In the standard formulation of the twin paradox an accelerated twin considers himself as at rest and his brother as moving. Hence, when formulating the twin paradox, one uses the general principle of relativity, i.e. that accelerated and rotational motion is relative. The significance of perfect inertial dragging for the validity of the principle of relativity is made clear. Three new results are reviewed in the discussion. A cosmic time effect which cannot be reduced to the gravitational or the kinematical time dilation. Perfect dragging in an exact solution of Einsteins field equations describing flat spacetime inside a shell with Kerr spacetime outside it. An extended model of Minkowski spacetime in order to avoid introducing absolute acceleration and rotation through the asymptotic emptiness of the Kerr spacetime.
One of the most discussed peculiarities of Einstein's theory of relativity is the twin paradox, the fact that the time between two events in space-time appears to depend on the path between these events. We show that this time discrepancy results only from faulty assumptions in the transition from one reference system to another. The twin paradox does not exist. But the Lorentz invariance of the theory has strong consequences, if we assume that it is valid not only locally, but also on cosmic scale.
The famous twin paradox of the Special Theory of Relativity by Einstein (1905) is revisited and revised. This paradox is not a paradox in the true sense of a paradox but a reflection of a misunderstanding of the problem and the Principle of Relativity. The currently accepted solution to this takes into account the accelerations and deceleration of the traveling twin thus introducing an asymmetry that solves the paradox. We argue here that, with the acceleration and deceleration neglected, the problem is asymmetric hence leading to the same conclusion that the traveling twin will age less than …
The twin paradox of the special theory of relativity has given rise to a large body of literature discussing its implications. In its standard form, the traveler changes velocity only at the destination of the trip, so that he appears to perceive an improbably instantaneous and non-continuous change in age of the stationary twin. In this work, a smooth velocity/acceleration profile is used that allows the abrupt velocity-change case as a limit. All gravitational effects are ignored in this treatment. Aside from mutual perception of simultaneous clock times in an accelerating frame, constant co…
A nomenclature for inertial frames and a notation for space and time coordinates is proposed to give an unambigous description of space-time experiments in special relativity. Of particular importance are the concepts of `base' and `travelling' frames and `primary' and `reciprocal' experiments. A detailed discussion of the twin paradox is presented. The physical basis of the differential aging effect is found to be a relativistic relative-velocity transformation relation, not, as hitherto supposed, the spurious `length contraction' effect.
It is shown that the "twin paradox" arises from comparing unlike entities, namely perceived intervals with eigenintervals. When this lacuna is closed, it is seen that there is no twin paradox and that eigentime can serve as the independent variable for mechanics in Special Relativity.
Observation of the decay of muons produced in the Earth's atmosphere by cosmic ray interactions provides a graphic illustration of the counter-intuitive space-time predictions of special relativity theory. Muons at rest in the atmosphere, decaying simultaneously, are subject to a universal time-dilatation effect when viewed from a moving frame and so are also observed to decay simultaneously in all such frames. The analysis of this example reveals the underlying physics of the differential aging effect in Langevin's travelling-twin thought experiment.
The special theory of relativity is the foundation of modern physics, but its unusual postulate of invariant vacuum speed of light results in a number of plausible paradoxes. This situation leads to radical criticisms and suspicions against the theory of relativity. In this paper, from the perspective that the relativity is nothing but a geometry, we give a uniform resolution to some famous and typical paradoxes such as the ladder paradox, the Ehrenfest's rotational disc paradox. The discussion shows that all the paradoxes are caused by misinterpretation of concepts. We misused the global simu…
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…
If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological invariant of their spatial geodesics, namely the homotopy class. This illustrates how the spacetime symmetry invariance group, although valid {\it locally}, is broken down {\it globally} as soon as some points of space are identified. As a consequence, any non--trivial space topology defines preferred inertial frames along which the proper time is longer than …
An in-depth and mathematically-detailed analysis of Langevin's popular 1911 article on the special theory of relativity is presented. For the reader's convenience, English translations of large parts of the original French text are given. The self-contradictory nature of many of Langevin's assertions is pointed out. Of special interest is the analysis of the exchange of light signals between the travelling and stay-at-home twins in Langevin's thought experiment, in which antinomies are found in the conventional relativistic treatment. Their resolution shows that the physical basis of the diffe…
Some known relativistic paradoxes are reconsidered for closed spaces, using a simple geometric model. For two twins in a closed space, a real paradox seems to emerge when the traveling twin is moving uniformly along a geodesic and returns to the starting point without turning back. Accordingly, the reference frames (RF) of both twins seem to be equivalent, which makes the twin paradox irresolvable: each twin can claim to be at rest and therefore to have aged more than the partner upon their reunion. In reality, the paradox has the resolution in this case as well. Apart from distinction between…
A "Two-Spaceship Paradox" in special relativity is resolved and discussed. We demonstrate a nonstandard resolution to the "two-spaceship paradox" by explicit calculation using Generalized Principle of limiting 4-dimensional symmetry proposed in previous paper [1].The physical and geometrical meaning of the nonholonomic transformations used in special relativity is determined.
