SPECIAL RELATIVITY - 1905

Einstein published his original paper on SRT in 1905. He begins it by questioning the idea that time is universal. He wants to show that time is local and that clocks which are separated in space, and on different bodies that are in motion, cannot be synchronized –that time ‘flows’ differently, as seen from one body, to the next. Here is the beginning of his argument:

"… a ray of light proceeds from A at time tA towards B, arrives and is reflected from B at time tB and returns to A at time t’A. According to the definition both clocks are synchronous if tB – tA = t’A – tB. We assume that this definition of synchronism is possible without invoking any inconsistency…"

The motivation behind this approach is easy to understand. The equation expresses the fact that the time the light travels from A to B is equal to the time required for the return path. If that is what defines synchronized clocks then it follows, from elementary logic, that if these times are not equal, the clocks are not synchronized. That was how Einstein came to the conclusion that clocks in motion will not tick at the same rate. The logic is correct –but the premise is wrong, so the conclusion is also wrong. If the clocks are synchronized and there is no motion, the equation is true, but not vice versa. The error in logic is analogous to defining ‘crime’ as the act of stealing, and then concluding that since you didn’t steal, you did not commit any crime.

He apparently does not realize that unless the clocks are synchronized in advance you can’t do the subtraction on either side. Further more, you can't write tB - tA without considering who knows this. So you need (a) previously synchronized clocks at A and B, because otherwise the subtraction makes no sense, and (b) you do the subtraction, tB – tA, as the observer at A, at a later time, when you find out (through communication at the speed of light or otherwise) what was the reading of the clock at B when the light pulse arrived. At that point you can also knows t'A - tB (the time it took the light on the return path to A) and can decide whether they are equal, in which case there was no movement between A and B while the light was going back and forth.

So we need the concept of synchronization ahead of this equation – and can’t define it by means of this equation. No way can you use the equality to define synchronization - much less to decide that if the equality does not hold (i.e. there is motion between A and B) that this implies that the clocks are (or were) not synchronized. The argument amounts to using synchronized clocks to prove that they were not synchronized – a contradiction, or whatever else you may call this logical fallacy. But without time dilation the Lorentz Transformation can't be derived and SRT vanishes - it loses its claim as a model of physical reality.

I can’t resist pointing out just how trivial the synchronization problem is if A and B are at fixed distance. Presumably the observer at A can let the one at B know ahead of time, that he will send him a light pulse at, say 3:00 PM (by A’s clock). B can send a light pulse on a round trip to A before 3PM ,and if he finds that the round trip took six seconds, he knows that a one way trip takes three seconds. So when the observer at A sends his pulse B knows his clock should read 3 PM plus three seconds. If it doesn’t, he can correct it, and the clocks are synchronized – the differences tB-tA and t’A-tB have not been used to define synchronization. The observers can easily check that the distance is fixed by sending out a short sequence of regularly spaced pulses. If the returning pulses are also regularly spaced with the same spacing as the sent pulses, the distance between A and B is constant. Einstein fails to see all this because he is unable to divorce communication from synchronization.

In transitioning to motion, in the next section, Einstein immediately introduces his second principle, that the velocity of light is independent of the motion of the source. He needs this principle to derive relative time, which is then used to derive the LT, which, in turn, is intended to resolve the conflict between his two principles. Assuming a principle in order to prove that it is valid is known as a circular argument, which is logically unacceptable.

We can show how to synchronize time with relatively moving bodies. Consider for example two bodies, one of which is in an elliptical orbit about the other. They periodically share a common moment – when they are at maximum distance and at minimum distance from one another. If each sends out a beam of light to the other, the Doppler will reverse for both, changing from blue to red at the point of closest approach, and from red to blue at the farthest point. Each can set his clock when this happens. The periodicity is the same for both bodies, so time flows at the same rate.

