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.
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 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…
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 descr…
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 …
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.
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…
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. …
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…
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 …
This article revisits the historiography of the problem of inertial frames. Specifically, the case of the twins in the clock paradox is considered to see that some resolutions implicitly assume inertiality for the non-accelerating twin. If inertial frames are explicitly identified by motion with respect to the large scale structure of the universe, it makes it possible to consider the relative inertiality of different frames.
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…
In this paper we deal analytically with a version of the so called clock paradox in which the moving clock performs a circular motion of constant radius. The rest clock is denoted as (1), the rotating clock is (2), the inertial frame in which (1) is at rest and (2) moves is I and, finally, the accelerated frame in which (2) is at rest and (1) rotates is A. By using the General Theory of Relativity in order to describe the motion of (1) as seen in A we will show the following features. I) A differential aging between (1) and (2) occurs at their reunion and it has an absolute character, i.e. the…
We consider a clock 'paradox' framework where an observer leaves an inertial frame, is accelerated and after an arbitrary trip comes back. We discuss a simple equation that gives, in the 1+1 dimensional case, an explicit relation between the time elapsed on the inertial frame and the acceleration measured by the accelerating observer during the trip. A non-closed trip with respect to an inertial frame appears closed with respect to another suitable inertial frame. Using this observation we define the differential aging as a function of proper time and show that it is non-decreasing. The recons…
We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient $β$, special relativity being recovered for $β=0$. The effect of differential aging is studied for the different values of $β$. Below the critical values $|β| =1/c$ the differential aging has the usual direction - after a round trip the accelerated observer returns younger than the twin at rest in the inertial frame - while above the cri…
A conventional space-time diagram is $r-ct$ one, which satisfies the Minkowski geometry. This geometry conflict the intuition from the Euclid geometry. In this work an Euclid space-time diagram is proposed to describe relativistic world lines with an exact Euclid geometry. The relativistic effects such as the dilation of moving clocks, the contraction of moving length, and the twin paradox can be geometrically expressed in the Euclid space-time diagram. It is applied to the case of a satellite clock to correct the gravitational effect. It is found that this Euclid space-time diagram is much mo…
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 an earlier paper the author expounded an interferometer scheme to communicate classical data over an entangled quantum channel. We return to this concept to show that the laws of Quantum Mechanics are not violated and that the device is able to affect the statistical blend of the quantum states (and that this can be detected) but not the statistics - i.e. the physics of observables. The ideas of superluminal information transfer, discussed in the previous paper, are taken forward to develop a notion of absolute space, time and motion with relativistic effects ascribed to motion through an a…
