Editing Zero-point energy (section)

== Chaotic and emergent phenomena ==
{{Beyond the Standard Model}}
{{See also|Chaos theory|Emergence|Self-organization}}
The mathematical models used in [[classical electromagnetism]], quantum electrodynamics (QED) and the [[Standard Model]] all view the [[QED vacuum|electromagnetic vacuum]] as a linear system with no overall observable consequence. For example, in the case of the Casimir effect, Lamb shift, and so on these phenomena can be explained by alternative mechanisms other than action of the vacuum by arbitrary changes to the normal ordering of field operators. See the [[#Alternative theories|alternative theories]] section. This is a consequence of viewing electromagnetism as a U(1) gauge theory, which topologically does not allow the complex interaction of a field with and on itself.<ref>{{cite book|last1=Barrett|first1=Terence W.|title=Topological Foundations of Electromagnetism|date=2008|publisher=World Scientific|location=Singapore|isbn=9789812779977|page=2|url=https://books.google.com/books?id=e0-QdLqT-pIC}}</ref> In higher symmetry groups and in reality, the vacuum is not a calm, randomly fluctuating, largely immaterial and passive substance, but at times can be viewed as a turbulent virtual [[Plasma (physics)|plasma]] that can have complex vortices (i.e. [[soliton]]s vis-à-vis particles), [[entangled state]]s and a rich nonlinear structure.{{sfnp|Greiner|Müller|Rafelski|2012|p=23}} There are many observed nonlinear physical electromagnetic phenomena such as [[Aharonov–Bohm effect|Aharonov–Bohm]] (AB)<ref>
{{cite journal
 |author=Ehrenberg, W
 |author2=Siday, RE
 |date=1949
 |title=The Refractive Index in Electron Optics and the Principles of Dynamics
 |journal=[[Proceedings of the Physical Society]] | series = Series B
 |volume=62 |issue=1
 |pages=8–21
 |doi=10.1088/0370-1301/62/1/303
 |bibcode = 1949PPSB...62....8E |citeseerx=10.1.1.205.6343
}}</ref><ref name="Significance of electromagnetic potentials in quantum theory">
{{cite journal
 |author=Aharonov, Y
 |author2=Bohm, D
 |date=1959
 |title=Significance of electromagnetic potentials in quantum theory
 |journal=[[Physical Review]]
 |volume=115 |issue=3
 |pages=485–491
 |doi=10.1103/PhysRev.115.485
 |arxiv=1911.10555
 |bibcode = 1959PhRv..115..485A |s2cid=121421318
}}</ref> and Altshuler–Aronov–Spivak (AAS) effects,<ref>{{cite journal|last1=Altshuler|first1=B. L.|last2=Aronov|first2=A. G.|last3=Spivak|first3=B. Z.|title=The Aaronov-Bohm effect in disordered conductors|journal=Pisma Zh. Eksp. Teor. Fiz.|date=1981|volume=33|page=101|bibcode=1981JETPL..33...94A|url=http://www.jetpletters.ac.ru/ps/1501/article_22943.pdf|access-date=3 November 2016|archive-date=4 November 2016|archive-url=https://web.archive.org/web/20161104023602/http://www.jetpletters.ac.ru/ps/1501/article_22943.pdf|url-status=dead}}</ref> [[Geometric phase|Berry]],<ref>{{cite journal|last1=Berry|first1=M. V.|title=Quantal Phase Factors Accompanying Adiabatic Changes|journal=Proc. R. Soc.|date=1984|volume=A392|issue=1802|pages=45–57|doi=10.1098/rspa.1984.0023|bibcode=1984RSPSA.392...45B|s2cid=46623507}}</ref> Aharonov–Anandan,<ref>{{cite journal|last1=Aharonov|first1=Y.|last2=Anandan|first2=J.|title=Phase change during a cyclic quantum evolution|journal=Physical Review Letters|date=1987|volume=58|issue=16|pages=1593–1596|doi=10.1103/PhysRevLett.58.1593|pmid=10034484|bibcode=1987PhRvL..58.1593A}}</ref> Pancharatnam<ref>{{cite journal|last1=Pancharatnam|first1=S.|title=Generalized theory of interference, and its applications|journal=Proceedings of the Indian Academy of Sciences|date=1956|volume=44|issue=5|pages=247–262|doi=10.1007/BF03046050|s2cid=118184376}}</ref> and Chiao–Wu<ref>{{cite journal|last1=Chiao|first1=Raymond Y.|last2=Wu|first2=Yong-Shi|title=Manifestations of Berry's Topological Phase for the Photon|journal=Physical Review Letters|date=1986|volume=57|issue=8|pages=933–936|doi=10.1103/PhysRevLett.57.933|bibcode=1986PhRvL..57..933C|pmid=10034203}}</ref> phase rotation effects, [[Josephson effect]],<ref>
{{cite journal |author=Josephson |first=B. D. |year=1962 |title=Possible new effects in superconductive tunnelling |journal=Phys. Lett. |volume=1 |issue=7 |pages=251–253 |bibcode=1962PhL.....1..251J |doi=10.1016/0031-9163(62)91369-0}}</ref><ref name=Joe>
{{cite journal
 |author=B. D. Josephson
 |year=1974
 |title=The discovery of tunnelling supercurrents
 |journal=Rev. Mod. Phys.
