who Made It: Dyson, Feynman, Schwinger and Tomonaga|url=https://archive.org/details/qedmenwhomadeitd0000schw|url-access=registration|date=1994|publisher=Princeton University Press|isbn=978-0-691-03327-3|pages=[https://archive.org/details/qedmenwhomadeitd0000schw/page/108 108]–112|oclc= 439849774}}</ref>

[[File:Paul Dirac, 1933.jpg|thumb|upright|Paul Dirac, 1933]]
Building on the work of Heisenberg and others, [[Paul Dirac]]'s theory of emission and absorption (1927){{sfnp|Dirac|1927}} was the first application of the quantum theory of radiation. Dirac's work was seen as crucially important to the emerging field of quantum mechanics; it dealt directly with the process in which "particles" are actually created: [[spontaneous emission]].<ref>{{cite journal|last1=Weinberg|first1=Steven|title=The Search for Unity: Notes for a History of Quantum Field Theory|journal=Daedalus|date=1977|volume=106|issue=4|pages=17–35|jstor=20024506}}</ref> Dirac described the quantization of the [[electromagnetic field]] as an ensemble of [[quantum harmonic oscillator|harmonic oscillator]]s with the introduction of the concept of [[creation and annihilation operators]] of particles. The theory showed that spontaneous emission depends upon the zero-point energy fluctuations of the electromagnetic field in order to get started.<ref name="Yokoyama">
{{cite book
 |last1=Yokoyama|first1=H.
 |last2=Ujihara|first2=K.
 |title=Spontaneous emission and laser oscillation in microcavities
 |publisher= CRC Press
 |location=Boca Raton
 |year=1995
 |isbn=978-0-8493-3786-4|oclc= 832589969
 |page=[https://books.google.com/books?id=J_0ZAwf6AQ0C&pg=PA6 6]
}}</ref>{{sfnp|Scully |Zubairy |1997|loc=[https://books.google.com/books?id=20ISsQCKKmQC&pg=PA22 §1.5.2 pp. 22–23]}} In a process in which a photon is annihilated (absorbed), the photon can be thought of as making a transition into the vacuum state. Similarly, when a photon is created (emitted), it is occasionally useful to imagine that the photon has made a transition out of the vacuum state. In the words of Dirac:{{sfnp|Dirac|1927}}

{{blockquote|The light-quantum has the peculiarity that it apparently ceases to exist when it is in one of its stationary states, namely, the zero state, in which its momentum and therefore also its energy, are zero. When a light-quantum is absorbed it can be considered to jump into this zero state, and when one is emitted it can be considered to jump from the zero state to one in which it is physically in evidence, so that it appears to have been created. Since there is no limit to the number of light-quanta that may be created in this way, we must suppose that there are an infinite number of light quanta in the zero state&nbsp;...}}

Contemporary physicists, when asked to give a physical explanation for spontaneous emission, generally invoke the zero-point energy of the electromagnetic field. This view was popularized by [[Victor Weisskopf]] who in 1935 wrote:<ref>{{cite journal|last1=Weisskopf|first1=Viktor|title=Probleme der neueren Quantentheorie des Elektrons|language=de|trans-title=Problems of the new quantum theory of the electron|journal=Naturwissenschaften|date=1935|volume=23|issue=37|pages=631–637|doi= 10.1007/BF01492012|bibcode= 1935NW.....23..631W|s2cid=6780937}}</ref>

{{blockquote|From quantum theory there follows the existence of so called zero-point oscillations; for example each oscillator in its lowest state is not completely at rest but always is moving about its equilibrium position. Therefore electromagnetic oscillations also can never cease completely. Thus the quantum nature of the electromagnetic field has as its consequence zero point oscillations of the field strength in the lowest energy state, in which there are no light quanta in space&nbsp;... The zero point oscillations act on an electron in the same way as ordinary electrical oscillations do. They can change the eigenstate of the electron, but only in a transition to a state with the lowest energy, since empty space can only take away energy, and not give it up. In this way spontaneous radiation arises as a consequence of the existence of these unique field strengths corresponding to zero point oscillations. Thus spontaneous radiation is induced radiation of light quanta produced by zero point oscillations of empty space}}

This view was also later supported by [[Theodore A. Welton|Theodore Welton]] (1948),<ref>{{cite journal|last1=Welton|first1=Theodore Allen|title=Some observable effects of the quantum-mechanical fluctuations of the electromagnetic field|journal=Physical Review|date=1948|volume=74|issue=9|page=1157|doi=10.1103/PhysRev.74.1157|bibcode=1948PhRv...74.1157W}}</ref> who argued that spontaneous emission "can be thought of as forced emission taking place under the action of the fluctuating field". This new theory, which Dirac coined [[quantum electrodynamics]] (QED), predicted a fluctuating zero-point or "vacuum" field existing even in the absence of sources.

