If textbook Lorentz invariance is actually a property of the equations describing a sector of the excitations of vacuum above some critical distance scale, several sectors of matter with different critical speeds in vacuum can coexist and an absolute rest frame (the vacuum rest frame) may exist without contradicting the apparent Lorentz invariance felt by "ordinary" particles (particles with critical speed in vacuum equal to $c$ , the speed of light). The sectorial Lorentz symmetry may be only a low-energy limit, in the same way as the relation $ω$ (frequency) = $c_s$ (speed of sound) $k$ (wave vector) holds for low-energy phonons in a crystal. We study the consequences of such a scenario, using an ansatz inspired by the Bravais lattice as a model for some vacuum properties. It then turns out that: a) the Greisen-Zatsepin-Kuzmin cutoff on high-energy cosmic protons and nuclei does no longer apply; b) high-momentum unstable particles have longer lifetimes than expected with exact Lorentz invariance, and may even become stable at the highest observed cosmic ray energies or slightly above. Some cosmological implications of superluminal particles are also discussed.
Although Lorentz symmetry has been tested at low energy with extremely good accuracy, its validity at very high energy is much less well established. If Lorentz symmetry violation (LSV) is energy-dependent (e.g. $\propto E^2$), it can be of order 1 at Planck scale and undetectable at GeV scale or below. Similarly, superluminal particles with positive mass and energy (superbradyons) can exist and be the ultimate building blocks of matter. We discuss a few cosmological consequences of such a scenario, as well as possible experimental tests.
The recent measurement of the neutrino velocity with the OPERA detector in the CNGS beam, on whose basis it was found that (v-c)/c = (2.48 \pm 0.28 (stat.) \pm 0.30 (sys.)) 10e-5, does not contain any significant violation of Local Lorentz Invariance (LLI), since the corresponding value of the parameter delta=(u/c)^2-1, that represents the upper limit of the breakdown of LLI, is at least three orders of magnitude higher than the known lower limit reported in literature and is compatible with the values estimated by other experiments carried out so far.
If textbook Lorentz invariance is actually a property of the equations describing a sector of matter above some critical distance scale, several sectors of matter with different critical speeds in vacuum can coexist and an absolute rest frame (the vacuum rest frame, possibly related to the local rest frame of the expanding Universe) may exist without contradicting the apparent Lorentz invariance felt by "ordinary" particles (particles with critical speed in vacuum equal to $c$ , the speed of light). Sectorial Lorentz invariance, reflected by the fact that all particles of a given dynamical sec…
While the OPERA experimental scrutiny is ongoing in the community, in the present article we construct a toy model of {\it extended Lorentz code} (ELC) of the uniform motion, which will be a well established consistent and unique theoretical framework to explain the apparent violations of the standard Lorentz code (SLC), the possible manifestations of which arise in a similar way in all particle sectors. We argue that in the ELC-framework the propagation of the superluminal particle, which implies the modified dispersion relation, could be consistent with causality. Furthermore, in this framew…
If textbook Lorentz invariance is actually a property of the equations describing a sector of the excitations of vacuum above some critical distance scale, several sectors of matter with different critical speeds in vacuum can coexist and an absolute rest frame (the vacuum rest frame) may exist without contradicting the apparent Lorentz invariance felt by "ordinary" particles (particles with critical speed in vacuum equal to $c$, the speed of light). Sectorial Lorentz invariance, reflected by the fact that all particles of a given dynamical sector have the same critical speed in vacuum, will t…
Since some experiments have found superluminality, we assume that the particles in the universe are divided into three classes: the subluminal, luminal and superluminal particles by the speed of light, their energy-momenum relations are E2 = m2c4 + c2p2, E2 = c2p2, and E2 + m2c4 = c2p2, respectively. The Einstein's theory of relativity still holds and is consummated by the existence of superluminal particles, and the Lorentz symmetry of the spacetime is also not violated. There should have two sets of inertial reference systems: subluminal and superluminal reference systems. Two inertial refer…
If textbook Lorentz invariance is actually a property of the equations describing a sector of matter above some critical distance scale, several sectors of matter with different critical speeds in vacuum can coexist and an absolute rest frame (the vacuum rest frame, possibly related to the local rest frame of the expanding Universe) may exist without contradicting the apparent Lorentz invariance felt by "ordinary" particles (particles with critical speed in vacuum equal to c , the speed of light). The real geometry of space-time will then be different from standard Lorentz invariance, and the …
First, some superluminal phenomena and experiments are introduced briefly. Next, based on the basic principles of the special relativity, the Lorentz transformation (LT) with smaller velocity and the general Lorentz transformation (GLT) with larger velocity should be derived simultaneously by the classification of the timelike and the spacelike intervals. In deriving LT, an additional independent hypothesis has been used, thus the values of velocity are restricted absolutely, and the spacelike interval is excluded. LT and GLT are connected by the de Broglie relation. The fundamental properties…
If textbook Lorentz invariance is actually a property of the equations describing a sector of the excitations of vacuum above some critical distance scale, several sectors of matter with different critical speeds in vacuum can coexist and an absolute rest frame (the vacuum rest frame) may exist without contradicting the apparent Lorentz invariance felt by "ordinary" particles (particles with critical speed in vacuum equal to $c$, the speed of light). Sectorial Lorentz invariance, reflected by the fact that all particles of a given dynamical sector have the same critical speed in vacuum, will t…
