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 light pulse motion observed in the stationary frame. Application of this velocity distribution in the Lorentz factor derivation showed the same travel time for the light pulse observed in the moving and stationary frames of reference. The moving light clock system was therefore found to be unsuitable for the Lorentz factor derivation and illustration of time dilation, and shown to illustrate the relativity of the observation of light rather than the relativity of time.
A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving stationary and uniformly-moving clocks. Physical predictions concern only the observed rate of a clock as a function of its relative speed, not its setting. How the failure to make this distinction leads to the conventional predictions of spurious `relativity of simultaneity' and `length contraction' effects in special relativity is explained.
An interpretation of the inertial mass increase due to an object's velocity which is derived from the theory of special relativity is discussed. A Lorentz transformation of the reference time causes the inertial mass increase. It is assumed that the real physical phenomenon that occurs is an expansion of the reference time by a Lorentz transformation (that is, a dilation of time). Only the reference time is assumed to be variant, which causes relativistic mass. Time dilation is real. Relativistic mass originates in a Lorentz transformation of reference time.
A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean or Lorentz transformations is then studied using new, simple, and practical clock synchronisation procedures. It is found that measured length intervals are Lorentz invariant, whereas moving clocks show a universal time dilatation effect. The `relativistic length contraction' and `relativity of simultaneity' effects of conventional special relativity theory…
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.
A geometric illustration of the Lorentz transformations is given. According to similarity between space and time and correspondence between a ruler and a clock, like the division number in a moving ruler, the tick number of a moving clock is independent of its relative speed and hence invariant under the Lorentz transformations. So the hand of the moving clock never runs slow but the time interval between its two consecutive ticks contracts. Thus it is Einstein's concept of slowing of the hands of moving clocks to create the clock paradox or twin paradox. Regrettably, the concept of the clock …
Lorentz Transformation is reinterpreted. It is shown that by admitting the existence of a frame of reference with synchronized clocks, we conclude that any other frame of reference that moves related to the first has desynchronized clocks. From this conclusion we will arrive at a new expression to relate the time of different frames of reference. We also arrive at a new expression to relate the contraction of different frames. We will show that if the maximum speed on a frame with synchronized clocks is the speed of light, then the speed of light varies accordingly to the velocity of the frame…
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.
The standard Lorentz transformations establish a relationship between the space-time coordinates of the same event when detected from two inertial reference frames I and I' in the standard arrangement. This event is characterized by the space-time coordinates E(x,tE) and E'(x',t'E), tE and t'E representing the readings of the standard synchronized clocks C(x) and C'(x') located in the two frames where the event takes place. We obtain the nonstandard Lorentz transformations establishing a "physically" correct relationship between the readings of the standard synchronized clocks and the readings…
We have realized that under Lorentz transformations the tick number of a moving common clock remains unchanged, that is, the hand of the clock never runs slow, but the time interval between its two consecutive ticks contracts, so the relative time has to be recorded by using the tau-clocks required by the transformations, instead of unreal slowing clocks. Thus it is argued that using rest common clocks or the equivalent the measured velocity of light emitted by a moving source, which is quasi-velocity of foreign light, is dependent of the source velocity. Nevertheless, the velocity of foreign …
The theory of special relativity derives from the Lorentz transformation. The Lorentz transformation implies differential simultaneity and light speed isotropy. Experiments to probe differential simultaneity should be able to distinguish the Lorentz transformation from a kinematically-similar alternate transformation that predicts absolute simultaneity, the absolute Lorentz transformation. Here, we describe how published optical tests of light speed isotropy/anisotropy cannot distinguish between the two transformations. We show that the shared equations of the two transformations, from the per…
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.
We present two new measurements constraining Lorentz and CPT violation using the Xe-129 / He-3 Zeeman maser and atomic hydrogen masers. Experimental investigations of Lorentz and CPT symmetry provide important tests of the framework of the standard model of particle physics and theories of gravity. The two-species Xe-129 / He-3 Zeeman maser bounds violations of CPT and Lorentz symmetry of the neutron at the 10^-31 GeV level. Measurements with atomic hydrogen masers provide a clean limit of CPT and Lorentz symmetry violation of the proton at the 10^-27 GeV level.
The time in an atomic clock in motion is discussed using the analogy of a sing around sound source. Sing around frequency is modified according to the motion of the sing around sound source, using the Lorentz transformation equation. Thus, if we use the sing around frequency as a reference, we can define the reference time. We propose that the time delay of an atomic clock in motion be derived using the sing around method. In this letter, we show that time is defined by a combination of light speed and motion.
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…
We present two new measurements constraining Lorentz and CPT violation using the Xe-129 / He-3 Zeeman maser and atomic hydrogen masers. Experimental investigations of Lorentz and CPT symmetry provide important tests of the framework of the standard model of particle physics and theories of gravity. The two-species Xe-129 / He-3 Zeeman maser bounds violations of CPT and Lorentz symmetry of the neutron at the 10^-31 GeV level. Measurements with atomic hydrogen masers provide a clean limit of CPT and Lorentz symmetry violation of the proton at the 10^-27 GeV level.
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…
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
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.
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.
The equation of the Doppler shift of two bodies in inertial motion in a reference frame at rest (i.e., stationary reference frame) is derived. In this derivation, the wave-particle duality of photons in the theory of special relativity is considered. The dilation of time of a moving clock, which is derived from the Lorentz transformation that depends on the velocity of the moving clock in the reference frame at rest, and wavefront counting by geometrical drawing are used to describe the longitudinal Doppler shift. We show that the equation of the Doppler shift depends on the velocities of the …
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…
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…
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…
We show that standard Relativistic Dynamics Equation F=dp/dτis only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational accele…
This work deals with the questions of absolute space and relativity. In particular, an alternative derivation of the effects described by special relativity is provided, which is based on a description that assumes a privileged reference frame. The present theory follows the ideas of Lorentz and Poincare, abandoning a strict view of Einstein's "equivalence" of all inertial frames. The meaning of the Principle of Relativity is discussed and elucidated, and it is shown that it is not incompatible with the existence of a preferred, absolute, frame. Most scientists nowadays still consider the basi…
