It is well known that simultaneity within an inertial frame is defined in relativity theory by a convention or definition. This definition leads to different simultaneities across inertial frames and the well known principle of relativity of simultan
eity. The lack of a universal present implies the existence of past, present and future as a collection of events on a four dimensional manifold or continuum wherein three dimensions are space like and one dimension is time like. However, such a continuum precludes the possibility of evolution of future from the present as all events exist forever so to speak on the continuum with the tenses past, present and future merely being perceptions of different inertial frames. Such a far-reaching ontological concept, created by a mere convention, is yet to gain full acceptance. In this paper, we present arguments in favour of an absolute present, which means simultaneous events are simultaneous in all inertial frames, and subscribe to evolution of future from the present.
In determining the classical Doppler Effect, two assumptions are used for computing the difference in distance travelled by consecutive signals: (a) the receptor is stationary, and (b) the emitter is stationary. The calculated Doppler Effect under th
e two assumptions are identical, provided the velocity of propagation with respect to source and the velocity of propagation with respect to the receptor differ exactly by the velocity of relative motion. We show that, in the case of light, the ratio of the two calculated classical Doppler Effects, with propagation speed c in the source and receptor inertial frames respectively, remains constant in all geometries and orientations. Furthermore, the observed Doppler Effect, as predicted by special relativity, is the geometric mean of the two expected classical Doppler Effects in all geometries and orientations. This leads to two simultaneous conclusions: (1) by the receptor that the clock associated with the emitter runs slow, and (2) by the emitter that the clock associated with the receptor runs slow. These differences can be resolved if we theorize that light travels at speed c with respect to the emitter as it leaves the emitter and travels at speed c with respect to the receptor as it approaches the receptor.
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 ret
urn 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.
The relationship between the harmonic mean and special relativity is concisely elucidated. The arguments in favor and against SRT are explored. It is shown that the ratio of the speed of light to the harmonic mean of the onward and return speeds of l
ight in a moving frame under Newtonian mechanics, when equitably distributed between space and time as a correction, leads to the Lorentz transformation. This correction implies an apparent contraction of objects and time dilation. However, the symmetry of the onward and inverse transformations give a different meaning to the gamma factor
We expand the IST transformation to three-dimensional Euclidean space and derive the speed of light under the IST transformation. The switch from the direction cosines observed in K to those observed in K-prime is surprisingly smooth. The formulation
thus derived maintains the property that the round trip speed is constant. We further show that under the proper synchronization convention of K-prime, the one-way speed of light becomes constant.
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 durin
g 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 distinctive synchronicity of the clocks co-moving with it. Published in Journal of Physical and Natural Sciences Volume 1, Issue 1, 2007 http://www.scientificjournals.org/journals2007/articles/1102.pdf
This contribution adds to the points on the <indeterminacy of special relativity> made 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.
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, wh
ich 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. The derivation has been done before using vector algebra. Such derivations assume that the axes of K and K-prime are parallel. Our method uses matrix algebra and shows that the axes of K and K-prime do not remain parallel, and in fact K and K-prime which are properly orthogonal are observed to be non-orthogonal by K-prime and K respectively. http://www.iop.org/EJ/abstract/0143-0807/28/2/004
In the usual rod and slot paradox, the rod, if it falls, was expected to fall into the 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, whereby the considerations come strictly under Special Relativity. In these experiments the line of motion is not parallel to either the axis of the rod or the slot. In this paper we consider in detail the two cases when the rod does fall into the slot and when 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 whether the rod falls into the slot as determined by Galilean kinematics is also valid under relativistic kinematics; this determination does not depend upon 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. Our conclusion emphasizes the fact that the passing (or crashing) of the rod as a wholesome event is unaffected by relativistic kinematics. We also provide a simple formula to determine whether or not the rod passes through the slot.
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 ex
plains 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.
