As Henri Poincaré pointed out
“In this theory, two lengths are equal, by definition, if they are traversed by light in equal times”
the lengths and herefore the measure of any distance is given by the way light does cross it. What if we don’t know exactly how the light acts, e.g. as a wave like Christiaan Huygens said or like corpuscles by following the arguments of Isaac Newton. Presumably it won’t be the best idea if all science is to be reduced to this kind of thinking, namely to use some given processes without analysing it before.
If we follow this path we might say:
“Two durations are equal, by definition, if they are given by traversing equal lengths by light.”
In order to fix some duration for reference purposes we have to use a straight line distance, e.g. 10 Meters, and read the time needed by some traversing light. Simple task, isn’t it?
The quite complicating fact here is that 10 Meters are not an acceptable definition of length because of the first statement. The distance used to gain some time interval must be equal in terms of „equal travel time“ which should be given by technical means, e.g. playing the reference signal.
There is an assumption of Hendrik Antoon Lorentz, which puts some more complication into our task. According to the Lorentzian contraction of moving bodies any line will be skrinking, depending on the relative speed. The only way to fix some length and to compare it is to do it while staying within our local environment which is often called a frame of reference. If we want to use a length as rule on a distant moving planet like the moon, we won’t be able to check the identity of the measure against that one on earth.
Even if we transport a copy of our standard meter bar to the moon and record the time of light travelling along this meter there is no guarantee to match the duration measured on earth. The time measured on the moon must be recorded and compared with that measure created on earth. How?Unfortunately their is no timer with precision and constancy to the usage between different frames of reference. Moreover there are theories of Albert Einstein and others showing that gravitation does have impact on time.
If we want to use the theories about the nature of light, the space and time providing the invariance of the speed of light we will fall flat. We do not have any measure to get the very first precondition: Comparability of physical measures between different frames of reference. In order to refer some rule of length we must have the identity of duration. In order to refer some fixed duration we are bound to the identity of length.
This is called circular reasoning.
Synchronously moving observers may assume that the speed of light is constant in all directions while staying at rest. When synchronizing clocks by sending and reveiving light signals, they will notify the signalling time only and ignore other modifications of the signal due to the motion of the sender or receiver. Therefore such a pair of moving clocks is not synchronous and does not indicate the same time. Henri Poincaré calculated that this synchronization error matches Lorentz’s local time.
Some difference of elapsed time measured by clocks with unknown synchronization error due to their movements is called time dilation effect.
Finally, there is one point of interest: The theory of relativity gives every frame of reference its very own time frame. Assume there are two frames with some relative speed. The time is given by some signal according to the Einstein rule. One frame states to the other: „Reset your clock and set this time!“ sending the value which is equal to the half of the round trip time. During the sending of the signals the two frames are receding or approaching with const velocity. Does the signalled value match the half of the real round trip time, at any time?