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 sector have the same critical speed in vacuum, will then be an expression of a fundamental sectorial symmetry (e.g. preonic grand unification or extended supersymmetry) protecting a parameter of the equations of motion. We study the breaking of Lorentz invariance in such a scenario, with emphasis on mixing between the "ordinary" sector and a superluminal sector, and discuss with examples the consequences of existing data. The sectorial universality of the value of the high-energy speed in vacuum, even exact, does not necessarily imply that Lorentz invariance is not violated and does not by itself exclude the possibility to produce superluminal particles at accelerators or to find them in experiments devoted to high-energy cosmic rays. Similarly, the stringent experimental bounds on Lorentz symmetry violation at low energy cannot be extrapolated to high-energy phenomena. Several basic questions related to possible effects of Lorentz symmetry violation are discussed, and potential signatures are examined.
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 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) $k$ (wav…
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…
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 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 …
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.
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…
Motivated by increased interest in experiments in which light appears to propagate by tunnelling at superluminal velocity, the Lorentz invariant theory proposed by Partha Ghose to explain these surprising effects is revisited. This theory is based on the Harish-Chandra formalism, which describes the relativistic dynamics of a massless spin-1 boson, like a photon. Via this formalism, the Bohmian average transport velocity of the electromagnetic energy is formulated. It is proved that, if the dielectric making the waveguide is nonabsorptive and nondispersive, this velocity can be superluminal. T…
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…
We show that starting with the addition law of parallel speeds derived as a consequence of the invariance of the speed of light, the Lorentz transformations for the space-time coordinates can be derived.
We show that the transformation equations for the parameters that characterize a plane acoustic wave: period, (frequency), wave vector, wave length and phase velocity can be derived without using phase invariance and Lorentz-Einstein transformation
Introducing the primed inertial coordinate system, for each inertial frame of reference, in addition to the usual inertial coordinate system, we assume that gravity-free space and time possess the Euclidean structures in the primed inertial coordinate system and the generalized Finslerian structures in the usual inertial coordinate system. We combine these assumptions with two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, to derive the localized Lorentz transformation as a linear transformation between …
