Zero Rest Mass Research Articles

Photon Characteristics and Behavior under Refractive Index

The effective mass, energy and momentum of photon in medium is described. The photon has both kinetic and potential energy and displays an effective mass when travelling through a medium. The photon is a type of elementary particle that serves as the quantum of the electromagnetic field and is explained through equations to have an elastic constant, volume, momentum, force, power and zero rest mass. The theory that photons a massless only applies to rest mass. A photon undergoes different dynamics such as strain and changes in effective mass under the influence of the refractive index that gives rise to a refractive force. This study synthesizes some properties of energy such as elastic constant, weight, and volume in order to explain the nature of photons and photon dynamics under refractive index. In this study, a helical spring model has been used to describe the behavior of a photon in the medium. The model connects together the exhibited properties such as energy, effective mass, spin, elastic constant and volume. Further explanation is given to the effect of gravitational force on wavelength and refractive index of air, and how gravitational force causes red and blue shifts in photon propagation. The quantization of energy has been extended to the quantization of space, time and matter. This study is consistent and consolidates the existing classical and quantum theories. There are further potential applications in optical communication, quantum cryptography, quantum optics, and medicine, especially in the use of two-photon excitation microscopy and photodynamic therapy.

James Clerk Maxwell and Inertia-Free Physics

It is shown that using the inertia-free process of transferring angular momentum, which was introduced by Maxwell in the model of luminiferous ether, it is possible to explain many physical phenomena, most of them have had no physical explanation as yet. Such phenomena are, in particular: spin supercurrent supporting the “stiffness” of spin part of the order parameter in superfluid 3He-B; quantum correlations between any quantum entities of both zero rest mass (photons) and non-zero rest mass; the vector magnetic potential; the generation of energy in a rotating nonlinear magnetic field; the energy of cavity structures. The inertia-free process may spread at the speed higher than the speed of light and this does not contradict Special Relativity as the latter postulates the speed limit only for an inertial process; besides, the inertia-free process is not characterized by kinetic energy and does not take part in gravitational interactions.

Zero rest-mass fields and the Newman–Penrose constants on flat space

Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman–Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the correspondence between data for these fields on a spacelike hypersurface and the value of their corresponding NP constants at future and past null infinity. To do so, Friedrich’s framework of the cylinder at spatial infinity is employed to show that, expanding the initial data in terms spherical harmonics and powers of the geodesic spatial distance ρ to spatial infinity, the NP constants correspond to the data for the second highest possible spherical harmonic at a fixed order in ρ. In addition, it is shown that for generic initial data within the class considered in this article, there is no natural correspondence between the NP constants at future and past null infinity—for both the Maxwell and spin-2 field. However, if the initial data are time-symmetric, then the NP constants at future and past null infinity have the same information.

Four states of matter and centrally symmetric de Broglie particle–wave mechanical systems

The dark issues of cosmological mechanics imply that our accounting for mass and energy at this scale is incorrect. On the other hand, existing theory not only accounts for atomic physics, but does so to a very high degree of accuracy. de Broglie was first to propose a concrete physical picture of the co-existence of both particle and its associated wave. We have previously proposed a Lorentz invariant modification of Newton’s second law that applies when the particle energy itself is of comparable magnitude to the potential energy of the applied external field. A dual particle–wave formulation is developed that allows exceptions to the law that matter cannot be created or destroyed, and accommodates both particle and wave energies. Here we examine this formulation in a centrally or spherically symmetric gravitating environment. A logical analysis of the integrated rate-of-working equation gives rise to four distinct states of matter; positive and negative energies with either non-zero rest mass or zero rest mass. This identification is meaningful only within the extended theory, and it has no meaning within conventional theory. We propose that dark matter and dark energy arise from a particular alignment of the spatial physical force f and the force g in the direction of time, such that the particle and wave energies coincide, and a consistent mathematical framework supports this proposal. Allowable potentials V(r, t) arise as the solutions of certain partial differential equations depending upon the assumed state of matter, and the mathematical framework corresponding to each state is briefly described and, where possible, some of the simpler and physically more interesting solutions are examined. The Newtonian gravitational potential arises from a variety of asymptotic limits, and can be identified as predominantly wave energy, which is entirely consistent with the post-Newtonian approximation.

