Chandru Iyer

A constructive formulation of the one-way speed of light

A formulation of the one-way speed of light in three-dimensional Euclidean space is derived by a constructive approach. This formulation is consistent with the result of the Michelson–Morley experiment in that the harmonic mean of the outward and return speeds is equal to c, the standard value for the speed of electromagnetic radiation in vacuum. It is also shown that a shift in synchronization, proportional to the distance along the line of motion, renders this speed a constant along all directions.

Reversal in the time order of interactive events: the collision of inclined rods

In the rod and hole paradox as described by Rindler (1961 Am. J. Phys. 29 365-6), a rigid rod moves at high speed over a table towards a hole of the same size. Observations from the inertial frames of the rod and slot are widely different. Rindler explains these differences by the concept of differing perceptions in rigidity. Gron and Johannesen (1993 Eur. J. Phys. 14 97-100) confirmed this aspect by computer simulation where the shapes of the rods are different as observed from the co-moving frames of the rod and slot. Lintel and Gruber (2005 Eur. J. Phys. 26 19-23) presented an approach based on retardation due to speed of stress propagation. In this paper we consider the situation when two parallel rods collide while approaching each other along a line at an inclination with their axis. The collisions of the top and bottom ends are reversed in time order as observed from the two co-moving frames. This result is explained by the concept of extended present derived from the principle of relativity of simultaneity.

Differing observations on the landing of the rod into the slot

In the usual rod and slot paradox a rod falls into a slot due to gravity. Many thought experiments have been conducted where the presence of gravity is eliminated with the rod and slot approaching each other along a line joining their centers. In these experiments the line of motion is not parallel to the axis of the rod or the slot. We consider the cases for which the rod falls into the slot and the rod does not fall into the slot, each from the perspective of the co-moving frames of the rod and the slot. We show that if the rod falls into the slot as determined by Galilean kinematics, the same conclusion is valid for relativistic kinematics. Our conclusion emphasizes that the passing (or crashing) of the rod is unaffected by relativistic kinematics. This determination does not depend on the magnitude of the velocity, but only on the proper lengths and the proper angles of the rod and slot with the line of motion.

Lorentz transformations with arbitrary line of motion

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x–y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with As chosen x- or y-axis. It becomes necessary in such cases to develop Lorentz transformations where the line of motion is not aligned with either the x- or the y-axis. In this paper we develop these transformations and show that under such transformations, two orthogonal systems (in their respective frames) appear non-orthogonal to each other. We also illustrate the usefulness of the transformation by applying it to three problems including the rod-slot problem.

Comment on ‘The principle of relativity and the indeterminancy of special relativity’

This contribution adds to the points on themade by De Abreu and Guerra. We show that the Lorentz Transformation can be composed by the physical observations made in a frame K of events in a frame K-prime viz i) objects in K-prime are moving at a speed v relative to K, ii) distances and time intervals measured by K-prime are at variance with those measured by K and iii) the concept of simultaneity is different in K-prime compared to K. The order in which the composition is executed determines the nature of the middle aspect (ii). This essential uncertainty of the theory can be resolved only by a universal synchronicity as discussed in [1] based on the unique frame in which the one way speed of light is constant in all directions.