We develop a geometro-dynamical approach to the cosmological constant problem (CCP) by invoking a geometry induced by the energy-momentum tensor of vacuum, matter and radiation. The construction, which utilizes the dual role of the metric tensor that it structures both the spacetime manifold and energy-momentum tensor of the vacuum, gives rise to a framework in which the vacuum energy induced by matter and radiation, instead of gravitating, facilitates the generation of the gravitational constant. The (...) non-vacuum sources comprising matter and radiation gravitate normally. At the level of classical gravitation, the mechanism deadens the CCP yet quantum gravitational effects, if strong, can keep it existent. (shrink)

In this paper I formulate Minimal Requirements for Candidate Predictions in quantum field theories, inspired by viewing the standard model as an effective field theory. I then survey standard effective field theory regularization procedures, to see if the vacuum expectation value of energy density ) is a quantity that meets these requirements. The verdict is negative, leading to the conclusion that \ is not a physically significant quantity in the standard model. Rigorous extensions of flat space quantum field (...) theory eliminate \ from their conceptual framework, indicating that it lacks physical significance in the framework of quantum field theory more broadly. This result has consequences for problems in cosmology and quantum gravity, as it suggests that the correct solution to the cosmological constant problem involves a revision of the vacuum concept within quantum field theory. (shrink)

We discuss a new theory of the universe in which the vacuum energy is of classical origin and dominates the energy content of the universe. As usual, the Einstein equations determine the metric of the universe. However, the scale factor is controlled by total energy conservation in contrast to the practice in the Robertson–Walker formulation. This theory naturally leads to an explanation for the Big Bang and is not plagued by the horizon and cosmological constant problem. (...) It naturally accommodates the notion of dark energy and proposes a possible explanation for dark matter. It leads to a dual description of the universe, which is reminiscent of the dual theory proposed by Milne in 1937. On the one hand one can describe the universe in terms of the original Einstein coordinates in which the universe is expanding, on the other hand one can describe it in terms of co-moving coordinates which feature in measurements. In the latter representation the universe looks stationary and the age of the universe appears constant. The paper describes the evolution of this universe. It starts out in a classical state with perfect symmetry and zero entropy. Due to the vacuum metric the effective energy density is infinite at the beginning, but diminishes rapidly. Once it reaches the Planck energy density of elementary particles, the formation of particles can commence. Because of the quantum nature of creation and annihilation processes spatial and temporal inhomogeneities appear in the matter distributions, resulting in residual proton (neutron) and electron densities. Hence, quantum uncertainty plays an essential role in the creation of a diversified complex universe with increasing entropy. It thus seems that quantum fluctuations play a role in cosmology similar to that of random mutations in biology. Other analogies to biological principles, such as recapitulation, are also discussed. (shrink)

A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the (...) final formulation of Quantum Gravity. (shrink)

Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the de Sitter solutions in terms of a family of radial functions R that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of ${10^{- 123} M_{\rm Planck}^4}$ is derived (...) in agreement with the experimental observations. A correct lower estimate of the mass of the observable universe related to the Dirac–Eddington–Weyl’s large number N = 1080 is also obtained. The presence of the radial function R is instrumental to understand why the cosmological constant is not zero and why it is so tiny. Finally, we rigorously prove why the proper use of Weyl’s Geometry within the context of Friedman–Lemaitre–Robertson–Walker cosmological models can account for both the origins and the value of the observed vacuum energy density. The source of dark energy is just the dilaton-like Jordan–Brans–Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. The full theory involving the dynamics of Weyl’s gauge field Aμ is very rich and may explain also the anomalous Pioneer acceleration and the temporal variations of the fundamental constants resulting from the expansion of the Universe. This is consistent with Dirac’s old idea of the plausible variation of the physical constants but with the advantage that it is not necessary to invoke extra dimensions. (shrink)

Using quantum liquids one can simulate the behavior of the quantum vacuum in the presence of the event horizon. The condensed matter analogs demonstrate that in most cases the quantum vacuum resists formation of the horizon, and even if the horizon is formed different types of the vacuum instability develop, which are faster than the process of Hawking radiation. Nevertheless, it is possible to create the horizon on the quantum-liquid analog of the brane, where the vacuum (...) life-time is long enough to consider the horizon as the quasistationary object. Using this analogy we calculate the Bekenstein entropy of the near-extremal and extremal black holes, which comes from the fermionic microstates in the region of the horizon—the fermion zero modes. We also discuss how the cancellation of the large cosmological constant follows from the thermodynamics of the vacuum. (shrink)

