Giovanni Zanella
The wave nature of the light, applied to the kinematics of the moving bodies, permits to investigate and find a coherent solution on some questions raised by the theory of special relativity about the Lorentz contraction.
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It has been more than a century since first Lorentz and later Einstein explored relativistic events and still important consequences of that remains unclear to everybody. The present study extensively focus on Lorentz (Length) contraction phenomenon and takes a different approaches to explain how the shrinking of the body appears if exists. We utilized two postulates of Special Relativity that emphasizes constancy of speed of light and same physical laws in any inertial frame. Finally, we propose Lorentz contraction exists in different form through the shape of the accelerated body. The deform…
An elementary thought experiment is used to show that once the time dilatation effect is established, there is no way to escape a dual length contraction.
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.
Incompatibility between the principle of the constancy of the speed of light and the Lorentz contraction in the global positioning system (GPS) is discussed. The GPS works precisely in the earth-centered locally inertial (ECI) coordinate system on the condition that the speed of light c is assumed to be constant regardless of the inertial motion of the GPS satellites and the earth. The inertial system of the earth travels not only in the solar system at the velocity 30 km/s but also in the cosmic microwave background (CMB) at the velocity 700 km/s. The deviation on the car navigation system by…
We look afresh at the deduction of the "Lorentz contraction" of a "rod" from the Lorentz transformation equations of the special theory of relativity. We show that under special conditions, which include acceleration of the "rod", length "expansion" and "invariance" are possible, and thus these are purely kinematical phenomena. We then take a closer look at Einstein's two famous papers on the special theory of relativity and point out a flaw in his argument. It seems that it is possible to have the times of the clocks of two, and indeed all, inertial systems to agree with each other.
It is demonstrated that the 3--vector $\bs{S}$ currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector $\bs{T}$ is individuated. The equation of motion for the two vectors is shown to contain two terms, a common linear rotation, identified with Thomas precession, and also a nonlinear rotation depending on the direction of the spin itself.
In a recent paper, Harada and Sachs suggested that the Fitzgerald-Lorentz contraction does not refer to a physical contraction but can perhaps best be seen as a 'currency conversion'. In the present paper, this view is inspected, and it is found, beyond the immediate frame of the interpretation, that the Fitzgerald-Lorentz contraction leads to a contradiction in a system of more than two observers. A possible physical system in which this can occur is a relativistic (ideal) gas or fluid.
Lorentz contraction of electric field lines for a point charge in uniform motion
本文重新审视匀速运动点电荷电场线洛伦兹收缩的逻辑基础，指出既有论证的缺陷，并基于钱学森半个世纪前的鲜为人知结果给出一个新证明，从而获得额外结论。
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of the light. The latter and Lorentz contraction imply the relativistic time dilation. The invariance of the light speed defined as the round-trip value follows from the time dilation and Lorentz contraction. An observer is incognizant about his motion relative to the absolute frame of reference. So, in order to synchronize spaced clocks in a moving reference fra…
This paper aims at demonstrating that: 1/ Assuming the equality of the two-way transit time of light in vacuo, along the two perpendicular arms of Michelson's interferometers (modern versions of Michelson's experiment), and the anisotropy of the one-way speed of light in the Earth frame, two facts supported today by strong experimental arguments, length contraction (in Lorentz and FitzGerald's approach) should no longer be regarded as an ad hoc hypothesis, it appears necessary and can be easily deduced. 2/ Builder and Prokhovnik had the great merit of having shown that, as a result of to lengt…
The Lorentz transformation is used to analyse space and time coordinates corresponding to two spatially-separated clocks in the same inertial frame. The time dilatation effect is confirmed, but not `relativity of simultaneity' or `relativistic length contraction'. How these latter, spurious, effects arise from misuse of the Lorentz transformation is also explained.
Visual perception of Fitzgerald-Lorentz contraction is known to be theoretically impossible, and this can be demonstrated pedagogically with the aid of simple spacetime diagrams of one spatial dimension. Such diagrams also demonstrate, simply and directly, that the apparent length of a moving meter stick changes as it passes by and can even look elongated. In addition, measurement of a moving meter stick with instruments, as opposed to visual perception, must be inherently ambiguous, as the length measured depends on clock synchronization, which is widely considered to be conventional. In fact…
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"
Space-like and time-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances. The former are found to be Lorentz invariant --there is no `relativistic length contraction', whereas the latter exhibit the experimentally confirmed `time dilatation' effect, without, however, `relativity of simultaneity'. It is shown how the spurious predictions of length contraction and relativity of simultaneity arise from the use of inconsistent synchronisation procedures for spatially separated clocks.
