The Dynamics of Relativistic Length Contraction and the Ehrenfest Paradox

Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically, on the energy-momentum tensor. We discuss a few examples, which illustrate the dynamical aspect of the length-contraction effect within the framework of Special Relativity. We show some pitfalls associated with direct application of the length contraction formula in cases when an extended object is accelerated. Our analysis reveals intimate connections between length contraction and the dynamics of internal forces within the accelerated system. The developed approach is used to analyze the correlation between two congruent disks - one stationary and one rotating (the Ehrenfest paradox). Specifically, we consider the transition of a disk from the state of rest to a spinning state under the applied forces. It reveals the underlying physical mechanism in the corresponding transition from Euclidean geometry of stationary disk to Lobachevskys (hyperbolic) geometry of the spinning disk in the process of its rotational boost. A conclusion is made that the rest mass of a spinning disk or ring of a fixed radius must contain an additional term representing the potential energy of non-Euclidean circumferential deformation of its material. Possible experimentally observable manifestations of Lobachevskys geometry of rotating systems are discussed.

A new paradox in superluminal signaling

A new causal paradox in superluminal signaling is presented. In contrast to the Tolman paradox with tachyon exchange between two parties, the new paradox appears already in a one-way superluminal signaling, even without creating the time loop. This produces a universal ban on superluminal signals, which is stronger than the ban imposed by the Tolman paradox. The analysis also shows that records of evolution of a superluminal object observed from two different reference frames may be time-reversed with respect to each other. Interactions with such objects could add some new features to spectroscopy. Even though relativity embraces superluminal motions, thus making the world symmetric with respect to the invariant speed barrier, their ineptness for signaling makes the symmetry incomplete. Key words: superluminal signaling, tachyons, the Tolman paradox

Relativistic Paradoxes and Lack of Relativity in Closed Spaces

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 two RF with respect to actual forces in play, they can be distinguished by clock synchronization. A closed space singles out a truly stationary RF with single-valued global time; in all other frames, time is not a single-valued parameter. This implies that even uniform motion along a spatial geodesic in a compact space is not truly inertial, and there is an effective force on an object in such motion. Therefore, the traveling twin will age less upon circumnavigation than the stationary one, just as in flat space-time. Ironically, Relativity in this case emerges free of paradoxes at the price of bringing back the pre-Galilean concept of absolute rest. An example showing the absence of paradoxes is also considered for a more realistic case of a time-evolving closed space.

On the Superluminal Quantum Tunneling and Causality Violation

This is an analysis of some aspects of an old but still controversial topic, superluminal quantum tunneling. Some features of quantum tunneling described in literature, such as definition of the tunneling time and a frequency range of a signal, are discussed. The argument is presented that claim of superluminal signaling allegedly observed in frustrated internal reflection experiment was based on the wrong interpretation of the tunneling process. A thought experiment similar to that in the Tolman paradox is discussed. It shows that a new factor, attenuation, comes in the interplay between tunneled signals and macroscopic causality.

Interactions Between Evanescent Photons and Environment

The evanescent waves named as EW1, EW2, EW3 are described in 3 respective experimental setups: 1) total internal reflection; 2) scattering on an inhomogeneous planar target; and 3) propagation along a waveguide. Some interactions are considered between EW2 and the environment. The latter may include a beam of probing particles and/or the screen on which the EW2 are formed. Some new properties of EW are described, such as complex energy eigenvalues in case of a movable screen, and evanescence exchange between the interacting objects. This reveals the connection between evanescent states and the Gamow states of the studied system. The 4-momentum exchange between EW2 and the probe is highly selective and may collapse the superposition of studied EW2- eigenstates to a single EW-eigenstate of the probing particle. Possible imprints of EW2 in the far field are briefly discussed and a simple experiment is suggested for their observation. .

Two Permanently Congruent Rods May Have Different Proper Lengths

We scrutinize congruence as one of the basic definitions of equality in geometry and pit it against physics of Special Relativity. We show that two non-rigid rods permanently kept congruent during their common expansion or compression may have different instantaneous proper lengths (when measured at the same time of their respective reference clocks) if they have different mass distributions over their lengths. Alternatively, their proper lengths can come out equal only when measured at different but strictly correlated moments of time of their respective clocks. The derived expression for the ratio of instantaneous proper lengths of two permanently congruent changing objects explicitly contains information about the objects mass distribution. The same is true for the ratio of readings of the two reference clocks, for which the instantaneous measurements of respective proper lengths produce the same result. In either case the characteristics usually considered as purely kinematic depend on mass distribution, which is a dynamic property. This is a spectacular demonstration of dynamic aspect of geometry already in the framework of Special Relativity.