We present the special theory of relativity taking the Doppler effect as the starting point, and derive several of its main effects, such as time dilation, length contraction, addition of velocities, and the mass-energy relation, and assuming energy and momentum conservation, we discuss how to introduce the 4-momentum in a natural way. We also use the Doppler effect to explain the "twin paradox", and its version on a cylinder. As a by-product we discuss Bell's spaceship paradox, and the Lorentz transformation for arbitrary velocities in one dimension.
Relativistic Doppler effect in a uniformly accelerated motion - III
在狭义相对论的背景下，我们详细地描述了静止的光源和线性运动和恒定的固有加速度的观察者之间的多普勒效应。要有这篇文章的英文版本，请询问作者。- ^Ce special-relativeco ni detale priskribas lum-Doppletion efikon inter restanta fonto kaj observanto kun rektilinia movado kaj constanta propra akcelo.
It is known that action is invariant in special relativity. The goal of this note is to show that the reverse statement is also correct, that special relativity follows from the postulate that action is invariant under the transformation from one inertial frame to another.
An approach to special relativity is outlined which emphasizes the wave and field mechanisms which physically produce the relativistic effects, with the goal of making them seem more natural to students by connecting more explicitly with prior studies of waves and oscillators.
Simply by assuming the first postulate of Special Relativity and by exploring Gedankenexperiments with electromagnetic forces, we suggest that there is a speed limit in the universe, which can be determined as a relation between vacuum permeability and permittivity. We also derive space contraction and time dilatation without referring to light. Finally, we argue that, based on previous works on the derivation of Lorentz s Transformation without light and from our results, it is possible to transform the epistemological status of the Einstein s second postulate from principle into derivation.
All of the experiments supporting Einstein's Special Relativity Theory are also supportive of the Lorentz ether theory, or many other ether theories. However, a growing number of experiments show deviations from Einstein's Special Relativity Theory, but are supporting more extended theories. Some of these experiments are reviewed and analyzed. Unfortunately, many experiments are not of high quality, never repeated and mostly both. It is proposed that the most promising experiments should be repeated.
The most general transformation connecting inertial frames is derived from rather general and simple assumptions, without the postulate of constancy of the speed of light in vacuo.
Solving special relativity paradoxes requires rigorous analysis of event timing, due to relative simultaneity in consequence of the Lorentz transformation. Since clock synchronisation is a convention in special theory of relativity, instead of the Einstein's procedure one may choose such that offers absolute simultaneity. We present in short the corresponding formalism in one spatial dimension. We show that paradoxes do not arise with this choice of synchronisation and descriptions of these issues are exceptionally simple and consistent for both observers involved.
Recent experiments with high-speed ions have investigated potential deviations from the time-dilation predicted by special relativity (SR). The main contribution of this article is to show that the SR predictions are matched by the experimental results only when the transverse Doppler effect in the observed emissions from the ions are neglected in the analysis. However, the Doppler effect in the emission cannot be neglected because it is similar to the time dilation effect. Thus, the article highlights the need to consider Doppler emission effects when validating SR time dilation using high-sp…
Arguments are reviewed and extended in favor of presenting special relativity at least in part from a more mechanistic point of view. A number of generic mechanisms are catalogued and illustrated with the goal of making relativistic effects seem more natural by connecting with more elementary aspects of physics, particularly the physics of waves.
The diagram showing off-center nested spheres which is traditionally used to illustrate the Doppler effect, is misleading and its trigonometric analysis leads to errors concerning light, because electromagnetic Doppler and aberration effects conform to a wavefront surface that is not a sphere but an ellipsoid stretched along the trajectory of the source. The Cartesian and polar equations of the spherical and ellipsoidal wavefronts are compared here and related to their respective angular Doppler functions. As wavefront surfaces directly link inter-frame coordinate transformations to the aberra…
We give a brief critical examination of the special theory of relativity and a similar Newtonian framework to the first order of the $v/c$ ratio, focusing on the phenomena of aberration, Fresnel dragging, and the Doppler effect. We will show that both frameworks yield the same equations modeling these phenomena up to first order. We do this at a level understandable to anyone with a working knowledge of calculus so that the underlying ideas do not get lost in abstruse mathematical formulations.
Relativeca Dopplera efekto ĉe unuforme akcelata movo -- II
延伸物理学/0701092，单色辐射的光源，在恒定的固有加速度下直线运动，通过附近的观察者在休息。在狭义相对论的背景下，我们描述所观察到的多普勒效应。我们还描述了有趣的不连续效应时，骑通过发生。这篇文章的英文版本是可用的。-- ^Ce la special-relativeco，ni priskribas la observatan Doppletenefikon.我不认为你对有效的内部利益有兴趣。
Although electromagnetic and acoustic waves profoundly differ in their nature, comparing their Doppler effects is instructive and reveals persistent conceptual traps. The principle of the Doppler effect was presented by Christian Doppler in 1842 long before the advent of relativity theory, but while the relativistic Doppler effect is now well established, its non-relativistic version retrospectively called classical, suffers from misleading intuitions such as: (1) there is no transverse classical Doppler effect; (2) the Galilean Doppler effect corresponds to the relativistic one without Lorent…
A map is discussed that connects, in 1+1 dimensions, Galilei's relativity to Einstein's special relativity. By means of this map it is possible to derive special-relativistic formulas from the corresponding Galilean ones. Beyond being interesting on its own, this map is also significant with respect to a recent debate on the extension of relativistic symmetries to the Planck scale (especially in the framework of the so-called doubly special relativity). The map in fact provides an explicit example of how can be misleading to interpret a mathematical correspondence between two relativity scheme…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special relativity and in distinguishing between dynamical and purely perspectival effects.
We present a novel paradox in special relativity together with its solution. We call it the four particles paradox. The purpose of this paradox is pedagogical and therefore directed towards students and lecturers of physics. Even if most paradoxes in special relativity theory are very interrelated and some are special cases of others, the paradox we present here is original and illuminates on the very nice subject and the literature of special relativity.
The special theory of relativity does not predict the existence of photons (quanta of electromagnetic radiation). However, it is demonstrated here that it follows from the special theory of relativity that if photons do exist---and we know that they do---then their energy must be proportional to their frequency. This means that the Planck-Einstein formula E=hν follows just from some results of the special theory of relativity and the assumption of the particle--wave duality.
We introduce a Lorentz-covariant description of tachyons, free of inconsistencies. Our approach is based on an appropriate extension of the special relativity beyond the light barrier, owing to the freedom of synchronization of distant clocks.
We present visual calculations in special relativity using spacetime diagrams drawn on graph paper that has been rotated by 45 degrees. The rotated lines represent lightlike directions in Minkowski spacetime, and the boxes in the grid (called "light-clock diamonds") represent units of measurement modeled on the ticks of an inertial observer's lightclock. We show that many quantitative results can be read off a spacetime diagram by counting boxes, using a minimal amount of algebra. We use the Doppler Effect, in the spirit of the Bondi k-calculus, to motivate the method.
