rmsgrey wrote:In an otherwise empty universe, the inside of a hollow neutronium sphere is at a lower gravitational potential than a point infinitely far away.

A flat plain, stretching infinitely far in all horizontal directions, and with uniform density and thickness would produce a linear gravitational potential, and a constant gravitational field - no matter how far you were above the surface, the effect of its gravity would be the same - so there would be no way to detect it purely from gravitational effects. On a human scale, the Earth is approximately such a plain, so gravity is more-or-less constant in daily life (unless you're an astronaut or something)

So what I'm asking is, does the gravitational potential make any difference to anything? Or is it only the gradient that matters?

gmalivuk wrote:But absolute velocity is in no way measurable, whereas absolute rotational velocity would be. An isolated Earth, if absolute rotational velocity is indeed a thing, would be shaped differently at equilibrium and would allow things to orbit differently if it were rotating than if it weren't. In other words, you could in principle test for the existence of absolute rotation, whereas you couldn't (according to any current theory) do so for absolute velocity.rmsgrey wrote:The concept of absolute rotation reminds me of the concept of absolute velocity that special relativity replaced.

And a hundred and thirty years ago (give or take), the Michelson-Morley experiments tested for the existence of absolute velocity.

There are experimentally verified effects that, in principle (I don't know whether this result has been observed in practice) would produce different results for the test for absolute rotation depending on how far you are from a rotating mass - that is to say, near a rotating mass (embedded in a universe of masses with no net rotation) the experimentally determined non-rotating frame would be rotating with respect to a similarly determined non-rotating frame further from the mass.

I can imagine that. I imagine a massive rotating sphere. Let's say it's rotating fast. One side of the sphere is heading directly toward you while the opposite side is heading directly away from you. So by special relativity, they will both have time dilation but one will have more than the other. So it has more time to do gravitation on you. That means the spinning mass will have its gravitation be unbalanced, it won't point directly at the center of mass but off to one side by something less than the diameter of the mass.

\(x'=\gamma\left(x-\beta ct\right)\)

\(ct'=\gamma\left(ct-\beta x\right)\)

The gamma x and gamma ct will be the same both ways. But with the sign of beta opposite, one side will seem to be both closer and its time goes faster. Will those effects cancel out so they both present the same amount of gravity? Probably only at one particular speed?

So that would imply that spinning masses would not behave the same as point masses concentrated at their center of mass. How strange. I wonder if I got that wrong. My intuition about relativity is so weak I can easily get stuff wrong and not notice. With lots of things when I make a big blunder I realize it can't be right and then find out where I went wrong. With relativity when it seems like it has to be wrong, likely as not it's right.