This post contains 2 thoughts, one an idea of how to show why time dilation in SR can't work, the other to point to interesting conclusions of various arguments.
First is a train on a large turntable, the larger the turn table the less G force needs to be. The turn table either accelerates to a significant fraction of the speed of light, or to more obtainable velocities with very precise clocks, each clock is initially stationary relative to the earth, all clocks can be easily synchronized, all clocks read 12:00 and then the turn table starts speeding up. It could speed up in an atto-second or slowly enough there are actually biological survivors. Those on earth see the train is moving and according to SR expect to see the clocks on the turn table to be running slow and getting increasingly behind. Those on the train expect to see earth clocks running slow and increasingly behind. But those on the train expect the clock on the carriage on the opposite side of the turn table (180 degrees away) to be the slowest of all since it has a relative velocity of double to that of the earth! You would notice the clock in your carriage is getting further and further ahead of this clock in the opposite carriage where time is plainly more sluggish, now you are hours ahead. If you went for a walk through the adjourning carriages (peeking at the clocks) until you got to the one that had the awfully slow clock on the other side on the turn table, you would now (according to SR) expect to see your old cabins clock to be slower and behind. Since all clocks on the train experience start out the same and have identical and symmetrical experiences there can be no justification for them differing, and yet because there is relative motion there must be time dilation (and for that matter length contraction). Ok, now the objections are even more interesting, first the objection of centrifugal force being equivalent to gravity, and gravity causing time dilation is relevant, I have no objection to this, but centrifugal force can be continually decreased by having a larger turn table, even to the point of being less than 1G while moving at near light speed. Another objection is that acceleration is often given as a reason to decide which twin will have aged less, and rotating things are constantly accelerating. But if because it is rotating time dilation doesn't occur when it otherwise should or only occurs in one frame and not the other, we can just have another object fly by with the same linear velocity as the train and they have a short window of opportunity to compare clock rates (or if it is another train, a long window of opportunity to share with different cabins) and agree on observations of how they see Earth's clock rate compared to theirs, it would seem very odd if they didn't match when they are momentarily in the same reference frame. Never the less, let's just propose that an orbiting object does not experience time dilation for some reason according to SR, you could simply wiggle something and it now would not appear to have time dilation relative to the virtual pivot point, in other words if you imagine that the earth is experiencing massing time dilation since we are moving at 99.99999% of the speed of light relative to some reference frame that a cosmic ray is inhabiting, all you would need to do is wiggle something so it followed the same arc momentarily that it would have if it was orbiting a point in that speeding reference frame, it would then have the same time rate as that reference frame, which should be both faster and slower than the earths rate depending on if you are the wiggler, or just watching. So obviously curved paths would have similar degrees of time dilation to straight paths since clearly that would have been noted by now. Finally since acceleration of the turn table can take place over a tiny moment if we wish, there is too little time spent accelerating, or decelerating to make up for any hour hours of time difference that may be expected. At the same time if the acceleration is thought to change the rate of time one experiences once at speed, then if one observer always existed in a given reference frame and the other had to accelerate to reach this reference frame, it would seem odd as they meet to find they they have different rates of time! Time dilation without a preferred reference frame is a total nonsense. John
