A Short History of the Concept of Relative Simultaneity in the Special Theory of Relativity

(Christopher Jon Bjerknes)

Abstract. There is a common misconception enunciated in numerous histories, that Albert Einstein was the first person to propose the relativity of simultaneity. It is often alleged that the paper, "Zur Elektrodynamik bewegter Körper", Annalen der Physik, Series 4, Volume 17, (1905), pp. 891-921, at 892-895, contained the first proposal of a clock synchronization method employing observers and light signals. Given the absence of references in Einstein's work, it has been further assumed by some that the revised thought-experiment regarding a midpoint and relative simultaneity, which appeared in Einstein's 1916 work, "Die Relativität der Gleichzeitigkeit", Über die spezielle und die allgemeine Relativitätstheorie, Chapter 9, Friedr. Vieweg & Sohn, Braunschweig, (1917), pp. 16-19, was also an original idea. The historic record proves otherwise.

Piecing together the Missing References in Einstein's Plagiarized Works

In 1887, Woldemar Voigt published the following relativistic transformation of space-time coordinates [1]:

x' = x - vt , y' = y /  , z' = z /  , t' = t - vx / c2 , where  = 1 / ( 1 - v2 / c2 )1/2 .

Poincaré asserted that simultaneity is relative, in 1898:

"XII. But let us pass to examples less artificial; to understand the definition implicitly supposed by the savants, let us watch them at work and look for the rules by which they investigate simultaneity.

I will take two simple examples, the measurement of the velocity of light and the determination of longitude.

When an astronomer tells me that some stellar phenomenon, which his telescope reveals to him at this moment, happened nevertheless fifty years ago, I seek his meaning, and to that end I shall ask him first how he knows it, that is, how he has measured the velocity of light.

He has begun by supposing that light has a constant velocity, and in particular that its velocity is the same in all directions. That is a postulate without which no measurement of this velocity could be attempted. This postulate could never be verified directly by experiment; it might be contradicted by it if the results of different measurements were not concordant. We should think ourselves fortunate that this contradiction has not happened and that the slight discordances which may happen can be readily explained.

The postulate, at all events, resembling the principle of sufficient reason, has been accepted by everybody; what I wish to emphasize is that it furnishes us with a new rule for the investigation of simultaneity, entirely different from that which we have enunciated above.

This postulate assumed, let us see how the velocity of light has been measured. You know that Roemer used eclipses of the satellites of Jupiter, and sought how much the event fell behind its prediction. But how is this prediction made? It is by the aid of astronomic laws, for instance Newton's law.

Could not the observed facts be just as well explained if we attributed to the velocity of light a little different value from that adopted, and supposed Newton's law only approximate? Only this would lead to replacing Newton's law by another more complicated. So for the velocity of light a value is adopted, such that the astronomic laws compatible with this value may be as simple as possible. When navigators or geographers determine a longitude, they have to solve just the problem we are discussing; they must, without being at Paris, calculate Paris time. How do they accomplish it? They carry a chronometer set for Paris. The qualitative problem of simultaneity is made to depend upon the quantitative problem of the measurement of time. I need not take up the difficulties relative to this latter problem, since above I have emphasized them at length.

Or else they observe an astronomic phenomenon, such as an eclipse of the moon, and they suppose that this phenomenon is perceived simultaneously from all points of the earth. That is not altogether true, since the propagation of light is not instantaneous; if absolute exactitude were desired, there would be a correction to make according to a complicated rule.

Or else finally they use the telegraph. It is clear first that the reception of the signal at Berlin, for instance, is after the sending of this same signal from Paris. This is the rule of cause and effect analyzed above. But how much after? In general, the duration of the transmission is neglected and the two events are regarded as simultaneous. But, to be rigorous, a little correction would still have to be made by a complicated calculation; in practise it is not made, because it would be well within the errors of observation; its theoretic necessity is none the less from our point of view, which is that of a rigorous definition. From this discussion, I wish to emphasize two things: (1) The rules applied are exceedingly various. (2) It is difficult to separate the qualitative problem of simultaneity from the quantitative problem of the measurement of time; no matter whether a chronometer is used, or whether account must be taken of a velocity of transmission, as that of light, because such a velocity could not be measured without measuring a time.

