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However, the results of the Michelson—Morley experiment in 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 completely eliminated by cooling thus eliminating all radiation or energy.

From this idea evolved the second concept of achieving a real vacuum: cool it down to absolute zero temperature after evacuation. Absolute zero was technically impossible to achieve in the 19th century, so the debate remained unsolved. The zero-point energy makes no contribution to Planck's original law, as its existence was unknown to Planck in The concept of zero-point energy was developed by Max Planck in Germany in as a corrective term added to a zero-grounded formula developed in his original quantum theory in In , Max Planck published the first journal article [28] to describe the discontinuous emission of radiation, based on the discrete quanta of energy.

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. It is therefore widely agreed that "Planck's equation marked the birth of the concept of zero-point energy. Soon, the idea of zero-point energy attracted the attention of Albert Einstein and his assistant Otto Stern.

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 Walther Nernst proposed that empty space was filled with zero-point electromagnetic radiation. 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 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. Kurt Bennewitz and Francis Simon [38] 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 led them to conclude that the results provided evidence for a zero-point energy. Moreover, they suggested correctly, as was later verified by Simon , [39] [40] that this quantity was responsible for the difficulty in solidifying helium even at absolute zero.

In Robert Mulliken [41] provided direct evidence for the zero-point energy of molecular vibrations by comparing the band spectrum of 10 BO and 11 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 , [42] with the development of matrix mechanics in Werner Heisenberg 's famous article " Quantum theoretical re-interpretation of kinematic and mechanical relations " the zero-point energy was derived from quantum mechanics.

In Niels Bohr had proposed what is now called the Bohr model of the atom, [44] [45] [46] 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. In Pascual Jordan [50] 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 infinite zero-point energy term. He was able to obtain the same fluctuation formula that Einstein had obtained in Building on the work of Heisenberg and others Paul Dirac 's theory of emission and absorption [55] 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.

The theory showed that spontaneous emission depends upon the zero-point energy fluctuations of the electromagnetic field in order to get started. 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: [59]. 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 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 wrote: [60]. From quantum theory there follows the existence of so called zero-point oscillations; for example each oscillator in its lowest 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 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 Welton , [61] who argued that spontaneous emission "can be thought of as forced emission taking place under the action of the fluctuating field. Throughout the s 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 , [62] and measurement of the magnetic moment of the electron. Renormalization was originally developed by Hans Kramers [64] and also Victor Weisskopf , [65] and first successfully applied to calculate a finite value for the Lamb shift by Hans Bethe In Wolfgang Pauli 's Nobel lecture [68] 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".

In Hendrik Casimir [69] [70] 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 "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 — long-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 , [71] [72] 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. 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 famous 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 [74] [75] [76] in the case of plane parallel 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.

In Herbert Callen and Theodore Welton [78] proved the quantum fluctuation-dissipation theorem FDT which was originally formulated in classical form by Nyquist [79] as an explanation for observed Johnson noise in electric circuits. 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.

In the Jaynes—Cummings model [85] was developed describing the system of a two-level atom interacting with a quantized field mode i. 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 s 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.

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" [88] [89] or amplified. Amplification was first predicted by Purcell in [90] the Purcell effect and has been experimentally verified.

Zero-point energy is fundamentally related to the Heisenberg uncertainty principle. In particular, there cannot exist a state in which the system simply sits motionless at the bottom of its potential well: for, then, its position and momentum would both be completely determined to arbitrarily great precision. Near the bottom of a potential well , the Hamiltonian of a general system the quantum-mechanical operator giving its energy can be approximated as a quantum harmonic oscillator ,. The idea of a quantum harmonic oscillator and its associated energy can apply to either an atom or subatomic particle.

In ordinary atomic physics, the zero-point energy is the energy associated with the ground state of the system.

In quantum mechanical terms, the zero-point energy is the expectation value of the Hamiltonian of the system in the ground state. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state and commutes with the Hamiltonian of the system. According to the third law of thermodynamics , a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state.

Many systems, such as a perfect crystal lattice , have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero temperature for systems that exhibit negative temperature. The wave function of the ground state of a particle in a one-dimensional well is a half-period sine wave which goes to zero at the two edges of the well.

The energy of the particle is given by:. In quantum field theory QFT , the fabric of "empty" space is visualized as consisting of fields , with the field at every point in space and time being a quantum harmonic oscillator , with neighboring oscillators interacting with each other. According to QFT the universe is made up of matter fields whose quanta are fermions e. In QFT this combination of fields is called the vacuum state , its associated zero-point energy is called the vacuum energy and the average expectation value of the Hamiltonian is called the vacuum expectation value also called condensate or simply VEV.

