October 14th, 2020


Curved space

It's 3:30am and my mind keeps ticking over the same annoying thing. I keep trying to think of some way to see gravity as curved space without it collapsing into contradictions. I can see the attraction of the idea. It almost looks like you can eliminate gravity as a force and just see it as geometry. Also, I'm very aware of the fact that a lot of very smart people who I respect think that this is how gravity works. Unfortunately I know that a lot of very smart people believed in planetary epicycles too.

My only solution to the problem is to genuinely understand it. However, no matter how I try a couple of basic problems always remain.

If space is curved, then an object without force acting on it will orbit another because its path is said to be a straight line that has been bent by the nearby mass. However if I momentarily push that object along its existing path so that it moves faster, then it will no longer continue the same path. It is obvious why it moves to a different path, but it is not explainable if the object was already following what was a straight path in curved space. It requires the person to believe two contradictory things at once: that space is both curved and flat at the same time. When an object travels passively through space, the curved path is a straight line bent by curved space, but add speed to that object and we now recalculate its path using flat space, but somehow still, at the same time, think space is curved.

When thinking of gravity as curved space people tend to use Einstein's weights on a rubber membrane metaphor. It is a very attractive model. It uses gravity pulling objects down on the membrane distorting it, to model how space is distorted, but in doing this gravity is being used to explain gravity. You can't do that. It is like the circular arguments of religion: god exists because of a book that says he does, and the book is true because it's god's book. It doesn't make sense.

If you hold a ball above the ground then release it, it suddenly moves. This seems to introduce a force acting on the ball. When considering space as distorted, you think of the membrane representing space as angled, so the ball rolls down the incline to the larger mass, Earth. But you haven't eliminated gravity and explained it as geometry. You've replaced the simple force of gravity with geometry distorted in some unexplained way, plus some hitherto unexplained force in order to explain how things are pushed against that geometry. It doesn't simplify gravity; it complicates it.

If anybody understands how I am wrong in all this, please, I beg of you, tell me how. I would be very happy and relieved to be shown how I am wrong. (Crossposted from https://miriam-e.dreamwidth.org/335464.html at my Dreamwidth account. Number of comments there so far: comment count unavailable)