XIII

To conclude: We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them.[2]"

Circa 1899, Poincaré clarified the fact that he saw no distinction between "time" and "local time":

"Allow me a couple of remarks regarding the new variable t': it is what Lorentz calls the local time. At a given point t and t' will not defer but by a constant, t' will, therefore, always represent the time, but the origin of the times being different for the different points serves as justification for his designation."

"Disons deux mots sur la nouvelle variable t': c'est ce que Lorentz appelle le temps locale. En un point donné t et t' ne différeront que par une constante, t' représentera donc toujours le temps mais l'origine des temps étant différente aux différents points: cela justifie sa dénomination.[3]"

In 1900, Poincaré stated:

"In order for the compensation to occur, the phenomena must correspond, not to the true time t, but to some determined local time t' defined in the following way.

I suppose that observers located at different points synchronize their watches with the aid of light signals; which they attempt to adjust to the time of the transmission of these signals, but these observers are unaware of their movement of translation and they consequently believe that the signals travel at the same speed in both directions, they restrict themselves to crossing the observations, sending a signal from A to B, then another from B to A. The local time t' is the time determined by watches synchronized in this manner.

If in such a case

V = 1 / K0 ½

is the speed of light, and v the translation of the Earth, that I imagine to be parallel to the positive x axis, one will have:

t' = t - vx / V 2."

"Pour que la compensation se fasse, il faut rapporter les phénomènes, non pas au temps vrai t, mais à un certain temps local 'N défini de la façon suivante.

Je suppose que des observateurs placés en différents points, règlent leurs montres à l'aide de signaux lumineux; qu'ils cherchent à corriger ces signaux du temps de la transmission, mais qu'ignorant le mouvement de translation dont ils sont animès et croyant par conséquent que les signaux se transmettent également vite dans les deux sens, ils se bornent à croiser les observations, en envoyant un signal de A en B, puis un autre de B en A. Le temps local tNest le temps marqué par les montres ainsi réglées.

Si alors

V = 1 / K0 ½

est la vitesse de la lumière, et v la translation de la Terre que je suppose parallèle à l'axe des x positifs, on aura:

t' = t - vx / V 2 . [4]"

In 1902, Poincaré asserted, and we know, from Solovine's accounts [6], that Einstein had read this work of Poincaré's:

"There is no absolute time. When we say that two periods are equal, the statement has no meaning, and can only acquire a meaning by convention. Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places. I have explained this in an article entitled 'Mesure du Temps.' [7]"

Again, in 1904, Poincaré asserted that simultaneity is relative, and elaborated on the light synchronization method that Mileva Einstein-Marity and Albert Einstein copied, in 1905, without citation to Poincaré. Poincaré stated in 1904,

"We come to the principle of relativity: this not only is confirmed by daily experience, not only is it a necessary consequence of the hypothesis of central forces, but it is imposed in an irresistible way upon our good sense, and yet it also is battered.

Consider two electrified bodies; though they seem to us at rest, they are both carried along by the motion of the earth; an electric charge in motion, Rowland has taught us, is equivalent to a current; these two charged bodies are, therefore, equivalent to two parallel currents of the same sense and these two currents should attract each other. In measuring this attraction, we measure the velocity of the earth; not its velocity in relation to the sun or the fixed stars, but its absolute velocity.

I well know what one will say, it is not its absolute velocity that is measured, it is its velocity in relation to the ether. How unsatisfactory that is! Is it not evident that from the principle so understood we could no longer get anything? It could no longer tell us anything just because it would no longer fear any contradiction.

If we succeed in measuring anything, we would always be free to say that this is not the absolute velocity in relation to the ether, it might always be the velocity in relation to some new unknown fluid with which we might fill space.

Indeed, experience has taken on itself to ruin this interpretation of the principle of relativity; all attempts to measure the velocity of the earth in relation to the ether have led to negative results. This time experimental physics has been more faithful to the principle than mathematical physics; the theorists, to put in accord their other general views, would not have spared it; but experiment has been stubborn in confirming it.

The means have been varied in a thousand ways and finally Michelson has pushed precision to its last limits; nothing has come of it. It is precisely to explain this obstinacy that the mathematicians are forced today to employ all their ingenuity.

