Imatfaal,

Thank you so much for your time.

Respectfully, the point is not that light literally travels the exact length of the rod. It is how long would light take to traverse the exact length. That may sound nit picky but I don’t want us to get on the wrong track. No light pulses are being used at all.

The statements “the speed of light is constant” and “the speed of light is the same for all observers” don’t mandate that a light pulse is generated and timed as it traverses the rod. More exactly, the statements taken together mean that if a light pulse went from one end of the measuring rod to the other end it would take the same amount of the time in the observers frame whether the observer is in the moving frame and, in essence, observing the rest length or in the rest frame observing the rod at any contracted length.

In other words if it would take time x for a light to traverse the exact length of the rod judged from inside the moving frame, it would take a light pulse the same amount of time, x, for light to traverse the exact length of the rod at any magnitude of contraction judged from the rest frame.

To determine what time x is for the measuring rod’s rest length, calculate the amount of time it would take for light to traverse the length of the measuring. If the length is already stated in terms of light speed i.e. light seconds, light microseconds etc. no calculation is necessary. The increment of time is the numeric value and the unit of time. The word “light” indicates at the speed of light. For example, the length of that measuring rod is 360 light nanoseconds. 360 is the number of the nanosecond time units that light would take to traverse a rod. If the length is not expressed in terms of light speed e.g. meters, yards, furlongs etc. it must be so converted.

To determine what time x is for the measuring rod’s contracted length, that length should be expressed in terms of light speed. Time in the moving frame that contains the rod is dilated relative to the rest frame. Therefore, the number of increments of time is multiplied by the time dilation factor for the moving frame. For example, for the relative velocity of the moving frame that results in the contraction factor of .5, the time dilation factor is 2, the reciprocal of the contraction factor. The measuring rod above has the contracted length of 180 light nanoseconds (360*.5). The increment of time of the contracted length (180) is multiplied by the time dilation factor for the frame, 180*2=360 increments of the unit of time. The number of increments of time is 360, the unit of time is nanoseconds. So, it would take 360 nanoseconds for light to traverse the contracted length. It would take 360 nanoseconds in the moving frame for light to traverse the non-contracted length. Light takes the same amount of time to traverse the contracted and non-contracted length.

This calculation is rarely done. The result is always the same. Light would always, by definition, take the same amount time as judged by all observers to traverse a particular length in the direction of motion.

As demonstrated above, any length can be expressed in terms of length or terms of light speed. Both are equally valid.

However, length perpendicular to the direction of motion can clearly be expressed in terms of the speed of light just as length in the direction of motion. Both lengths consist of increments of time. In the circumstance that both lengths are in a frame in motion relative to a rest frame, judged from the rest frame the time in the moving frame that contains both lengths is dilated relative to the rest frame. Repeat time in the FRAME that contains BOTH lengths is relatively dilated. The increments of time for both lengths MUST be multiplied by the time dilation factor for that frame. If anyone knows a legitimate explanation to the contrary, PLEASE enlighten me. I have no explanation.

Thank you,

Butch