The QED vacuum is a part of the vacuum state which specifically deals with quantum electrodynamics e. Recent experiments advocate 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 with the zero-point field. In cosmology , the vacuum energy is one possible explanation for the cosmological constant [95] and the source of dark energy.

Scientists are not in agreement about how much energy is contained in the vacuum. Quantum mechanics requires the energy to be large as Paul Dirac claimed it is, like a sea of energy. Other scientists specializing in General Relativity require the energy to be small enough for curvature of space to agree with observed astronomy. The Heisenberg uncertainty principle allows the energy to be as large as needed to promote quantum actions for a brief moment of time, even if the average energy is small enough to satisfy relativity and flat space.

To cope with disagreements, the vacuum energy is described as a virtual energy potential of positive and negative energy. In quantum perturbation theory , it is sometimes said that the contribution of one-loop and multi-loop Feynman diagrams to elementary particle propagators are the contribution of vacuum fluctuations , or the zero-point energy to the particle masses.

The oldest and best known quantized force field is the electromagnetic field. Maxwell's equations have been superseded by quantum electrodynamics QED. By considering the zero-point energy that arises from QED it is possible to gain a characteristic understanding of zero-point energy that arises not just through electromagnetic interactions but in all quantum field theories.

The fact that:. The reconciliation of wave and particle attributes of the field is accomplished via the association of a probability amplitude with a classical mode pattern. It is often argued that the entire universe is completed bathed in the zero-point electromagnetic field, and as such it can add only some constant amount to expectation values. Physical measurements will therefore reveal only deviations from the vacuum state. Thus the zero-point energy can be dropped from the 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.

Thus we can choose to declare by fiat that the ground state has zero energy and a field Hamiltonian, for example, can be replaced by: [11]. The new Hamiltonian is said to be normally ordered or Wick ordered and is denoted by a double-dot symbol. The normally ordered Hamiltonian is denoted : H F , i. This is especially reasonable in the case of the field Hamiltonian, since the zero-point term merely adds a constant energy which can be eliminated by a simple redefinition for the zero of energy.

However, things are not quite that simple. The zero-point energy cannot be eliminated by dropping its energy from the Hamiltonian: When we do this and solve the Heisenberg equation for a field operator, we must include the vacuum field, which is the homogeneous part of the solution for the field operator. In fact we can show that the vacuum field is essential for the preservation of the commutators and the formal consistent of QED. When we calculate the field energy we obtain not only a contribution from particles and forces that may be present but also a contribution from the vacuum field itself i.

In other words, the zero-point energy reappears even though we may have deleted it from the Hamiltonian. From Maxwell's equations, the electromagnetic energy of a "free" field i. We introduce the "mode function" A 0 r that satisfies the Helmholtz equation:. We wish to "quantize" the electromagnetic energy of free space for a multimode field. The field intensity of free space should be independent of position such that A 0 r 2 should be independent of r for each mode of the field.

The mode function satisfying these conditions is:. This allows us to consider the field in any one of the imaginary cubes and to define the mode function:. Thus we define the mode functions:. This gives the vector potential for a plane wave mode of the field. The condition for k x , k y , k z shows that there are infinitely many such modes. The linearity of Maxwell's equations allows us to write:. This is the Hamiltonian for an infinite number of uncoupled harmonic oscillators. Thus different modes of the field are independent and satisfy the commutation relations:.

This state describes the zero-point energy of the vacuum. It appears that this sum is divergent — in fact highly divergent, as putting in the density factor. It diverges proportional to v 4 for large v. There are two separate questions to consider. First, is the divergence a real one such that the zero-point energy really is infinite? If we consider the volume V is contained by perfectly conducting walls, very high frequencies can only be contained by taking more and more perfect conduction. No actual method of containing the high frequencies is possible. Such modes will not be stationary in our box and thus not countable in the stationary energy content.

So from this physical point of view the above sum should only extend to those frequencies which are countable; a cut-off energy is thus eminently reasonable. However, on the scale of a "universe" questions of general relativity must be included. Suppose even the boxes could be reproduced, fit together and closed nicely by curving spacetime.

Then exact conditions for running waves may be possible. However the very high frequency quanta will still not be contained. As per John Wheeler's "geons" [98] these will leak out of the system. So again a cut-off is permissible, almost necessary. The question here becomes one of consistency since the very high energy quanta will act as a mass source and start curving the geometry. This leads to the second question.

