247 research outputs found
Deriving relativistic momentum and energy. II. Three-dimensional case
We generalise a recent derivation of the relativistic expressions for
momentum and kinetic energy from the one-dimensional to the three-dimensional
case.Comment: 7 page
The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited
We study the effect of the cosmological constant on the bending of
light by a concentrated spherically symmetric mass. Contrarily to previous
claims, we show that when the Schwarzschild-de Sitter geometry is taken into
account, does indeed contribute to the bending.Comment: 5 pages, 2 figure
Relativistic Hall Effect
We consider the relativistic deformation of quantum waves and mechanical
bodies carrying intrinsic angular momentum (AM). When observed in a moving
reference frame, the centroid of the object undergoes an AM-dependent
transverse shift. This is the relativistic analogue of the spin Hall effect,
which occurs in free space without any external fields. Remarkably, the shifts
of the geometric and energy centroids differ by a factor of 2, and both
centroids are crucial for the correct Lorentz transformations of the AM tensor.
We examine manifestations of the relativistic Hall effect in quantum vortices,
and mechanical flywheels, and also discuss various fundamental aspects of this
phenomenon. The perfect agreement of quantum and relativistic approaches allows
applications at strikingly different scales: from elementary spinning
particles, through classical light, to rotating black-holes.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let
Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant
The contribution of the cosmological constant to the deflection angle and the
time delays are derived from the integration of the gravitational potential as
well as from Fermat's Principle. The findings are in agreement with recent
results using exact solutions to Einstein's equations and reproduce precisely
the new -term in the bending angle and the lens equation. The
consequences on time delay expressions are explored. While it is known that
contributes to the gravitational time delay, it is shown here that a
new -term appears in the geometrical time delay as well. Although
these newly derived terms are perhaps small for current observations, they do
not cancel out as previously claimed. Moreover, as shown before, at galaxy
cluster scale, the contribution can be larger than the second-order
term in the Einstein deflection angle for several cluster lens systems.Comment: 6 pages, 1 figure, matches version published in PR
The equivalence principle, uniformly accelerated reference frames, and the uniform gravitational field
The relationship between uniformly accelerated reference frames in flat
spacetime and the uniform gravitational field is examined in a relativistic
context. It is shown that, contrary to previous statements in the pages of this
journal, equivalence does not break down in this context. No restrictions to
Newtonian approximations or small enclosures are necessary
Reciprocal relativity of noninertial frames: quantum mechanics
Noninertial transformations on time-position-momentum-energy space {t,q,p,e}
with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and
the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of
transformations contains the Lorentz group as the inertial special case. In the
limit of small forces and velocities, it reduces to the expected Hamilton
transformations leaving invariant the symplectic metric and the nonrelativistic
line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by
c and relative forces by b. Spacetime is no longer an invariant subspace but is
relative to noninertial observer frames. Born was lead to the metric by a
concept of reciprocity between position and momentum degrees of freedom and for
this reason we call this reciprocal relativity.
For large b, such effects will almost certainly only manifest in a quantum
regime. Wigner showed that special relativistic quantum mechanics follows from
the projective representations of the inhomogeneous Lorentz group. Projective
representations of a Lie group are equivalent to the unitary reprentations of
its central extension. The same method of projective representations of the
inhomogeneous U(1,3) group is used to define the quantum theory in the
noninertial case. The central extension of the inhomogeneous U(1,3) group is
the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the
Weyl-Heisenberg group. A set of second order wave equations results from the
representations of the Casimir operators
Fields of accelerated sources: Born in de Sitter
This paper deals thoroughly with the scalar and electromagnetic fields of
uniformly accelerated charges in de Sitter spacetime. It gives details and
makes various extensions of our Physical Review Letter from 2002. The basic
properties of the classical Born solutions representing two uniformly
accelerated charges in flat spacetime are first summarized. The worldlines of
uniformly accelerated particles in de Sitter universe are defined and described
in a number of coordinate frames, some of them being of cosmological
significance, the other are tied naturally to the particles. The scalar and
electromagnetic fields due to the accelerated charges are constructed by using
conformal relations between Minkowski and de Sitter space. The properties of
the generalized `cosmological' Born solutions are analyzed and elucidated in
various coordinate systems. In particular, a limiting procedure is demonstrated
which brings the cosmological Born fields in de Sitter space back to the
classical Born solutions in Minkowski space. In an extensive Appendix, which
can be used independently of the main text, nine families of coordinate systems
in de Sitter spacetime are described analytically and illustrated graphically
in a number of conformal diagrams.Comment: 37 pages, 23 figures, reformatted version of the paper published in
JMP; low-resolution figures due to arXiv size restrictions; for the version
with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers
Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics
When ground state atoms are accelerated through a high Q microwave cavity,
radiation is produced with an intensity which can exceed the intensity of Unruh
acceleration radiation in free space by many orders of magnitude. The cavity
field at steady state is described by a thermal density matrix under most
conditions. However, under some conditions gain is possible, and when the atoms
are injected in a regular fashion, the radiation can be produced in a squeezed
state
Charges and fields in a current-carrying wire
Charges and fields in a straight, infinite, cylindrical wire carrying a
steady current are determined in the rest frames of ions and electrons,
starting from the standard assumption that the net charge per unit length is
zero in the lattice frame and taking into account a self-induced pinch effect.
The analysis presented illustrates the mutual consistency of classical
electromagnetism and Special Relativity. Some consequences of the assumption
that the net charge per unit length is zero in the electrons frame are also
briefly discussed
Classical 5D fields generated by a uniformly accelerated point source
Gauge fields associated with the manifestly covariant dynamics of particles
in spacetime are five-dimensional. In this paper we explore the old
problem of fields generated by a source undergoing hyperbolic motion in this
framework. The 5D fields are computed numerically using absolute time
-retarded Green-functions, and qualitatively compared with Maxwell fields
generated by the same motion. We find that although the zero mode of all fields
coincides with the corresponding Maxwell problem, the non-zero mode should
affect, through the Lorentz force, the observed motion of test particles.Comment: 36 pages, 8 figure
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