This book provides a comprehensive review of the experiments and theories of transport properties of charge carriers in liquid helium. It is a subject about which no other monograph exists to date. The book is intended for graduate and postgraduate students and for condensed matter physicists who will benefit from its completeness and accuracy. This is an appropriate time for a comprehensive archival review.
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Be the first to write a review. 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.
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.
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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.
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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". One may query what this has to do with zero-point energy.