Throughout the 1940s improvements in [[microwave]] technology made it possible to take more precise measurements of the shift of the levels of a [[hydrogen atom]], now known as the Lamb shift,<ref name=lamb>
{{cite journal
 | author-link1= Willis Lamb
 | author-link2=Robert Retherford
 | year=1947
 | title=Fine Structure of the Hydrogen Atom by a Microwave Method
 | journal=[[Physical Review]]
 | volume=72 | pages= 241–243
 | doi=10.1103/PhysRev.72.241
 | bibcode = 1947PhRv...72..241L
 | issue=3
 | last1= Lamb
 | first1= Willis
 | last2= Retherford
 | first2= Robert
 | doi-access=free
}}</ref> and measurement of the [[magnetic moment]] of the electron.<ref name=foley>
{{cite journal
 | author-link2=Polykarp Kusch
 | author-link1=Henry M. Foley
 | year=1948
 | title=On the Intrinsic Moment of the Electron
 | journal=[[Physical Review]]
 | volume=73 | pages=412
 | doi=10.1103/PhysRev.73.412
 | bibcode = 1948PhRv...73..412F
 | issue=3
 | last1= Foley
 | first1= H.
 | last2= Kusch
 | first2= P.
}}</ref> Discrepancies between these experiments and Dirac's theory led to the idea of incorporating [[renormalisation]] into QED to deal with zero-point infinities. Renormalization was originally developed by [[Hans Kramers]]<ref>{{cite book|last1=Dresden|first1=M.|title=H. A. Kramers: Between Tradition and Revolution|date=1987|publisher=Springer|location=New York|isbn=978-1-461-29087-2|oclc= 1015092892}}</ref> and also [[Victor Weisskopf]] (1936),{{sfnp|Weisskopf|1936|p=6}} and first successfully applied to calculate a finite value for the Lamb shift by [[Hans Bethe]] (1947).<ref>{{cite journal|last1=Bethe|first1=Hans Albrecht|title=The Electromagnetic Shift of Energy Levels|journal=Physical Review|date=1947|volume=72|issue=4|page=339|doi=10.1103/PhysRev.72.339|bibcode=1947PhRv...72..339B|s2cid=120434909 }}</ref> As per spontaneous emission, these effects can in part be understood with interactions with the zero-point field.{{sfnp|Power|1964|p=35}}{{sfnp|Milonni|1994|p=111}} But in light of renormalisation being able to remove some zero-point infinities from calculations, not all physicists were comfortable attributing zero-point energy any physical meaning, viewing it instead as a mathematical artifact that might one day be eliminated. In [[Wolfgang Pauli]]'s 1945 [[Nobel lecture]]<ref>{{cite web|last1=Pauli|first1=Wolfgang|title=Exclusion principle and quantum mechanics|url=https://www.nobelprize.org/nobel_prizes/physics/laureates/1945/pauli-lecture.pdf|website=nobelprize.org|publisher=Royal Swedish Academy of Sciences|access-date=20 October 2016|date=1946}}</ref> he made clear his opposition to the idea of zero-point energy stating "It is clear that this zero-point energy has no physical reality".