 |volume=46 |issue=2 |pages=251–254
 |bibcode=1974RvMP...46..251J
 |doi=10.1103/RevModPhys.46.251|url=https://www.europhysicsnews.org/10.1051/epn/19740503001/pdf
}}</ref> [[Quantum Hall effect]],<ref name=vonKlitzing:1980>
{{cite journal
 |author1=K. v. Klitzing
 |author2=G. Dorda
 |author3=M. Pepper
 |year=1980
 |title=New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance
 |journal=Physical Review Letters
 |volume=45 |issue=6 |pages=494–497
 |bibcode=1980PhRvL..45..494K
 |doi=10.1103/PhysRevLett.45.494|doi-access=free
}}
</ref> the [[De Haas–Van Alphen effect]],<ref>{{cite journal|last1=De Haas|first1=W. J.|last2=Van Alphen|first2=P. M.|title=The dependance of the susceptibility of diamagnetic metals upon the field|journal=Proc. Netherlands R. Acad. Sci.|date=1930|volume=33|page=1106}}</ref> the [[Sagnac effect]] and many other physically observable phenomena which would indicate that the electromagnetic potential field has real physical meaning rather than being a mathematical artifact{{sfnp|Penrose|2004|pages=453–454}} and therefore an all encompassing theory would not confine electromagnetism as a local force as is currently done, but as a SU(2) gauge theory or higher geometry. Higher symmetries allow for nonlinear, aperiodic behaviour which manifest as a variety of complex non-equilibrium phenomena that do not arise in the linearised U(1) theory, such as multiple stable states, symmetry breaking, chaos and [[emergence]].<ref>{{cite book|last1=Feng|first1=J. H.|last2=Kneubühl|first2=F. K.|editor1-last=Barrett|editor1-first=Terence William|editor2-last=Grimes|editor2-first=Dale M.|title=Solitons and Chaos in Periodic Nonlinear Optical Media and Lasers: Advanced Electromagnetism: Foundations, Theory and Applications|date=1995|publisher=World Scientific|location=Singapore|isbn=978-981-02-2095-2|page=438|url=https://books.google.com/books?id=OdnsCgAAQBAJ}}</ref>

What are called Maxwell's equations today, are in fact a simplified version of the original equations reformulated by [[Oliver Heaviside|Heaviside]], [[George Francis FitzGerald|FitzGerald]], [[Oliver Lodge|Lodge]] and [[Heinrich Hertz|Hertz]]. The original equations used [[William Rowan Hamilton|Hamilton]]'s more expressive [[quaternion]] notation,<ref>{{cite book|last1=Hunt|first1=Bruce J.|title=The Maxwellians|date=2005|publisher=Cornell University Press|location=Cornell|isbn=9780801482342|page=17|url=https://books.google.com/books?id=23rBH11Q9w8C}}</ref> a kind of [[Clifford algebra]], which fully subsumes the standard Maxwell vectorial equations largely used today.<ref>{{Cite journal |doi = 10.1049/pi-c.1959.0012|title = The Heaviside papers found at Paignton in 1957|journal = Proceedings of the IEE - Part C: Monographs|volume = 106|issue = 9|pages = 70|year = 1959|last1 = Josephs|first1 = H.J.}}</ref> In the late 1880s there was a debate over the relative merits of vector analysis and quaternions. According to Heaviside the electromagnetic potential field was purely metaphysical, an arbitrary mathematical fiction, that needed to be "murdered".<ref>{{cite book|last1=Hunt|first1=Bruce J.|title=The Maxwellians|date=2005|publisher=Cornell University Press|location=Cornell|isbn=9780801482342|pages=165–166|url=https://books.google.com/books?id=23rBH11Q9w8C}}</ref> It was concluded that there was no need for the greater physical insights provided by the quaternions if the theory was purely local in nature. Local vector analysis has become the dominant way of using Maxwell's equations ever since. However, this strictly vectorial approach has led to a restrictive topological understanding in some areas of electromagnetism, for example, a full understanding of the energy transfer dynamics in [[Nikola Tesla|Tesla's]] oscillator-shuttle-circuit can only be achieved in quaternionic algebra or higher SU(2) symmetries.