A model of a three-dimensional quantum vacuum based on Planck energy density as a universal property of a granular space is suggested. The possibility to provide an unifying explanation of dark matter and dark energy as phenomena linked with the fluctuations of the three-dimensional quantum vacuum is explored. The changes and fluctuations of the quantum vacuum energy density generate a curvature of space–time similar to the curvature produced by a “dark energy” density. The (...) formation of large scale structures in the universe associated to the flattening of the orbital speeds of the spiral galaxies can be explained in terms of primary fluctuations of the quantum vacuum energy density without attracting the idea of dark matter. (shrink)

According to modern physics and cosmology, the universe expands at an increasing rate as the result of a “dark energy” that characterizes empty space. Although dark energy is a modern concept, some elements in it can be traced back to the early part of the twentieth century. I examine the origin of the idea of zero-point energy, and in particular how it appeared in a cosmological context in a hypothesis proposed by Walther Nernst in 1916. The hypothesis (...) of a zero-point vacuum energy attracted some attention in the 1920s, but without attempts to relate it to the cosmological constant that was discussed by Georges Lemaître in particular. Only in the late 1960s, was it recognized that there is a connection between the cosmological constant and the quantum vacuum. As seen in retrospect, many of the steps that eventually led to the insight of a kind of dark energy occurred isolated and uncoordinated. (shrink)

The structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom in interaction with a quantum electromagnetic field is investigated. Our main purpose is to rewrite the formalism in Zhu et al. and to deduce the general expressions of the Einstein A coefficients of an atom on an arbitrary stationary trajectory. The total rate of change of the energy and Einstein coefficients of the atom near a plate with finite temperature (...) or acceleration are also investigated. (shrink)

Motivated by analogous applications to sonoluminescence, neutron stars mergers are examined in the context of Schwinger's dynamical Casimir effect. When the dielectric properties of the QED vacuum are altered through the introduction of dense matter, energy shifts in the zero-point fluctuations can appear as photon bursts at gamma-ray frequencies. The amount of radiation depends upon the properties and amount of matter in motion and the suddenness of the transition. It is shown that the dynamical Casimir effect can convert (...) sufficient energy of neutron star mergers into gamma rays. Using information extracted from simulations of matter flow in neutron star mergers by Ruffert and Janka, we estimate that the total Casimir energy released can exceed 10 53 ergs in gamma-ray frequencies. The Casimir energy approach is capable of explaining the most energetic gamma-ray bursts. (shrink)

The cosmological constant problem arises at the intersection between general relativity and quantum field theory, and is regarded as a fundamental problem in modern physics. In this paper we describe the historical and conceptual origin of the cosmological constant problem which is intimately connected to the vacuum concept in quantum field theory. We critically discuss how the problem rests on the notion of physically real vacuum energy, and which relations between general relativity and quantum field theory are (...) assumed in order to make the problem well-defined. (shrink)

We describe vacuum as a system of virtual particles, some of which have negative energies. Any system of vacuum particles is a part of a keneme, i.e., of a system of n particles which can, without violating the conservation laws, annihilate in the strict sense of the word (transform into nothing). A keneme is a homogeneous system, i.e., its state is invariant by all transformations of the invariance group. But a homogeneous system is not necessarily a keneme. In (...) the simple case of a spin system, where the invariance group is SU(2), a homogeneous system is a system whose total spin is unpolarized; a keneme is a system whose total spin is zero. The state of a homogeneous system is described by a statistical operator with infinite trace (von Neumann), to which corresponds a characteristic distribution. The characteristic distributions of the homogeneous systems of vacuum are defined and studied. Finally it is shown how this description of vacuum can be used to solve the frame problem posed in paper (I). (shrink)

First the “frame problem” is sketched: The motion of an isolated particle obeys a simple law in Galilean frames, but how does the Galilean character of the frame manifest itself at the place of the particle? A description of vacuum as a system of virtual particles will help to answer this question. For future application to such a description, the notion of global particle is defined and studied. To this end, a systematic use of the Fourier transformation on the (...) Poincaré group is needed. The state of a system of n free particles is represented by a statistical operator W, which defines an operator-valued measure on ^Pn (^P is the dual of the Poincaré group). The inverse Fourier–Stieltjes transform of that measure is called the characteristic function of the system; it is a function on Pn. The main notion is that of global characteristic function: it is the restriction of the characteristic function to the diagonal subgroup of Pn; it represents the state of the system, considered as a single particle. The main properties of characteristic functions, and particularly of global characteristic functions, are studied. A mathematical Appendix defines two functional spaces involved. (shrink)