Their task was not easy, and if Lorentz has gotten through it, it is only by accumulating hypotheses. The most ingenious idea has been that of local time.

Imagine two observers who wish to adjust their watches by optical signals; they exchange signals, but as they know that the transmission of light is not instantaneous, they take care to cross them.

When the station B perceives the signal from the station A, its clock should not mark the same hour as that of the station A at the moment of sending the signal, but this hour augmented by a constant representing the duration of the transmission. Suppose, for example, that the station A sends its signal when its clock marks the hour o, and that the station B perceives it when its clock marks the hour t. The clocks are adjusted if the slowness equal to t represents the duration of the transmission, and to verify it, the station B sends in its turn a signal when its clock marks o; then the station A should perceive it when its clock marks t. The timepieces are then adjusted. And in fact, they mark the same hour at the same physical instant, but on one condition, which is that the two stations are fixed. In the contrary case the duration of the transmission will not be the same in the two senses, since the station A, for example, moves forward to meet the optical perturbation emanating from B, while the station B flies away before the perturbation emanating from A. The watches adjusted in that manner do not mark, therefore, the true time, they mark what one may call the local time, so that one of them goes slow on the other. It matters little since we have no means of perceiving it. All the phenomena which happen at A, for example, will be late, but all will be equally so, and the observer who ascertains them will not perceive it since his watch is slow; so as the principle of relativity would have it, he will have no means of knowing whether he is at rest or in absolute motion.[8]"

Mileva Einstein-Marity and Albert Einstein parroted Poincaré's clock synchronization procedures, without acknowledging that Poincaré had stated them first. From the Einsteins' 1905 paper:

"I. KINEMATICAL PART

§ 1. Definition of Simultaneity

[Consider a system of coordinates, in which the Newtonian mechanical equations are valid. In order to put the contradistinction from the [moving] systems of coordinates to be introduced later into words, and for the exact definition of the conceptualization, we call this system of coordinates the 'resting system'.]

If a material point is at rest relatively to this system of co-ordinates, its position can be defined relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean geometry, and can be expressed in Cartesian co-ordinates.

If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by 'time.' We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, 'That train arrives here at 7 o'clock,' I mean something like this: 'The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.'

It might appear possible to overcome all the difficulties attending the definition of 'time' by substituting 'the position of the small hand of my watch' for 'time.' And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or - what comes to the same thing - to evaluate the times of events occurring at places remote from the watch.

We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought.

If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an 'A time' and a 'B time.' We have not defined a common 'time' for A and B, for the latter cannot be defined at all unless we establish by definition that the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A. Let a ray of light start at the 'A time' from A towards B, let it at the 'B time' be reflected at B in the direction of A, and arrive again at A at the 'A time'.

In accordance with definition the two clocks synchronize if

tB - tA = t'A - tB.

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid: -

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.

2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous resting clocks located at different places, and have evidently obtained a definition of 'simultaneous,' or 'synchronous,' and of 'time.' The 'time' of an event is that which is given simultaneously with the event by a resting clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.

[We set forth, according to present experience, that the magnitude

( 2 A B ) / ( t'A - tA ) = c

is a universal constant (the velocity of light in empty space).]

It is essential to have time defined by means of resting clocks in the resting system, and the time now defined being appropriate to the resting system we call it 'the time of the resting system.'[9]"

Albert Einstein believed he had a right to plagiarize, if he could put a new spin on an old idea. He asserted this "privilege" in 1907:

"It appears to me that it is the nature of the business that what follows has already been partly solved by other authors. Despite that fact, since the issues of concern are here addressed from a new point of view, I believe I am entitled to leave out a thoroughly pedantic survey of the literature, all the more so because it is hoped that these gaps will yet be filled by other authors, as has already happened with my first work on the principle of relativity through the commendable efforts of Mr. Planck and Mr. Kaufmann.[10]"

D. F. Comstock wrote, in 1910, in his popular exposition on the theory of relativity:

"The whole principle of relativity may be based on an answer to the question: When are two events which happen at some distance from each other to be considered simultaneous? The answer, 'When they happen at the same time,' only shifts the problem. The question is, how can we make two events happen at the same time when there is a considerable distance between them.

Most people will, I think, agree that one of the very best practical and simple ways would be to send a signal to each point from a point halfway between them. The velocity with which signals travel through space is of course the characteristic 'space velocity,' the velocity of light.

