Hi, sorry for my enforced absence, I’m joining in again.
I got so carried away with the ongoing arguments about 1G gravity versus 1G acceleration that I forgot my original mission. I was wrong in pursuing the argument about the 1G accelerated frame not going out of sync with the reference clock as I had the wrong parameters. Here are the correct parameters, and why I have been keen to establish the time connection between 1G gravity and 1G acceleration.
There is a closed chest resting on the surface of the Earth. Naturally the man inside experiences 1G. During the course of this experiment he is not allowed outside the chest.
There is a closed chest with a man inside in a rocket ship which is about to be accelerated at 1G. During the course of this experiment he is not allowed outside the chest.
The Earth and the rocket to be accelerated are both placed in intergalactic space, far away from any other bodies so there are no reference points except each other. They are aware of each other, and know they are eg 1 million Km apart.
Their clocks are synchronised and the rocket motor is fired up. The distance between the two then rapidly increases at 9.8m/s^2. The man in the rocket (he does not know he is in a rocket remember) experiences 1G, and time for him passes normally - ie he cannot detect any change in the passage of time. He can also conduct experiments which tell him he is experiencing 1G, and all experiments he conducts behave normally, just as they did when he performed them on Earth before this experiment began. The man in the chest on Earth experiences 1G and for him the passage of time is “normal” also. He can also conduct experiments which tell him he is experiencing 1G, and all experiments he conducts behave normally, just as they did previously on Earth before this experiment began.
After 2,191.5 hours by the clock on the rocket, the motor on the rocket is cut, the rocket is rotated round 180 degrees, and the motor restarted. The man in the chest on board does not know this, all he knows is that he was weightless for 60 seconds, then all was normal again. Unknown to the man in the rocket, 2,191.5 hours after that period of weightlessness, the rocket very briefly (almost instantaneously) stops (relative to Earth) and starts accelerating back. 4,383 hours after the first period of weightlessness, the procedure is repeated. All he knows is he was weightless again for 60 seconds. Another 2,191.5 hours passes, and the Earth and the rocket are adjacent to each other again. One year has passed on the rocket. The experiment has now ended, they are back again to the 1 million Km apart. The rocket cuts its motor and the clocks are compared. Note that the man in the chest on Earth did not undergo two 60 seconds periods of weightlessness, and this will cause a disparity between the clocks of 0.00008 seconds, a trifling amount.
With the above scenario, any GR effects are present in both FRs, and therefore cancel each other out. Are the clocks in sync to within a few seconds. If not, which clock is slow, and why?
We have here of course the twin paradox, as each man can justifiably say that he was the one who was stationary, and the other was moving. Their only reference was each other. They both experienced 1G for one year (except for one man who experienced 0G for 120 seconds, wich will not affect the outcome.
It can be arranged for the man in the chest on Earth to be weightless also for 2 periods of 60 seconds, by having him suspended and dropped, but the experiment is simpler as laid out here, and just as accurate.