Zero rest mass soliton solutions

In this paper, extended Klein-Gordon field systems will be introduced. Theoretically, it will be shown that for a special example of these systems, it is possible to have a single zero rest mass soliton solution, which is forced to move at the speed of light provided it is considered a non-deformed rigid object. This special soliton solution has the minimum energy among the other solutions, i.e. any arbitrary deformation in its internal structure leads to an increase in the total energy.

New Discoveries and the Necessity of Reconsidering the Perspectives on Newton's Second Law

According to the mainstream physicists the observation and record of the motion of neutrinos at ultra relativistic speeds apparently seem to violate relativity postulate and to violate the speed of light as a universal constant. The Einstein mass-energy equation E=mc2, the relativistic mass, relativistic form of Newton's second law, the fundamental principles and equations of modern physics by generalizing this anomaly will be challenged. Some other observations and results make possible the speeds higher than speed of light which is not rather incredible and it will not be impossible; it only requires a change in today's attitudes towards relativity and quantum mechanics. Thus this paper, from a new approach, turns out to merge the fundamental principles of quantum physics, relativity and classical mechanics through a new definition of quiescent state of particles like photon, and attempts to present the reasons and the possibilities of the existence of the superluminal speeds. At the beginning of the 20th century, Newton's second law was corrected considering the limit speed c and the relativistic mass. At that time there has not been a clear understanding of the subatomic particles and basically there was little research in high energy physics, if we ignore the zero rest mass of photon, much better and more real physical phenomena may be investigated.The speed of the created particles is a function of the internal interaction and the mechanism of creation of subatomic particles, and the external forces that are exerted on them.

Proca Effects of Axion-Like Particle-Photon Interactions on Light Polarization in External Magnetic Fields

Photon can mix with the axion-like particles (ALPs) on light polarization when the laser beam travels through a magnetic field. Since there is no conclusive evidence of an exact zero rest mass for the photon in various experiments and observations, we study the Proca effects in various ALP-photon regeneration experiments and develop a formalism which can be adopted to study the evolution of a massive photon in the presence of external magnetic fields. We find that the Proca effects are much smaller than the effects of the standard QCD axions. But if the masses of such particles are comparable, the Proca effects can not be neglected. Furthermore, we get the implied photon mass limit and discuss the feasibility of extending the search for the photon mass limit in this area.

Robinson-Trautman radiating metrics with zero news and photonrockets

We show that a Robinson-Trautman radiating metric has zeroBondi news if and only if it is a Kinnersley metric for apoint mass accelerating arbitrarily with the emission of matter of zerorest mass. This corrects a statement, which we made in arecent paper (1999 Class. Quantum Grav. 16 611-7),that the news function vanishes only for those Kinnersleymetrics that have axial symmetry. It follows that none of the`photon rockets' of the Kinnersleyfamily generate gravitational waves.

Polyhomogeneous solutions of wave equations in the radiation regime

While the physical properties of the gravitational field in the radiation regime are reasonably well understood, several mathematical questions remain unanswered. The question here is that of existence and properties of gravitational fields with asymptotic behavior compatible with existence of gravitational radiation. A framework to study those questions has been proposed by R. Penrose (R. Penrose, “Zero rest-mass fields including gravitation”, Proc. Roy. Soc. London A284 (1965), 159-203), and developed by H. Friedrich (H. Friedrich, “Cauchy problem for the conformal vacuum field equations in general relativity”, Commun. Math. Phys. 91 (1983), 445-472.), (H. Friedrich, “On the existence of n-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure”, Commun. Math. Phys. 107 (1986), 587-609.), (-,“On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations”, Jour. Diff. Geom. 34 (1991), 275-345) using conformal completions techniques. In this conformal approach one has to 1) construct initial data, which satisfy the general relativistic constraint equations, with appropriate behavior near the conformal boundary, and 2) show a local (and perhaps also a global) existence theorem for the associated evolution problem. In this context solutions of the constraint equations can be found by solving a nonlinear elliptic system of equations, one of which resembles the Yamabe equation (and coincides with this equation in some cases), with the system degenerating near the conformal boundary. In the first part of the talk I (PTC) will describe the existence and boundary regularity results about this system obtained some years ago in collaboration with Helmut Friedrich and Lars Andersson. Some new applications of those techniques are also presented. In the second part of the talk I will describe some new results, obtained in collaboration with Olivier Lengard, concerning the evolution problem.