Vacuum (leer, frei) bezeichnete bis zum 19. Jahrhundert allein den körperlosen Raum. Unter dem Einfluss physikalischer (Feld-) Theorien meint der Terminus inzwischen diejenige residuale physische Entiät, die einen vorgegebenen Raum ausfüllt bzw. im Prinzip ausfüllen würde, nachdem alles, was mit physikalischen Mitteln entfernt werden kann, aus dem Raum entfernt wurde. Theorien über das V. sind daher eng mit Theorien über die Struktur des Raumes, die Bewegung, die physikalischen Gegenstände und deren Wechselwirkungen verbunden. In der Quantentheorie bezeichnet V. den Zustand (...) niedrigster Energie (Grundzustand) eines Systems. (shrink)

According to the BSM- Supergravitation Unified Theory (BSM-SG), the energy is indispensable feature of matter, while the matter possesses hierarchical levels of organization from a simple to complex forms, with appearance of fields at some levels. Therefore, the energy also follows these levels. At the fundamental level, where the primary energy source exists, the matter is in its primordial form, where two super-dense fundamental particles (FP) exist in a classical pure empty space (not a physical vacuum). (...) They are associated with the Planck scale parameters of frequency and distance and interact by Supergravitational forces. These forces are inverse proportional to the cube of distance at pure empty space and they are based on frequency interactions. Since the two FPs have different intrinsic frequencies, the SG forces appear different for interactions between the like and unlike FPs and may change the sign. This primordial form of matter exists in the super-heavy black holes located in the center of each well formed galaxy. The next upper level of matter organization includes the underlying structure of the physical vacuum, called a Cosmic Lattice, and the structure of elementary particles. They have common substructure elements obtained by specific crystallization process preceding the formation of the observable galaxies. The Cosmic Lattice, forming a space known as a physical vacuum, is responsible for the existence and propagation of the physical fields: electrical, magnetic, Newtonian gravity and inertia. The energy of physical vacuum is in two forms: Static (enormous) and Dynamic (weak). The Static energy is directly related to the Newtonian mass by the Einstein equation E = mc^2 and it is a primary source of the nuclear energy. The Dynamic energy is responsible for the existence of the electric and magnetic fields, the constant speed of light and the quantum mechanical properties of the physical vacuum. The next upper energy level is the dynamical energy of excited atoms and molecules. At this level a hidden energy wells exit, such as the internal energy of the electron and the internal energy of atoms with more than one electron. The next upper energy level is at some organic molecules and particularly in the biomolecules that contain ring atomic structures. In such a structure, some quantum states are not emitted immediately, but rotating in the ring. While in organic molecules the energy stored in such a ring is released by a chemical process, in the long chain molecule of proteins in the living organism the stored energy can be released simultaneously by triggering. A huge number of atomic rings are contained in the DNA strands. The release of the energy stored in DNA, for example, is an avalanche process that causes an emission of entangled photons possessing a strong penetrating capability. A sequence of entangled photons emitted by DNA should carry the genetic information encoded by the cordons. This mechanism, predicted in BSM-SG theory, is very important for intercommunication between the cells of the living organism. The next upper level of energy organization may exist in the brain. The brain is an organ of a most abundant number of atomic rings, while its tissue environment might permit complex energy interactions. The human brain contains billions of atomic rings. The next hypothetical upper level of energy organization is an information field, physically existed outside, but connected with the living brain. It corresponds to a specific field known as aura, while the possibility of its existence is still not accepted by the main stream science. The problem is that this field could not be detected by the currently existing technical means used for EM communications. The BSM-SG predicts that this field might differ from the EM field we use for communication, but it is a subject of a further theoretical development that must be supported by experiments using specifically designed technical means. According to the BSM-SG theory, the energy conversion from the primary energy source to the complex levels of matter and field organization is a permanent syntropic process based on complex resonance interactions. (shrink)

