1100f said:
Your post is appreciated, however there is a major short-coming in the fiat declaring time dilation. While I didn't respond to James R above because it has been repeated to many times and he ignores the issue, it is the same issue that I will clarify here.
The assumption that time has dilated always is based on disregarding the parallel claim that there is length contraction in the direction of motion.
In the clock scenario that was being discussed here James R showed that distance of 9 lhr had contracted to 3.92 lhr. And to accumulate 10 hours travel in one view and only 4.356 hours in the other view is perfectly accounted for by the distance traveled WITH AN IDENTICAL TICK RATE.
James has tried to glaze over this issue by saying that the tick rate of one tick/second is still one tick/second locally but therein implies that the designation is superflous and that somehow A's 1 tick/second has a different duration than B's 1 tick/second.
1 - There is simply no basis to make that assumption.
2 - Mathematically A's tick rate and B's tick rate in direct comparison MUST be identical or else the accumulated times and clock displays would not be as claimed in the first instance.
3 - Having the clocks produce a flash of light with each tick and having them travel the respective distances stipulated at a common velocity of 0.9c shows that the flash interval between ticks is absolutely identical. If they were not the accumulated times would not be as claimed.
4 - So with accumulated time being fully accounted for due to lorentz contraction, time dilation becomes an impossible feature to claim.
Only as in your example above can you claim time dilation in that no calculation of lorentz contraction has been made. Both length contraction and time dilation employ the exact same formula and produce the exact same result on time accumulation; because they are arbitrary views of cause for change in accumulated time.
The most important point which is being disregarded however, is that you cannot declare BOTH as being physical realities. A physical reality is not something which can be turned on or off as a matter of choice.
If length contraction is physical it occurs if you calculate it or not. If you do not calculate it and then claim time dilation, the numbers still work out but you have ignored what you call a physical reality and that is length contraction. They are one and the same using different names and causes.
If you try to claim length contraction and time dilation are both physical realities then the clock time no longer matches d = vt (t = d/v) but becomes t2 = t1(1 - v<sup>2</sup>/c<sup>2</sup>)<sup>1/2</sup> * (1 - v<sup>2</sup>/c<sup>2</sup>)<sup1/2</sup> so as to accommodate both length and time changes as being physical.
That would cause clock B to only accumulate 1.9 hours where t = 3.92/0.9 = 4.35, not 1.9. So BOTH cannot be claimed as physically real.
This really is a very simple and straight forward issue. It is amazing how easily many choose to disregard the macroscopic view and vary the microscopic detail to suit their desired result. But that violates physical reality.