Massless fields on Minkowski space-time with quantized, Kerr sources

Solutions to the zero rest mass field equations generated by spinning Kerr sources are reviewed. It is shown that the act of quantization removes the singularity when the source has spin ½ . For a Maxwell field, the integrated self-energy is also finite.

Minkowski Bessel modes.

The global Minkowski Bessel (M-B) modes, whose explicit form allows the identification and description of the condensed vacuum state resulting from the operation of a pair of accelerated refrigerators, are introduced. They span the representation space of the unitary representation of the Poincare group on 2-D Lorentz space-time. Their three essential properties are: (1) they are unitarily related to the familiar Minkowski plane waves; (2) they form a unitary representation of the translation group on two dimensional Minkowski spacetime. (3) they are eigenfunctions of Lorentz boosts around a given reference event. In addition the global Minkowski Mellin modes are introduced. They are the singular limit of the M-B modes. This limit corresponds to the zero transverse momentum solutions to the zero rest mass wave equation. Also introduced are the four Rindler coordinate representatives of each global mode. Their normalization and density of states are exhibited in a (semi-infinite) accelerated frame with a finite bottom. In addition we exhibit the asymptotic limit as this bottom approaches the event horizon and thereby show how a mode sum approaches a mode integral as the frame becomes bottomless.

A generalization of Penrose’s helicity theorem for space-times with nonzero dual mass

An algebraic definition of the helicity operator ℋ is proposed for vacuum stationary and asymptotically flat wormholes (i.e., space-times where the manifold of orbits of the stationary Killing field has S2×R topology). The definition avoids the use of momentum space or Fourier decomposition of the gravitational degrees of freedom into positive and negative frequency parts, and is essentially geared to emphasize the role of nontrivial topology. It is obtained via the introduction of a total spin vector Sα derived from the dual Bondi four-momentum *Pα, both vectors originating in the presence of nontrivial homotopy groups. (Space-times with nonzero dual mass can be characterized by a conformal null boundary ℐ having the topology of an S1 fiber bundle over S2 with possible identifications along the fiber—lens space—or equivalently vanishing Bondi–News.) It is shown that Sα is a constant multiple of Pα, the total Bondi four-momentum, and if in addition the space-time admits a point at spacelike infinity, there is strong support for the past limit of Sα to be a null vector. This can be viewed as a generalization of Penrose’s result on the Pauli–Lubanski vector for classical zero rest-mass particles. The helicity operator at null infinity is rooted in the topology and turns out to be essentially the Hodge duality operator(*). The notion of duality appears as a global concept. Under such conditions, self- and anti-self-dual modes of the Weyl curvature could be viewed as states originating in the nontrivial topology. These results depend crucially on the presence of topological charges; it is tempting to speculate that such wormholes might be basic building blocks.

Electromagnetic, neutrino and gravitational fields in the Kasner space-time with rotational symmetry

The Hertz-Debye superpotential formalism has been applied to study the behaviour of the perturbative zero rest-mass fields, namely, the electromagnetic, massless neutrino and gravitational fields in the rotationally symmetric Kasner Universe. The formalism yields a single decoupled equation for the superpotential in each of the three cases. A considerable amount of information is obtained from these equations themselves and the equations are subjected to various methods of solution. The effects of anisotropy of the Kasner space-time on the superposed fields are analysed. The relative behaviour of the three fields is studied with the similarities and differences in their evolution being highlighted. Finally in the geometric optics approximation the propagation of the fields is compared with the null geodesics.

