IF you mean that it accelerates at the SAME RATE in the SAME DIRECTION everywhere, it tells you that time runs at different rates in different places (that is at different "heights" where "height" is a variable perpendicular to the [parallel] surfaces of "constant time rate").
However that does NOT tell you that SPACE, per se, is curved. Thus you could say that "Time is bent," or "Time is curved," but wedding that to space would not involve what is normally meant by "curvature of space-time."
Suppose instead that g has a uniform modulus on (say) a given spherical surface. I suspect that:
a) It cannot have that same value on all other (internal or external) spheres, and
b) That space curvature would also be mandated then.
Those are just my gut impressions --- I have no idea how I would prove them!
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Another provocative Alexander question.
My answer is: It depends on what you mean!
IF you mean that it accelerates at the SAME RATE in the SAME DIRECTION everywhere, it tells you that time runs at different rates in different places (that is at different "heights" where "height" is a variable perpendicular to the [parallel] surfaces of "constant time rate").
However that does NOT tell you that SPACE, per se, is curved. Thus you could say that "Time is bent," or "Time is curved," but wedding that to space would not involve what is normally meant by "curvature of space-time."
Suppose instead that g has a uniform modulus on (say) a given spherical surface. I suspect that:
a) It cannot have that same value on all other (internal or external) spheres, and
b) That space curvature would also be mandated then.
Those are just my gut impressions --- I have no idea how I would prove them!
Live long and prosper. (Thank you, "cat")
He forgot to add "Live long and prosper".