Divergent or not, finite or infinite, is the zero-point energy of any physical significance? The ignoring of the whole zero-point energy is often encouraged for all practical calculations. The reason for this is that energies are not typically defined by an arbitrary data point, but rather changes in data points, so adding or subtracting a constant even if infinite should to be allowed. However this is not the whole story, in reality energy is not so arbitrarily defined: in general relativity the seat of the curvature of spacetime is the energy content and there the absolute amount of energy has real physical meaning.

There is no such thing as an arbitrary additive constant with density of field energy. Energy density curves space, and an increase in energy density produces an increase of curvature. Furthermore, the zero-point energy density has other physical consequences e. The vacuum state, like all stationary states of the field, is an eigenstate of the Hamiltonian but not the electric and magnetic field operators.

In the vacuum state, therefore, the electric and magnetic fields do not have definite values. We can imagine them to be fluctuating about their mean value of zero. In a process in which a photon is annihilated absorbed , we can think of the photon as making a transition into the vacuum state. We can make the replacement:. This can be large even in relatively narrow "low frequency" regions of the spectrum.

We showed in the above section that the zero-point energy can be eliminated from the Hamiltonian by the normal ordering prescription. However, this elimination does not mean that the vacuum field has been rendered unimportant or without physical consequences. To illustrate this point we consider a linear dipole oscillator in the vacuum. The Hamiltonian for the oscillator plus the field with which it interacts is:. This has the same form as the corresponding classical Hamiltonian and the Heisenberg equations of motion for the oscillator and the field are formally the same as their classical counterparts.

Above we have made the electric dipole approximation in which the spatial dependence of the field is neglected. Alternatively, we can argue that these operators must commute if we are to obtain the correct equations of motion from the Hamiltonian, just as the corresponding Poisson brackets in classical theory must vanish in order to generate the correct Hamilton equations. The formal solution of the field equation is:. It can be shown that in the radiation reaction field, if the mass m is regarded as the "observed" mass then we can take:.

The total field acting on the dipole has two parts, E 0 t and E RR t. E 0 t is the free or zero-point field acting on the dipole. It is the homogeneous solution of the Maxwell equation for the field acting on the dipole, i. E RR t is the source field, the field generated by the dipole and acting on the dipole. Classically, a dipole in the vacuum is not acted upon by any "external" field: if there are no sources other than the dipole itself, then the only field acting on the dipole is its own radiation reaction field. In quantum theory however there is always an "external" field, namely the source-free or vacuum field E 0 t.

The expectation value of the free field is therefore at all times equal to zero:. We can therefore drop the zero-point field energy from the Hamiltonian, as is usually done. But the zero-point field re-emerges as the homogeneous solution for the field equation.

A charged particle in the vacuum will therefore always see a zero-point field of infinite density. The free field is in fact necessary for the formal consistency of the theory. In particular, it is necessary for the preservation of the commutation relations, which is required by the unitary of time evolution in quantum theory:.

We can calculate [ z t , p z t ] from the formal solution of the operator equation of motion. For the dipole oscillator under consideration it can be assumed that the radiative damping rate is small compared with the natural oscillation frequency, i. A similar result is easily worked out for the case of a free particle instead of a dipole oscillator. What we have here is an example of a "fluctuation-dissipation elation". Generally speaking if a system is coupled to a bath that can take energy from the system in an effectively irreversible way, then the bath must also cause fluctuations.

The fluctuations and the dissipation go hand in hand we cannot have one without the other. In the current example the coupling of a dipole oscillator to the electromagnetic field has a dissipative component, in the form of the zero-point vacuum field; given the existence of radiation reaction, the vacuum field must also exist in order to preserve the canonical commutation rule and all it entails.

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The fact that the canonical commutation relation for a harmonic oscillator coupled to the vacuum field is preserved implies that the zero-point energy of the oscillator is preserved. It is an example of a non-perturbative vacuum state, characterized by a non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks.

The presence of these condensates characterizes the confined phase of quark matter. In technical terms, gluons are vector gauge bosons that mediate strong interactions of quarks in quantum chromodynamics QCD.

Gluons themselves carry the color charge of the strong interaction. This is unlike the photon , which mediates the electromagnetic interaction but lacks an electric charge. Gluons therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than QED quantum electrodynamics as it deals with nonlinear equations to characterize such interactions. It can have this effect because of its unusual "Mexican hat" shaped potential whose lowest "point" is not at its "centre". Below a certain extremely high energy level the existence of this non-zero vacuum expectation spontaneously breaks electroweak gauge symmetry which in turn gives rise to the Higgs mechanism and triggers the acquisition of mass by those particles interacting with the field.