Scattering theory and the geometry of multitwistor spaces

Existing results which show the zero rest mass field equations to be encoded in the geometry of projective twistor space are extended, and it is shown that the geometries of spaces of more than one twistor contain information concerning the scattering of such fields. Some general constructions which describe spacetime interactions in terms of cohomology groups on subvarieties in twistor space are obtained and are used to construct a purely twistorial description of spacetime propagators and of first order ϕ 4 {\phi ^4} scattering. Spacetime expressions concerning these processes are derived from their twistor counterparts, and a physical interpretation is given for the twistor constructions.

Ultrageneralised complex analysis

The zero rest mass Euclidean Dirac equations in 2 (4) dimensions may be regarded as ‘square roots’ of the second order harmonic equation, and give rise to the crucial integral theorem and integral formula of complex (quaternionic) analysis. Recently discovered ‘2rth root’ equations for the 2rth order ‘harmonic’ equations are here shown to give rise to a similar integral theorem and integral formula.

Behaviour of scalar perturbations of a Reissner-Nordström black hole inside the event horizon

This paper considers general scalar perturbations of a Reissner-Nordstrdöm black hole and examines the qualitative behaviour of these perturbations in the region between and on the inner and outer horizons ( r - ≼ r ≼ r + ). Initial data are specified in terms of the ingoing radiation crossing the outer (event) horizon. The only essential restriction on these data is that the radiation should not die away too slowly on this horizon. The resultant perturbations are shown to be bounded and continuous. It is also shown that if ũ is any retarded null coordinate such that ũ = 0 on the event horizon, then the perturbations tend to zero along lines of constant radius as ũ ↓ 0. In particular, all these properties hold for pertur­bations on the inner horizon. For certain types of scalar field (including the zero rest mass scalar field) perturbations vanish at the crossover point on the inner horizon.

Instability of black hole inner horizons

Linear perturbations of black hole models by a variety of fields are considered. Perturbing fields include the zero rest mass scalar field in the case of Reissner-Nordstrom, and gravitational, electromagnetic and zero rest mass scalar perturbation in the case of the Kerr model. The analysis deals with the Ψ 0 components (in the Newman-Penrose (1962) formalism) of non-zero spin fields. The symmetry properties of the models are used to derive the crucial condition th at the field be singular on the inner horizon. This condition is independent of the field propagation equation. Initial data are then given in terms of incoming radiation from f - is shown that there exist wellbehaved initial data sets for which the resultant fields are singular on the inner horizon. It is emphasized that this instability result is dependent only on the global symmetries and causal structure of the models considered, and is independent of the precise nature of the perturbing field.

Existence and construction of neutrino fields with geodesic and shear-free rays and of other zero rest-mass fields in curved space-time

The Newman-Penrose formalism (1962) allows a unified treatment of unquantised Weyl neutrino fields with geodesic and shear-free rays (( kappa , sigma ) fields) and of other zero rest-mass fields of type null with different spin. Taking Robinson's theorem about Maxwell null fields as a starting point, the necessary and sufficient conditions for a space-time to admit a neutrino ( kappa , sigma ) field or another null-type zero rest-mass field are given. In addition, a method of construction is developed which relates null-type fields and neutrino ( kappa , sigma ) fields with other null-type fields of different spin or, in an empty space-time, with the background conformal tensor.

A nonstatic plane symmetric solution of Einstein's field equations for zero-rest mass scalar fields

An exact solution of Einstein's field equations of general relativity is given for a plane symmetric zero-rest-mass scalar field in the nonstatic case. The solution generalizes Singh's solution, which itself extends Taub's empty space-time.

Some zero rest mass test fields in general relativity

Zero rest mass test fields of pure algebraic type are defined and studied via the newly developed GHP formalism. The field equations are written explicitly and an immediate generalisation of Robinson's theorem is obtained. The form for the general zero rest mass test field of pure type is determined in terms of the tetrad components of the background Weyl spinor and an additional gauge dependent function which can be thought of as representing a test neutrino field.