The paper is intended to clarify operational meaning of mass and time quantities as main characteristics of an atomic clock, which is considered a quantum oscillator in association with the de Broglie wave concept. The specification of the concept of clock in quantum terms reflects the idea of relativistic mass and time complementarity, which is important for avoiding ambiguity of such notions as ``time rate'', ``time record'', and ``elapsed time'' under relativistic conditions. We used this approach in SRT Kinematics to conduct a detailed analysis of the clock paradox; results are discussed. …
Recently a New Relativity Principle has been proposed by one of the authors as the underlying physical and geometrical foundations of String and {\bf M} Theory. It is explicitly shown that within the framework of the New Relativity Theory, some Quantum Mechanical Paradoxes like the Einstein-Rosen Podolsky and the Black Hole Information Loss, are easily resolved. Such New Relativity Theory requires the introduction of an Infinite Dimensional Quantum Spacetime as has been shown recently by one of us. This can be viewed as just another way of looking at Feynman's path integral formulation of Quan…
The distinction between the real positions of moving objects in a single reference frame and the apparent positions of objects at rest in one inertial frame and viewed from another, as predicted by the space-time Lorentz Transformations, is discussed. It is found that in the Rockets-and-String paradox the string remains unstressed and does not break and that the pole in the Barn-and-Pole paradox never actually fits into the barn. The close relationship of the Lorentz-Fitzgerald Contraction and the relativity of simultaneity of Special Relativity is pointed out and an associated paradox, in whi…
The thought experiment (called the clock paradox or the twin paradox)proposed by Langevin in 1911 of two observers, one staying on Earth and the other making a trip toward a star with a velocity near the light velocity is very well known for its surprising result. When the traveler comes back, he is younger that the stay on Earth. This astonishing situation deduced from the theory of Special relativity sparked a huge amount of articles, discussions and controversies such it remains a particular phenomenon probably unique in Physics. We propose to study it. First we looked for the simplest solu…
We resolve a paradox in special relativity proposed by F. W. Sears for the action of forces on a rigid body. In the paradox, a moving rigid rod is struck at different times by impulsive forces, but continues to move with unchanged velocity, with the forces having no effect. Our conclusion is that the usual laws of mechanics can be applied to a rigid body only in its rest system
We present a solution for the apparent paradox regarding an incompatibility between the Lorentz force law and special relativity presented by Mansuripur [Phys. Rev. Lett. 108, 193901 (2012)]. A connection between the apparent paradox and the Abraham-Minkowski debate about the momentum of electromagnetic waves in material media is also presented.
The clock paradox is analyzed for the case when the onward and return trips cover the same <<distance>> (as observed by the traveling twin) but at unequal velocities. In this case the stationary twin observes the distances covered by her sister during the onward and return trips to be different. The analysis is presented using formulations of special relativity and the only requirement for consistency is that all observations are made from any one chosen inertial frame. The analysis suggests that a defining feature of an inertial frame should be based on the continued maintenance of the distin…
The field equations of general relativity are shown to derive from the existence of a limit force or of a limit power in nature. The limits have the value of c^4/4G and c^5/4G. The proof makes use of a result by Jacobson. All known experimental data is consistent with the limits. Applied to the universe, the limits predict its darkness at night and the observed scale factor. Some experimental tests of the limits are proposed. The main counter-arguments and paradoxes are discussed, such as the transformation under boosts, the force felt at a black hole horizon, the mountain problem, and the con…
In this paper it is shown that in the approach to special relativity which exclusively deals with the four-dimensional geometric quantities (4D GQs), the invariant special relativity (ISR), there is not recently posed paradox that in a static electric field a magnetic dipole moment (MDM) is subject to a torque in some frames and not in others. In the ISR, there is no need either for the change of the Lorentz force, but as a 4D GQ, or for the introduction of some "hidden" 3D quantities. Furthermore, in the ISR, contrary to all previous approaches, an electrically neutral current-loop in its res…
The essence of special relativity is hiding in the equal existence of particle and antiparticle, which can be expressed by two discrete symmetries within one inertial frame --- the invariance under the (newly defined) space-time inversion (${\bf x}\to -{\bf x},t\to -t$), or equivalently, the invariance under a mass inversion ($m\to -m$). The problems discussed are: the evolution of the $CPT$ invariance into a basic postulate, an unique solution to the original puzzle in Einstein-Podolsky-Rosen paradox, the reduced Dirac equation for hydrogenlike atoms, and the negative mass paradox leading to …
Special relativity theory is well established and confirmed by experiments. This research establishes an operational measurement way to express the great theory in a geometrical form. This may be valuable for understanding the underlying concepts of relativity theory. In four-dimensional spacetime continuum, the displacement field of matter motion is measurable quantities. Based on these measurements, a finite geometrical field can be established. On this sense, the matter motion in physics is viewed as the deformation of spacetime continuum. Suppose the spacetime continuum is isotropic, based…
It has been recently argued that the Lorentz force is incompatible with Special Relativity and should be amended in the presence of magnetization and polarization in order to avoid a paradox involving a magnet in the presence of an electric field. Here we stress the well-known fact among relativists that such an incompatibility is simply impossible and show that the appearance of such a "paradox" is a mere consequence of not fully considering the relativistic consequences of the covariant form of the Lorentz force. It should be mentioned, though, that this criticism does not invalidate the deb…
In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear. No inertial motion steps are considered. The rest clock is denoted as (1), the to-and-fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: I) What is t…
In this Comment it is shown that the principle of relativity is naturally satisfied and there is no paradox if an independent physical reality is attributed to the four-dimensional (4D) geometric quantities (GQs) and not, as usual, to the 3D quantities. Hence, there is no need either for the change of the expression for the Lorentz force, but as a 4D GQ, or for the introduction of some "hidden" 3D quantities.