[[File:Hendrik Casimir (1958).jpg|thumb|left|upright|Hendrik Casimir (1958)]]
In 1948 [[Hendrik Casimir]]<ref>{{cite journal|last1=Casimir|first1=Hendrik Brugt Gerhard|last2=Polder|first2=Dirk|title=The Influence of Retardation on the London–Van der Waals Forces|journal=Physical Review|date=1948|volume=73|issue=4|page=360|doi=10.1103/PhysRev.73.360|bibcode=1948PhRv...73..360C}}</ref><ref>{{cite journal|last1=Casimir|first1=Hendrik Brugt Gerhard|title=On the attraction between two perfectly conducting plates|journal=Proceedings of the Royal Netherlands Academy of Arts and Sciences|date=1948|volume=51|pages=793–795|url=http://www.dwc.knaw.nl/DL/publications/PU00018547.pdf|access-date=19 October 2016}}</ref> showed that one consequence of the zero-point field is an attractive force between two uncharged, perfectly conducting parallel plates, the so-called Casimir effect. At the time, Casimir was studying the properties of [[colloid|colloidal solutions]]. These are viscous materials, such as paint and mayonnaise, that contain micron-sized particles in a liquid matrix. The properties of such solutions are determined by [[Van der Waals forces]] – short-range, attractive forces that exist between neutral atoms and molecules. One of Casimir's colleagues, Theo Overbeek, realized that the theory that was used at the time to explain Van der Waals forces, which had been developed by [[Fritz London]] in 1930,<ref>{{cite journal|first1=R. |last1=Eisenschitz |first2=F. |last2=London |name-list-style=amp |journal=Zeitschrift für Physik|volume=60|pages= 491–527 |year=1930|doi=10.1007/BF01341258|title=Über das Verhältnis der Van der Waalsschen Kräfte zu den homöopolaren Bindungskräften|language=de|trans-title=On the relationship of van der Waals forces to homeopolar binding forces|issue=7–8|bibcode=1930ZPhy...60..491E|s2cid=125644826 }}</ref><ref>{{cite journal|first=F. |last=London|journal= Zeitschrift für Physik |volume=63|page= 245 |year=1930|doi=10.1007/BF01421741|title=Zur Theorie und Systematik der Molekularkräfte|language=de|trans-title=On the theory and systematics of molecular forces|issue=3–4|bibcode=1930ZPhy...63..245L|s2cid=123122363}}</ref> did not properly explain the experimental measurements on colloids. Overbeek therefore asked Casimir to investigate the problem. Working with [[Dirk Polder]], Casimir discovered that the interaction between two neutral molecules could be correctly described only if the fact that light travels at a finite speed was taken into account.<ref>{{cite journal|last1=Lambrecht|first1=Astrid|title=The Casimir effect: a force from nothing|journal=Physics World|date=2002|volume=15|issue=9|pages=29–32|url=https://indico.cern.ch/event/247728/contributions/1569920/attachments/426300/591724/Casimir_Force_PhysWorld_2002.pdf|access-date=24 October 2016|publisher=Institute of Physics Publishing|doi=10.1088/2058-7058/15/9/29|issn=0953-8585}}</ref> Soon afterwards after a conversation with [[Niels Bohr|Bohr]] about zero-point energy, Casimir noticed that this result could be interpreted in terms of vacuum fluctuations. He then asked himself what would happen if there were two mirrors – rather than two molecules – facing each other in a vacuum. It was this work that led to his prediction of an attractive force between reflecting plates. The work by Casimir and Polder opened up the way to a unified theory of van der Waals and Casimir forces and a smooth continuum between the two phenomena. This was done by Lifshitz (1956)<ref>{{Cite journal|title = The Theory of Molecular Attractive Forces between Solids|last = Lifshitz|first = E. M.|date = 1954|journal = Journal of Experimental Theoretical Physics USSR|volume = 29|pages = 94–110}}</ref><ref>{{Cite journal|title = The theory of molecular Attractive Forces between Solids|last = Lifshitz|first = E. M.|date = 1956|journal = Soviet Physics|volume = 2|number = 1|pages = 73–83}}</ref><ref>{{Cite journal|title = Direct measurement of molecular attraction between solids separated by a narrow gap|last1 = Derjaguin|first1 = B. V.|date = 1956|journal = Quarterly Reviews, Chemical Society|doi = 10.1039/qr9561000295|last2 = Abrikosova|first2 = I. I.|last3 = Lifshitz|first3 = E. M.|volume = 10|issue = 3|pages = 295–329}}</ref> in the case of plane parallel [[Dielectric|dielectric plates]]. The generic name for both van der Waals and Casimir forces is dispersion forces, because both of them are caused by dispersions of the operator of the dipole moment.<ref>{{cite book|last1=Mahanty|first1=J.|last2=Ninham|first2=B. W.|title=Dispersion Forces|date=1976|publisher=Academic Press|isbn=978-0-124-65050-3|oclc= 925046024}}</ref> The role of relativistic forces becomes dominant at orders of a hundred nanometers.

