Relativity 'controversy' 1. “The actual one-way speed of light (in vacuum) equals the constant ‘c’ in every inertial frame of reference”. The correct interpretation of the facts is that although the two-way speed of light is an absolute constant of nature, the one-way speed of light is a convenient convention. Why? Because one has to define 'simultaneity' before you can measure speed as time over a distance.

In his 1905 paper on Special Relativity, Einstein wrote in his paragraph on the definition of simultaneity (1923 English translation):

"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" t

_{A}from A towards B, let it at the "B time" t

_{B}be reflected at B in the direction of A, and arrive again at A at the "A time" t'

_{A}.”

Einstein then proceeded to show:

“In agreement with experience we further assume the quantity

2AB/(t'

_{A}- t

_{A}) = c

to be a universal constant―the velocity of light in empty space.”

Because of the 2 above the line, it is clearly a two-way definition of the speed of light. It uses a measurable distance (AB) and a single clock (A) to measure the round trip time of a light signal. In order to measure the one-way speed of light, you need clocks A and B and then they have to be synchronized somehow. One can immediately spot Einstein’s method of synchronization: he simply defines simultaneity so that the one-way speed of light is the same as the two-way speed and then use this definition to set the time on clock B.

This convention is often defended as a universal truth, but it has now been accepted by most in the scientific community for what it is – a convention.

^{[1]}It is not really a relativistic effect, because it works just as well in Newtonian dynamics. Newton could have decided to abandon absolute simultaneity (or time) and to define clock synchronization just like Einstein did; nothing fundamental in his theory would have changed. Similarly, Einstein could have decided on a different clock synchronization scheme and nothing fundamental would have changed in his special theory of relativity. It would just have made all relativistic calculations much, much more difficult. Einstein simply applied Occam’s razor and chose the scheme that makes the physics as simple as possible.

^{[2]}

The two-way speed of light is a totally different matter, because we can use a single clock and clock synchronization does not enter the discussion. Here we have a fundamental difference between the Newton and the Einstein case. For Newton, the two-way speed of light is not the same in every direction, because it depends on how the measurement apparatus is moving through the ether. For Einstein, the two-way speed of light is always the same, irrespective of how the apparatus is moving. This is the principle of relativity at work, which has been confirmed by numerous Michelson-Morley type experiments.

When I originally studied relativity, had I realized that “the one-way speed of light is a universal constant” is a misstatement, it would have saved me from many fruitless searches for explanations that are not required. I should have taken Einstein more literally - it is the the two-way speed of light that is a universal constant.

In the next Blog entry I will investigate another 'controversy': that the tick rates of clocks in relative inertial motion are necessarily different.

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Regards

Jorrie

References

[1] http://chaos.swarthmore.edu/courses/PDG/AJP000384.pdf: Debs, T. and Redhead M. (The twin "paradox" and the conventionality of simultaneity, Am. J. Phys. 64 (4), April 1996)

[2] http://arxiv.org/pdf/0812.1294: Foundations of anisotropic relativistic mechanics, Sonego, Sebastiano; Pin, Massimo (Universit`a di Udine, Via delle Scienze 208, 33100 Udine, Italy); Journal of Mathematical Physics, Volume 50, Issue 4, pp. 042902-042902-28 (2009)