Editing Zero-point energy (section)

== Overview ==
[[File:Zero-point energy v.s. motion.jpg|thumb|right|Kinetic energy vs temperature]]
In [[classical mechanics]] all [[particle]]s can be thought of as having some [[energy]] made up of their [[potential energy]] and [[kinetic energy]]. [[Temperature]], for example, arises from the intensity of random particle motion caused by kinetic energy (known as [[Brownian motion]]). As temperature is reduced to [[absolute zero]], it might be thought that all motion ceases and particles come completely to rest. In fact, however, kinetic energy is retained by particles even at the lowest possible temperature. The random motion corresponding to this zero-point energy never vanishes; it is a consequence of the [[uncertainty principle]] of [[quantum mechanics]].{{cn|date=September 2024}}

[[File:Zero-point energy of harmonic oscillator.svg|thumb|left|Zero-point radiation continually imparts random impulses on an [[electron]], so that it never comes to a complete stop. Zero-point radiation gives the [[Harmonic oscillator|oscillator]] an average energy equal to the frequency of oscillation multiplied by one-half of the [[Planck constant]].]]
The uncertainty principle states that no object can ever have precise values of position and velocity simultaneously. The total energy of a quantum mechanical object (potential and kinetic) is described by its [[Hamiltonian (quantum mechanics)|Hamiltonian]] which also describes the system as a harmonic oscillator, or [[wave function]], that fluctuates between various energy states (see [[wave-particle duality]]). All quantum mechanical systems undergo fluctuations even in their ground state, a consequence of their [[wave]]-like nature. The uncertainty principle requires every quantum mechanical system to have a fluctuating zero-point energy greater than the minimum of its classical [[potential well]]. This results in motion even at absolute zero. For example, [[liquid helium]] does not freeze under atmospheric pressure regardless of temperature due to its zero-point energy.

Given the equivalence of mass and energy expressed by [[Albert Einstein]]'s {{math|[[E = mc2|''E'' {{=}} ''mc''<sup>2</sup>]]}}, any point in [[Spacetime|space]] that contains energy can be thought of as having mass to create particles. Modern physics has developed quantum field theory (QFT) to understand the fundamental interactions between matter and forces; it treats every single point of space as a [[Harmonic oscillator (quantum)|quantum harmonic oscillator]]. According to QFT the universe is made up of matter fields, whose quanta are [[fermions]] (i.e. [[lepton]]s and quarks), and force fields, whose quanta are [[boson]]s (e.g. [[photon]]s and [[gluon]]s). All these fields have zero-point energy.{{sfnp|Milonni|1994|p=35}} Recent experiments support the idea that particles themselves can be thought of as excited states of the underlying [[quantum vacuum]], and that all properties of matter are merely vacuum fluctuations arising from interactions of the zero-point field.{{sfnp|Battersby|2008}}

The idea that "empty" space can have an intrinsic energy associated with it, and that there is no such thing as a "true vacuum" is seemingly unintuitive. It is often argued that the entire universe is completely bathed in the zero-point radiation, and as such it can add only some constant amount to calculations. Physical measurements will therefore reveal only deviations from this value.{{sfnp|Itzykson|Zuber|1980|p=111}} For many practical calculations zero-point energy is dismissed by fiat in the mathematical model as a term that has no physical effect. Such treatment causes problems however, as in Einstein's theory of [[general relativity]] the absolute energy value of space is not an arbitrary constant and gives rise to the [[cosmological constant]]. For decades most physicists assumed that there was some undiscovered fundamental principle that will remove the infinite zero-point energy (discussed further below) and make it completely vanish. If the vacuum has no intrinsic, absolute value of energy it will not gravitate. It was believed that as the universe expands from the aftermath of the [[Big Bang]], the energy contained in any unit of empty space will decrease as the total energy spreads out to fill the volume of the universe; [[galaxies]] and all matter in the universe should begin to decelerate. This possibility was ruled out in 1998 by the discovery that the expansion of the universe is not slowing down but is in fact accelerating, meaning empty space does indeed have some intrinsic energy. The discovery of [[dark energy]] is best explained by zero-point energy, though it still remains a mystery as to why the value appears to be so small compared to the huge value obtained through theory – the [[cosmological constant problem]].{{sfnp|Weinberg|2015|p=376}}

Many physical effects attributed to zero-point energy have been experimentally verified, such as [[spontaneous emission]], [[Casimir force]], [[Lamb shift]], [[Electron magnetic moment|magnetic moment of the electron]] and [[Delbrück scattering]].{{sfnp|Milonni|1994|p=111}}{{sfnp|Greiner|Müller|Rafelski|2012|p=12}} These effects are usually called "radiative corrections".{{sfnp|Bordag et al.|2009|p=4}} In more complex nonlinear theories (e.g. QCD) zero-point energy can give rise to a variety of complex phenomena such as [[Bistability|multiple stable states]], [[Spontaneous symmetry breaking|symmetry breaking]], [[chaos theory|chaos]] and [[emergence]]. Active areas of research include the effects of virtual particles,{{sfnp|Cho|2015}} [[quantum entanglement]],{{sfnp|Choi|2013}} the difference (if any) between [[Mass#Inertial mass|inertial and gravitational mass]],<ref name="Haisch et al. 1994">See {{harvp|Haisch|Rueda|Puthoff|1994}} for proposal and {{harvs|txt|last1=Matthews|year1=1994|year2=1995}}, {{harvp|Powell|1994}} and {{harvp|Davies|1994}} for comment.</ref> variation in the [[speed of light]],<ref>See {{harvp|Urban et al.|2013}}, {{harvp|Leuchs|Sánchez-Soto|2013}} and {{harvp|O'Carroll|2013}} for comment.</ref> a reason for the observed value of the [[cosmological constant]]{{sfnp|Rugh|Zinkernagel|2002}} and the nature of dark energy.<ref name="Dark Energy May Be Vacuum">{{cite press release|date=19 January 2007|publisher=Niels Bohr Institute|title=Dark Energy May Be Vacuum|url=http://dark.nbi.ku.dk/Public_Outreach/pressreleases/dark_energy_may_be_vacuum/|archive-url=https://archive.today/20170531094844/http://dark.nbi.ku.dk/Public_Outreach/pressreleases/dark_energy_may_be_vacuum/|archive-date=31 May 2017|url-status=dead}}</ref>{{sfnp|Wall|2014}}