crowman

Thanks Genady, I think that’s makes it a bit more clearer for me. IOW, It’s not a leap-frog situation with one part then the other part and so on. Thank you Markus. So, that would be like ending up with the spacetime geometry around a central symmetrical mass (sphere) Schwarzschild model.

Would a roundabout way of saying that be, there is no absolute spacetime and so no frame is special? Hence, no background dependency when it comes to spacetime. That’s how I’m making sense of it. Something to do with the field equations being in two parts, the movements of mass / energy dictates the spacetime geometry and vice versa?

Yes, you're right, thanks. On Earth, a thrown stone will naturally take a path that results in maximum ageing between launch and impact. The stone didn't read a clock or use a ruler. I only say this because your "gravity affects all rulers and clocks" leaves the backdoor open to calls of "it only affects the instruments of measurement."

Would it be fair to say that 'reality' certainly acts like space-time is a non-euclidean curved manifold, and that physics can't show that it's not? I don't know if that's a catch 22 or not?

In my first post on this site, I was puzzled as to why an apple seeking to accumulate the greatest proper time on its wristwatch, would head ''down'' to where time is slower and hence slowing its accumulating of proper time. In other words, the apple is stopping its ageing by going ''down''. Compounding my puzzlement, is that time dilation in the schwarzschild coordinates is only between stationary observers, that is, a stationary far away observer and a stationary ''shell'' observer near a black hole. So, for the falling apple there is no time dilation to travel down to, so to speak. If there was a slowing of time for the apple it would never reach the event horizon. help someone. I'm muddled in my thinking and know it's down to my incorrect understanding of things.🙂

I hope you chaps don't mind me not saying anything in replies, but I'm reading your replies and learning new things. All best

Howdy all.

Hello all. The principle of Maximum ageing says a stone (with wristwatch) in free fall takes the path which accumulates the greatest proper time on the stone's wristwatch. Time runs slower at at sea level than at the summit of Mt Everest. When an apple falls from a tree, its path is down to the ground. Yet, this free fall path would slow the accumulation of the apple's proper time. What am I misunderstanding?