<ref>{{cite journal|last1=Barrett|first1=T. W.|title=Tesla's Nonlinear Oscillator-Shuttle-Circuit (OSC) Theory|journal=Annales de la Fondation Louis de Broglie|date=1991|volume=16|issue=1|pages=23–41|url=http://www.cheniere.org/references/TeslaOSC.pdf|issn=0182-4295|access-date=3 November 2016|archive-date=13 September 2016|archive-url=https://web.archive.org/web/20160913052650/http://www.cheniere.org/references/TeslaOSC.pdf|url-status=dead}}</ref> It has often been argued that quaternions are not compatible with special relativity,{{sfnp|Penrose|2004|page=201}} but multiple papers have shown ways of incorporating relativity.<ref>{{cite journal|last1=Rocher|first1=E. Y.|title=Noumenon: Elementary entity of a new mechanics|journal=J. Math. Phys.|date=1972|volume=13|issue=12|page=1919|doi=10.1063/1.1665933|bibcode=1972JMP....13.1919R}}</ref><ref>{{cite journal|last1=Imaeda|first1=K.|title=A new formulation of classical electrodynamics|journal=Il Nuovo Cimento B|date=1976|volume=32|issue=1|pages=138–162|doi=10.1007/BF02726749|bibcode=1976NCimB..32..138I|s2cid=123315936}}</ref><ref>{{cite journal|last1=Kauffmann|first1=T.|last2=Sun|first2=Wen IyJ|title=Quaternion mechanics and electromagnetism|journal=Annales de la Fondation Louis de Broglie|date=1993|volume=18|issue=2|pages=213–219}}</ref><ref>{{cite web |last1=Lambek |first1=Joachim |title=QUATERNIONS AND THREE TEMPORAL DIMENSIONS |url=https://www.math.mcgill.ca/barr/lambek/pdffiles/Quater2014.pdf}}</ref>

A good example of nonlinear electromagnetics is in high energy dense plasmas, where [[Vortex|vortical phenomena]] occur which seemingly violate the [[second law of thermodynamics]] by increasing the energy gradient within the electromagnetic field and violate [[Maxwell's laws]] by creating ion currents which capture and concentrate their own and surrounding magnetic fields. In particular [[Lorentz force|Lorentz force law]], which elaborates Maxwell's equations is violated by these force free vortices.{{sfnp|Bostick et al.|1966}}<ref>{{cite book|last1=Ferraro|first1=V .|last2=Plumpton|first2=C.|title=An Introduction to Magneto-Fluid Mechanics|url=https://archive.org/details/introductiontoma00ferr|url-access=registration|date=1961|publisher=Oxford University Press|location=Oxford|bibcode=1961itmf.book.....F }}</ref><ref>{{cite book|last=White|first=Carol|date=1977|title=Energy potential: Toward a new electro-magnetic field theory|publisher=Campaigner Pub.|location=New York|isbn=978-0918388049}}</ref> These apparent violations are due to the fact that the traditional conservation laws in classical and quantum electrodynamics (QED) only display linear U(1) symmetry (in particular, by the extended [[Noether theorem]],<ref>{{cite journal|last=Noether|first=E.|year=1918|title=Invariante Variationsprobleme|journal=Nachr. D. König. Gesellsch. D. Wiss. Zu Göttingen, Math-phys. Klasse|volume=1918|pages=235–257}}</ref> [[conservation law]]s such as the [[laws of thermodynamics]] need not always apply to [[dissipative systems]],{{sfnp|Scott|2006|p=[https://books.google.com/books?id=KC7gZmIEAiwC&pg=PA163 163]}}<ref>{{cite book|last1=Pismen|first1=L. M.