The Higgs mechanism occurs whenever a charged field has a vacuum expectation value. This effect occurs because scalar field components of the Higgs field are "absorbed" by the massive bosons as degrees of freedom, and couple to the fermions via Yukawa coupling, thereby producing the expected mass terms.

The Higgs mechanism is a type of superconductivity which occurs in the vacuum. It occurs when all of space is filled with a sea of particles which are charged and thus the field has a nonzero vacuum expectation value. Interaction with the vacuum energy filling the space prevents certain forces from propagating over long distances as it does in a superconducting medium; e. Zero-point energy has many observed physical consequences. It implies a cosmological constant larger than the limits imposed by observation by about orders of magnitude. This "cosmological constant problem" remains one of the greatest unsolved mysteries of physics.

A phenomenon that is commonly presented as evidence for the existence of zero-point energy in vacuum is the Casimir effect , proposed in by 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. Results have been repeatedly replicated since then. In Munday et al. 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 []. An interesting hypothetical side effect of the Casimir effect is the Scharnhorst effect , a hypothetical phenomenon in which light signals travel slightly faster than c between two closely spaced conducting plates.

The quantum fluctuations of the electromagnetic field have important physical consequences. Charged particles can interact with the fluctuations of the quantized vacuum field, leading to slight shifts in energy, [] this effect is called the Lamb shift. 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.

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. It means that a short distance implies large momentum and therefore high energy i. QED concludes that the fine structure constant is an increasing function of energy.

In the presence of strong electrostatic fields it is predicted that virtual particles become separated from the vacuum state and form real matter. 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. 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 birefringent medium , thus in principle a rotation of the polarization frame the Faraday effect can be observed in empty space. 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 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. The consequences of this discovery probably will also have to be realised on a longer timescale.

Definitive proof would require repeating the observation at other wavelengths and on other neutron stars. In the late s it was discovered that very distant supernova were dimmer than expected suggesting that the universe's expansion was accelerating rather than slowing down. This would indicate empty space exerted some form of negative pressure or energy. There is no natural candidate for what might cause what has been called dark energy but the current best guess is that it is the zero-point energy of the vacuum.

In general relativity , mass and energy are equivalent; both produce a gravitational field and therefore the theorized vacuum energy of quantum field theory should have led the universe ripping itself to pieces. This obviously has not happened and this issue, called the cosmological constant problem , is one of the greatest unsolved mysteries in physics.

The European Space Agency is building the Euclid telescope. Due to launch in it will map galaxies up to 10 billion light years away. By seeing how dark energy influences their arrangement and shape, the mission will allow scientists to see if the strength of dark energy has changed. If dark energy is found to vary throughout time it would indicate it is due to quintessence , where observed acceleration is due to the energy of a scalar field , rather than the cosmological constant.

No evidence of quintessence is yet available, but it has not been ruled out either. It generally predicts a slightly slower acceleration of the expansion of the universe than the cosmological constant. Some scientists think that the best evidence for quintessence would come from violations of Einstein's equivalence principle and variation of the fundamental constants in space or time. Cosmic inflation is a faster-than-light expansion of space just after the Big Bang.

It explains the origin of the large-scale structure of the cosmos. It is believed quantum vacuum fluctuations caused by zero-point energy arising in the microscopic inflationary period, later became magnified to a cosmic size, becoming the gravitational seeds for galaxies and structure in the Universe see galaxy formation and evolution and structure formation.

The mechanism for inflation is unclear, it is similar in effect to dark energy but is a far more energetic and short lived process. As with dark energy the best explanation is some form of vacuum energy arising from quantum fluctuations. It may be that inflation caused baryogenesis , the hypothetical physical processes that produced an asymmetry imbalance between baryons and antibaryons produced in the very early universe , but this is far from certain. Schwinger , in particular, attempted to formulate QED without reference to zero-point fluctuations via his "source theory".

Such a derivation was first given by Schwinger [] for a scalar field, and then generalized to the electromagnetic case by Schwinger, DeRaad, and Milton More recently Jaffe [] has highlighted a similar approach in deriving the Casimir effect stating "the concept of zero-point fluctuations is a heuristic and calculational aid in the description of the Casimir effect, but not a necessity in QED. Nevertheless, as Jaffe himself notes in his paper, "no one has shown that source theory or another S-matrix based approach can provide a complete description of QED to all orders.