The cosmological constant problem arises at the intersection between general relativity and quantum field theory, and is regarded as a fundamental problem in modern physics. In this paper, we describe the historical and conceptual origin of the cosmological constant problem which is intimately connected to the vacuum concept in quantum field theory. We critically discuss how the problem rests on the notion of physically real vacuum energy, and which relations between general relativity and quantum field theory are (...) assumed in order to make the problem well-defined. (shrink)

Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t 1/2, and the fractional changes in momentum and energy are proportional to t −1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change (...) in momentum of a particle in a gas is very small. However, at the end of the mean free path each particle undergoes an interaction that magnifies the preceding change, and the net result is that the momentum distribution of the particles in a gas is randomized in a few collision times. In this way the random action of vacuum radiation and its subsequent magnification by molecular interaction produces entropy increase. This process justifies the assumption of molecular chaos used in the Boltzmann transport equation. (shrink)

Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be (...) the vacuum fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an inexplicable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment. (shrink)

The quantum vacuum may in certain circumstances be regarded as a type of fluid medium, or aether, exhibiting energy density, pressure, stress and friction. Vacuum friction may be thought of as being responsible for the spontaneous creation of particles from the vacuum state when the system is non-stationary. Examples include the expanding universe, rotating black holes, moving mirrors, atoms passing close to surfaces, and the activities of sub-cellular biosystems. The concept of vacuum friction will be (...) reviewed and illustrated, and some suggestions for future experiments made. (shrink)

In this paper we review the evolution of the concept of “ vacuum ” according to different theories formulated in the last century, like Quantum Mechanics, Quantum Electrodynamics, Quantum Chromodynamics in Particle Physics and Cosmology. In all these theories a metastable vacuum state is considered which transforms from one state to another according to the energy taken into consideration. It is a “fluid” made up by matter and radiation present in the whole Universe, which may be identified (...) with a modern definition of ether. (shrink)

Physical vacuum is a special superfluid medium populated by enormous amount of virtual particle-antiparticle pairs. Its motion is described by the modified Navier–Stokes equation: the pressure gradient divided by the mass density is replaced by the gradient from the quantum potential; time-averaged the viscosity vanishes, but its variance is not zero. Vortex structures arising in this medium show infinitely long lifetime owing to zero average viscosity. The nonzero variance is conditioned by exchanging the vortex energy with zero-point (...) class='Hi'>vacuum fluctuations. The vortex has a non-zero core where the orbital speed vanishes. The speed reaches a maximal value on the core wall and further it decreases monotonically. The vortex trembles around some average value and possesses by infinite life time. The vortex ball resulting from topological transformation of the vortex ring is considered as a model of a particle with spin. Anomalous magnetic moment of electron is computed. (shrink)

Conventional rockets are not a suitable technology for interstellar missions. Chemical rockets require a very large weight of propellant, travel very slowly compared to light speed, and require significant energy to maintain operation over periods of years. For example, the 722 kg Voyager spacecraft required 13,600 kg of propellant to launch and would take about 80,000 years to reach the nearest star, Proxima Centauri, about 4.3 light years away. There have been various attempts at developing ideas on which one (...) might base a spacecraft that would permit interstellar travel, such as spacewarps. In this paper we consider another suggestion from science fiction and explore how the quantum vacuum might be utilized in the creation of a novel spacecraft. The spacecraft is based on the dynamic Casimir effect, in which electromagnetic radiation is emitted when an uncharged mirror is properly accelerated in vacuum. The radiative reaction produces a dissipative force on the mirror that tends to resist the acceleration of the mirror. This force can be used to accelerate a spacecraft attached to the mirror. We also show that, in principle, one could obtain the power to operate the accelerated mirror in such a spacecraft using energy extracted from the quantum vacuum using the standard Casimir effect with a parallel plate geometry. Unfortunately the method as currently conceived generates a miniscule thrust, and is no more practical than a spacewarp, yet it does provide an interesting demonstration of our current understanding of the physics of the quantized electromagnetic field in vacuum. (shrink)

