THE DUAL PROBLEM OF THE INDUBITABLY CONSTANT VELOCITY OF LIGHT

In his first work on the theory of relativity, the famous treatise "Zur Elektrodinamik bewegter Körper" ("On the Electrodynamics of Moving Bodies") published in 1905 in "Annalen der Physik" Einstein did not account for the postulate about the constant velocity of light... However, judging by a later, popular scientific publication – Relativity: The Special and the General Theory – one cannot really say that he knew how to account for his own postulate. In Chapter IX of the book1 Einstein writes:

 We suppose a very long train travelling along the rails with the constant velocity v… People travelling in this train will with a vantage view the train as a rigid reference-body (co­ordinate system); … Then every event which takes place along the line also takes place at a particular point of the train. (Spaced by M. N.) … As a natural consequence, however, the following question arises:

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A—B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M1 be the mid-point of the distance A—B on the travelling train. Just when the flashes of lightning occur (as judged from the embankment), this point M1 naturally coincides with the point M but it moves… with the velocity v of the train. If an observer sitting in the position M1 in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously… Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. (Spaced by M. N.) Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

Etc.

This short Einstein's text, this unfortunate example and this inadequate interpretation wreaked such havoc in the understanding of the theory of relativity that it has not recovered to this day. Namely, if c is constant, if, that is, the velocity of light is the same whether the source of light is moving or not, whether approached or not, then it is absurd to claim that the ray will reach point M' first just because it is coming towards it. And this puzzles not only perplexed students, because the lesser they think about these flashes of lightning the better they fare at examinations, but — judging at least from what I could lay my hands on (at this moment only I have four books and two articles on the relativity theory before me), this is the state of affairs in general. And how else could it be if Einstein himself was unable to explain his c = const?! When for a long time science as a whole was not up the real explanation?! Because, let's not forget, at the time when Einstein invented those lightning, Rutherford's model of atom still held, i. e. only two elementary particles, electron and proton, were known. Or more exactly, Einstein had to thrust upon people the third one: photon as a quantum of light was not yet considered a particle even though it earned Einstein the Nobel Prize at the time. And just think: only two particles; in Einstein's lifetime (died in 1955) slightly over a dozen, and today more then one hundred fifty!!! A whole new god, our God in fact! And indeed, these Einstein’s lightning would also perplex us if we had not found our own God. Oh yes, as we have seen, to lay down the special theory of relativity only one its half suffices, the one about the Absence of Reason. But to understand this theory, well, here one needs the second half too, yes, the one about the All-Encompassing Possibility. How? Well, just like that, a simple application of the simple § 43 and § 45 — and nothing else.

§ 50

So, if it is true that all properties of all elementary particles depend on all properties of all other particles, if it is also true that equal elementary particles are not identical — the minimum of difference deriving from their own environment — then there are no two identical photons. Or, relative to the problem v + c = c, it means that now holds the following

Postulate: Even the photons from one and the same source of light are not identical; each will be the such one to get to its own receiver at velocity c whether this receiver is moving with respect to the emitter of light or not.

This may prove of utmost importance for the theoretical physics2, and thus warrants a few more words. You see, in an atom photon is only a virtual particle, only a possible difference in electron's energy levels. Accordingly, photon becomes real only when an electron changes its energy level. In relation to what it becomes real? One could say that it was also real before, i.e. per se, in the atom, even if only as a possibility (things that are real in atoms!) Now it also becomes real relative to the receiver. And conversely: since it has lost its original point of support in the atom, its only other reality is the emitter-receiver part, the distance . However transitory for any other specificity, i.e. longer or shorter from one moment to the other, for this photon it is everything: all that is real and constant during its lifetime, or more exactly, its only modus vivendi. This Δl = const. is what makes it specific as against the generality of all possible photons, the basis and the minimum of its specificity. On the other hand, c=const. is a property of all photons and constitutes the minimum of their togetherness. Hence the conclusion: since cΔt = Δl and since this Δl is practically the specific measure of every photon, in all inertial systems, i.e. every photon individually, the relation has to be invariant. And that is the famous invariance with which Einstein begins to lay down the mathematical foundations of his theory, i.e. its mathematical outcome v + c = c becomes comprehensible only when interpreted as an expression of a specific difference between photons.)

* * *

The immediate consequences of this state of affairs are as follows:

§ 51

a) To the traveller in the train (at pant M') and the man on the embankment (at point M) both lightning will flash simultaneously. All rays of light from A and all rays from B will reach point M' simultaneously. And all rays from A and from B will also arrive simultaneously at point M.

§ 52

b) The difference, however, rests with the following: whilst to the man on the embankment both lightning are of the same colour, to the traveller the flash from A will be ever so redder and the flash from B ever so slightly bluer because of the Doppler effect. (Just as to the traveller the thunder from A will sound deeper than the thunder from B whilst to the man on the embankment they will sound the same.) And this difference is not negligible. Namely, blue is not only an indication of higher frequency but also of higher photon energy. Photon energy, on the other hand, equals the energy difference of electron levels in atoms, the levels that define every atom. Not only that lightning A in one reference system is not the same as that selfsame lightning in another reference system, but even the atoms themselves vary from one reference system to the other. Hence the

Postulate: Every event is unique, complete and unrepeatable, only what it is in its own reference system.

§ 53

c) Accordingly, it is not true that all events taking place in a reference system necessarily take place in another system as well. The observer in a system cannot see, or measure, or record with any instrument whatsoever, a single event from another system: as soon as he has seen it, measured it, recorded it, it has happened within his own system, in his own way, or more exactly, as his own event. There is, however, another possibility. Since the traveller in the train realises that he cannot record a single event as it is happening on the embankment, he asks for information the man on the embankment. He stops at point A in the train and when the man on the embankment, also standing at point A, tells him that the embankment was struck by lightning he will note that time on his watch. He also asks a fellow traveller to do the same with another man on the embankment standing at point B. The two travellers can thus note the discrepancy between the recorded times. And it is only in this sense that one can speak of the relativity of simultaneity. Otherwise the travellers can calculate themselves the simultaneity of both lightning on the embankment (the only place where they have any raison d' être) on the basis of times recorded by them.

* * *

And so, all this trouble was needed to solve just one problem of the indubitably constant velocity of light. And a less important one at that, by and large the problem of man's ability or inability to fully grasp v + c = c. But on the way to the solution of this almost purely subjective problem a non-negligible objective consequence arose: light propagates by virtue of difference between individual photons. What revelation might then bring us the solution of the other riddle of light, the objective, virtually the only real problem posed by light? Even it is constant, why is the velocity of light such as it is?! Having come face to face with this question, one is also inevitably faced with a whole range of questions of the same order:

Why is the gravitational constant exactly 6.67·10 -11?

And Planck's 6.62·10 –34?

Why is the electron’s electric charge exactly 1.6·10 -19?

And its mass 9.1· 10 -31?

Why is proton mass 1936 that of electron mass?

And generally, how is it that these very elementary particles are stable, i.e. exactly an atom with protons and neutrons in its core and not some other atom?


1 For example:

http://www.marxists.org/reference/archive/einstein/works/1910s/relative

2 If for no other reason then because it is high time indeed for the physics textbooks to rectify the interpretation of Einstein’s lightning…

 

Back to Contents

Back to Beginning

(From ESSAY ON GOD,

translated by Miroslava-Mirka Janković)