452 research outputs found
Can Maxwell's equations be obtained from the continuity equation?
We formulate an existence theorem that states that given localized scalar and
vector time-dependent sources satisfying the continuity equation, there exist
two retarded fields that satisfy a set of four field equations. If the theorem
is applied to the usual electromagnetic charge and current densities, the
retarded fields are identified with the electric and magnetic fields and the
associated field equations with Maxwell's equations. This application of the
theorem suggests that charge conservation can be considered to be the
fundamental assumption underlying Maxwell's equations.Comment: 14 pages. See the comment: "O. D. Jefimenko, Causal equations for
electric and magnetic fields and Maxwell's equations: comment on a paper by
Heras [Am. J. Phys. 76, 101 (2008)].
The general relativistic infinite plane
Uniform fields are one of the simplest and most pedagogically useful examples
in introductory courses on electrostatics or Newtonian gravity. In general
relativity there have been several proposals as to what constitutes a uniform
field. In this article we examine two metrics that can be considered the
general relativistic version of the infinite plane with finite mass per unit
area. The first metric is the 4D version of the 5D "brane" world models which
are the starting point for many current research papers. The second case is the
cosmological domain wall metric. We examine to what extent these different
metrics match or deviate from our Newtonian intuition about the gravitational
field of an infinite plane. These solutions provide the beginning student in
general relativity both computational practice and conceptual insight into
Einstein's field equations. In addition they do this by introducing the student
to material that is at the forefront of current research.Comment: Accepted for publication in the American Journal of Physic
Using the Uncharged Kerr Black Hole as a Gravitational Mirror
We extend the study of the possibility to use the Schwarzschild black hole as
a gravitational mirror to the more general case of an uncharged Kerr black
hole. We use the null geodesic equation in the equatorial plane to prove a
theorem concerning the conditions the impact parameter has to satisfy if there
shall exist boomerang photons. We derive an equation for these boomerang
photons and an equation for the emission angle. Finally, the radial null
geodesic equation is integrated numerically in order to illustrate boomerang
photons.Comment: 11 pages Latex, 3 Postscript figures, uufiles to compres
Gravitational coupling to two-particle bound states and momentum conservation in deep inelastic scattering
The momentum conservation sum rule for deep inelastic scattering (DIS) from
composite particles is investigated using the general theory of relativity. For
two 1+1 dimensional examples, it shown that covariant theories automatically
satisy the DIS momentum conservation sum rule provided the bound state is
covariantilly normalized. Therefore, in these cases the two DIS sum rules for
baryon conservation and momentum conservation are equivalent
Bohmian Quantum Gravity in the Linear Field Approximation
In this paper we have applied Bohmian quantum theory to the linear field
approximation of gravity and present a self--consistent quantum gravity theory
in the linear field approximation. The theory is then applied to some specific
problems, the Newtonian limit, and the static spherically symmetric solution.
Some observable effects of the theory are investigated
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
Expansion-induced contribution to the precession of binary orbits
We point out the existence of new effects of global spacetime expansion on
local binary systems. In addition to a possible change of orbital size, there
is a contribution to the precession of elliptic orbits, to be added to the
well-known general relativistic effect in static spacetimes, and the
eccentricity can change. Our model calculations are done using geodesics in a
McVittie metric, representing a localized system in an asymptotically
Robertson-Walker spacetime; we give a few numerical estimates for that case,
and indicate ways in which the model should be improved.Comment: revtex, 7 pages, no figures; revised for publication in Classical and
Quantum Gravity, with minor changes in response to referees' comment
What is the topology of a Schwarzschild black hole?
We investigate the topology of Schwarzschild's black hole through the
immersion of this space-time in spaces of higher dimension. Through the
immersions of Kasner and Fronsdal we calculate the extension of the
Schwarzschild's black hole.Comment: 7 pages. arXiv admin note: substantial text overlap with
arXiv:1102.446
Formal analogies between gravitation and electrodynamics
We develop a theoretical framework that allows us to compare electromagnetism
and gravitation in a fully covariant way. This new scenario does not rely on
any kind of approximation nor associate objects with different operational
meaning as it's sometime done in the literature. We construct the
electromagnetic analogue to the Riemann and Weyl tensors and develop the
equations of motion for these objects. In particular, we are able to identify
precisely how and in what conditions gravity can be mapped to electrodynamics.
As a consequence, many of the gemometrical tools of General Relativity can be
applied to Electromagnetism and vice-versa. We hope our results would shed new
light in the nature of electromagnetic and gravitational theories.Comment: 9pages, submitted to General Relativity and Gravitatio
A Deeper Look at Student Learning of Quantum Mechanics: the Case of Tunneling
We report on a large-scale study of student learning of quantum tunneling in
4 traditional and 4 transformed modern physics courses. In the transformed
courses, which were designed to address student difficulties found in previous
research, students still struggle with many of the same issues found in other
courses. However, the reasons for these difficulties are more subtle, and many
new issues are brought to the surface. By explicitly addressing how to build
models of wave functions and energy and how to relate these models to real
physical systems, we have opened up a floodgate of deep and difficult questions
as students struggle to make sense of these models. We conclude that the
difficulties found in previous research are the tip of the iceberg, and the
real issue at the heart of student difficulties in learning quantum tunneling
is the struggle to build the complex models that are implicit in experts'
understanding but often not explicitly addressed in instruction.Comment: v2, v3 updated with more detailed analysis of data and discussion;
submitted to Phys. Rev. ST: PE
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