_{1}

^{*}

Special Relativity Theory (SRT) is from time to time subject to critical assaults. There are several logically deduced discrepancies inherent in SRT (paradoxes) which demand a scrupulous examination. In this paper a new thought experiment, including two frames of reference is presented. Two trains are hurtling in opposite directions past one another in a symmetrical manner, but substantially asymmetrical events occur. This consideration leads to a contradiction in the notion of “relativity of simultaneity” — the basic tenet of SRT.

The Special Relativity Theory (SRT) is from time to time subject to critical assaults. It is worth to mention a rather recent paper [

It should notice an interesting attempt to cope with the curse of relativity of simultaneity due to introducing of a global space-time coordinate system: “Given the definition of a global coordinate system… the definition of global simultaneousness is trivial [

Two almost identical locomotives A (alighting) and B (bombing) are rushing along a double track railway in opposite directions, and they pass one by another during a small stretch of time (

Locomotive B differs structurally from A due to small round windows, replacing the lamps, but maintaining the same levels of centres, at the “down” for the front window and “up” for the rear one (

horizontal distance between their centres is

locomotive A relative to locomotive B, and c ― speed of light. These windows, facing the correspondent lamps speed of the (whilst passing of locomotives one near another) are the inputs to two identical guide-tubes, conducting light from the correspondent lamp into central compartment of the second locomotive (

At the centre of the locomotive B is situated an exploding device with a special controller operating a detonating fuse. This controller is represent by an optoelectronic apparatus, working according to binary logic. It implements the well-known function of logical multiplication-the double input operation

In the proper reference frame

receives two signals simultaneously, and engages the exploding device, ― the bomb blows up.

However, in its own reference frame of locomotive A symmetry is absent (Fitzgerald-Lorentz contraction!). In the reference frame of the light source (

The length of the tubes becomes

Let us insert explicitly the relativistic factor

We obtain identical zero for the time difference

Let us substitute the vacuum tubes for fiberglass cables. The speed of light in a moving medium does obey the rule (1) according to special relativity, but instead of c we have to use

and for the right cable:

Substituting (3) and (4) into (2) gives:

Here also the bomb blasts as viewing from both reference frames.

For the speed

Rejecting the terms of higher order, we come to the formula

Consider the situation from the point of view light source reference frame

So, in place of (2), we get

Let us calculate the difference

Using (6) in (5) gives

This resulting time difference in (7) is evidently more than zero. If

Transition from phase velocity to group velocity changes nothing in this paradoxical situation. In this case the group velocity of light in the moving medium according to Fresnel is

where

Substituting (9) into expression for signal’s time difference we get

which is obvious for

On this condition the Einstein formula for group velocity is as follows:

That is different than the Fresnel Formula (8) in this case [

Calculation gives the following expression:

The signal’s time difference would be

For the real values of refractive index the denominator and the numerator are always positive, which is to say that sign of total expression (12) is always plus. We have

For the locomotive velocities that are small with respect to the velocity of light

The Formulae (8) and (11) lead to cardinally different results (10) and (12). Notice, the delay

A number of paradoxes have been noticed in the realm of SRT and their solutions have been found also within the same theory. However, in the case of “bomb paradox” there does not appear to be any in the field of vision. If the truth is to be told, such a fancy trick could not be tolerated for a domain of knowledge, pretending to be treated as natural science. This “bombing attack” casts doubt on the principal tenet of the theory ― relativity of simultaneity, valid for each pair of events separated by a space-like interval. Unfortunately, locomotive speed, reaching a quarter of that of the light, is unattainable for railways in the meantime (smile!), so the opportunity of experimental checking does not present itself any time soon. That is why either real experimental testing of the relativity of simultaneity would be of great importance. Such an acceptable experiment is suggested in a paper by Wagner [

There is something inconsequential in how Einstein treats the light in the medium: it loses the property of speed invariance. The value

The author thanks Mr Barry Smith from the University of Liverpool for valuable help while preparing this paper.

Vladimir A. Leus, (2015) On an Optical Paradox in Special Relativity. Open Access Library Journal,02,1-7. doi: 10.4236/oalib.1101963