The idea that the mass m of an elementary particle is explained in the semi-classical approximation by quantum-mechanical zero-point vacuum fluctuations has been applied previously to spin-1/2 fermions to yield a real and positive constant value for m, expressed through the spinorial connection Γ i in the curved-space Dirac equation for the wave function ψ due to Fock. This conjecture is extended here to bosonic particles of spin 0 and spin 1, starting from the basic assumption that all fundamental (...) fields must be conformally invariant. As a result, in curved space-time there is an effective scalar mass-squared term $m_{0}^{2}=-R/6=2\varLambda_{\mathrm{b}}/3$ , where R is the Ricci scalar and Λ b is the cosmological constant, corresponding to the bosonic zero-point energy-density, which is positive, implying a real and positive constant value for m 0, through the positive-energy theorem. The Maxwell Lagrangian density $\mathcal{L} =- \sqrt{-g}F_{ij}F^{ij}/4$ for the Abelian vector field F ij ≡A j,i −A i,j is conformally invariant without modification, however, and the equation of motion for the four-vector potential A i contains no mass-like term in curved space. Therefore, according to our hypothesis, the free photon field A i must be massless, in agreement with both terrestrial experiment and the notion of gauge invariance. (shrink)

The discovery of the Higgs boson at LHC confirms that what we experience as empty space should actually be thought as a condensate of elementary quanta. This condensate characterizes the physically realized form of relativity and could play the role of preferred reference frame in a modern Lorentzian approach. This observation suggests a new interpretative scheme to understand the unexplained residuals in the old ether-drift experiments where light was still propagating in gaseous systems. Differently from present vacuum experiments, where (...) anyhow deviations from Special Relativity are expected to be at the limit of visibility, these now acquire a crucial importance and become consistent with the Earth’s velocity of 370 km/s which characterizes the CMB anisotropy. In the same scheme, one can also understand the difference with the other experiments where light propagates in strongly bound systems such as solid or liquid transparent media. This non-trivial level of consistency motivates a new generation of precise laser interferometry experiments which explore the same particle physics vacuum and, in this sense, are complementary to those with high-energy accelerators. (shrink)

According to the BSM Supergravitation Unified Theory, the physical vacuum contains energy that is not of electromagnetic origin. The Heterodyne Resonance Mechanism (HRM) predicted by the theory permits access to this hidden energy by a process involving the anomalous magnetic moment and the quantum mechanical spin flipping of the electron. Plasma experiments and analysis of lightning observations indicate that the HRM effect could be involved in the natural lightning phenomena. Although the energy density of this hidden (...) source is much smaller than nuclear energy, the opportunity to access this energy will lead to some new practical applications. The derived physical model of the HRM effect provides the opportunity for development of new technologies. This book could be an useful handbook for researchers and experimenters. (shrink)

We interpret the probability rule of the CSL collapse theory to mean to mean that the scalar field which causes collapse is the gravitational curvature scalar with two sources, the expectation value of the mass density (smeared over the GRW scale a) and a white noise fluctuating source. We examine two models of the fluctuating source, monopole fluctuations and dipole fluctuations, and show that these correspond to two well-known CSL models. We relate the two GRW parameters of CSL to fundamental (...) constants, and we explain the energy increase of particles due to collapse as arising from the loss of vacuum gravitational energy. (shrink)

Stemming from our energy localization hypothesis that energy in general relativity is localized in the regions of the energy-momentum tensor, we had devised a test with the classic Eddington spinning rod. Consistent with the localization hypothesis, we found that the Tolman energy integral did not change in the course of the motion. This implied that gravitational waves do not carry energy in vacuum, bringing into question the demand for the quantization of gravity. Also if (...) information is conveyed by the waves, the traditional view that information transfer demands energy is challenged. Later, we showed that the “body” angular momentum changed at a rate indicating that the moment of inertia increased to higher order, contrary to traditional expectations. We consider the challenges facing the development of a localized expression for the total angular momentum of the body including the contribution from gravity. We find that Komar's expression does not lead to an adequate formulation of localized angular momentum. (shrink)

References to energy of the universe have focussed upon the matter contribution, whereas the conservation laws must include a gravitational contribution as well. The conservation laws as applied to FRW cosmologies suggest a zero total energy irrespective of the spatial curvature when the value of the cosmological constant is taken to be zero. This result provides a useful constraint on models of the early universe and lends support to currently studied theories of the universe arising as a quantum (...) fluctuation of the vacuum. (shrink)

In Newtonian gravity it is a moot question whether energy should be localized in the field or inside matter. An argument from relativity suggests a compromise in which the contribution from the field in vacuum is positive definite. We show that the same compromise is implied by Noether’s theorem applied to a variational principle for perfect fluids, if we assume Dirichlet boundary conditions on the potential. We then analyse a thought experiment due to Bondi and McCrea that gives (...) a clean example of inductive energy transfer by gravity. Some history of the problem is included. (shrink)

