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In order to generalize the relativistic kinematics of rigid bodies in rectilinear uniform motion to whatever kind of motion, following Minkowski’s ideas we obtain the following statement: To say that a body remains relativistically rigid means: it deforms continuously by arbitrary motion so that each of its infinitesimal elements Lorentz contract (relative to its rest length) all the time in...
I let a horizontal platform rotate uniformly, at one or two revolutions per second, around a vertical axis; on the platform I have firmly fixed the pieces of an interferometer equal to that I used in my previous experiments, described in 1910 (Comptes rendus,150, 1676). The two interfering beams, which are reflected by four mirrors placed on the rim of the rotating platform, are superimposed after...
In the Global Positioning System (GPS) the reference frame used for navigation is an earth-centered, earth-fixed rotating frame, the WGS-84 frame. The time reference is defined in an underlying earth-centered locally inertial frame, freely falling with the earth but non-rotating, with a time unit determined by atomic clocks at rest on earth’s rotating geoid. Therefore GPS receivers must apply significant...
The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than in the special theory. This line of thinking was confused, however. To clarify the situation we investigate the relation between coordinates and the results of space-time...
The hypothesis of locality, its origin and consequences are discussed. This supposition is necessary for establishing the local spacetime frame of accelerated observers; in this connection, the measurement of length in a rotating system is considered in detail. Various limitations of the hypothesis of locality are examined.
Transformations of space and time depending on a synchronization parameter, e1, indicate the existence of a privileged inertial system S0. The Lorentz transformations are obtained for a particular e1 ≠ 0. No classical experiment on inertial frames depends on the choice of e1, but if accelerations are considered only e1 = 0 remains possible. The choice e...
The Sagnac effect allows a plain geometrical interpretation in Minkowskian spacetime, involving a geometrical time-like gap known in the literature as the “time-lag”. However the time-lag seems to be a mere ‘theoretical artefact’, whose crucial feature is the use of Einstein synchronization, extrapolated from local to global along the rim of the rotating disk. This paper straightforwardly shows the...
Although most physicists presume the theoretical basis of relativistically rotating systems is well established, there may be grounds to call the traditional analysis of such systems into question. That analysis is argued to be inconsistent with regard to its prediction for circumferential Lorentz contraction, and via the hypothesis of locality, the postulates of special relativity. It is also contended...
Elementary methods of synchronization on rotating systems are discussed. It is argued that the continuous time synchronization preferred by Klauber and others is not the time synchronization for making distance measurements but rather leads to a velocity of light which depends on direction. A paradox discovered by Selleri will also be discussed. This paradox involves a limiting case of the rotating...
We briefly review Lorentz invariance and the locality principle, which are the grounds of the theory of Relativity. Subsequently we discuss some recent claims about local anisotropy in the speed of light, as observed in a non inertial frame, and especially in a rotating frame. We show that a standard analysis of a typical physical measurement of the speed of light performed in a rotating frame leads...
In this paper, it is shown, using a geometrical approach, the isotropy of the velocity of light measured in a rotating frame in Minkowski space-time, and it is verified that this result is compatible with the Sagnac effect. Furthermore, we find that this problem can be reduced to the solution of geodesic triangles in a Minkowskian cylinder. A relationship between the problems established on the cylinder...
The phase shift due to the Sagnac Effect, for relativistic matter and electromag-netic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in...
Rotating observers and circular test particle orbits in Minkowski spacetime are used to illustrate the transport laws and derivative operators needed to define the various “inertial forces” one can introduce using the natural relative observer approach to describing spacetime. Various centripetal accelerations (often called centrifugal forces when multiplied by the mass) are evaluated and compared...
Simple ideas that shed new light on the physics of rotation as it concerns two famous experiments: The Wilson and Wilson, and the Michelson and Morley experiments.
The paper discusses the issue of time and length measurements on a rotating disk. Considering operational procedures it is shown that the only relevant phenomena related to the rotation of the disk are the ones affecting clocks. Direct measurements of length do not give results in contrast with the ones obtainable for a non-rotating disk. The space geometry on the disk is also discussed and again...
By proper co-ordinates of non-inertial observers (shortly — proper non-inertial co-ordinates) we understand the proper co-ordinates of an arbitrarily moving local observer. After a brief review of the theory of proper non-inertial coordinates, we apply these co-ordinates to discuss the relativistic effects seen by observers at different positions on a rotating ring. Although there is no relative motion...
The problem of giving a relativistic description of the geometry of a rotating disk has a history nearly as old as that of the theory of relativity itself. Already in 1909 Ehrenfest formulated his famous paradox in the context of the special theory of relativity. A few years later Einstein made heuristic use of this problem in order to motivate the introduction of non-Euclidean geometry in a relativistic...
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise in models that incorporate Born reciprocity principle and the notion of a maximal acceleration. Some specific examples are discussed in detail.
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