The Higgs mechanism , Hawking Radiation and the Unruh effect are also theorized to be dependent on zero-point vacuum fluctuations, the field contribution being an inseparable parts of these theories. Jaffe continues "Even if one could argue away zero-point contributions to the quantum vacuum energy, the problem of spontaneous symmetry breaking remains: condensates [ground state vacua] that carry energy appear at many energy scales in the Standard Model.

So there is good reason to be skeptical of attempts to avoid the standard formulation of quantum field theory and the zero-point energies it brings with it. The mathematical models used in classical electromagnetism , quantum electrodynamics QED and the standard model all view the electromagnetic vacuum as a linear system with no overall observable consequence e. See 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.

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. What are called Maxwell's equations today, are in fact a simplified version of the original equations reformulated by Heaviside , FitzGerald , Lodge and Hertz. The original equations used Hamilton 's more expressive quaternion notation, [] a kind of Clifford algebra , which fully subsumes the standard Maxwell vectorial equations largely used today.

According to Heaviside the electromagnetic potential field was purely metaphysical, an arbitrary mathematical fiction, that needed to be "murdered". 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 Tesla's oscillator-shuttle-circuit can only be achieved in quaternionic algebra or higher SU 2 symmetries. A good example of nonlinear electromagnetics is in high energy dense plasmas, where 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 law , which elaborates Maxwell's equations is violated by these force free vortices. 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. The Nobel Prize in Chemistry was awarded to thermodynamicist Ilya Prigogine [] for his theory of dissipative systems that described this notion. Prigogine described the principle as "order through fluctuations" [] or "order out of chaos".

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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 transitions 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. 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. In particular it has been asserted that the Beltrami vortices in the plasma focus display the same paired flux-tube morphology as Type II superconductors.

In essence, it has been asserted that Beltrami plasma vortex structures are able to at least simulate the morphology of Type I and 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. Furthermore, the pair production of Beltrami vortices has been compared to the morphology of pair production of virtual particles in the vacuum.

The idea that the vacuum energy can have multiple stable energy states is a leading hypothesis for the cause of cosmic inflation. In fact, it has been argued that these early vacuum fluctuations led to the expansion of the universe and in turn have guaranteed the non-equilibrium conditions necessary to drive order from chaos, as without such expansion the universe would have reached thermal equilibrium and no complexity could have existed. With the continued accelerated expansion of the universe, the cosmos generates an energy gradient that increases the "free energy" i.

The sun's fusion power is only possible due to the gravitational disequilibrium of matter that arose from cosmic expansion. In this essence, the vacuum energy can be viewed as the key cause of the negative entropy i. That humanity might alter the morphology of the vacuum energy to create an energy gradient for useful work is the subject of much controversy. Physicists overwhelmingly reject any possibility that the zero-point energy field can be exploited to obtain useful energy work or uncompensated momentum; such efforts are seen as tantamount to perpetual motion machines.

Nevertheless, the allure of free energy has motivated such research, usually falling in the category of fringe science. As long ago as before quantum theory or discovery of the zero point energy Nikola Tesla proposed that useful energy could be obtained from free space, or what was assumed at that time to be an all-pervasive aether. A common assumption is that the Casimir force is of little practical use; the argument is made that the only way to actually gain energy from the two plates is to allow them to come together getting them apart again would then require more energy , and therefore it is a one-use-only tiny force in nature.

The battery can be recharged by making the electrical forces slightly stronger than the Casimir force to reexpand the plates. In and Maclay et al. While not exploiting the Casimir force for useful work, the papers drew attention from the MEMS community due to the revelation that Casimir effect needs to be considered as a vital factor in the future design of MEMS. The paper showed that continuous positive net exchange of energy from the Casimir effect was possible, even stating in the abstract "In the event of no other alternative explanations, one should conclude that major technological advances in the area of endless, by-product free-energy production could be achieved.

When they brought a metallized sphere close up to the plate, the attractive Casimir force between the two objects made the plate rotate. They also studied the dynamical behaviour of the MEMS device by making the plate oscillate. The Casimir force reduced the rate of oscillation and led to nonlinear phenomena, such as hysteresis and bistability in the frequency response of the oscillator.

