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Vesselin Petkov

Publications and source records attributed to Vesselin Petkov.

51 records · Page 3Linked to original sources
arXiv2009

Correlations for pairs of periodic trajectories for open billiards

In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiards similar to those established by Pollicott and Sharp for closed geodesics on negatively curved compact surfaces. The first of these estimates holds for general open billiards in any dimension. The more intricate second estimate is established for open billiards satisfying the so called Dolgopyat type estimates. This class of billiards includes all open billiards in the plane and open billiards in $\R^N, N \geq 3$ satisfying some additional conditions.

math.DS↗
arXiv2009

Singularities of the scattering kernel related to trapping rays

An obstacle $K \subset \R^n,\: n \geq 3,$ $n$ odd, is called trapping if there exists at least one generalized bicharacteristic $γ(t)$ of the wave equation staying in a neighborhood of $K$ for all $t \geq 0.$ We examine the singularities of the scattering kernel $s(t, θ, ω)$ defined as the Fourier transform of the scattering amplitude $a(λ, θ, ω)$ related to the Dirichlet problem for the wave equation in $Ω= \R^n \setminus K.$ We prove that if $K$ is trapping and $γ(t)$ is non-degenerate, then there exist reflecting $(ω_m, θ_m)$-rays $δ_m,\: m \in \N,$ with sojourn times $T_m \to +\infty$ as $m \to \infty$, so that $-T_m \in {\rm sing}\:{\rm supp}\: s(t, θ_m, ω_m),\: \forall m \in \N$. We apply this property to study the behavior of the scattering amplitude in $\C$.

math-ph↗
arXiv2009

Estimates of holomorphic functions in zero-free domains

We study functions f(z) holomorphic in the upper half plane and having no zeros when the imaginary part of z is between 0 and 1, and we obtain a lower bound for the modulus of f(z) in this strip. In our analysis we deal with scalar functions f(z) as well as with operator valued holomorphic functions I+A(z) assuming that A(z) is a trace class operator in the upper half plane and I+A(z) is invertible in the same strip and is unitary on the real line.

math.CV↗
arXiv2009

Accelerating spaceships paradox and physical meaning of length contraction

A fifty-year old apparently paradoxical thought experiment involving two accelerating spaceships and a thread hat connects them states that the thread will break due to length contraction. This paradox still appears to be regarded by some physicists as a proof that (i) only physical bodies, but not space, undergo relativistic length contraction and (ii) a relativistically contracted body experiences a stress. This note, dedicated to the one hundredth anniversary of Hermann Minkowski's paper "Space and Time", shows that a proper relativistic treatment of the paradox demonstrates that it is a manifestation of a specific relativistic acceleration phenomenon, which does not have a classical analog. This means that length contraction plays no role in the resolution of the paradox. It is also shown that no stress is involved in the length contraction effect.

physics.class-ph↗
arXiv2008

Time and Reality of Worldtubes

In this essay, dedicated to the one hundredth anniversary of Hermann Minkowski's talk "Space and Time", I argue that physicists should face the issue of the reality of spacetime and worldtubes of physical objects for two reasons. First, this issue is not a philosophical question, as some appear to think, since the kinematical special relativistic effects would be impossible, as will be demonstrated, if the physical objects involved in these effects did not exist as four-dimensional worldtubes. Second, taking into account that worldtubes are real four-dimensional objects provides an unexpected insight into the origin of inertia, the nature of the force acting on a body supported in a gravitational field, and possibly even the nature of quantum objects.

physics.gen-ph↗
arXiv2007

On the Reality of Minkowski Space

Should physicists deal with the question of the reality of Minkowski space (or any relativistic spacetime)? It is argued that they should since this is a question about the dimensionality of the world at the macroscopic level and it is physics that should answer it.

physics.gen-ph↗
arXiv2003

Propagation of light in non-inertial reference frames

It is shown that the complete description of the propagation of light in a gravitational field and in non-inertial reference frames in general requires an average coordinate and an average proper velocity of light. The need for an average coordinate velocity of light in non-inertial frames is demonstrated by considering the propagation of two vertical light rays in the Einstein elevator (in addition to the horizontal ray originally discussed by Einstein). As an average proper velocity of light is implicitly used in the Shapiro time delay (as shown in the Appendix) it is explicitly derived and it is shown that for a round trip of a light signal between two points in a gravitational field the Shapiro time delay not only depends on which point it is measured at, but in the case of a parallel gravitational field it is not always a delay effect. The propagation of light in rotating frames (the Sagnac effect) is also discussed and an expression for the coordinate velocity of light is derived. The use of this coordinate velocity naturally explains why an observer on a rotating disk finds that two light signals emitted from a point on the rim of the disk and propagating in opposite directions along the rim do not arrive simultaneously at the same point.

