66 research outputs found
Operational indistinguishably of varying speed of light theories
The varying speed of light theories have been recently proposed to solve the
standard model problems and anomalies in the ultra high energy cosmic rays.
These theories try to formulate a new relativity with no assumptions about the
constancy of the light speed. In this regard, we study two theories and want to
show that these theories are not the new theories of relativity, but only
re-descriptions of Einstein's special relativity.Comment: 5 pages, 2 figures, title changed, minor changes in notations and
formulae, a paragraph added, Int. J. Mod. Phys. D (in press) v
A Note on the correspondence between Qubit Quantum Operations and Special Relativity
We exploit a well-known isomorphism between complex hermitian
matrices and , which yields a convenient real vector
representation of qubit states. Because these do not need to be normalized we
find that they map onto a Minkowskian future cone in , whose
vertical cross-sections are nothing but Bloch spheres. Pure states are
represented by light-like vectors, unitary operations correspond to special
orthogonal transforms about the axis of the cone, positive operations
correspond to pure Lorentz boosts. We formalize the equivalence between the
generalized measurement formalism on qubit states and the Lorentz
transformations of special relativity, or more precisely elements of the
restricted Lorentz group together with future-directed null boosts. The note
ends with a discussion of the equivalence and some of its possible
consequences.Comment: 6 pages, revtex, v3: revised discussio
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
Relative entropy, Haar measures and relativistic canonical velocity distributions
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS)
entropy is reconsidered by combining elements from group and measure theory.
Our analysis starts by noting that the BGS entropy is a special case of
relative entropy. The latter characterizes probability distributions with
respect to a pre-specified reference measure. To identify the canonical BGS
entropy with a relative entropy is appealing for two reasons: (i) the maximum
entropy principle assumes a coordinate invariant form; (ii) thermodynamic
equilibrium distributions, which are obtained as solutions of the maximum
entropy problem, may be characterized in terms of the transformation properties
of the underlying reference measure (e.g., invariance under group
transformations). As examples, we analyze two frequently considered candidates
for the one-particle equilibrium velocity distribution of an ideal gas of
relativistic particles. It becomes evident that the standard J\"uttner
distribution is related to the (additive) translation group on momentum space.
Alternatively, imposing Lorentz invariance of the reference measure leads to a
so-called modified J\"uttner function, which differs from the standard
J\"uttner distribution by a prefactor, proportional to the inverse particle
energy.Comment: 15 pages: extended version, references adde
Uniqueness of the mass in the radiating regime
The usual approaches to the definition of energy give an ambiguous result for
the energy of fields in the radiating regime. We show that for a massless
scalar field in Minkowski space-time the definition may be rendered unambiguous
by adding the requirement that the energy cannot increase in retarded time. We
present a similar theorem for the gravitational field, proved elsewhere, which
establishes that the Trautman-Bondi energy is the unique (up to a
multiplicative factor) functional, within a natural class, which is monotonic
in time for all solutions of the vacuum Einstein equations admitting a smooth
``piece'' of conformal null infinity Scri.Comment: 8 pages, revte
Relativistic entanglement of two particles driven by continuous product momenta
In this paper we explore the entanglement of two relativistic spin-1/2 particles with continuous momenta. The spin state is described by the Bell state and the momenta are given by Gaussian distributions of product form. Transformations of the spins are systematically investigated in different boost scenarios by calculating the orbits and concurrence of the spin degree of freedom. By visualizing the behavior of the spin state we get further insight into how and why the entanglement changes in different boost situations
A Lorentz-Poincar\'e type interpretation of the Weak Equivalence Principle
The validity of the Weak Equivalence Principle relative to a local inertial
frame is detailed in a scalar-vector gravitation model with Lorentz-Poincar\'e
type interpretation. Given the previously established first Post-Newtonian
concordance of dynamics with General Relativity, the principle is to this order
compatible with GRT. The gravitationally modified Lorentz transformations, on
which the observations in physical coordinates depend, are shown to provide a
physical interpretation of \emph{parallel transport}. A development of
``geodesic'' deviation in terms of the present model is given as well.Comment: v1: 9 pages, 2 figures, v2: version to appear in International
Journal of Theoretical Physic
Relativistic Chasles' theorem and the conjugacy classes of the inhomogeneous Lorentz group
This work is devoted to the relativistic generalization of Chasles' theorem,
namely to the proof that every proper orthochronous isometry of Minkowski
spacetime, which sends some point to its chronological future, is generated
through the frame displacement of an observer which moves with constant
acceleration and constant angular velocity. The acceleration and angular
velocity can be chosen either aligned or perpendicular, and in the latter case
the angular velocity can be chosen equal or smaller than than the acceleration.
We start reviewing the classical Euler's and Chasles' theorems both in the Lie
algebra and group versions. We recall the relativistic generalization of
Euler's theorem and observe that every (infinitesimal) transformation can be
recovered from information of algebraic and geometric type, the former being
identified with the conjugacy class and the latter with some additional
geometric ingredients (the screw axis in the usual non-relativistic version).
Then the proper orthochronous inhomogeneous Lorentz Lie group is studied in
detail. We prove its exponentiality and identify a causal semigroup and the
corresponding Lie cone. Through the identification of new Ad-invariants we
classify the conjugacy classes, and show that those which admit a causal
representative have special physical significance. These results imply a
classification of the inequivalent Killing vector fields of Minkowski spacetime
which we express through simple representatives. Finally, we arrive at the
mentioned generalization of Chasles' theorem.Comment: Latex2e, 49 pages. v2: few typos correcte
Semiclassical approximation to supersymmetric quantum gravity
We develop a semiclassical approximation scheme for the constraint equations
of supersymmetric canonical quantum gravity. This is achieved by a
Born-Oppenheimer type of expansion, in analogy to the case of the usual
Wheeler-DeWitt equation. The formalism is only consistent if the states at each
order depend on the gravitino field. We recover at consecutive orders the
Hamilton-Jacobi equation, the functional Schrodinger equation, and quantum
gravitational correction terms to this Schrodinger equation. In particular, the
following consequences are found:
(i) the Hamilton-Jacobi equation and therefore the background spacetime must
involve the gravitino, (ii) a (many fingered) local time parameter has to be
present on (the space of all possible tetrad and gravitino
fields), (iii) quantum supersymmetric gravitational corrections affect the
evolution of the very early universe. The physical meaning of these equations
and results, in particular the similarities to and differences from the pure
bosonic case, are discussed.Comment: 34 pages, clarifications added, typos correcte
Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates
The conservative dynamics of two point masses given in harmonic coordinates
up to the third post-Newtonian (3pN) order is treated within the framework of
constrained canonical dynamics. A representation of the approximate Poincar\'e
algebra is constructed with the aid of Dirac brackets. Uniqueness of the
generators of the Poincar\'e group resp. the integrals of motion is achieved by
imposing their action on the point mass coordinates to be identical with that
of the usual infinitesimal Poincar\'e transformations. The second
post-Coulombian approximation to the dynamics of two point charges as predicted
by Feynman-Wheeler electrodynamics in Lorentz gauge is treated similarly.Comment: 42 pages, submitted to Phys. Rev.
- …