Synchronism of Distant Clocks.
(First development : November
6th,
1999 (in Spanish)
Last Update: September 6th, 2003)
I need to be very clear with the following exposition and its associated conclusions. I am not trying to trick, I only intent to reach logical conclusions, based on fundamental concepts accepted as valid or reasonable.
Example: If I see a stone hitting another, 300 m distance from where I am observing, and the sound I receive delay one second, I accept that everything behaves agreeing with the laws I know, since the speed of sound is about 300 m/s. But if, as a consequence of a strong wind, the sound signal takes more time in arriving, not for that I will say that synchronism got lost. Neither I will conclude that crash took place farther than 300 m because the delay overcomes 1 s. Simply, I will accept that sound delays as a consequence of the strong wind. This is not more than classical Physics. And Special Relativity (SR) is not opposed to classical Physics.
What I am trying to analyze from the beginning is, how we know or how we determine that an event happened at 300 m distance?. Analyzing these basic suppositions Einstein did reach the astonishing conclusion (brilliant intuition?) that, to measure distances we use an electromagnetic phenomenon (light, in its more popular version). And it does not worth say that, instead of using an electromagnetic phenomenon, we can use a bar or a rule of well-known longitude. In that case, we have to change the question to: how we know the rule measures 1 m, or 10 cm, or 1 mm, or...?. And that is what makes the SR been applied from astronomical scale to sub-atomic scale phenomenon.
It's good to clarify from the beginning that, except for the force of gravity, all other interactions we observe in the physical world are electromagnetic interactions (the other exception constitutes the nuclear forces but we don't observe them so regularly). A ball bounces in the floor as consequence of interactions between the atoms' outer electrons of the ball and the floor constituents. The color, the chemical reactions, the rebounds, the sound, the music, the aging etc., etc., are electromagnetic interactions.
Example: we age (Not our atoms, at least NOT in the same way) as consequence of changes which are originated because electromagnetic interactions among substances.
At this point, given its conceptual importance, I want to transcribe a paragraph from Einstein's original 1905 paper, introducing the so called Special Relativity Theory:
"The theory to be developed bases, like the whole electrodynamics, in the kinematics of the rigid body since the statements of such theories are linked to relationships among rigid bodies (coordinated systems), clocks and electromagnetic processes. The root of the difficulties found, presently, by the electrodynamics of bodies in movement lies in an insufficient consideration of these circumstances."
At risk of exaggerating the importance of the fundamental concepts, I want to rescue from previous paragraph the enumeration: "... rigid bodies (coordinated systems), clocks and electromagnetic processes..." as bases of the entire physical structure we are discussing. This astonishing synthesis, speaks by itself about the Einstein capacity to go to the theoretical foundations.
How do we know a tree is 100 m from our position, or Moon is 360,000 Km from Earth? Well, in both cases it is because we have used some measuring instrument. Fundamentally we can say that it is because we have a rule of well-known longitude, with which, direct or indirectly, we perform measurements. Later we will return to this point to make a deepest analysis.
Let us accept, then, that we can affirm that certain object (we call B) is at 3,000,000 Km from our position (we call A). For that we have used a 1 m rule or some triangulating process (based on the 1 m rule)
Let us ask then, how do we know that a clock at B is synchronized with a clock at A?
In principle the answer is operative. Leaving aside any theoretical abstraction, we can say that if it happens the following sequence of events:
We are able to conclude that data seem to be consistent. This measuring agrees with a luminous ray round trip, 10 s for the going and 10 s for the return. And 10 s is what takes light in traveling 3,000,000 Km at speed 300,000 Km/s
But.... What we had thought if the return signal had arrived at 10:00:36 (according to the clock at A)?
That would mean that light took 36 s in traveling the round trip between A and B. And that could be interpreted in two alternative ways:
Could we decide among both alternatives?
To opt for the first alternative, we should have a distance measuring system that doesn't involve the speed of light as a measuring tool. In other words, we need a rule whose longitude was determined with independence of the electromagnetic waves speed.
Question: Is it possible?
Answer: "A priori" our first impulse is to answer yes.
The second alternative is the one selected by Einstein when founding the Special Relativity Theory.
Einstein postulated the speed of light as an universal constant defined as:
2 AB
----------------
= c
t'A - tA
where AB is the distance between A and B and, t'A - tA, is the time used for light in the round trip. Both times are measured with the clock at A.
This postulate doesn't admit doubts: The speed of light ("c") is used to measure distances. If the clock at A indicates 36 s elapsed for the round trip between A and B, then the distance between A and B is:
300,000 Km/s * 36 s
--------------------------------------
= 5,400,000 Km
2
But now the question is: Is this postulate reasonable?
Einstein postulate it in a pragmatic way accepting something like this: "The entire efforts carried out to measure absolute movements indicate that Nature behaves as if 'c' was an universal constant".