Two clocks, one at A and the other at B, can therefore be set running in unison by means of a light signal sent to each from a place midway between them.

Now suppose both clock A and clock B are on a kind of sidewalk or platform moving uniformly past us with velocity v. In Fig. 1 (2) is the moving platform and (1) is the fixed one, on which we consider ourselves placed. Since the observer on platform (2) is moving uniformly he can have no reason to consider himself moving at all, and he will use just the method we have indicated to set his two clocks A and B in unison. He will, that is,

send a light flash from C, the point midway between A and B, and when this flash reaches the two clocks he will start them with the same reading.

To us on the fixed platform, however, it will of course be evident that the clock B is really a little behind clock A, for, since the whole system is moving in the direction of the arrow, light will take longer to go from C to B than from C to A. Thus the clock on the moving platform which leads the other will be behind in time.

Now it is very important to see that the two clocks are in unison for the observer moving with them (in the only sense in which the word 'unison' has any meaning for him), for if we adopt the first postulate of relativity, there is no way in which he can know that he is moving. In other words, he has just as much fundamental right to consider himself stationary as we have to consider ourselves stationary, and therefore just as much right to apply the midway signal method to set his clocks in unison as we have in the setting of our 'stationary clocks.' 'Stationary' is, therefore, a relative term and anything which we can say about the moving system dependent on its motion, can with absolutely equal right be said by the moving observer about our system.

We are, therefore, forced to the conclusion that, unless we discard one of the two relativity postulates, the simultaneity of two distant events means a different thing to two different observers if they are moving with respect to each other.

The fact that the moving observer disagrees with us as to the reading of his two clocks as well as to the reading of two similar clocks on our 'stationary' platform, gives us a complete basis for all other differences due to point of view.

A very simple calculation will show that the difference in time between the two moving clocks is

[The time it takes light to go from C to B is ½ / (V - v) and the time to go from C to A is ½ / (V + v). The difference in these two times is the amount by which the clocks disagree and this difference becomes, on simplification, the expression given above. - Notation found in the original.]

1/ / (1 - )

where

l = distance between clocks A and B;

v = velocity of moving system;

V = velocity of light;

= v / V.

The way in which this difference of opinion with regard to time between the moving observer and ourselves leads to a difference of opinion with regard to length also may very easily be indicated as follows:

Suppose the moving observer desires to let us know the distance between his clocks and says he will have an assistant stationed at each clock and each of these, at a given instant, is to make a black line on our platform. He will, therefore, he says, be able to leave marked on our platform an exact measure of the length between his clocks and we can then compare it at leisure withy any standard we choose to apply.

We, however, object to this measure left with us, on the ground that the two assistants did not make their marks simultaneously and hence the marks left on our platform do not, we say, represent truly the distance between his clocks. The difference is readily shown in Fig. 2, where M represents the black mark made on our platform at a certain time by the assistant at A, and N that made by the assistant at B at a later time. The latter assistant waited, we say, until his clock read the same as clock A, waited, that is, until B was at B'; and then made the mark N. The moving observer declares, therefore, that the distance MN is equal to the distance AB, while we say that MN is greater than AB.

Again it must be emphasized that, because of the first fundamental postulate, there is no universal standard to be applied in settling such a difference of opinion. Neither the standpoint of the 'moving' observer nor our standpoint is wrong. The two merely represent two different sides of reality. Any one could ask: What is the 'true' length of a metal rod? Two observers working at different temperatures come to different conclusions as to the 'true length.' Both are right. It depends on what is meant by 'true.' Again, asking a question which might have been asked centuries ago, is a man walking toward the stern of an east bound ship really moving west? We must answer 'that depends' and we must have knowledge of the questioner's view-point before we can answer yes or no.

A similar distinction emerges from the principle of relativity. What is the distance between the two clocks? Answer: that depends. Are we to consider ourselves with the clock system when we answer, or passing the clocks with a hundredth the velocity of light or passing the clocks with a tenth the velocity of light? The answer in each case must be different, but in each case may be true.

