arXiv physics/07021912007-02-22physics.gen-ph

A simple derivation of the Lorentz transformation and of the related velocity and acceleration formulae

Jean-Michel Levy

备注：: Update of physics/0606103 4 pages, 1 figure, a slightly modified version is to appear in the American Journal of Physics
发表信息：: American Journal of Physics 75, 7 (2007) 615-618
DOI：: 10.1119/1.2719700

英文摘要：

The Lorentz transformation is entirely derived from length contraction, itself established through the known light-clock thought experiment . This makes the derivation accessible to beginning students once Eintein's two postulates have been admitted. The formula derived for the space part of the general rotation-free Lorentz transformation is very compact and allows for an easy derivation of the velocity and acceleration transformations. A possibly new and very simple relation is found between proper acceleration and acceleration in an inertial frame.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

An alternative derivation of Einstein's Doppler shift and aberration formulae

I propose an alternative, purely kinematical, derivation of Einstein's Doppler formula. It is valid for periodic signals of any shape that propagate with the velocity of light. The formula is asymptotic in a parameter proportional to the relative variation of the distance source-receiver during one period. As a by-product, I also derive an alternative proof of Einstein's aberration formulae.

2009-02-06physics.gen-ph

A faster than "World fastest derivation of the Lorentz transformation"

We show that a derivation of the Lorentz-Einstein transformation based on length contraction or on time dilation is faster then "World's fastest derivation of the Lorentz transformation"

2006-02-22physics.gen-ph

Full Physical Derivation and Meaning of Lorentz Transformation

In the line of thought of Einstein's 1905 paper on relativity, I get a physical derivation of Lorentz transformation (LT) answering its main criticism and considerably enlarging the area of applications of the theory of relativity.

1999-11-25physics.gen-ph

A brief and transparent derivation of the Lorentz-Einstein transformations via thought experiments

Starting with a thought experiment proposed by Kard, which derives the formula that accounts for the relativistic effect of length contraction, we present a "two line" transparent derivation of the Lorentz-Einstein transformations for the space-time coordinates of the same event. Our derivation make uses of Einstein's clock synchronization procedure

2006-02-08physics.gen-ph

Derivation of transformation equations for the parameters that characterize a plane acoustic wave without using phase invariance and Lorentz-Einstein transformation

We show that the transformation equations for the parameters that characterize a plane acoustic wave: period, (frequency), wave vector, wave length and phase velocity can be derived without using phase invariance and Lorentz-Einstein transformation

2005-06-20physics.gen-ph

The simplest derivation of the Lorentz transformation

Starting from the well-known light-clock thought experiment to derive time dilation and length contraction, it is shown that finding the Lorentz Transformation requires nothing more than the most trivial vector addition formula. The form which is obtaine for the L.T. allows an easy derivation of the velocity and acceleration transformations which are also given.

2006-10-09physics.gen-ph

更多相关论文收起更多论文

Derivation of the Lorentz Transformations

The Lorentz Transformations are derived without any linearity assumptions and without assuming that y and z coordinates transform in a Galilean manner. Status of the invariance of the speed of light is reduced from a foundation of the Special Theory of Relativity to just a property which allows to determine a value of the physical constant. While high level of rigour is maintained, this paper should be accessible to a second year university physics student.

2001-10-26physics.gen-ph

Le groupe de Lorentz-Einstein comme consequence d'un quantum d'action

It is shown that the natural quantization of intervals between events (in the relativistic sense) leads to the definition of two units, c and h, implying the formulae for the transformation of co-ordinates as well as the fundamental quantum formulae. ----- On montre comment la quantification naturelle des intervalles entre evenements (au sens relativiste) conduit a la definition de deux unites, c et h, entrainant aussi bien les formules de transformation de coordonnees que les formules quantiques fondamentales.