I want to remark from this moment that the definition of "c" constancy, employed to develop Special Relativity, imply round trip journeys. Independently from later interpretations, it is not necessary to make special suppositions for going travel or return travel alone. In fact Einstein added a second statement when settling down by definition that the time used during the going is equal to the time used in the return trip. This statement was added to define the synchronism between distant events. And, in my opinion, it was not by accident that he chose this definition of synchronism, but because it allowed him to eliminate the influence of ether in the transmission of electromagnetic signals. Einstein didn't eliminate the ether, only its influence. And in this statements I am practically using Einstein words when he says - "... The introduction of a "luminiferous ether" will prove to be superfluous..."
Let us see with an example, the implications of this postulate.
Let us suppose that a supporting medium for light waves exists (something like the old "ether" just mentioned) and, A and B are on a rigid axis that moves at speed " v " = 200,000 km/s relative to the supporting medium.
If the “true" distance (later we will discuss this point) between A and B is 3,000,000 km the light will travel at 100,000 Km/s (300,000 minus 200,000) from A towards B, and at 500,000 Km/s (200,000 added to 300,000) during the trip from B towards A. During the Going the light uses:
3,000,000 Km
--------------------------
= 30 s
100,000 Km/s
and during the Return:
3,000,000 Km
--------------------------
= 6 s.
500,000 Km/s
And this would give a total time of 30 s + 6 s = 36 s for the journey
Applying the postulate of the constancy of "c" we would conclude that the distance AB is:
300,000 Km/s * 36 s
---------------------------------------
= 5,400,000 Km
2
|
|
|
| Fig. 1 -
If A and B are stationary (v=0), the signal speed is the same for the going that for the return.. |
Fig. 2 -
If A and B are moving at speed "v", the signal travels more slowly in one direction than in the other one (c+v and c-v, respectively). |
Summarizing the example:
And summarizing it a little bit more:
We take for granted that two objects are at 3.000.000 km one from the other and later we “demonstrate " (by means of a series of additional suppositions) that they are at 5.400.000 km (!!??!!).
Outlined in such later way it seems evident that the mistake in this reasoning, is in point 4, because we know, based on how we build the example, that the speed of light varies with the direction in the system AB.
However Einstein during the development of the Special Relativity Theory makes exactly this supposition, for the only simple (or deep) reason that physical measuring seem to indicate that it is necessary to do that. However Einstein doesn't deny in any moment that if somebody travels toward the source of a luminous ray he will find it in advance to those that remains at rest in relation with the source. In fact he uses this example to show the lack of absolute synchronism.
If you don't agree with Einstein, probably you believe that you can measure the distance AB (the supposed 3,000,000 Km) without using light (or any electromagnetic phenomenon) as reference. Basically, the great majority of "complaints" I have listened about Special Relativity is based (direct or indirectly) in this point. In other words: If I use a 1 m stick to measure 3,000,000 Km (just as a bricklayer does to measure a wall), with independence of the effort making to do it, where in this process am I using "c"?
Difficult to see?.
Sure!!
This is a very long topic and, in these pages, we will crumble it until its foundations.
Then, let us return to the synchronism:
If now we accept that distance AB is of 5,400,000 Km and
We could say that clocks A and B are synchronous.
... Sure?
So, to do this statement valid, it is necessary to assume that light takes the same time going than turning back. And this is the definition made by Einstein when developing the Special Relativity.
But.... What would happen if we are already in the case outlined at 3,000,000 Km with a system moving at 200,000 km/s in relation with the medium where the light travels at 300,000 Km/s?.
In this case, although in an absolute sense the ray arrives to B 30 s after having abandoned the position A, we would be accepting that clock B should mark in that moment 10:00:18, and not 10:00:30 as in that moment (in the naive sense of absolute synchronism) reads the clock at A.
Well, the problem arises because we accept that we can measure the distance with independence of the luminous rays. Einstein accepted that it is not possible and therefore he took as standard of length measurements the speed "c". In other words he postulated that if the luminous ray takes 36 s in the round trip journey, then it consumes 18 in the going and 18 in the turn. By definition. And fundamentally (from my own point of view) because the physical world seems to behave in this way.
As a direct consequence, this leads to accept that a ray of light moves at 300,000 Km/s in relation with a stationary object and in relation with another that moves at 100,000 in relation with the first.
Does it sound difficult to accept?.
Of course!! It is like if somebody affirm that an automobile moves at 100 km/h in relation with all other cars in the road (those that go in its own direction, those that are stopped and those oncoming) Or, if somebody affirmed that the summit of Everest is 8,000 m higher than all other points in Earth. Including the 7900 and 7999 m summits. It is like say that the difference of height between the base and the summit of Everest is 8,000 m and the difference of height among the Aconcagua Mt. (7,000 m) and Everest is also of 8,000 m ¿¿!!??
Yes, there are not doubts, this is what the Special Relativity assumes when postulating the constancy of "c". And this is the main reason for which so much people refuse to accept it, although its results (equations) describe the physical world amazingly well.
The synchronism of two distant clocks must be defined by means of some mechanism or process of measurement.
Einstein did not demonstrate, but he postulated, that light takes the same time during the Going that during the Return way.
The postulates of Einstein lead to formulations that describe very well the physical world.
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