50 research outputs found
Hamiltonian Formulation of Two Body Problem in Wheeler-Feynman electrodynamics
A Hamiltonian formulation for the classical problem of electromagnetic
interaction of two charged relativistic particles is found.Comment: 22 pages, 8 Uuencoded Postscript figure
Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics
In this article, we analyze the third of three papers, in which Einstein
presented his quantum theory of the ideal gas of 1924-1925. Although it failed
to attract the attention of Einstein's contemporaries and although also today
very few commentators refer to it, we argue for its significance in the context
of Einstein's quantum researches. It contains an attempt to extend and exhaust
the characterization of the monatomic ideal gas without appealing to
combinatorics. Its ambiguities illustrate Einstein's confusion with his initial
success in extending Bose's results and in realizing the consequences of what
later became to be called Bose-Einstein statistics. We discuss Einstein's
motivation for writing a non-combinatorial paper, partly in response to
criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments
are based on Einstein's belief in the complete analogy between the
thermodynamics of light quanta and of material particles and invoke
considerations of adiabatic transformations as well as of dimensional analysis.
These techniques were well-known to Einstein from earlier work on Wien's
displacement law, Planck's radiation theory, and the specific heat of solids.
We also investigate the possible role of Ehrenfest in the gestation of the
theory.Comment: 57 pp
Action at a distance as a full-value solution of Maxwell equations: basis and application of separated potential's method
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of
the examples related to the inconsistency of the conventional classical
electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe
the whole electromagnetic phenomena and the incompleteness of a set of
solutions of Maxwell equations are discussed and mathematically proved. Reasons
of the introduction of the so-called ``electrodynamics dualism concept"
(simultaneous coexistence of instantaneous Newton long-range and
Faraday-Maxwell short-range interactions) have been displayed. It is strictly
shown that the new concept presents itself as the direct consequence of the
complete set of Maxwell equations and makes it possible to consider classical
electrodynamics as a self-consistent and complete theory, devoid of inward
contradictions. In the framework of the new approach, all main concepts of
classical electrodynamics are reconsidered. In particular, a limited class of
motion is revealed when accelerated charges do not radiate electromagnetic
field.Comment: ReVTeX file, 24pp. Small corrections which do not have influence
results of the paper. Journal reference is adde
The Stern-Gerlach Experiment Revisited
The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment
of quantum physics providing evidence for several fundamental properties of
quantum systems. Based on today's knowledge we illustrate the different
benchmark results of the SGE for the development of modern quantum physics and
chemistry.
The SGE provided the first direct experimental evidence for angular momentum
quantization in the quantum world and thus also for the existence of
directional quantization of all angular momenta in the process of measurement.
It measured for the first time a ground state property of an atom, it produced
for the first time a `spin-polarized' atomic beam, it almost revealed the
electron spin. The SGE was the first fully successful molecular beam experiment
with high momentum-resolution by beam measurements in vacuum. This technique
provided a new kinematic microscope with which inner atomic or nuclear
properties could be investigated.
The original SGE is described together with early attempts by Einstein,
Ehrenfest, Heisenberg, and others to understand directional quantization in the
SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are
presented. The first realization of these proposals by Stern, Phipps, Frisch
and Segr\`e is described. The set-up suggested by Einstein can be considered an
anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which
the directional quantization process and possible interference effects of the
two different spin states are investigated.
In full agreement with the results of the new quantum theory directional
quantization appears as a general and universal feature of quantum
measurements. One experimental example for such directional quantization in
scattering processes is shown. Last not least, the early history of the
`almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig
Exact Solution of Photon Equation in Stationary G\"{o}del-type and G\"{o}del Space-Times
In this work the photon equation (massless Duffin-Kemmer-Petiau equation) is
written expilicitly for general type of stationary G\"{o}del space-times and is
solved exactly for G\"{o}del-type and G\"{o}del space-times. Harmonic
oscillator behaviour of the solutions is discussed and energy spectrum of
photon is obtained.Comment: 9 pages,RevTeX, no figure, revised for publicatio
Quantum Theory in Accelerated Frames of Reference
The observational basis of quantum theory in accelerated systems is studied.
The extension of Lorentz invariance to accelerated systems via the hypothesis
of locality is discussed and the limitations of this hypothesis are pointed
out. The nonlocal theory of accelerated observers is briefly described.
Moreover, the main observational aspects of Dirac's equation in noninertial
frames of reference are presented. The Galilean invariance of nonrelativistic
quantum mechanics and the mass superselection rule are examined in the light of
the invariance of physical laws under inhomogeneous Lorentz transformations.Comment: 25 pages, no figures, contribution to Springer Lecture Notes in
Physics (Proc. SR 2005, Potsdam, Germany, February 13 - 18, 2005
Spin, gravity, and inertia
The gravitational effects in the relativistic quantum mechanics are
investigated. The exact Foldy-Wouthuysen transformation is constructed for the
Dirac particle coupled to the static spacetime metric. As a direct application,
we analyze the non-relativistic limit of the theory. The new term describing
the specific spin (gravitational moment) interaction effect is recovered in the
Hamiltonian. The comparison of the true gravitational coupling with the purely
inertial case demonstrates that the spin relativistic effects do not violate
the equivalence principle for the Dirac fermions.Comment: Revtex, 12 pages, no figures, accepted in Phys. Rev. Let