2003-03-25physics.gen-ph

Unsuitability of the moving light clock system for the Lorentz factor derivation

The moving light clock system was analyzed with respect to the orientation of the wavefront of the light pulse observed in the moving and stationary frames of reference. The plane wavefront of the light pulse was oriented horizontally in both the frames. The wavefront observed in the stationary frame was not perpendicular to the direction of the light pulse propagation. This showed different characteristics of the light pulse than that assumed in the Lorentz factor derivation. According to the horizontal orientation of the wavefront, velocity c was determined as the vertical component of the l…

2009-06-26physics.gen-ph

Derivation and New Interpretation of the Lorentz Transformations and Einstein's Theorem of Velocity Addition

It is traditionally believed that the Lorentz transformations (LT) and Einstein's theorem of velocity addition (ETVA), underlying special relativity, cannot be obtained from non-relativistic (classical) mechanics. In the present paper it is shown, however, that both the LT and the ETVA are derivable within the framework of classical kinematics if the speeds of material points are bounded above by a certain universal limit $c_+$ which can coincide with the speed of light $c$ in a vacuum.

2013-03-27physics.gen-ph

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 f…

2007-02-19physics.gen-ph

Reflection of light from a moving mirror: derivation of the relativistic Doppler formula without Lorentz transformations

A special case of the relativistic Doppler effect, which occurs when light reflects from a moving mirror, is discussed. The classic formula for the Doppler shift is derived in a fully non-relativistic fashion using basic facts from geometry. The derivation does not involve Lorentz transformations, length contractions and time dilations, and therefore is conceptually simpler than the standard derivations in physics textbooks. This discussion can be useful for teaching introductory physics and also for understanding the foundations of special relativity.

2006-05-11physics.ed-phphysics.gen-ph

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.

2007-12-04physics.gen-ph

A New Kinematical Derivation of the Lorentz Transformation and the Particle Description of Light

The Lorentz Transformation is derived from only three simple postulates: (i) a weak kinematical form of the Special Relativity Principle that requires the equivalence of reciprocal space-time measurements by two different inertial observers; (ii) Uniqueness, that is the condition that the Lorentz Transformation should be a single valued function of its arguments; (iii) Spatial Isotropy. It is also shown that to derive the Lorentz Transformation for space-time points lying along a common axis, parallel to the relative velocity direction, of two inertial frames, postulates (i) and (ii) are suffi…

2004-10-27physics.class-phphysics.gen-ph

Emergence of complex and spinor wave functions in Scale Relativity. II. Lorentz invariance and bi-spinors

Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity field of geodesics of a continuous and non-differentiable (therefore fractal) space-time. In a first paper (Paper I), we have presented the general argument which leads to this result using an elaborate and more detailed derivation than previously displayed. We have therefore been able to show how the complex wave function emerges naturally from the doubling …

2014-06-04physics.gen-ph

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.

2007-09-24physics.gen-ph

An investigation of Lorentz transformation

A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is presented for clarification. I consider the most general form of transformations between two sets of events in two inertial reference frames and use the most basic properties expected from such a transformation together with the principle of the constancy of the velocity of light to derive LT. The method is very simple, succinct and useful for students tryin…

2013-04-13physics.gen-ph

Special relativity as classical kinematics of a particle with the upper bound on its speed. Part II. The general Lorentz transforrmation and the generalized velocity composition theorem

The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical mechanics without employing any concepts , associated with the time dilatation or/and length contraction. It yielded the 1-D Lorentz transformation (LT), free of inconsistencies (inherent in the canonical derivation and interpretations of the LT). Here we apply the same approach to derive the LT for the 3-dimensional motion of a particle and the attendant law of velocity co…

2014-05-09physics.gen-ph

Lorentz transformations with arbitrary line of motion

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with As chosen x or y axis. It becomes necessary in such cases to develop Lorentz transformations where the line of motion is not aligned with either the x or the y-axis. In this paper we develop these transformations and show that under such transformations, two orthogonal systems (in their respective frames) appear non-orthog…

2008-09-18physics.gen-ph

Lorentz Transformation as a 'Complementary Time-Dependent Coordinate Transformation'. The Physical Foundation of Einstein' Special Relativity

We here deduce Lorentz transformation (LT) as a member of a class of time-dependent coordinate transformations, complementary to those already known as spatial translations and rotations. This exercise validates the principle of physical determination of equations within special relativity theory (SRT), in accordance with the derivation of the LT in Einstein's original paper on relativity. This validation is possible because our LT deduction also discloses the real physics warranting Einstein's manipulations of several equations in that paper, thus proving the correctness of his derivation of …

2006-03-05physics.gen-phphysics.soc-ph