gr-qc↗
arXiv2003

Acceleration-dependent self-interaction effects as a possible mechanism of inertia

The paper pursues two aims. First, to revisit the classical electromagnetic mass theory and develop it further by making use of a corollary of general relativity - that the propagation of light in non-inertial reference frames is anisotropic. Second, to show that the same type of acceleration-dependent self-interaction effects that give rise to the inertia and mass of the classical electron appear in quantum field theory as well when the general relativistic frequency shift of the virtual quanta, mediating the electromagnetic, weak, and strong interactions between non-inertial particles, is taken into account. Those effects may account for the origin of inertia and mass of macroscopic objects.

physics.class-ph↗
arXiv2001

On the nature of the force acting on a charged classical particle deviated from its geodesic path in a gravitational field

In general relativity the gravitational field is a manifestation of spacetime curvature and unlike the electromagnetic field is not a force field. A particle falling in a gravitational field is represented by a geodesic worldline which means that no force is acting on it. If the particle is at rest in a gravitational field, however, its worldline is no longer geodesic and it is subjected to a force. The nature of that force is an open question in general relativity. The aim of this paper is to outline an approach toward resolving it in the case of classical charged particles which was initiated by Fermi in 1921.

gr-qc↗
arXiv2001

On the gravitational redshift

The purpose of this paper is twofold - to demonstrate that in the gravitational redshift it is the frequency a photon that is constant, and to describe the mechanism responsible for the change of its wavelength.

gr-qc↗
arXiv2001

Is the active gravitational mass of a charged body distance-dependent?

It appears to follow from the Reissner-Nordstrom solution of Einstein's equations that the charge of a body reduces its gravitational field. In a recent note Hushwater offered an explanation of this apparent paradox. His explanation, however, raises more questions than solves since it implies that the active gravitational mass of a charged body is distance-dependent and therefore is not equal to its inertial mass.

gr-qc↗
arXiv2000

Did 20th century physics have the means to reveal the nature of inertia and gravitation?

At the beginning of the 20th century the classical electron theory (or, perhaps more appropriately, the classical electromagnetic mass theory) - the first physical theory that dared ask the question of what inertia and mass were - was gaining momentum and there were hopes that physics would be finally able to explain their origin. It is argued in this paper that if that promising research path had not been inexplicably abandoned after the advent of relativity and quantum mechanics, the contemporary physics would have revealed not only the nature of inertia, mass, and gravitation, but most importantly would have outlined the ways of their manipulation. Another goal of the paper is to try to stimulate the search for the mechanism responsible for inertia and gravitation by outlining a research direction, which demonstrates that the classical electromagnetic mass theory in conjunction with the principle of equivalence offers such a mechanism.

physics.gen-ph↗
arXiv1999

Propulsion Through Electromagnetic Self-Sustained Acceleration

As is known the repulsion of the volume elements of an uniformly accelerating charge or a charge supported in an uniform gravitational field accounts for the electromagnetic contribution to the charge's inertial and gravitational mass, respectively. This means that the mutual repulsion of the volume elements of the charge produces the resistance to its accelerated motion. Conversely, the effect of electromagnetic attraction of opposite charges enhances the accelerated motion of the charges provided that they have been initially uniformly accelerated or supported in an uniform gravitational field. The significance of this effect is that it constitutes a possibility of altering inertia and gravitation.

physics.gen-ph↗
arXiv1998

On the Possibility of a Propulsion Drive Creation Through a Local Manipulation of Spacetime Geometry

Since the shape of a free body's worldline is determined by the geometry of spacetime a local change of spacetime geometry will affect a body's worldline, i.e. a body's state of motion. The exploration of this possibility constitutes a radically new approach to the idea of how a body can be propelled: instead of applying a force to the body itself, the geometry of spacetime is subjected to a local manipulation which in turn results in the body's motion.

physics.gen-ph↗