|title=Patterns and Interfaces in Dissipative Dynamics|date=2006|publisher=Springer|isbn=9783540304319|page=3|url=https://books.google.com/books?id=Wje3RXlQdaMC}}</ref> which are expressed in gauges of higher symmetry). The second law of thermodynamics states that in a closed linear system entropy flow can only be positive (or exactly zero at the end of a cycle). However, negative entropy (i.e. increased order, structure or self-organisation) can spontaneously appear in an open nonlinear thermodynamic system that is far from equilibrium, so long as this emergent order accelerates the overall flow of entropy in the total system. The 1977 [[Nobel Prize in Chemistry]] was awarded to thermodynamicist [[Ilya Prigogine]]<ref>{{cite web|author1=The Nobel Foundation|title=The Nobel Prize in Chemistry 1977|url=https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1977/|website=nobelprize.org|publisher=Royal Swedish Academy of Sciences|access-date=3 November 2016|date=1977}}</ref> for his theory of dissipative systems that described this notion. Prigogine described the principle as "order through fluctuations"<ref>{{cite book|last1=Nicolis|first1=G.|last2=Prigogine|first2=I.|title=Self-organization in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations|date=1977|publisher=Wiley-Blackwell|isbn=978-0471024019}}</ref> or "order out of chaos".<ref>{{cite book|last1=Prigogine|first1=Ilya|last2=Stengers|first2=Isabelle|title=Order out of Chaos|date=1984|publisher=Flamingo|isbn=978-0-00-654115-8}}</ref> It has been argued by some that all emergent order in the universe from galaxies, solar systems, planets, weather, complex chemistry, evolutionary biology to even consciousness, technology and civilizations are themselves examples of thermodynamic dissipative systems; nature having naturally selected these structures to accelerate entropy flow within the universe to an ever-increasing degree.<ref>{{cite book|last1=Gleick|first1=James|title=Chaos: Making a New Science|date=1987|publisher=Vintage|isbn=9780749386061|page=308|edition=1998}}</ref> For example, it has been estimated that human body is 10,000 times more effective at dissipating energy per unit of mass than the sun.<ref>{{cite book|last1=Chaisson|first1=Eric J.|title=Cosmic Evolution: The Rise of Complexity in Nature|date=2002|publisher=Harvard University Press|isbn=978-0674009875|url=https://books.google.com/books?id=KG2SZouhFuIC|page=139}}</ref>

One may query what this has to do with zero-point energy. Given the complex and adaptive behaviour that arises from nonlinear systems considerable attention in recent years has gone into studying a new class of [[phase transition]]s which occur at absolute zero temperature. These are quantum phase transitions which are driven by EM field fluctuations as a consequence of zero-point energy.<ref>{{cite book|last1=Kais|first1=Sabre|editor1-last=Popelier|editor1-first=Paul|title=Finite Size Scaling for Criticality of the Schrödinger Equation: Solving the Schrödinger Equation: Has Everything Been Tried?|date=2011|publisher=Imperial College Press|location=Singapore|isbn=978-1-84816-724-7|pages=91–92|url=https://books.google.com/books?id=zFK7CgAAQBAJ}}</ref> A good example of a spontaneous phase transition that are attributed to zero-point fluctuations can be found in [[superconductor]]s. Superconductivity is one of the best known empirically quantified macroscopic electromagnetic phenomena whose basis is recognised to be quantum mechanical in origin. The behaviour of the electric and magnetic fields under superconductivity is governed by the [[London equations]]. However, it has been questioned in a series of journal articles whether the quantum mechanically canonised London equations can be given a purely classical derivation.<ref>{{cite news|title=Classical Physics Makes a Comeback|newspaper=The Times|date=14 January 1982|location=London}}</ref> Bostick,<ref>{{cite journal|last1=Bostick|first1=W.|title=On the Controversy over Whether Classical Systems Like Plasmas Can Behave Like Superconductors (Which Have Heretofore Been Supposed to Be Strictly Quantum Mechanically Dominated)|journal=International Journal of Fusion Energy|date=1985|volume=3|issue=2|pages=47–51|url= https://wlym.com/archive/fusion/ijfe/19850404-IJFE.pdf|access-date=2020-05-22|url-status=live|archive-url= https://web.archive.org/web/20160403190424/http://wlym.com/archive/fusion/ijfe/19850404-IJFE.pdf|archive-date=2016-04-03}}</ref><ref>{{cite journal|last1=Bostick|first1=W.