In this paper, we consider the apparent superluminal speed of neutrinos in their travel from CERN to Gran Susso, as measured by the OPERA experiment, within the framework of the Extended Lorentz Transformation Model. The model is based on a natural extension of Lorentz transformation by wick rotation. Scalar and Dirac's fields are considered and invariance under the new lorentz group is discussed. Moreover, an extension of quantum mechanics to accommodate new particles is considered using the newly proposed Generalized-$\mathbb{C}$ quantum mechanics. A two dimensional representation of the new…
Lorentz symmetry has been tested at low energy with great accuracy, but its extrapolation to very high-energy phenomena is much less well established. We expect a possible breaking of Lorentz symmetry to be a very high energy and very short distance phenomenon, compatible with existing data. If textbook special relativity is only an approximate property of the equations describing a sector of matter above some critical distance scale, superluminal sectors of matter may exist related to new degrees of freedom not yet discovered experimentally. The new superluminal particles ("superbradyons") wo…
Some arguments in favour of the existence of tachyons and extensions of the Lorentz Group are presented. On the former, it is observed that with a slight modification to standard electromagnetic theory a single superluminal charge will bind to itself in a self-sustaining circular orbit, suggestive of a (modified) electromagnetic interpretation of the strong force. Symmetries in that theory are used in the subsequent analysis as a starting point in the search for physically-motivated extensions of the Lorentz Group. There is some discussion of the validity of imaginary coordinates in superlumin…
The significance of the Lorentz gauge as a constraint on solutions of Maxwellian waves is discussed. It is proved that recent claims of superluminal propagation of electromagnetic waves rely on an erroneous basis.
The Poincaré relativity principle has been tested at low energy with great accuracy, but its extrapolation to very high-energy phenomena is much less well established. Lorentz symmetry can be broken at Planck scale due to the renormalization of gravity or to some deeper structure of matter: we expect such a breaking to be a very high energy and very short distance phenomenon. If textbook special relativity is only an approximate property of the equations describing a sector of matter above some critical distance scale, an absolute local frame (the "vacuum rest frame", VRF) can possibly be foun…
Recent experiments by OPERA with high energy neutrinos, as well as astrophysics observation data, may possibly prove violations of underlying principles of special relativity theory. This paper attempts to present an elementary modification of relativistic mechanics that is consistent both with the principles of mechanics and with Dirac's approach to derivation of relativistic quantum equations. Our proposed hyper-relativistic model is based on modified dispersion relations between energy and momentum of a particle. Predictions of the new theory significantly differ from the standard model, as…
First, we extend the special relativity into the superluminal case and put forward a superluminal theory of kinematics, in which we show that the temporal coordinate need exchanging with one of the spatial coordinates in a superluminal inertial frame, and that the coordinate transformations from any superluminal inertial frame to the rest frame (here rest just says in a relative sense) are the same as the Lorentz transformations from some normal inertial frame to the rest frame. Consequently, the causality can not be violated. Secondly, we investigate the superluminal theory of dynamics and fi…
In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in terms of the ordinary, so-called "X-shaped waves". Moeover, by the present formalism we obtain the first analytical localized Superluminal approximate solutions which represent beams propagating in dispersive media. Our solutions may find application in different fields, like optics, microwaves, radio waves, and so on. [PACS nos.: 03.50.De ; 41.20.Jb ; 83.50.…
All Lorentz invariant solutions of vacuum Einstein's equations are found. It is proved that these solutions describe space-times of constant curvature.
Modification of special theory of relativity is proposed to describe the propagation of signals with superluminal velocity. Modified kinematics and Lorentz transformations of Maxwell's equations are described. A possible experiment on measuring the speed of light for verification of the theory is discussed. It is shown that replacing the maximum speed in special theory of relativity by the neutrino superluminal velocity measured by the OPERA collaboration leads to lower value of the muon mass reconstructed from the muon decay products with the modified relativistic kinematics. This value is in…
The modified Lorentz transformation of a distance-dependent special theory of relativity - which will be briefly summarized - predicts the possibility of superluminal velocity of very distantly moving material bodies to be connected with the generation of Cerencov radiation off the quantum vacuum. It is shown that vacuum Cerencov radiation due to the superluminal propagation of extraterrestrial spaceprobes in the interstellar space would account for all known properties of gamma ray bursts (GRBs) and the "afterglow" at lower frequencies. Distances and other parameter prove to be calculable and…
Applying a non-diagonal spherically symmetric tetrad field having arbitrary function, $S(r)$, that is corresponding to local Lorentz transformation, to the field equations of f(T) gravity theories. An analytic vacuum solutions with constants of integration are derived. These constants are studied by calculating the total conserved charge associated to each solution. The study has shown that the obtained solutions represent Schwarzschild-Ads spacetime.
