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Bernhard Rothenstein

Publications and source records attributed to Bernhard Rothenstein.

63 records · Page 4Linked to original sources
arXiv2005

Watching an uniformly moving source of light using a telescope and a frequency-meter

We propose a scenario that involves a stationary observer who detects a point like source of light moving with constant velocity at a constant altitude, using a telescope and a frequency-meter. We derive a formula for the angular velocity at which we should rotate the axis of the telescope and a formula that relates the proper period at which the source emits successive wave crests and the proper period at which the stationary observer receives them

physics.gen-ph↗
arXiv2005

Graphical aids for relativistic optics

The paper presents a relativistic space-time diagram, which displays in true values the space (Cartesian and polar) and the time coordinates of the same event detected from two inertial reference frames in relative motion related by the Lorentz-Einstein transformations, the aberration angles and the Doppler shifted periods and wavelengths. We use it in order to illustrate the reflection of light on moving mirrors (horizontal and vertical) and the way in which a single observer could measure the length of a moving rod. It displays in true values the space-time coordinates of the same event generated by a light signal.

physics.gen-ph↗
arXiv2005

From one space dimension to two space dimensions in special relativity

Authors derive the Lorentz-Einstein transformation for the space-time coordinates starting with a one-space dimension approach. They add to the results the invariance of the space coordinates measured perpendicular to the direction of relative motion. Students often ask if the transition does not affect the transformation equation for the time coordinate. Our paper shows that the transformation of the time coordinate depends only on the x space coordinate.

physics.gen-ph↗
arXiv2004

Three levels of understanding physical relativity: Galileo's relativity, Up-to-date Galileo's relativity and Einstein's relativity: A historical survey

We present a way of teaching Einstein's special relativity. It starts with Galileo's relativity, the learners know from previous lectures. The lecture underlines that we can have three transformation equations for the space-time coordinates of the same event, which lead to absolute clock readings, time intervals and lengths (Galileo's relativity), to absolute clock readings but to relative time intervals and lengths (up-to-date Galileo transformations) and to relative clock readings time intervals and lengths.

physics.gen-ph↗
arXiv2004

"An analysis of the classical Doppler Effect"[1] revisited

After having shown that the formula which describes the Doppler effect in the general case holds only in the case of the "very high" frequency assumption, we derive free of assumptions Doppler formulas for two scenarios presented in the revisited paper.

physics.gen-ph↗
arXiv2003

Doppler shift experiments with source in periodic motion: Parametrized Doppler shift formulas

Doppler shift formulas are derived for two less studied scenarios: stationary receiver and source in harmonic oscillatory motion and stationary receiver and source in uniform circular motion. For each of the scenarios we derive a formula, one which works when the emission period is small enough that it can be considered that two successive signals are emitted from the same point in space (locality assumption) and another which takes into account that two successive signals are emitted from two different points in space (non-locality assumption). The results furnished by the two Doppler shift formulas are compared, showing that increasing the emission frequency decreases the difference between the results obtained with the two formulas.

physics.gen-ph↗
arXiv2003

The game of the "very small" and the "very big": The case of the Doppler Effect

In the study of the Doppler Effect, non-locality is not taken into account. We present two cases in which a continuous change in the receiver's speed and in the angle at which the successive wavecrests are received takes place. In each case the error committed by not taking into account the non-locality is evaluated.

physics.gen-ph↗
arXiv2003

With the relativistic velocity addition law through special relativity

It is shown that if we can define a physical quantity with proper character in a given inertial reference frame (kinematic, dynamic, electromagnetic in its nature) which transforms when detected from a reference frame relative to which it moves with velocity $u_x$ as $F=\f{F^o}{\sqrt{1-\f{u_x^2}{c^2}}}$ then we can derive for it transformation equations following one and the same procedure, which involves the addition law of relativistic velocities which can be derived without using the Lorentz transformations. The transformation equation derived that way, generates the physical quantities $u_xF$ and $u_x'F'$, for which physicists invent names reflecting theirs physical meaning.

physics.gen-ph↗