|title=The Morphology of the Electron|journal=International Journal of Fusion Energy|date=1985|volume=3|issue=1|pages=9–52|url= http://wlym.com/archive/fusion/ijfe/19850101-IJFE.pdf|access-date=2020-05-22|url-status=live|archive-url= https://web.archive.org/web/20160403183310/http://wlym.com/archive/fusion/ijfe/19850101-IJFE.pdf|archive-date=2016-04-03}}</ref> for instance, has claimed to show that the London equations do indeed have a classical origin that applies to superconductors and to some collisionless plasmas as well. In particular it has been asserted that the [[Beltrami vector field|Beltrami vortices]] in the plasma focus display the same paired [[Flux tube|flux-tube]] morphology as [[Type II superconductor]]s.<ref>{{cite journal|last1=Bostick|first1=W.|title=Recent Experimental Results of The Plasma-Focus Group at Darmstadt, West Germany: A Review and Critique|journal=International Journal of Fusion Energy|date=1985|volume=3|issue=1|page=68|url= http://wlym.com/archive/fusion/ijfe/19850101-IJFE.pdf|access-date=2020-05-22|url-status=live|archive-url= https://web.archive.org/web/20160403183310/http://wlym.com/archive/fusion/ijfe/19850101-IJFE.pdf|archive-date=2016-04-03}}</ref><ref>{{cite journal|last1=Edwards|first1=W. Farrell|title=Classical Derivation of the London Equations|journal=Physical Review Letters|date=1981|volume=47|issue=26|pages=1863–1866|doi=10.1103/PhysRevLett.47.1863|bibcode=1981PhRvL..47.1863E}}</ref> Others have also pointed out this connection, Fröhlich<ref>{{cite journal |last1=Fröhlich |first1=H. |date=1966 |title=Macroscopic wave functions in superconductors |journal=Proceedings of the Physical Society |volume=87 |issue=1 |pages=330–332 |bibcode=1966PPS....87..330F |doi=10.1088/0370-1328/87/1/137}}</ref> has shown that the hydrodynamic equations of compressible fluids, together with the London equations, lead to a macroscopic parameter (<math>\mu</math> = electric charge density / mass density), without involving either [[phase factor|quantum phase factors]] or the Planck constant. In essence, it has been asserted that Beltrami plasma vortex structures are able to at least simulate the morphology of [[Type-I superconductor|Type I]] and [[Type-II superconductor|Type II superconductors]]. This occurs because the "organised" dissipative energy of the vortex configuration comprising the ions and electrons far exceeds the "disorganised" dissipative random thermal energy. The transition from disorganised fluctuations to organised helical structures is a phase transition involving a change in the condensate's energy (i.e. the ground state or zero-point energy) but ''without any associated rise in temperature''.{{sfnp|Reed|1995|p=[https://books.google.com/books?id=OdnsCgAAQBAJ&pg=PA226 226]}} This is an example of zero-point energy having multiple stable states (see [[Quantum phase transition]], [[Quantum critical point]], [[Topological degeneracy]], [[Topological order]]<ref>{{cite journal|last1=Chen|first1=Xie|last2=Gu|first2=Zheng-Cheng|last3=Wen|first3=Xiao-Gang|title=Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order|journal=Physical Review B|year=2010|volume=82|issue=15|page=155138|doi=10.1103/PhysRevB.82.155138|arxiv=1004.3835|bibcode=2010PhRvB..82o5138C|s2cid=14593420}}</ref>) and where the overall system structure is independent of a reductionist or deterministic view, that "classical" macroscopic order can also causally affect quantum phenomena. Furthermore, the pair production of Beltrami vortices has been compared to the morphology of pair production of virtual particles in the vacuum.