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. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate (...) operators (ISaTCO) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

We study the response of switched particle detectors to static negative energy densities and negative energy fluxes. It is demonstrated how the switching leads to excitation even in the vacuum and how negative energy can lead to a suppression of this excitation. We obtain quantum inequalities on the detection similar to those obtained for the energy density by Ford and co-workers and in an ‘‘operational’’ context by Helfer. We reexamine the question ‘‘Is there a quantum (...) equivalence principle?’’ in terms of our model. Finally, we briefly address the issue of negative energy and the second law of thermodynamics. (shrink)

This column is about a new development in the theory of wormholes. At Vanderbilt University, David Hochberg and Thomas W. Kephart have discovered that gravity itself can produce regions of negative energy. Within these regions, we may conjecture, stable wormholes may form naturally, particularly during the early Big Bang. A wormhole is a geometrical shortcut in curved space-time with the topology of a cup handle which, in principle, allows movement from one point in space-time to another without the necessity (...) of traversing the intervening space-time interval. This provides a physical basis for two traditional gimmicks of science fiction: faster-than-light travel and time travel into the past and the future. (shrink)

Dirac’s relativistic theory of electron generally results in two possible solutions, one with positive energy and other with negative energy. Although positive energy solutions accurately represented particles such as electrons, interpretation of negative energy solution became very much controversial in the last century. By assuming the vacuum to be completely filled with a sea of negative energy electrons, Dirac tried to avoid natural transition of electron from positive to negative energy state using Pauli’s (...) exclusion principle. However, many scientists like Bohr objected to the idea of sea of electrons as it indicates infinite density of charge and electric field and consequently infinite energy. In addition, till date, there is no experimental evidence of a particle whose total energy (kinetic plus rest) is negative. In an alternative approach, Feynman, in quantum field theory, proposed that particles with negative energy are actually positive energy particles running backwards in time. This was mathematically consistent since quantum mechanical energy operator contains time in denominator and the negative sign of energy can be absorbed in it. However, concept of negative time is logically inconsistent since in this case, effect happens before the cause. To avoid above contradictions, in this paper, we try to reformulate the Dirac’s theory of electron so that neither energy needs to be negative nor the time is required to be negative. Still, in this new formulation, two different possible solutions exist for particles and antiparticles (electrons and positrons). (shrink)

A new hypothesis for energy localization in general relativity is introduced which is based upon the fact that the energy-momentum conservation laws are devoid of content in vacuum. The vanishing of pseudotensor components forms the basis of coordinate conditions consistent with the above. The implication is that energy is localized where the energy-momentum tensor is nonvanishing. As a consequence, gravitational waves are not carriers of energy in vacuum. A detailed analysis of a Feynman (...) detector interacting with a plane gravitational wave is consistent with the hypothesis. The fact that there has never been a confirmed direct energy transfer to a detector via gravitational radiation is also consistent with the hypothesis. (shrink)

According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical (...) theory, which degeneracy allegedly arises from the fact that “large” (but not “small”) local gauge transformations connect physically distinct states of zero field energy. If that is right, then some local gauge transformations do generate empirical symmetries. In defending conventional wisdom against this challenge I hope to clarify the meaning of empirical symmetry while deepening our understanding of gauge transformations. I distinguish empirical from theoretical symmetries. Using Galileo’s ship and Faraday’s cube as illustrations, I say when an empirical symmetry is implied by a theoretical symmetry. I explain how the theta-vacuum arises, and how “large” gauge transformations differ from “small” ones. I then present two analogies from elementary quantum mechanics. By applying my analysis of the relation between empirical and theoretical symmetries, I show which analogy faithfully portrays the character of the vacuum state of a classical non-Abelian Yang-Mills gauge theory. The upshot is that “large” as well as “small” gauge transformations are purely formal symmetries of non-Abelian Yang-Mills gauge theories, whether classical or quantized. It is still worth distinguishing between these kinds of symmetries. An analysis of gauge within the constrained-Hamiltonian formalism yields the result that “large” gauge transformations should not be classified as gauge transformations; indeed, nor should “global” gauge transformations. In a theory in which boundary conditions are modeled dynamically, “global” gauge transformations may be associated with physical symmetries, corresponding to translations of these extra dynamical variables. Such translations are symmetries if and only if charge is conserved. But it is hard to argue that these symmetries are empirical, and in any case they do not correspond to any constant phase change in a quantum state. (shrink)