It must be remembered that the results of the principle of relativity are as true and no truer than its postulates. If future experience bears out these postulates then the length of the body, even of a geometrical line, in fact the very meaning of 'length,' depends on the point of view, that is, on the relative motion of the observer and the object measured. The reason this conclusion seems at first contrary to common sense is doubtless because we, as a race, have never had occasion to observe directly velocities high enough to make such effects sensible. The velocities which occur in some of the newly investigated domains of physics are just as new and outside our former experience as the fifth dimension.[11]"

Citing Comstock's above quoted work, Robert Daniel Carmichael wrote, in 1912:

"§ 9. Simultaneity of Events Happening at Different Places. - Let us now assume two systems of reference S and S' moving with a uniform relative velocity v. Let an observer on S' undertake to adjust two clocks at different places so that they shall simultaneously indicate the same time. We will suppose that he does this in the following very natural manner:

[Compare Comstock, Science, N. S., 31 (1900) [sic]: 767-772. - Notation found in the original.]

Two stations A and B are chosen in the line of relative motion of S and S' and at a distance d apart. The point C midway between these two stations is found by measurement.

The observer is himself stationed at C and has assistants at A and B. A single light signal is flashed from C to A and to B, and as soon as the light ray reaches each station the clock there is set at an hour agreed upon beforehand. The observer on S' now concludes that his two clocks, the one at A and the other at B, are simultaneously marking the same hour; for, in his opinion (since he supposes his system to be at rest), the light has taken exactly the same time to travel from C to A as to travel from C to B.

Now let us suppose that an observer on the system S has watched the work of regulating these clocks on S'. The distances CA and CB appear to him to be

½ d (1 -  )1/2

instead of ½ d. Moreover, since the velocity of light is independent of the velocity of the source, it appears to him that the light ray proceeding from C to A has approached A at the velocity c + v, where c is the velocity of light, while the light ray going from C to B has approached B at the velocity c - v. Thus to him it appears that the light has taken longer to go from C to B than from C to A by the amount

½ d (1 -  )1/2 / ( c - v ) - ½ d (1 -  )1/2 / ( c + v )

= vd (1 -  )1/2 / ( c2 - v2 ) .

But since  = v / c the last expression is readily found to be equal to

( v / c2 ) [ d / (1 -   )1/2 ] .

Therefore, to an observer on S the clocks on S' appear to mark different times; and the difference is that given by the last expression above.

Thus we have the following conclusion:

Theorem VII. Let two systems of reference S and S' have a uniform relative velocity v. Let an observer on S' place two clocks at a distance d apart in the line of relative motion of S and S' and adjust them so that they appear to him to mark simultaneously the same time. Then to an observer on S the clock on S' which is forward in point of motion appears to be behind in point of time by the amount

( v / c2 ) [ d / (1 -  )1/2 ] ,

where c is the velocity of light and  = v / c (MVLR).

It should be emphasized that the clocks on S' are in agreement in the only sense in which they can be in agreement for an observer on that system who supposes (as he naturally will) that his own system is at rest-notwithstanding the fact that to an observer on the other system there appears to be an irreconcilable disagreement depending for its amount directly on the distance apart of the two clocks.

According to the result of the last theorem the notion of simultaneity of events happening at different places is indefinite in meaning until some convention is adopted as to how simultaneity is to be determined. In other words, there is no such thing as the absolute simultaneity of events happening at different places.[12]"

Albert Einstein, who sought a "new point of view" from plagiarizing Poincaré's 1900 clock synchronization method, plagiarized Comstock (1910) and Carmichael (1912), in Einstein's book of 1916:

"THE RELATIVITY OF SIMULTANEITY

UP to now our considerations have been referred to a particular body of reference, which we have styled a 'railway embankment.' We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. I. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train.

Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. 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 the 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 Aà B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance Aà B on the traveling train. Just when the flashes

[As judged from the embankment. - Notation found in the original.]

of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M' 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, i.e. they would meet just where he is situated. 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. 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.

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.

We were led to that conflict by the considerations of Section VI, which are now no longer tenable. In that section we concluded that the man in the carriage, who traverses the distance w per second relative to the carriage, traverses the same distance also with respect to the embankment in each second of time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distance w relative to the railway line in a time which is equal to one second as judged from the embankment.