In 1951 [[Herbert Callen]] and Theodore Welton<ref name="ReferenceB">{{cite journal|last1=Callen|first1=Herbert|last2=Welton|first2=Theodore A.|title=Irreversibility and Generalized Noise|journal=Physical Review|date=1951|volume=83|issue=1|pages=34–40|doi=10.1103/PhysRev.83.34|bibcode=1951PhRv...83...34C}}</ref> proved the quantum [[fluctuation-dissipation theorem]] (FDT) which was originally formulated in classical form by [[Harry Nyquist|Nyquist]] (1928)<ref name="ReferenceC">{{cite journal|last1=Nyquist|first1=Harry|title=Thermal Agitation of Electric Charge in Conductors|journal=Physical Review|date=1928|volume=32|issue=1|pages=110–113|doi=10.1103/PhysRev.32.110|bibcode=1928PhRv...32..110N}}</ref> as an explanation for observed [[Johnson noise]] in electric circuits.<ref name="ReferenceD">{{cite journal|last1=Johnson|first1=John Bertrand|title=Thermal Agitation of Electricity in Conductors|journal=Physical Review|date=1928|volume=32|issue=1|pages=97–109|doi=10.1103/PhysRev.32.97|bibcode=1928PhRv...32...97J}}</ref> The fluctuation-dissipation theorem showed that when something dissipates energy, in an effectively irreversible way, a connected heat bath must also fluctuate. The fluctuations and the dissipation go hand in hand; it is impossible to have one without the other. The implication of FDT being that the vacuum could be treated as a heat bath coupled to a dissipative force and as such energy could, in part, be extracted from the vacuum for potentially useful work.{{sfnp|Milonni|1994|p=54}} FDT has been shown to be true experimentally under certain quantum, non-classical, conditions.<ref name="cloudfront.escholarship.org">{{cite journal|last1=Koch|first1=Roger H.|last2=Van Harlingen|first2=D. J.|last3=Clarke|first3=John|title=Observation of Zero-Point Fluctuations in a Resistively Shunted Josephson Tunnel Junction|journal=Physical Review Letters|date=1981|volume=47|issue=17|pages=1216–1219|doi=10.1103/PhysRevLett.47.1216|bibcode=1981PhRvL..47.1216K|osti=1136482|s2cid=119728862 |url=https://cloudfront.escholarship.org/dist/prd/content/qt7cb912p9/qt7cb912p9.pdf?t=maz7le}}</ref><ref name=Allahverdyan-2000>{{cite journal|last1=Allahverdyan|first1=A. E.|last2=Nieuwenhuizen|first2=Th. M.|title=Extraction of Work from a Single Thermal Bath in the Quantum Regime|journal=Physical Review Letters|date=2000|volume=85|issue=9|pages=1799–1802|doi=10.1103/PhysRevLett.85.1799|pmid=10970617|bibcode=2000PhRvL..85.1799A|arxiv=cond-mat/0006404|s2cid=32579381|url=https://pure.uva.nl/ws/files/3031844/12613_88222y.pdf}}</ref>{{sfnp|Scully et al.|2003}}

In 1963 the [[Jaynes–Cummings model]]<ref>{{cite journal|last1=Jaynes|first1=E. T.|last2=Cummings|first2=F. W.|title=Comparison of quantum and semiclassical radiation theories with application to the beam maser|journal=Proceedings of the IEEE|date=1963|volume=51|issue=1|doi=10.1109/PROC.1963.1664|pages=89–109}}</ref> was developed describing the system of a [[Two-level system|two-level atom]] interacting with a quantized field mode (i.e. the vacuum) within an optical cavity. It gave nonintuitive predictions such as that an atom's spontaneous emission could be driven by field of effectively constant frequency ([[Rabi frequency]]). In the 1970s experiments were being performed to test aspects of quantum optics and showed that the rate of spontaneous emission of an atom could be controlled using reflecting surfaces.{{sfnp|Drexhage|1970}}{{sfnp|Drexhage|1974|p={{page needed|date=May 2020}}}} These results were at first regarded with suspicion in some quarters: it was argued that no modification of a spontaneous emission rate would be possible, after all, how can the emission of a photon be affected by an atom's environment when the atom can only "see" its environment by emitting a photon in the first place? These experiments gave rise to [[cavity quantum electrodynamics]] (CQED), the study of effects of mirrors and cavities on radiative corrections. Spontaneous emission can be suppressed (or "inhibited")<ref>{{cite journal|last1=Hulet|first1=Randall G.|last2=Hilfer|first2=Eric S.|last3=Kleppner|first3=Daniel|title=Inhibited Spontaneous Emission by a Rydberg Atom|journal=Physical Review Letters|date=1985|volume=55|issue=20|pages=2137–2140|doi=10.1103/PhysRevLett.55.2137|pmid=10032058|bibcode=1985PhRvL..55.2137H|url=https://scholarship.rice.edu/bitstream/1911/79433/1/PhysRevLett.55.2137.pdf|hdl=1911/79433}}</ref><ref>{{cite journal|last1=Yablonovitch|first1=Eli|title=Inhibited Spontaneous Emission in Solid-State Physics and Electronics|journal=Physical Review Letters|date=1987|volume=58|issue=20|pages=2059–2062|doi=10.1103/PhysRevLett.58.2059|bibcode=1987PhRvL..58.2059Y|pmid=10034639|doi-access=free}}</ref> or amplified. Amplification was first predicted by Purcell in 1946<ref>{{cite journal|last1=Purcell|first1=E. M.|title=Proceedings of the American Physical Society|journal=Physical Review|date=1946|volume=69|issue=11–12|page=674|doi=10.1103/PhysRev.69.674|bibcode=1946PhRv...69Q.674.}}</ref> (the [[Purcell effect]]) and has been experimentally verified.{{sfnp|Goy et al.|1983}} This phenomenon can be understood, partly, in terms of the action of the vacuum field on the atom.{{sfnp|Milonni|1983}}