Mach versus Einstein

[sol invictus]

Yes, but also in fact there's a lot more stuff in the universe than a pair of rockets. Doesn't rotation relative to that stuff correspond well with "absolute" rotation? Is this merely a coincidence, according to GR?

OK, I thought about this a little more. I don't see any sense in which the other stuff in the universe defines a rest frame for acceleration which coincides with the one we see. In our universe matter more or less obeys a Hubble law, which means that distant objects move relative to us at a speed proportional to their distance. If you go sufficiently far away that would correspond to a speed greater than the speed of light, which means there is a horizon. Anyway, the point is that distant masses in our universe are not in any sense "fixed". Of course Mach didn't know that - it was discovered after his death.

I do not think this would even present a problem when considering the frame dragging of a rotating black hole alone in the universe but I’m not sure.

It can't, because all of the calculations of those effects are done exactly in that case. The exact metric describing even two masses is not known.

I think that the best interpretation of Mach’s principle, that I have seen so far, is that without mass (or energy) there is no space (or space-time).

OK, maybe. But then again that puts it into total conflict with GR, in which space exists independently of mass.

 

[The Man]

OK, maybe. But then again that puts it into total conflict with GR, in which space exists independently of mass.

Well I guess that might be true since GR deals with the curvature of space-time by mass and without mass there is no curvature but not necessarily no space-time. Does GR specifically require the existence of space time without the presence of mass and how can that be demonstrated?

This is kind of where I run into some problems, I have no real problems understanding the concepts of GR or Tensors, however when it comes to actually doing the calculations, I kind of run into a (mental) road block.

Does anyone know of any web sites that have some simple GR problems worked out step by step that might help me breakthrough my mental road block?

 

[sol invictus]

Well I guess that might be true since GR deals with the curvature of space-time by mass and without mass there is no curvature but not necessarily no space-time. Does GR specifically require the existence of space time without the presence of mass and how can that be demonstrated?

I'm not sure what it would mean for GR to "require" the existence of spacetime. GR is an equation (or really a set of equations). When there is no matter or energy present, the solution to those equations is flat Minkowski space. It's not quite unique - for example a torus also works, and there are weird things like Taub-NUT spacetimes - but roughly speaking it's the only solution.

I don't know any websites like that; I'd just buy a book on GR if you want to learn how to calculate things in it.

 

[The Man]

I'm not sure what it would mean for GR to "require" the existence of spacetime. GR is an equation (or really a set of equations). When there is no matter or energy present, the solution to those equations is flat Minkowski space. It's not quite unique - for example a torus also works, and there are weird things like Taub-NUT spacetimes - but roughly speaking it's the only solution.

I don't know any websites like that; I'd just buy a book on GR if you want to learn how to calculate things in it.

Well, that’s precisely what I meant, that no space-time is not a GR solution for no mass or energy.

Thanks