IIRC, Einstein wasn’t the first to try to develop a curvature theory of gravity. Riemann himself apparently tried. And, IIRC, Einstein was one of Riemann’s students. Einstein brought to the table the whole thing about having to deal with spacetime rather than space.
As far as Mach’s principle, I believe it’s something a little different than what you said. It’s more the whole thing of acceleration rather than velocity. It’s sorta a notion that the inertia of an object derives from the distribution of all the rest of the mass in the universe. I beleive in pure form it’s more a vague notion rather than a formalized principle. But it does inform GR and aspects of GR conform to it.
More generally, I’d like to toss out a bit wild guess/wild eyed thought based on this sort of thinking: even if Barbour’s timeless universe is false, I’m going to guess that his type of configuration space is the “actual” configuration space. That is, it’s a configuration space of relations between particles or whatever, rather than configurations of absolute positions. Now, instead of demanding that the relevant triangle inequalities hold, as he does… don’t demand that. Then configurations where the inequality is violated would correspond to curvature. Maybe. Anyways, that’s juat a vague notion on my part. If/when I have more of the relevant theoretical sophistication, I’ll see if I can make this work, or of it goes kablewey.
Hopefully: nature vs nurture and all that. We probably would want to figure out how to reproduce the relevant training too. Further, that could apply to other people, not just the clones. And that, actually, seems to be what Eliezer is trying to do here in general, actually.
Now, instead of demanding that the relevant triangle inequalities hold, as he does… don’t demand that. Then configurations where the inequality is violated would correspond to curvature.
Nope… dS^2 between me and my future self 2 seconds from now is 2 seconds squared. But both have zero dS^2 with a sphere one light second away. No curvature is present.
If on the other hand you’re talking about just the space part, then not even curvature can do what you’re talking about.
Good post, minor nitpicks though:
IIRC, Einstein wasn’t the first to try to develop a curvature theory of gravity. Riemann himself apparently tried. And, IIRC, Einstein was one of Riemann’s students. Einstein brought to the table the whole thing about having to deal with spacetime rather than space.
As far as Mach’s principle, I believe it’s something a little different than what you said. It’s more the whole thing of acceleration rather than velocity. It’s sorta a notion that the inertia of an object derives from the distribution of all the rest of the mass in the universe. I beleive in pure form it’s more a vague notion rather than a formalized principle. But it does inform GR and aspects of GR conform to it.
More generally, I’d like to toss out a bit wild guess/wild eyed thought based on this sort of thinking: even if Barbour’s timeless universe is false, I’m going to guess that his type of configuration space is the “actual” configuration space. That is, it’s a configuration space of relations between particles or whatever, rather than configurations of absolute positions. Now, instead of demanding that the relevant triangle inequalities hold, as he does… don’t demand that. Then configurations where the inequality is violated would correspond to curvature. Maybe. Anyways, that’s juat a vague notion on my part. If/when I have more of the relevant theoretical sophistication, I’ll see if I can make this work, or of it goes kablewey.
Hopefully: nature vs nurture and all that. We probably would want to figure out how to reproduce the relevant training too. Further, that could apply to other people, not just the clones. And that, actually, seems to be what Eliezer is trying to do here in general, actually.
Nope… dS^2 between me and my future self 2 seconds from now is 2 seconds squared. But both have zero dS^2 with a sphere one light second away. No curvature is present.
If on the other hand you’re talking about just the space part, then not even curvature can do what you’re talking about.