@deepthought said
I'm not loving the way he's expressed this. He is not talking about time dilation here. This is the relativistic version of Fermat's principle, the principle of least time from optics. The falling object's motion is such that the proper time is minimised over the motion. Proper time is the time as measured by a clock that is in the same place and moving at the same sp ...[text shortened]... re for eternal youth to objects. This quote is consistent with the post I made in the other thread.
Time dilation from matter is what causes things to fall. Greene explained it well. You are in denial.
Einstein knew time dilation caused gravity after he invented the equivalence principal in a thought experiment. Knowing this made perfect sense he then needed to work out the mathematics to prove the validity of his theory. That was the hard part.
When he came up with GR field equations he didn't later come to the surprise conclusion that his equations predicted time dilation as has been suggested. He knew that time dilation caused gravity all along. He just needed to confirm it with the math. Not a prediction, a confirmation of what he already knew with equations. It just appears that way when looking at the equations from a limited perspective.
He worked his butt off to confirm it, otherwise people like kazetnaggora would say it was a fringe theory and he would get plenty of cheerleaders to put the patent clerk in his place and you would have never heard of GR until years later.
If it were not for Einstein's friend Marcel Grossmann it may not have happened when it did. Not just because he helped him with the math for GR either, he helped him with his notes in college and Marcel's father got him the job at the patent clerk office. What if he had never met Grossmann? What if instead he had a friend like kazetnagorra?
Einstein used the term bending of space/time because it included all the known dimensions of space with the dimension of time. It was a more complete explanation. Unfortunately the term stuck so well the time dilation part of those four dimensions got lost in the teaching process.
Time dilation and space/time are just different descriptions of the same thing. The former is one dimension and the latter is the other 3 from space. They are inexorably linked. Time dilation bends space with it. Space cannot bend without time dilation.
The assertion that the bending of space/time causes time dilation is a fallacy. You took the word "cause" literally, just as people took the word "predicted" literally. Maybe some day you will finally understand Einstein's field equations well enough to accept that. The = sign is not a trivial matter!