Moreover, the considerations of Section VI are based on yet a second assumption, which, in the light of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the introduction of the theory of relativity.[13]"

This chapter "by Einstein" has often been criticized as being "absolutist" and "Lorentzian". One understands why it was written in the fashion that it was, when one reads the source material, which Einstein plagiarized to produce it.

References and Notes

1. W. Voigt, "Ueber das Doppler'sche Princip", Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen, (1887), pp. 41-51; republished Physikalische Zeitschrift, Volume 16, Number 20, (October15, 1915), pp. 381-386; English translation, as well as very useful commentary, are found in A. Ernst and Jong-Ping Hsu (W. Kern is credited with assisting in the translation), "First Proposal of the Universal Speed of Light by Voigt in 1887", Chinese Journal of Physics (The Physical Society of the Republic of China), Volume 39, Number 3, (June, 2001), pp. 211-230; URL: http://psroc.phys.ntu.edu.tw/cjp/v39/211.pdf . Lorentz acknowledged Voigt's priority, and suggested that the "Lorentz Transformation" be called the "Transformations of Relativity": See: H. A. Lorentz, Theory of Electrons, B. G. Teubner, Leipzig, (1909), p. 198 footnote; and H. A. Lorentz, "Deux memoirs de Henri Poincaré", Acta Mathematica, Volume 38, (1921), p. 295; reprinted in Œuvres de Henri Poincaré, Volume XI, Gautier-Villars, (1956), pp. 247-261. Minkowski also acknowledged Voigt's priority: See: The Principle of Relativity, Dover, New York, (1952), p. 81; and Physikalische Zeitschrift, Volume 9, Number 22, (November 1, 1908), p. 762. For further discussion of Voigt's relativistic transformation, see: R. Dugas, A History of Mechanics, Dover, New York, (1988), pp. 468, 484, 494; A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York, Toronto, Melbourne, (1982), pp. 121-122.

2. H. Poincaré, "La Mesure du Temps", Revue de Métaphysique et de Morale, Volume 6, (January, 1898) pp. 1-13; The Value of Science, The Science Press, New York, (1907), pp. 26-36.

3. H. Poincaré, Electrité et Optique, Gauthier-Villars, Paris, (1901), p. 530.

4. H. Poincaré, "La Théorie de Lorentz et le Principe de la Réaction", Archives Néerlandaises des Sciences Exactes et Naturelles, Series 2, Volume 5, (1900), pp. 252-278, at 272-273.

5. A. Einstein, "Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie", Annalen der Physik, Volume 20, (1906), pp. 627-633, at 627.

6. J. Stachel, Ed., The Collected Papers of Albert Einstein, Volume 2, Princeton University Press, (1989), pp. xxiv-xxv.

7. H. Poincaré, Science and Hypothesis, Dover, New York, (1952), p. 90.

8. H. Poincaré's St. Louis lecture from September of 1904, La Revue des Idées, 80, (November 15, 1905); "L'État Actuel et l'Avenir de la Physique Mathématique", Bulletin des Sciences Mathématique, Series 2, Volume 28, (1904), p. 302-324; English translation, "The Principles of Mathematical Physics", The Monist, Volume 15, Number 1, (January, 1905), pp. 1-24.

9. The Principle of Relativity, Dover, New York, (1952), pp. 38-40. In order to maintain conformity with the original German text, necessary corrections have been made, as indicated by bracketed text. "Resting" has been substituted for "stationary", in conformity with the original German text.

10. A. Einstein, "Ueber die vom Relativitaetsprinzip gefordterte Traegheit der Energie", Annalen der Physik, Series 4, Volume 23, (1907), pp. 371-384, at 373.

11. D. F. Comstock, "The Principle of Relativity", Science, New Series, Volume 31, Number 803, (20 May 1910), pp. 767-772, at 768-770.

12. R. D. Carmichael, "On the Theory of Relativity", The Physical Review, Volume 35, Number 3, (September 1912), pp. 153-176, at 170-171; republished in "The Theory of Relativity", Mathematical Monographs No. 12, John Wiley & Sons, New York, (1914/1920), pp. 40-41.

13. A. Einstein, "The Relativity of Simultaneity", Relativity: The Special and the General Theory, Chapter 9, Methuen, London, (1920), pp. 30-33.

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[A presentation of the author is given at the end of the first of his previous two papers published in this same issue of Episteme]

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