Gravity and the quantum vacuum inertia hypothesis

In previous work it has been shown that the electromagnetic quantum vacuum, or electromagnetic zero‐point field, makes a contribution to the inertial reaction force on an accelerated object. We show that the result for inertial mass can be extended to passive gravitational mass. As a consequence the weak equivalence principle, which equates inertial to passive gravitational mass, appears to be explainable. This in turn leads to a straightforward derivation of the classical Newtonian gravitational force. We call the inertia and gravitation connection with the vacuum fields the quantum vacuum inertia hypothesis . To date only the electromagnetic field has been considered. It remains to extend the hypothesis to the effects of the vacuum fields of the other interactions. We propose an idealized experiment involving a cavity resonator which, in principle, would test the hypothesis for the simple case in which only electromagnetic interactions are involved. This test also suggests a basis for the free parameter η(ν) which we have previously defined to parametrize the interaction between charge and the electromagnetic zero‐point field contributing to the inertial mass of a particle or object.     

Contrasting Classical and Quantum Vacuum States in Non-inertial Frames

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories.     

Spontaneous excitation of a circularly accelerated atom coupled to electromagnetic vacuum fluctuations

We study, using the formalism proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji, the contributions of the vacuum fluctuation and radiation reaction to the rate of change of the mean atomic energy for a circularly accelerated multilevel atom coupled to vacuum electromagnetic fields in the ultrarelativistic limit. We find that the balance between vacuum fluctuation and radiation reaction is broken, which causes spontaneous excitations of accelerated ground state atoms in vacuum. Unlike for a circularly accelerated atom coupled to vacuum scalar fields, the contribution of radiation reaction is also affected by acceleration, and this term takes the same form as that of a linearly accelerated atom coupled to vacuum electromagnetic fields. For the contribution of vacuum fluctuations, we find that in contrast to the linear acceleration case, terms proportional to the Planckian factor are replaced by those proportional to a non-Planck exponential term, and this indicates that the radiation perceived by a circularly orbiting observer is no longer thermal as is in the linear acceleration case. However, for an ensemble of two-level atoms, an effective temperature can be defined in terms of the atomic transition rates, which is found to be dependent on the transition frequency of the atom. Specifically, we calculate the effective temperature as a function of the transition frequency and find that in contrast to the case of circularly accelerated atoms coupled to the scalar field, the effective temperature in the current case is always larger than the Unruh temperature.     

Momentum transfer from vacuum field to anisotropic electromagnetic media

It is demonstrated that many novel vacuum effects will be caused if an anisotropic electromagnetic environment, which can break the universal symmetry of vacuum, is achieved. It is thus possible for the momentum to be transferred from the vacuum zero-point field to the anisotropic electromagnetic media. In addition to the effect considered by Feigel more recently [A. Feigel, Phys. Rev. Lett. 92 (2004) 020404], there may exist another vacuum-fluctuation contribution to the momentum of a medium. Such an effect has a relativistic origin (resulting from the relativistic transformation of the optical constants), which, however, was not taken into account by Feigel.     

The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell’s equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics.     

Gravity, Inertia, and Quantum Vacuum Zero Point Fields

Over the past several years Haisch, Rueda, and others have made the claim that the origin of inertial reaction forces can be explained as the interaction of electrically charged elementary particles with the vacuum electromagnetic zero-point field expected on the basis of quantum field theory. After pointing out that this claim, in light of the fact that the inertial masses of the hadrons reside in the electrically chargeless, photon-like gluons that bind their constituent quarks, is untenable, the question of the role of quantum zero-point fields generally in the origin of inertia is explored. It is shown that, although non-gravitational zero-point fields might be the cause of the gravitational properties of normal matter, the action of non-gravitational zero-point fields cannot be the cause of inertial reaction forces. The gravitational origin of inertial reaction forces is then briefly revisited. Recent claims critical of the gravitational origin of inertial reaction forces by Haisch and his collaborators are then shown to be without merit.     

The Equivalence Principle and an Electric Charge in a Gravitational Field II. A Uniformly Accelerated Charge Does Not Radiate

The electromagnetic field of a charge supported in a uniform gravitational field is examined from the viewpoint of an observer falling freely in the gravitational field. It is argued that such a charge, which from the principle of equivalence is moving with a uniform acceleration with respect to the (inertial) observer, could not be undergoing radiation losses at a rate implied by Larmor's formula. It is explicitly shown that the total energy in electromagnetic fields, including both velocity and acceleration fields, of a uniformly accelerated charge, at any given instant of the inertial observer's time, is just equal to the self-energy of a non-accelerated charge moving with a velocity equal to the instantaneous present velocity of the accelerated charge. At any given instant of time, and as seen with respect to the present position of the uniformly accelerated charge, although during the acceleration phase there is a radially outward component of the Poynting vector, there is throughout a radially inward Poynting flux component during the deceleration phase, and a null Poynting vector at the instant of the turn around. From Poynting's theorem, defined for any region of space strictly in terms of fixed instants of time, it is shown that a uniformly accelerated charge does not emit electromagnetic radiation, in contrast to what is generally believed. Contrary to some earlier suggestions in the literature, there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer.     

Majorana,Pauling and the quantum theory of the chemical bond

Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process in order to account for the impossibility of instantaneous measurement of physical fields. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of locality that assumes an accelerated observer simultaneously equivalent to a comoving inertial frame of reference. In this scenario, the transformation between an inertial and accelerated observer is generalized which affects the properties of physical fields. In particular, we analyze how an uniformly accelerated observer perceives a homogeneous and isotropic black body radiation. We show that all nonlocal effects are transient and most relevant in the first period of acceleration.     