Despite this and several similar peer reviewed papers, there is not a consensus as to whether such devices can produce a continuous output of work. Garret Moddel at University of Colorado has highlighted that he believes such devices hinge on the assumption that the Casimir force is a nonconservative force , he argues that there is sufficient evidence e. A patent by Haisch and Moddel [] details a device that is able to extract power from zero-point fluctuations using a gas that circulates through a Casimir cavity.

As gas atoms circulate around the system they enter the cavity. Upon entering the electrons spin down to release energy via electromagnetic radiation. This radiation is then extracted by an absorber. On exiting the cavity the ambient vacuum fluctuations i. A published test of this concept by Moddel [] was performed in and seemed to give excess energy that could not be attributed to another source. However it has not been conclusively shown to be from zero-point energy and the theory requires further investigation. In Callen and Welton [78] proved the quantum fluctuation-dissipation theorem FDT which was originally formulated in classical form by Nyquist [79] as an explanation for observed Johnson noise [80] in electric circuits.

Fluctuation-dissipation theorem showed that when something dissipates energy, in an effectively irreversible way, a connected heat bath must also fluctuate. Grau and Kleen [] and Kleen , [] argued that the Johnson noise of a resistor connected to an antenna must satisfy Planck's thermal radiation formula, thus the noise must be zero at zero temperature and FDT must be invalid.

Kiss [] pointed out that the existence of the zero-point term may indicate that there is a renormalization problem—i. Later, Abbott et al. Despite such criticism, FDT has been shown to be true experimentally under certain quantum, non-classical conditions. Zero-point fluctuations can, and do, contribute towards systems which dissipate energy. There have been a growing number of papers showing that in some instances the classical laws of thermodynamics, such as limits on the Carnot efficiency, can be violated by exploiting negative entropy of quantum fluctuations.

Despite efforts to reconcile quantum mechanics and thermodynamics over the years, their compatibility is still an open fundamental problem. The full extent that quantum properties can alter classical thermodynamic bounds is unknown []. The use of zero-point energy for space travel is highly speculative. A complete quantum theory of gravitation that would deal with the role of quantum phenomena like zero-point energy does not yet exist.

Speculative papers explaining a relationship between zero-point energy and gravitational shielding effects have been proposed, [17] [] [] [] but the interaction if any is not yet fully understood. According to the general theory of relativity , rotating matter can generate a new force of nature, known as the gravitomagnetic interaction, whose intensity is proportional to the rate of spin. In neutrons stars for example it can produce a gravitational analogue of the Meissner effect , but the force produced in such an example is theorized to be exceedingly weak.

In Robert Forward , [] a physicist and aerospace engineer at Hughes Research Laboratories , published a paper showing how within the framework of general relativity "anti-gravitational" effects might be achieved. Since all atoms have spin , gravitational permeability may be able to differ from material to material. A strong toroidal gravitational field that acts against the force of gravity could be generated by materials that have nonlinear properties that enhance time-varying gravitational fields.

Such an effect would be analogous to the nonlinear electromagnetic permeability of iron making it an effective core i. Dewitt demonstrated that a magnetic-type gravitational field must result in the presence of fluxoid quantization. In , Dewitt's work was substantially expanded by Ross. In his three patents, Wallace describes three different methods used for detection of the gravitomagnetic field — change in the motion of a body on a pivot, detection of a transverse voltage in a semiconductor crystal, and a change in the specific heat of a crystal material having spin-aligned nuclei.

There are no publicly available independent tests verifying Wallace's devices. Such an effect if any would be small. The military may now regret that the patents have already been granted and so are available for anyone to read. Attempts were made to contact Wallace using patent addresses and other sources but he was not located nor is there a trace of what became of his work.

The concept can be somewhat justified on general relativistic grounds since rotating frames of time varying fields are expected to emit gravitational waves. In the U. One of the six areas of interest was "Esoteric energy sources for propulsion, including the quantum dynamic energy of vacuum space In Kip Thorne et al. In Scharnhorst and Barton [] showed that the speed of a photon will be increased if it travels between two Casimir plates, an example of negative energy.

In the most general sense, the exotic matter needed to create wormholes would share the repulsive properties of the inflationary energy , dark energy or zero-point radiation of the vacuum. The ship would then ride this wave inside a region of flat space, known as a warp bubble and would not move within this bubble but instead be carried along as the region itself moves due to the actions of the drive.