In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time dilation factors. It is shown that this limitation has led to mathematical and physical inconsistencies. The paper explains the conditions for a successful theory of time dilation and length contraction, and provides a simple proof to a new generalized transformation of coordinate systems as the only possible solution that meets those conditions. It discusses …
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.
Some reasons are given to suggest that the interpretation of the Lorentz' transformations as if they referred to coordinates instead of to intervals could be incorrect. Besides, the usual form of such transformations, by using variables that represent finite values instead of differentials, could be another error. Later it is shown that the Lorentz contraction factor must not have the form currently accepted for it if the Lorentz contraction factor is assumed to be equal to the quotient between time differentials.
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.
Time-like and space-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances defined by two spatially-separated clocks. The time dilatation effect is confirmed, but not `relativity of simultaneity' or `relativistic length contraction'. How these latter, spurious, effects arise from misuse of the Lorentz transformation is also explained.
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not spatial intervals, so breaking space-time exchange symmetry and forbidding relativity of simultaneity and length contraction. Two satellite-borne experiments to test these predictions are proposed.
Observations of the apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not spatial intervals, so breaking space time exchange symmetry and forbidding relativity of simultaneity and length contraction. A satellite cesium clock experiment to test these predictions is proposed.
The Bell Spaceship Paradox has promoted confusion and numerous resolutions since its first statement in 1959, including resolutions based on relativistic stress due to Lorentz contractions. The paradox is that two ships, starting from the same reference frame and subject to the same acceleration, would snap a string that connected them, even as their separation distance would not change as measured from the original reference frame. This paper uses a Simple Relativity approach to resolve the paradox and explain both why the string snaps, and how to adjust accelerations to avoid snapping the st…
The usual transformations (UT) of the 3-vectors E and B that are found by Lorentz, Poincaré and independently by Einstein in 1905. are generally considered to be the Lorentz transformations (LT) of E and B. According to the UT E in one frame is 'seen' as E' and B' in a relatively moving frame. In Minkowski's last paper, in 1908. in section 11.6, he defined the vectors (with four components) of the electric $Φ$ and magnetic $Ψ$ fields and discovered that, e.g., $Φ$ correctly transforms by the LT again to $Φ^{\prime}$. His correct LT are reinvented in, e.g., [11] ([11] Ivezić T 2005 Found. Phys.…
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…
The conventional discussion of the observed distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations, from a stationary frame, of : (i) objects moving with constant velocity and uniformly illuminated during a short time $τ_L$ (their `Luminous Proper Time') in their rest frame; these may be called `Transient Luminous Objects' and (ii) a moving, extended, array of synchronised `equivalent clocks' in a common inertial frame. Application of the Lorentz Transformation to (i) shows that such objects, observed…
In this work, according to the electromagnetic field tensor in the framework of generalized uncertainty principle (GUP), we obtain the Lorentz force and Faraday's law of induction in the presence of a minimal length. Also, the ponderomotive force and pomderomotive pressure in the presence of a measurable minimal length are found.
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.
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 construc…
The behavior of mass is well known, as described by Newton's Laws of Motion, the Lorentz Contractions, and Einstein's mass - energy equivalence. But just what mass is, how those behaviors come about, what in material reality produces the effects of mass, has been little understood. The only extant hypothesis is that of the "Higgs Field" and its related particle, the Higgs Boson. Neither has been detected in spite of significant efforts to do so. Further, that hypothesis is not so much a description of the mechanics of mass as a further abstraction away from the problem by substituting another …
In this paper a geometric approach to the special relativity (SR) is used that is called the "invariant special relativity" (ISR). In the ISR it is considered that in the four-dimensional (4D) spacetime physical laws are geometric, coordinate-free relationships between the 4D geometric, coordinate-free quantities. It is mathematicaly proved that in the ISR the electric and magnetic fields are properly defined vectors on the 4D spacetime. According to the first proof the dimension of a vector field is mathematicaly determined by the dimension of its domain. Since the electric and magnetic field…
According to the postulates of the special theory of relativity (STR), physical quantities such as proper times and Doppler shifts can be obtained from any inertial frame by regarding it as isotropic. Nonetheless many inconsistencies arise from the postulates, as shown in this paper. However, there are numerous experimental results that agree with the predictions of STR. It is explained why they are accurate despite the inconsistencies. The Lorentz transformation (LT), unless subject to the postulates of STR, may be a useful method to approach physics problems. As an example to show the useful…
It is shown that time intervals Delta t' measured for photons moving with speed v > c can be of the same sign for all observers according to special relativity, thereby avoiding any violation of Einstein causality. Previous assertions to the contrary have led to unnecessarily complicated interpretations of experiments which indicate that single photons do travel with faster-than-c speeds in regions of anomalous dispersion
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