A Thought Experiment

This thought experiment relates to the speed of light. A and B each have two wonderful devices that are far more capable than our current technological capabilities would permit. Device-1 is about a meter long with a light source at one end and a mirror system providing an extended folded light path. There is one sensor just after the light source that can detect the passage of light through it. It is set up to record the passage of light through it and to calculate the difference in local time that it took for the light to go through it between the emission and return of the light pulse. The sensor will also cause a flash of light from an external light source as light passes through the sensor. Device-2 will sense external light flashes and calculate the difference in local time between the flashes. The two Device-1s are essentially identical as are the two Device-2s.

B takes one set of devices to the surface of a rather massive planet, while A keeps one set on a space platform that is orbiting the planet in such a manner that the platform remains exactly over the position where B is on the planet. A uses Device-1 to measure the speed of light on the platform and finds the value to be c. B uses Device-1 to measure the speed of light on the planet and finds the value to be c (this of course being a generally accepted fundamental assumption). It is assumed that the clock rate on the planet is slower than the clock rate on the platform.

Under the conditions of the special and general theories of relativity, where light must have the exact same speed on the platform and the planet, why does B, who is using the clock rate on the planet, measure the same speed for light as A. One possibility is that B’s Device-1 has increased in length. If that is the case, then the device must approach infinite length as the mass of the planet increases (and would become a hazard to inter-stellar navigation). So that does not seem like a reasonable possibility. Another possibility is that the length of a measuring rod decreases so the device is measured as being longer. If a physical measuring rod decreased in size, so would the device, and its measured length would remain the same. Trying to find a physical example of such a measuring rod seems a hopeless task. So maybe it is space that changes so that B measures the rod as being longer. However, B cannot measure the rod as being longer unless B has a physical measuring device to do so. It would seem, then, that if light had a constant speed that the measurements by A and B could not result in the same value.

 While B was doing the measuring, A pointed Device-2 at B’s position and measured the time between the flashes in platform time. The local time interval recorded by A for the flashes from B’s position must be greater than the local time interval recorded by A for Device-1 on the platform. Thus, to A, the speed of light on the planet must be slower than the speed of light on the platform.

So A must conclude that the speed of light on the planet is less than on the platform regardless of any measuring rod peculiarities on the planet. Also, B measures the speed of light on the platform to be faster than on the planet when using Device-2 to determine the interval between flashes from Device-1 on the platform. Thus the speed of light cannot be the same for all observers regardless of the circumstances. One logical conclusion that satisfies the above conditions is that the speed of light must depend upon the clock rate in the area through which it is traveling. The speed of light would then correspond with that clock rate, which would result in the speed being measured as the generally accepted value of c in any location where the clock rate was uniform throughout the light path in the region where the measurement is made. This would also result in the speed not having the accepted value of c when the measurement is made using an external clock rate that is different from that in the system in which the light is traveling.