In Evgeny Podkletnov [] published a heavily debated [] [] [] [] journal article claiming a specific type of rotating superconductor could shield gravitational force. Independently of this, from to Ning Li and Douglas Torr published a number of articles [] [] [] about gravitational effects in superconductors. One finding they derived is the source of gravitomagnetic flux in a type II superconductor material is due to spin alignment of the lattice ions. Quoting from their third paper: "It is shown that the coherent alignment of lattice ion spins will generate a detectable gravitomagnetic field, and in the presence of a time-dependent applied magnetic vector potential field, a detectable gravitoelectric field.

The grant period ended in but no results from this research were ever made public. In Phantom Works , Boeing 's advanced research and development facility in Seattle , approached Evgeny Podkletnov directly. Phantom Works was blocked by Russian technology transfer controls. At this time Lieutenant General George Muellner, the outgoing head of the Boeing Phantom Works, confirmed that attempts by Boeing to work with Podkletnov had been blocked by Moscow, also commenting that "The physical principles — and Podkletnov's device is not the only one — appear to be valid There is basic science there.

They're not breaking the laws of physics. The issue is whether the science can be engineered into something workable" []. Froning and Roach [] put forward a paper that builds on the work of Puthoff, Haisch and Alcubierre. They used fluid dynamic simulations to model the interaction of a vehicle like that proposed by Alcubierre with the zero-point field. Vacuum field perturbations are simulated by fluid field perturbations and the aerodynamic resistance of viscous drag exerted on the interior of the vehicle is compared to the Lorentz force exerted by the zero-point field a Casimir-like force is exerted on the exterior by unbalanced zero-point radiation pressures.

They find that the optimized negative energy required for an Alcubierre drive is where it is a saucer-shaped vehicle with toroidal electromagnetic fields. The EM fields distort the vacuum field perturbations surrounding the craft sufficiently to affect the permeability and permittivity of space. In the paper, the authors identify and discuss nine potential sources of experimental errors, including rogue air currents, leaky electromagnetic radiation, and magnetic interactions. Not all of them could be completely ruled out, and further peer reviewed experimentation is needed in order to rule these potential errors out.

From Wikipedia, the free encyclopedia. For related articles, see Quantum vacuum disambiguation. Not to be confused with Zero Point photometry. For other uses, see Zero point disambiguation. Lowest possible energy of a quantum system or field. Classical mechanics Old quantum theory Bra—ket notation Hamiltonian Interference. Advanced topics. Quantum annealing Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum gravity Quantum information science Quantum machine learning Perturbation theory quantum mechanics Relativistic quantum mechanics Scattering theory Spontaneous parametric down-conversion Quantum statistical mechanics.

Main article: Uncertainty principle. Main article: Ground state. Feynman diagram. Standard Model. Quantum electrodynamics Electroweak interaction Quantum chromodynamics Higgs mechanism. Incomplete theories. Anderson P. Main articles: Vacuum expectation value , Vacuum energy , and Vacuum state.

Main article: QED vacuum. Main article: QCD vacuum. Main article: Higgs mechanism. Main article: Casimir effect. Main article: Lamb shift. Main article: Fine structure constant. Main articles: Lorentz-violating electrodynamics and Euler—Heisenberg Lagrangian. Play media. Main article: Dark energy. What cancels it out? Why does the observable universe have more matter than antimatter? Main article: Inflation cosmology. Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons. Quantum gravity.

String theory Loop quantum gravity Loop quantum cosmology Causal dynamical triangulation Causal fermion systems Causal sets Event symmetry Canonical quantum gravity Superfluid vacuum theory. See also: Chaos theory , Emergence , and Self-organization. Physics portal mathematics portal. Annalen der Physik. Bibcode : AnP Klein, Martin J. Princeton: Princeton University Press. Verhandlungen der Deutschen Physikalischen. Many systems have degenerate ground states.

The energy of the particle is given by:. The vacuum can be viewed, not as empty space, but the combination of all zero-point fields. Scientists are not in agreement about how much energy is contained in the vacuum. It is often argued that the entire universe is completed bathed in the zero-point electromagnetic field, and as such it can add only some constant amount to expectation values.

Physical measurements will therefore reveal only deviations from the vacuum state. Thus the zero-point energy can be dropped from the 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. Thus we can choose to declare by fiat that the ground state has zero energy and a field Hamiltonian, for example, can be replaced by:. This is especially reasonable in the case of the field Hamiltonian, since the zero-point term merely adds a constant energy which can be eliminated by a simple redefinition for the zero of energy.

