Ah but sandpaper is not smoothThat's a reasonable analogy. I usually use a loaf of bread cut into slices. Looks smooth from a distance but actually full of holes and strings; the strings are networks of galaxy clusters and the holes are voids.
Sandpaper works fairly well as well though.
Thing is neither are 'smooth', they just look it on average. And the very phrase 'on average' is dubious in general relativity, because to define an average you have to define a coordinate system in which to take that average, and then average across vector or tensor fields, immediately rendering your results meaningless. There's ways of doing it, which aren't ideal, and they're what I've been using. (We're working on other approaches too which are much nicer, but currently, err, don't work.)
Basically the problem is if you take an average, and then evolve it through time (which is what cosmology normally does) you don't get the same answer as if you evolved through time and then took an average. We can't actually do the latter cos we don't know how everything was exactly distributed, but in principle it's what we should be doing.
TOO MANY WORDS.
I'm going to hide the fact I've changed my previous answers by changing my definition of what 'acceleration' means in an averaged universe. There's a few ways of doing it when you use the time coordiante I'm using so I'll exploit that.
That'll leave me more time to go drinking with Russian ladies and have a high quality of life.
(Sandpaper works fairly well as well though.
Thing is neither are 'smooth', they just look it on average. And the very phrase 'on average' is dubious in general relativity, because to define an average you have to define a coordinate system in which to take that average, and then average across vector or tensor fields, immediately rendering your results meaningless. There's ways of doing it, which aren't ideal, and they're what I've been using. (We're working on other approaches too which are much nicer, but currently, err, don't work.)
Basically the problem is if you take an average, and then evolve it through time (which is what cosmology normally does) you don't get the same answer as if you evolved through time and then took an average. We can't actually do the latter cos we don't know how everything was exactly distributed, but in principle it's what we should be doing.
TOO MANY WORDS.
I'm going to hide the fact I've changed my previous answers by changing my definition of what 'acceleration' means in an averaged universe. There's a few ways of doing it when you use the time coordiante I'm using so I'll exploit that.
That'll leave me more time to go drinking with Russian ladies and have a high quality of life.
boris the spider,
Fri 11 Jun 2010, 12:18,
archived)
It took me at least three attempts for Einstein's General and Special Theory of Relativity to go in.It wasn't that the concept was unbearably hard to grasp - the problem was the language he used to convey the concept. He had a wonderful ability to complicate a simply analogy to the point wherein it became irritatingly hard to understand.
Still, good book, that.
(Still, good book, that.
Ttssattsr,
Fri 11 Jun 2010, 12:23,
archived)
I've actually never read itI may give it a shot. If your maths is fine then Carroll's "Spacetime and Geometry" is probably the best GR (and SR though he assumes you know a lot of SR at the outset) textbook I've found. Easier to read than Wald, a shitload less up its own arse and irritatingly smug than Misner, Thorne and Wheeler, more up-to-date and less heavily based in SR and coordinates than Weinberg.
At heart, general relativity is extremely simple. Just as centrifugal force is a fictional force that only exists when you sit in an accelerating reference frame, gravity is a fictional force that only exists when you sit in an accelerating reference frame. Real forces don't give the same acceleration to any mass - it doesn't make sense for them to. Gravity does. Either nature is fucked up and playing games and making inertial and gravitational mass identical for no good reason or, much more simply, gravity doesn't actually exist as a force.
It's beautiful.
(At heart, general relativity is extremely simple. Just as centrifugal force is a fictional force that only exists when you sit in an accelerating reference frame, gravity is a fictional force that only exists when you sit in an accelerating reference frame. Real forces don't give the same acceleration to any mass - it doesn't make sense for them to. Gravity does. Either nature is fucked up and playing games and making inertial and gravitational mass identical for no good reason or, much more simply, gravity doesn't actually exist as a force.
It's beautiful.
boris the spider,
Fri 11 Jun 2010, 12:30,
archived)
I only read this stuff for personal pleasure, buddy - I don't want to get all math-y.SHUDDER.
( Ttssattsr,
Fri 11 Jun 2010, 12:32,
archived)
Avoid Carroll, thenThere's maths in there I don't know and I do this stuff for a living.
( boris the spider,
Fri 11 Jun 2010, 12:39,
archived)