Zero-point oscillations and radiative-resonant interactions

We discuss new results describing the relationship between quantum radiation caused by zero-point oscillations and radiative resonant wave-particle interactions. We show that the formation of a power-law spectrum of fast particles produced by radiative resonant interactions [V.N. Tsytovich, Phys. Rep. 178 (1989) 261; Physica 210 (1981) 136; Physica Scripta 52 (1982) 54] is related to the interaction of zero-point oscillations with resonant particle acceleration. Possible experiments to measure the electromagnetic radiation produced by this process are suggested.     

Black Hole Thermodynamics, Casimir Effect and Induced Gravity

An analogy between the subtraction procedure in the Gibbons-Hawking Euclidean path integral approach to black hole thermodynamics and the Casimir effect is shown. Then a conjecture about a possible Casimir nature of the Gibbons-Hawking subtraction is made in the framework of Sakharov's induced gravity. In this framework it appears that the degrees of freedom involved in the Bekenstein-Hawking entropy can be naturally identified with zero-point modes of the matter fields. Some consequences of this view are sketched.     

Division of the energy and of the momentum of electromagnetic waves in linear media into electromagnetic and material parts

We defend a natural division of the energy density, energy flux and momentum density of electromagnetic waves in linear media in electromagnetic and material parts. In this division, the electromagnetic part of these quantities have the same form as in vacuum when written in terms of the macroscopic electric and magnetic fields, the material momentum is calculated directly from the Lorentz force that acts on the charges of the medium, the material energy is the sum of the kinetic and potential energies of the charges of the medium and the material energy flux results from the interaction of the electric field with the magnetized medium. We present reasonable models for linear dispersive non-absorptive dielectric and magnetic media that agree with this division. We also argue that the electromagnetic momentum of our division can be associated with the electromagnetic relativistic momentum, inspired on the recent work of Barnett [Phys. Rev. Lett. 104 (2010) 070401] that showed that the Abraham momentum is associated with the kinetic momentum and the Minkowski momentum is associated with the canonical momentum.     

各向异性磁电介质量子真空水平上的动量转移

通过计算各向异性磁电材料内电磁场模式的本征方程研究了任意方向量子真空模式对磁电材料动量转移总贡献，并指出介质由真空动量转移所获得速度可以由目前发展起来的光纤光学传感器(能测量纳米量级速度)所探测.对该量子真空宏观力学效应的物理机理与潜在应用也做了讨论.     

Electrodynamics in accelerated frames revisited

Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space‐time. We assume the existence of a general distribution of charges and currents in an inertial frame. Tetrad fields are used to project the electromagnetic fields and sources on accelerated frames. The purpose is to study several configurations of fields and observers that in the literature are understood as paradoxes. For instance, are the two situations, (i) an accelerated charge in an inertial frame, and (ii) a charge at rest in an inertial frame described from the perspective of an accelerated frame, physically equivalent? Is the electromagnetic radiation the same in both frames? Normally in the analysis of these paradoxes the electromagnetic fields are transformed to (uniformly) accelerated frames by means of a coordinate transformation of the Faraday tensor. In the present approach coordinate and frame transformations are disentangled, and the electromagnetic field in the accelerated frame is obtained through a frame (local Lorentz) transformation. Consequently the fields in the inertial and accelerated frames are described in the same coordinate system. This feature allows the investigation of paradoxes such as the one mentioned above.     

THE ROLE OF ACCELERATION AND LOCALITY IN THE TWIN PARADOX

We study the role of acceleration in the twin paradox. From the coordinate transformation that relates an accelerated and an inertial observer we find that, from the point of view of the accelerated observer, the rate of the differential lapses of time depends not only on the relative velocity, but also on the product of the acceleration and the distance between the observers. However, this result does not have a direct operational interpretation because an observer at a certain position can measure only physical quantities that are defined at the same position. For local measurements, the asymmetry between the two observers can be attributed to the fact that noninertial coordinate systems, contrary to inertial coordinate systems, can be correctly interpreted only locally.     

Spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations

We study the spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations by separately calculating the contribution to the excitation rate of vacuum fluctuations and a cross term which involves both vacuum fluctuations and radiation reaction, and demonstrate that although the spontaneous excitation for the atom in its ground state would occur in vacuum, such atoms in circular motion do not perceive a pure thermal radiation as their counterparts in linear acceleration do since the transition rates of the atom do not contain the Planckian factor characterizing a thermal bath. We also find that the contribution of the cross term that plays the same role as that of radiation reaction in the scalar and electromagnetic fields cases differs for atoms in circular motion from those in linear acceleration. This suggests that the conclusion drawn for atoms coupled with the scalar and electromagnetic fields that the contribution of radiation reaction to the mean rate of change of atomic energy does not vary as the trajectory of the atom changes from linear acceleration to circular motion is not a general trait that applies to the Dirac field where the role of radiation reaction is played by the cross term.     

Dynamically Generated Inertia

A (Higgs vacuum)–(spacetime geometry) reciprocity principle is proposed and its consequences are explored. While it has been established that configurations of the spacetime metric tensor field, associated with acceleration with respect to local inertial frames, cause the vacuum to become thermalized, it is asserted that the converse is also possible. An appropriate thermal vacuum, through dynamical mass generation, can cause particles to propagate in a spacetime with a Minkowski metric, as if they were in a spacetime with a non-Minkowski metric. The two points of view are equivalent and interchangeable. Invoking the reciprocity principle in the case of the Unruh effect in an accelerated frame, a mechanism is analyzed whereby in the context of the minimal standard model a gradient in the vacuum expectation value of the Higgs field in the direction of acceleration produces an effective inertial force on an accelerated material body.