The discrete light-cone quantization (DLCQ) of a supersymmetric gauge theory in 1+1 dimensions is discussed, with particular attention given to the inclusion of the gauge zero mode. Interestingly, the notorious “zero-mode” problem is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the nonsupersymmetric case. An analysis of the vacuum structure is provided by deriving the effective quantum mechanical Hamiltonian of the (...) gauge zero mode. It is shown that the inclusion of the zero modes of the adjoint scalars and fermions is crucial for probing the phase properties of the vacua. We find that the ground-state energy is zero and thus consistent with unbroken supersymmetry and conclude that the light-cone Fock vacuum is unchanged with or without the presence of matter fields. (shrink)

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (...) (1999); Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper. (shrink)

The questions of what represents space-time in GR, the status of gravitational energy, the substantivalist-relationalist issue, and the exceptional status of gravity are interrelated. If space-time has energy-momentum, then space-time is substantival. Two extant ways to avoid the substantivalist conclusion deny that the energy-bearing metric is part of space-time or deny that gravitational energy exists. Feynman linked doubts about gravitational energy to GR-exceptionalism, as do Curiel and Duerr; particle physics egalitarianism encourages realism about gravitational (...) class='Hi'>energy. In that spirit, this essay proposes a third possible view about space-time, one involving a particle physics-inspired non-perturbative split that characterizes space-time with a constant background _matrix_, a sort of vacuum value, thus avoiding the inference from gravitational _energy to substantivalism. On this proposal, space-time is, where eta=diag is a spatio-temporally constant numerical signature matrix, a matrix already used in GR with spinors. The gravitational potential, to which any gravitational energy can be ascribed, is g_{\mu\nu}- eta, an _affine_ geometric object with a tensorial Lie derivative and a vanishing covariant derivative. This non-perturbative split permits strong fields, arbitrary coordinates, and arbitrary topology, and hence is pure GR by almost any standard. This razor-thin background, unlike more familiar backgrounds, involves no extra gauge freedom and so lacks their obscurities and carpet lump-moving. After a discussion of Curiel's GR exceptionalist denial of the localizability of gravitational energy and his rejection of energy conservation, the two traditional objections to pseudotensors, coordinate dependence and nonuniqueness, are explored. Both objections are inconclusive and getting weaker. A literal interpretation involving infinitely many energies corresponding by Noether's first theorem to the infinite symmetries of the _action_ largely answers Schroedinger's false-negative coordinate dependence problem. Bauer's false-positive objection has multiple answers. Non-uniqueness might be handled by Nester et al.'s finding physical meaning in multiplicity in relation to boundary conditions, by an optimal candidate, or by Bergmann's identifying the non-uniqueness and coordinate dependence ambiguities as one. (shrink)

This paper charts P.A.M. Dirac’s development of his theory of the electron, and its radical picture of empty space as an almost-full plenum. Dirac’s Quantum Electrodynamics famously accomplished more than the unification of special relativity and quantum mechanics. It also accounted for the ‘duplexity phenomena’ of spectral line splitting that we now attribute to electron spin. But the extra mathematical terms that allowed for spin were not alone, and this paper charts Dirac’s struggle to ignore or account for them as (...) a sea of strange, negative-energy, particles with positive ‘holes’. This work was not done in solitude, but rather in exchanges with Dirac’s correspondence network. This social context for Dirac’s work contests his image as a lone genius, and documents a community wrestling with the ontological consequences of their work. Unification, consistency, causality, and community are common factors in explanations in the history of physics. This paper argues on the basis of materials in Dirac’s archive that — in addition — mathematical beauty was an epistemological factor in the development of the electron and hole theory. In fact, if we believe that Dirac’s beautiful mathematics captures something of the world, then there is both an epistemology and an ontology of mathematical beauty. (shrink)

