Searcharxiv⌕ Search

arXiv subjects

Bernhard Rothenstein

Publications and source records attributed to Bernhard Rothenstein.

At least 19 recordsLinked to original sources
arXiv2008

Synchrony parameter dependent transformation equations and some of their particular values - Kinematics

We show that alternative relativity theories that are essentially based on varied distant clock synchronization procedures can be recovered by using the standard Lorentz-Einstein transformations for the space-time coordinates of the same event. Through this approach we offer modest support for the Rizzi et al. stating that: "Once correctly and explicitly phrased, the principles of special relativity theory allow for a wide range of theories that differ from the standard Einstein's theory only for the difference in the chosen synchronization procedure, but are wholly equivalent to special relativity theory in predicting empirical facts." Our approach requires of the reader no more then a correct understanding of the physics behind the Lorentz-Einstein transformations equations which we use.

physics.gen-ph↗
arXiv2008

Relativistic dynamics without collisions and conservation laws

We show that the relativistic expressions for momentum and energy as well as the way in which they transform could be derived without involving collisions and conservation laws. Our approach involves relativistic kinematics via the addition law of relativistic velocities.

physics.gen-ph↗
arXiv2008

Nonstandard Lorentz-Einstein transformations

The standard Lorentz transformations establish a relationship between the space-time coordinates of the same event when detected from two inertial reference frames I and I' in the standard arrangement. This event is characterized by the space-time coordinates E(x,tE) and E'(x',t'E), tE and t'E representing the readings of the standard synchronized clocks C(x) and C'(x') located in the two frames where the event takes place. We obtain the nonstandard Lorentz transformations establishing a "physically" correct relationship between the readings of the standard synchronized clocks and the readings of other clocks (ta,t'a) of the same inertial reference frames. This relationship of the type tE=f(x,ta), expresses the standard Lorentz transformations as a function of ta and t'a respectively. We present several cases of nonstandard Lorentz transformation (the case of radar detection, the case when one reference frame is filled with an ideal transparent dielectric and the case of relativity of the apparent, actual and synchronized positions of the same moving particle).

physics.gen-ph↗
arXiv2008

A look at Einsteins clocks synchronization

While Einstein clocks synchronization process is performed, one has a well defined region in which the clocks are synchronized and another one in which the clocks are not yet synchronized. The frontier between them evolves differently from the perspective of observers in relative motion. A discussion is conducted upon direct observation of the phenomenon and Minkowski diagrams.

physics.gen-ph↗
arXiv2007

Transformation equations for the kinetic energy of the same particle: Filling the gap in special relativity literature

Transformation equations for the kinetic energy of a tardyon are derived in the limits of classical and of special relativity theory. Two formulas are presented. In the first one the energy of the particle in one of the involved reference frames is presented as a function of its proper energy, of the relative velocity of the two frames and of its speed in the second one. In the second one the kinetic energy in one of the involved reference frames is expressed as a function of its kinetic energy in the second one of its proper energy, of the relative velocity of the involved inertial reference frames and of its velocity relative to that frame. The obtained results are extended to the case of a photon that moves under the same geometrical conditions, recovering the formulas that account for the relativistic Doppler Effect, illustrating the behavior of a transformation equation when it should account for the properties of an electron and for those of a photon as well.

physics.gen-ph↗
arXiv2007

Lorentz transformation, time dilation, length contraction and Doppler Effect - all at once

We present a simple derivation of the Lorentz transformations for the space-time coordinates of the same event. It is based on the relative character of length and time interval as measured by observes in relative motion. We begin by accepting that the relative motion modifies in some particular way the result of these measurements. However we do not postulate the character of this distortion i.e. whatever it is dilation or contraction. The formulas accounting for length contraction, time dilation and Doppler shift are a byproduct of this derivation.

physics.gen-ph↗
arXiv2007

Relativistic electrodynamics as an extrapolation of relativistic kinematics

After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is involved via the addition law of parallel speeds or via the Lorentz transformations for the space-time coordinates of the same event. Electricity and magnetism are involved via Gauss's and Ampere's laws. In this way we avoid the transformation equations for the Lorenz force components which are used in most derivations of the transformation equations for E and B fields.

physics.gen-ph↗
arXiv2007

Lorentz transformation by mimicking the Lorentz transformation

We show that starting with the fact that special relativity theory is concerned with a distortion of the observed length of a moving rod, without mentioning if it is a "contraction" or "dilation", we can derive the Lorentz transformations for the spacetime coordinates of the same event. This derivation is based on expressing the length of the moving rod as a sum of components with all the lengths involved in this summation being measured by the observers of the same inertial reference frame.