However, things are not quite that simple. The zero-point energy cannot be eliminated by dropping its energy from the Hamiltonian: When we do this and solve the Heisenberg equation for a field operator, we must include the vacuum field, which is the homogeneous part of the solution for the field operator. When we calculate the field energy we obtain not only a contribution from particles and forces that may be present but also a contribution from the vacuum field itself i.

In other words, the zero-point energy reappears even though we may have deleted it from the Hamiltonian. From Maxwell's equations, the electromagnetic energy of a "free" field i.


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There are two separate questions to consider. First, is the divergence a real one such that the zero-point energy really is infinite? No actual method of containing the high frequencies is possible. Such modes will not be stationary in our box and thus not countable in the stationary energy content. So from this physical point of view the above sum should only extend to those frequencies which are countable; a cut-off energy is thus eminently reasonable. However, on the scale of a "universe" questions of general relativity must be included.

Suppose even the boxes could be reproduced, fit together and closed nicely by curving spacetime. Then exact conditions for running waves may be possible.

The Zero Point Field: How Thoughts Become Matter?

However the very high frequency quanta will still not be contained. As per John Wheeler's "geons" these will leak out of the system. So again a cut-off is permissible, almost necessary. The question here becomes one of consistency since the very high energy quanta will act as a mass source and start curving the geometry.

This leads to the second question. Divergent or not, finite or infinite, is the zero-point energy of any physical significance? The ignoring of the whole zero-point energy is often encouraged for all practical calculations. The reason for this is that energies are not typically defined by an arbitrary data point, but rather changes in data points, so adding or subtracting a constant even if infinite should to be allowed.

However this is not the whole story, in reality energy is not so arbitrarily defined: in general relativity the seat of the curvature of spacetime is the energy content and there the absolute amount of energy has real physical meaning. There is no such thing as an arbitrary additive constant with density of field energy. Energy density curves space, and an increase in energy density produces an increase of curvature. Furthermore, the zero-point energy density has other physical consequences e. The vacuum state, like all stationary states of the field, is an eigenstate of the Hamiltonian but not the electric and magnetic field operators.

In the vacuum state, therefore, the electric and magnetic fields do not have definite values. We can imagine them to be fluctuating about their mean value of zero. In a process in which a photon is annihilated absorbed , we can think of the photon 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. An atom, for instance, can be considered to be "dressed" by emission and reabsorption of "virtual photons" from the vacuum.

We can make the replacement:. This has the same form as the corresponding classical Hamiltonian and the Heisenberg equations of motion for the oscillator and the field are formally the same as their classical counterparts.

References

Alternatively, we can argue that these operators must commute if we are to obtain the correct equations of motion from the Hamiltonian, just as the corresponding Poisson brackets in classical theory must vanish in order to generate the correct Hamilton equations. The formal solution of the field equation is:. A similar result is easily worked out for the case of a free particle instead of a dipole oscillator.

What we have here is an example of a "fluctuation-dissipation elation". Generally speaking if a system is coupled to a bath that can take energy from the system in an effectively irreversible way, then the bath must also cause fluctuations. The fluctuations and the dissipation go hand in hand we cannot have one without the other. In the current example the coupling of a dipole oscillator to the electromagnetic field has a dissipative component, in the form of the zero-point vacuum field; given the existence of radiation reaction, the vacuum field must also exist in order to preserve the canonical commutation rule and all it entails.

It can have this effect because of its unusual "Mexican hat" shaped potential whose lowest "point" is not at its "centre". The Higgs mechanism occurs whenever a charged field has a vacuum expectation value. This effect occurs because scalar field components of the Higgs field are "absorbed" by the massive bosons as degrees of freedom, and couple to the fermions via Yukawa coupling, thereby producing the expected mass terms. It has units of mass, and is the only free parameter of the Standard Model that is not a dimensionless number. It occurs when all of space is filled with a sea of particles which are charged and thus the field has a nonzero vacuum expectation value.

Interaction with the vacuum energy filling the space prevents certain forces from propagating over long distances as it does in a superconducting medium; e. This mystical substance is everywhere and within it is recorded every action, emotion, thought, feeling and experience of every living being. It is like a huge database that contains a record of everything. Mystics have long suggested that this information can be accessed in certain states of raised consciousness and the data can be downloaded for future use. It states that if we know the position of a sub-atomic particle we cannot know its speed, and if we know its speed we cannot know its momentum.

If a particle were at rest we would know both. As such particles can never be at rest, not even at absolute zero, the coldest state known to science. This is minus This is three degrees above the temperature of the vacuum of space. Why this is of significance is that there should be no energy at absolute zero but there is. Lots of it.