We investigate the novel problem of what happens in special relativity and in relativistic field theories whenthree-dimensional space is quantized. First we examine the equation for elastic waves on a linear chain, the simplest example of a quantized medium, and propose, on its analogy, a nonlinearp-k relationp=ħk(sinhkl)/kl for light and material waves. Here,kl is a new variable which represents the space-quantization effect on the plane wave of wave numberk=|k|. (Note thatkl=0 givesp=ħk.) This relation makes the light velocity in vacuum (...) dependent onkl. We postulate, however, that the phase and group velocities of each individual light wave are still invariant, and try to generalize special relativity to the case ofkl ≠ 0. This can be simply done if the invariance ofkl is assumed. Our results suggest that “localization” might be a relative concept. One interesting consequence of our proposal is that relativistic field theories become automatically finite. This comes out without violating unitarity or causality. A precise measurement of velocities of high-energy photons or massive particles is desirable for checking our proposal. (shrink)

In response to Cushing it is urged that the vicissitudes of quantum field theory do not press towards a nonrealist attitude towards the theory as strongly as he suggests. A variety of issues which Redhead raises are taken up, including photon localizability, the wave-particle distinction in the classical limit, and the interpretation of quantum statistics, vacuum fluctuations, virtual particles, and creation and annihilation operators. It is urged that quantum field theory harbors an unacknowledged inconsistency connected with the fact that (...) the zero point energy has observable consequences, while to avoid infinities it must be "thrown away". Finally, Redhead's conception of ephemerals is pressed and the paper concludes with the suggestion that the particle concept largely drops out of quantum field theory. (shrink)

We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non-null escape rate over the potential barrier at low temperatures (T → 0). It is found (...) that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results. (shrink)

A contrarian scientist wrestles with the big questions that modern physics raises, and what physics says about the human condition Not only can we not currently explain the origin of the universe, it is questionable we will ever be able to explain it. The notion that there are universes within particles, or that particles are conscious, is ascientific, as is the hypothesis that our universe is a computer simulation. On the other hand, the idea that the universe itself is conscious (...) is difficult to rule out entirely. According to Sabine Hossenfelder, it is not a coincidence that quantum entanglement and vacuum energy have become the go-to explanations of alternative healers, or that people believe their deceased grandmother is still alive because of quantum mechanics. Science and religion have the same roots, and they still tackle some of the same questions: Where do we come from? Where do we go to? How much can we know? The area of science that is closest to answering these questions is physics. Over the last century, physicists have learned a lot about which spiritual ideas are still compatible with the laws of nature. Not always, though, have they stayed on the scientific side of the debate. In this lively, thought-provoking book, Hossenfelder takes on the biggest questions in physics: Does the past still exist? Do particles think? Was the universe made for us? Has physics ruled out free will? Will we ever have a theory of everything? She lays out how far physicists are on the way to answering these questions, where the current limits are, and what questions might well remain unanswerable forever. Her book offers a no-nonsense yet entertaining take on some of the toughest riddles in existence, and will give the reader a solid grasp on what we know-and what we don't know. (shrink)

The ‘cosmological constant problem’ has historically been understood as describing a conflict between cosmological observations in the framework of general relativity and theoretical predictions from quantum field theory, which a future theory of quantum gravity ought to resolve. I argue that this view of the CCP is best understood in terms of a bet about future physics made on the basis of particular interpretational choices in GR and QFT, respectively. Crucially, each of these choices must be taken as itself grounded (...) in the sucesses of the respective theory for this bet to be justified. 1 Introduction 2 The Cosmological Constant Problem 2.1 The physics that anticipates ‘vacuum energy’ 2.2 Getting to zero-point energies 2.3 Getting to the cosmological constant 3 The Epistemology of Physical Interpretation 4 The View from High-Energy Physics 5 Concluding Remarks. (shrink)

The cosmological constant problem is widely viewed as an important barrier and hint to merging quantum field theory and general relativity. It is a barrier insofar as it remains unsolved, and a solution may hint at a fuller theory of quantum gravity. I critically examine the arguments used to pose the cosmological constant problem, and find many of the steps poorly justified. In particular, there is little reason to accept an absolute zero point energy scale in quantum field theory, (...) and standard calculations are badly divergent. It is also unclear exactly how a semiclassical treatment of gravity would include a vacuum energy contribution to the total stress-energy. Large classes of solution strategies are also found to be conceptually wanting. I conclude that one should not accept the cosmological constant problem as standardly stated. (shrink)

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale $$(\hbar \lambda / R)$$. Previous work led us to show from (...) first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship $$\rho \sim L_{\rm Planck}^{-2}R^{-2} = L_{P}^{-4} (L_{\rm Planck} / R)^{2} \sim 10^{-122}M_{\rm Planck}^4$$, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles,....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit. (shrink)