125 research outputs found
On the emergence of Lorentzian signature and scalar gravity
In recent years, a growing momentum has been gained by the emergent gravity
framework. Within the latter, the very concepts of geometry and gravitational
interaction are not seen as elementary aspects of Nature but rather as
collective phenomena associated to the dynamics of more fundamental objects. In
this paper we want to further explore this possibility by proposing a model of
emergent Lorentzian signature and scalar gravity. Assuming that the dynamics of
the fundamental objects can give rise in first place to a Riemannian manifold
and a set of scalar fields we show how time (in the sense of hyperbolic
equations) can emerge as a property of perturbations dynamics around some
specific class of solutions of the field equations. Moreover, we show that
these perturbations can give rise to a spin-0 gravity via a suitable
redefinition of the fields that identifies the relevant degrees of freedom. In
particular, we find that our model gives rise to Nordstrom gravity. Since this
theory is invariant under general coordinate transformations, this also shows
how diffeomorphism invariance (albeit of a weaker form than the one of general
relativity) can emerge from much simpler systems.Comment: 10 pages, revtex4. Replaced with the published versio
Subluminal OPERA Neutrinos
The OPERA collaboration has announced to have observed superluminal neutrinos
with a mean energy 17.5 GeV, but afterward the superluminal interpretation of
the OPERA results has been refuted theoretically by Cherenkov-like radiation
and pion decay. In a recent work, we have proposed a kinematical resolution to
this problem. A key idea in our resolution is that the OPERA neutrinos are not
superluminal but subluminal since they travel faster than the observed speed of
light in vacuum on the earth while they do slower than the true speed of light
in vacuum determining the causal structure of events. In this article, we dwell
upon our ideas and present some concrete models, which realize our ideas, based
on spin 0, 1 and 2 bosonic fields. We also discuss that the principle of
invariant speed of light in special relativity can be replaced with the
principle of a universal limiting speed.Comment: 17 page
Space-Time Exchange Invariance: Special Relativity as a Symmetry Principle
Special relativity is reformulated as a symmetry property of space-time: Space-Time Exchange Invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the traditional form of the Principle of Special Relativity. The kinematical version of the latter is shown to be a consequence of the Lorentz transformation. As a dynamical application, the laws of electrodynamics and magnetodynamics are derived from those of electrostatics and magnetostatics respectively. The 4-vector nature of the electromagnetic potential plays a crucial role in the last two derivations
Nothing but Relativity, Redux
Here we show how spacetime transformations consistent with the principle of
relativity can be derived without an explicit assumption of the constancy of
the speed of light, without gedanken experiments involving light rays, and
without an assumption of differentiability, or even continuity, for the
spacetime mapping. Hence, these historic results could have been derived
centuries ago, even before the advent of calculus. This raises an interesting
question: Could Galileo have derived Einsteinian relativity
Foundations of anisotropic relativistic mechanics
We lay down the foundations of particle dynamics in mechanical theories that
satisfy the relativity principle and whose kinematics can be formulated
employing reference frames of the type usually adopted in special relativity.
Such mechanics allow for the presence of anisotropy, both conventional (due to
non-standard synchronisation protocols) and real (leading to detectable
chronogeometrical effects, independent of the choice of synchronisation). We
give a general method for finding the fundamental dynamical quantities
(Lagrangian, energy and momentum), and write their explicit expression in all
the kinematics compatible with the basic requirements. We also write the
corresponding dispersion relations and outline a formulation of these theories
in terms of a pseudo-Finslerian spacetime geometry. Although the treatment is
restricted to the case of one spatial dimension, an extension to three
dimensions is almost straightforward.Comment: 41 pages, 4 figure
Velocity of Light in Dark Matter with Charge
We propose an interesting mechanism to reconcile the recent experiments of
the Michelson-Morley type and slowdown of the velocity of light in dark matter
with a fractional electric charge when the index of refraction of dark matter
depends on the frequency of a photon. After deriving the formula for the
velocity of light in a medium with the index of refraction in a
relativistic regime, it is shown that the local anisotropy of the light speed
is proportional to the second order in . This result implies
that the experiments of the Michelson-Morley type do not give rise to a
stringent constraint on the slowdown of the velocity of light in dark matter
with electric charge.Comment: 10 page
Getting the Lorentz transformations without requiring an invariant speed
The structure of the Lorentz transformations follows purely from the absence
of privileged inertial reference frames and the group structure (closure under
composition) of the transformations---two assumptions that are simple and
physically necessary. The existence of an invariant speed is \textit{not} a
necessary assumption, and in fact is a consequence of the principle of
relativity (though the finite value of this speed must, of course, be obtained
from experiment). Von Ignatowsky derived this result in 1911, but it is still
not widely known and is absent from most textbooks. Here we present a
completely elementary proof of the result, suitable for use in an introductory
course in special relativity.Comment: 4 pages, 1 figur
Faster-than-c signals, special relativity, and causality
Motivated by the recent attention on superluminal phenomena, we investigate
the compatibility between faster-than-c propagation and the fundamental
principles of relativity and causality. We first argue that special relativity
can easily accommodate -- indeed, does not exclude -- faster-than-c signalling
at the kinematical level. As far as causality is concerned, it is impossible to
make statements of general validity, without specifying at least some features
of the tachyonic propagation. We thus focus on the Scharnhorst effect
(faster-than-c photon propagation in the Casimir vacuum), which is perhaps the
most plausible candidate for a physically sound realization of these phenomena.
We demonstrate that in this case the faster-than-c aspects are ``benign'' and
constrained in such a manner as to not automatically lead to causality
violations.Comment: Plain LaTeX2E; 25 pages; 4 embedded figures (LaTeX pictures). V2:
Some discussion clarified, minor rearrangements, references updated, no
change in physics conclusions. To appear in Annals of Physic
Apparent superluminal advancement of a single photon far beyond its coherence length
We present experimental results relative to superluminal propagation based on
a single photon traversing an optical system, called 4f-system, which acts
singularly on the photon's spectral component phases. A single photon is
created by a CW laser light down{conversion process. The introduction of a
linear spectral phase function will lead to the shift of the photon peak far
beyond the coherence length of the photon itself (an apparent superluminal
propagation of the photon). Superluminal group velocity detection is done by
interferometric measurement of the temporal shifted photon with its correlated
untouched reference. The observed superluminal photon propagation complies with
causality. The operation of the optical system allows to enlighten the origin
of the apparent superluminal photon velocity. The experiment foresees a
superluminal effect with single photon wavepackets.Comment: 11 pages, 2 figure
Deriving relativistic momentum and energy
We present a new derivation of the expressions for momentum and energy of a
relativistic particle. In contrast to the procedures commonly adopted in
textbooks, the one suggested here requires only the knowledge of the
composition law for velocities along one spatial dimension, and does not make
use of the concept of relativistic mass, or of the formalism of four-vectors.
The basic ideas are very general and can be applied also to kinematics
different from the Newtonian and Einstein ones, in order to construct the
corresponding dynamics.Comment: 15 pages, 2 figure
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