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Bernhard Rothenstein

Publications and source records attributed to Bernhard Rothenstein.

At least 37 records · Page 2Linked to original sources
arXiv2007

Special Relativity properties from Minkowski diagrams

This paper has pedagogical motivation. It is not uncommon that students have great difficulty in accepting the new concepts of standard special relativity, since these seem contrary to common sense. Experience shows that geometrical or graphically exposition of the basic ideas of relativity theory improves student understanding of the algebraic expressions of the theory. What we suggest here may complement standard textbook approaches.

physics.gen-ph↗
arXiv2007

Lorentz transformations: Einstein's derivation simplified

We show that the Lorentz transformations for the space-time coordinates of the same event are a direct consequence of the principle of relativity and of Einstein's distant clocks synchronization procedure. In our approach, imposing the linear character of the Lorentz transformations we guess that the transformation equation for the space coordinate has the form x=ax'+cbt'. Imposing the condition that it accounts for the time dilation relativistic effect and taking into account the fact that due to the clock synchronization a la Einstein the space-time coordinates of the same event in the two frames are related by x=ct and x'=ct', we find out expressions for a and b. Dividing the transformation equation for the space coordinate by c we obtain the transformation equation for the time coordinate t=at'+b/cx'. Combining the two transformation equations we obtain directly the inverse Lorentz transformations.

physics.gen-ph↗
arXiv2007

Quantization, Doppler shift and the invariance of the speed of light via the invariance of the counted numbers of photons: An interesting pedagogical problem

We show that when the observers are located in a plane electromagnetic wave it is not compulsory for them to take into account the time dilation and length contraction effects when the wave is detected from two inertial reference frames in relative motion. We also illustrate the difference between the approach that uses Einstein type of observers confronted with time dilation and length contraction effects and an unconventional approach that uses observers detecting information from the energy that arrives at their location.

physics.gen-ph↗
arXiv2006

Landing the uniformly accelerating observers

Observers of the uniformly accelerating observers or the observers who make up the system of uniformly accelerating observers reach the same velocity V at different times ti which depends on V and on theirs acceleration gi. Considering a platform that moves with constant velocity V, the observers can land smoothly on it. Their ages and locations in the inertial reference frame attached to the platform are reckoned and compared.

physics.gen-ph↗
arXiv2006

The system of uniformly accelerating observers

We begin with a scenario that involves point-like observers starting at t=0 from the origin O of an inertial reference frame. They move with all possible proper accelerations in the positive direction of the OX axis. Equipped with light sources the accelerating observers get involved in experiments like Doppler Effect, radar detection and radar echo. We derive formulas accounting for the experiments mentioned above. In the case of the Doppler Effect we take into account the non-locality aspect in the time interval measurement by accelerating observers.

physics.gen-ph↗
arXiv2006

Radar echo, Doppler Effect and Radar detection in the uniformly accelerated reference frame

The uniformly accelerated reference frame described by Hamilton, Desloge and Philpott involves the observers who perform the hyperbolic motion with constant proper acceleration gi. They start to move from different distances measured from the origin O of the inertial reference frame K(XOY), along its OX axis with zero initial velocity. Equipped with clocks and light sources they are engaged with each other in Radar echo, Doppler Effect and Radar detection experiments. They are also engaged in the same experiments with an inertial observer at rest in K(XOY) and located at its origin O. We derive formulas that account for the experiments mentioned above. We study also the landing conditions of the accelerating observers on a uniformly moving platform.

physics.gen-ph↗
arXiv2006

Relativistic aberration effect on the the light reflection law and the form of reflecting surface in a moving reference frame

The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays. The form of the reflection law in the moving reference frame is substantially modified and includes an additional parameter which is the velocity vector of the reference frame. It is shown that the reflected ray, as measured by a moving observer, would not in general be in the same plane as the incident and normal rays. A general method to transform the form of any rigid surface in 3-dimensional space with respect to the arbitrary directed relative motion of the reference frame is detailed. This method is based on the light signals processes and the invariance of the light velocity under Lorentz transformations. It is shown that a moving observer will measure a plane surface as a hyperboloid. That observer will also measure a spherical surface as an ellipsoid. A right line in the plane is seen by a moving observer as a hyperbola. The whole analysis is extended to the case of a uniform media.

physics.gen-ph↗
arXiv2006

Relativistic addition of parallel velocities from time dilation

The relativistic addition of parallel velocities is derived involving relativity only via the time dilation formula, avoiding the length contraction used by many authors in conjunction with time dilation. The followed scenario involves a machine gun that fires successive bullets, considered from its rest frame and from the rest frame of the target, the bullets hit.

physics.gen-ph↗
arXiv2006

Accelerating observers measure the period of the oscillations taking place in an acoustic wave (non-longitudinal case)

We consider a scenario that involves a stationary source of acoustic waves located at the origin of the K(XOY) inertial reference frame and a receiver that performs the hyperbolic motion at a constant altitude. The observer measures the proper reception time of successive wave crests. We investigate its dependence on the propagation speed of the wave and on the altitude at which the motion takes place.

physics.gen-ph↗
arXiv2006

Time interval measurements by uniformly accelerating observers (non-longitudinal case)

We consider two non-longitudinal Doppler Effect experiments. The first one involves a stationary source of monochromatic light located at the origin O of the K(XOY) inertial reference frame and an observer R who performs the hyperbolic motion at a constant altitude. The second involves a stationary observer located at the origin O and a monochromatic source of light that performs the hyperbolic motion. In both cases we compare the relationship between emission and reception times of the same light signal and the relationship between the emission and the reception time intervals of two successive light signals.

physics.gen-ph↗
arXiv2006

Special relativity from a single scenario using the same strategy

Following an approach proposed by Rosser for deriving the transformation equations of volume charge density and current density we derive the transformation equations for the space-time coordinates of the same event, for the mass and the momentum of the same particle and for the electric and the magnetic field generated by the same distribution of electric charges.

physics.gen-ph↗
arXiv2006

Period measurement by accelerating observers

We consider the problem of the period measurement in the case of the following scenarios: stationary source of successive light signals and accelerating receiver, stationary receiver and accelerating source of successive light signals and stationary machine gun that fires successive bullets received by an accelerating receiver. The accelerated motion is the hyperbolic one.

physics.gen-ph↗
arXiv2006

Relativistic dynamics without conservation laws

We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The derivations are based on the principle of relativity and on its direct consequence, the addition law of relativistic velocities.

physics.gen-ph↗
arXiv2006

Illustrating delta(E)=c^2 delta(m)

We present a thought experiment that involves a high sensitivity balance initially in a state of mechanical equilibrium but not in a state of thermal equilibrium. After reaching the state of thermal equilibrium it is no longer in a state of mechanical equilibrium.

physics.gen-ph↗
arXiv2006

Is the assumption of a special system of reference consistent with Special Relativity? Definitely yes, special approaches show it!

We compare the results obtained by interpreting some fundamental relativistic experiments from the point of view of two alternative theories: Einstein's special relativity theory and the Lorentz-Poincare theory admitting the existence of a special reference frame relative to which we can measure absolute velocities. The experiments that we consider here are the time dilation, the radar echo, the Doppler Effect and the radar detection. The most important result is that both theories lead to the Lorentz-Einstein transformations for the space-time coordinates of the same event. This conclusion enables us to assert that the anisotropy in the light propagation fades away in the case of these particular experiments

physics.gen-ph↗