We can, and need to be more precise with respect to the idea of ‘synchronization’. As with other concepts that Einstein uses, or misuses, this one also has two or more parts which we can call I-synchronization, B-synchronization, and T-synchronization. The first relates to having equal intervals, or, say, seconds of equal duration, the third refers to setting two clocks to the same point, or position, as we do when we adjust our wrist watch to another reference clock. That is what we are concerned with in the case of two points A and B that are stationary, or fixed to a body or platform. The first, I-synchronization, is the issue when it comes to bodies in motion. – that is the question of time dilation. B-synchronization occurs when the points, indicating the beats between intervals are simultaneous. It is important in music, such as drumming, or synchronizing all the violins in an orchestra when they are plucked. A good dictionary often gives several definitions of ‘synchronization’, corresponding to those above.

IF THE CLOCKS ARE FULLY SYNCHRONIZED AND THE DISTANCE BETWEEN THEM AT LOCATIONS A AND B IS FIXED, THE DIFFERENCES BETWEEN tA AND tB WILL CORRESPOND TO THE TIME IT TAKES FOR A PULSE OF LIGHT TO MOVE FROM A TO B AND SIMILARLY FOR THE RETURN PATH FROM B TO A. IN THAT CASE THE DIFFERENCES tB-tA and t’A-tB WILL BE EQUAL.

THE CONVERSE OF THIS THEN BECOMES: IF THE DIFFERENCES tB-tA and t’A-tB ARE NOT EQUAL THEN EITHER THERE IS MOTION DURING THE TIME OF TRAVEL OF THE LIGHT FROM A TO B AND BACK, OR, ALTENATIVELY, THE CLOCKS ARE NOT FULLY SYNCHRONIZED. AT MOST YOU CAN USE THESE DIFFERENCES TO CREATE OR VERIFY T-SYNCHRONIZATION – NOT TO ESTABLLSH, VERIFY OR DEFINE I-SYNCHRONIZATION – WHICH IS THE ISSUE FOR SRT.

That would have been the correct logical inference.

To summarize the three strikes against the 1905 paper: (1) An inappropriate definition of synchronization which presupposes synchronization. (2) The use of his second principle to derive relative time, then using relative time to derive the LT in order to justify his second principle – a circular argument. (3) A counter example showing that you can have synchronized clocks on two bodies in relative motion.

Note (added 8-31-03): It turns out that it is possible to generate a simple procedure that synchronizes clocks for two bodies that are in relative uniform motion - the motion that is called for under SRT.

The procedure is similar to the one discussed above, which produces t-synchronization for bodies that are fixed in their relative positions. For the case of uniform relative motion we need only invoke the principle of relativity. It will turn out, as a consequence of this procedure, that the second principle, that the velocity of light is independent of the motion of the source, must be false.

The procedure can best be illustrated by a specific thought experiment: Assume that two bodies, A and B, are separating at a uniform, but unknown rate. They are in outer space so we can't say that either is stationary. A sequence of light pulses, sent out at one-second intervals by either one, will experience a Doppler effect which increases the spacing of these pulses by a factor F (a constant, larger than 1) when received by the other body. Since the principle of relativity requires symmetry, this will be the same factor in either direction. If the observer at A sends out this sequence, and it is reflected at B, then on the return to A the sequence is again stretched by the factor F, so now the spacing is FxF. This enables the observer at A to know what the factor F is, by simply taking the square root of the increased spacing.

Now, let the observer at B send out a sequence of pulses at one second intervals – by the clock at B. If the observer at A receives them with a spacing different from F, he can advise the observer at B to increase or decrease the rate at which B's clock runs, so as to produce the same Doppler effect, F.

Voila - I-synchronization.

PUBLISHED BOOK 2005

HOME PAGE
INTRODUCTION
THE PRINCIPLE OF RELATIVITY
SPECIAL RELATIVITY - 1905
SPECIAL RELATIVITY - 1917

THE MICHELSON-MORLEY EXPERIMENT
THE LORENTZ TRANSFORMATION
MICHELSON-MORLEY PLUS LORENTZ, CONDENSED

THE DOPPLER EFFECT
A COUNTER EXAMPLE TO SRT
A COUNTER EXAMPLE TO GRT
THE AGE OF THE UNIVERSE
THE SPEED OF LIGHT