physics.gen-ph↗
arXiv2007

A simple superluminal but not physical motion

We discuss a superluminal unphysical motion which, we believe, has a high pedagogical potential. It highlights the physics behind the concept of simultaneity in special relativity and illustrates the non-physical character of superluminal speeds offering a rewarding exercise in handling the Minkowski space-time diagram.

physics.gen-ph↗
arXiv2007

A generic rule that simplifies the derivation of the transformation equations accounting for the properties of the photon

We show that the transformation equation for the tardyon velocity involves two generic functions which in turn depend on the relative velocity of the involved reference frames, on the tardyon velocity u and on the polar angle which define the direction along which the tardyon moves. The same functions are further involved in the transformation equations for the space-time coordinates of the same event generated by a moving tardyon and for its relativistic mass, momentum and energy. Taking the limits of these functions for u approaching c we obtain exactly the transformation equations for the space-time coordinates of the same event generated by a photon and for its momentum and energy. The same procedure works also for the transition from a plane acoustic wave to an electromagnetic wave.

physics.gen-ph↗
arXiv2007

Extending the abilities of the Minkowski spacetime diagram

A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane. However the Euclidean lengths of the lines on the diagram do not correspond to the true values of physical quantities in spacetime, except for those referring to the stationary reference frame. In order to extend its abilities to other inertial reference frames, we derive a factor which, multiplied by the magnitude of the actually displayed values (on the diagram), leads to the corresponding true measured values by any other inertial observers. Doing so, the student can infer from the Euclidean diagram plot the expressions that account for Lorentz length contraction, time dilation and also Lorentz Transformations just by using regular trigonometry.

physics.gen-ph↗
arXiv2007

Counting energy packets in the electromagnetic wave

We discuss the concept of energy packets in respect to the energy transported by electromagnetic waves and we demonstrate that this physical quantity can be used in physical problems involving relativistic effects. This refined concept provides results compatible to those obtained by simpler definition of energy density when relativistic effects apply to the free electromagnetic waves. We found this concept further compatible to quantum theory perceptions and we show how it could be used to conciliate between different physical approaches including the classical electromagnetic wave theory, the special relativity and the quantum theories.

physics.gen-ph↗
arXiv2007

Learning more from the Lorentz transformations

Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or dilation effects. Furthermore we quantify the simultaneity error occurring in the relativity theory. Having done this, we analyse the root cause of these effects and identify it with a finite phase velocity associated with the moving frame. We define this phase velocity by analogy to the de Broglie wave associated with a moving particle. Based on this construct we demonstrate that the phase of the de Broglie waves further extended for stationary particles is a relativistic invariant being the same for all corresponding observers. Also the phase of the electromagnetic waves transporting energy at light speed is a relativistic invariant. Therefore the universe and its matter / energy may be seen as a superposition of waves propagating such that their phase is the same for all corresponding observers. The wave phase may replace the time as an invariant and universal reference.

physics.gen-ph↗
arXiv2007

On spacetime coordinates in special relativity

Starting with two light clocks to derive time dilation expression, as many textbooks do, and then adding a third one, we work on relativistic spacetime coordinates relations for some simple events as emission, reflection and return of light pulses. Besides time dilation, we get, in the following order, Doppler k-factor, addition of velocities, length contraction, Lorentz Transformations and spacetime interval invariance. We also use Minkowski spacetime diagram to show how to interpret some few events in terms of spacetime coordinates in three different inertial frames.

physics.gen-ph↗
arXiv2007

Relativity and quantum mechanics: Jorgensen revisited

We first define the functions which ensure the transformation of momentum and energy of a tardyon, the transformation of the wave vector and the frequency of the associated wave. Having done this, we show that they ensure the relativistic invariance of the quotient between momentum and wave vector and between energy and frequency if the product between particle velocity u and phase velocity w is a relativistic invariant (uw=c^2), a condition which is a natural combination of special relativity theory and quantum mechanics.

physics.gen-ph↗
arXiv2007

Relativistic velocity addition law derived from a machine gun analogy and time dilation only

We consider a scenario that involves a machine gun, the bullets it fires and a moving target, considered from the rest frame of the machine gun and from the rest frame of the target respectively. Involving the special relativity via its two postulates and the time dilation formula we derive the relativistic velocity addition law showing that it leads to the Lorentz transformations for the space-time coordinates of the same event.

physics.gen-ph↗