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I'm new on the forum (been browsing threads for some time though) and this post is both an introduction of myself and a first question.

I have a huge interest for physics but my working knowledge (having studied it in school, oh well some 15 years ago) is limited to classical physics, let's say up to the turn of the twentieth century, electromagnetism included. I've been reading here and there about more modern physics for some years, in a casual way, just to realize eventually that "popular" science books, including those written by serious researchers, articles on the Italian edition of Scientific American, or random readings on the web, only served to build misconceptions since they are at least unexact, and at most downright wrong. And since these sources systematically avoid working out the maths, my knowledge remained quite superficial. So I decided to start to actually learn it the hard way. With no schedules of course, it's just to satisfy my personal curiosity.

On to the question. The way I understand it, the four coordinates in GR don't necessarily correspond to one time coordinate and three space coordinates. I tend to think of them more as four independent parameters, defining a space on which the theory is set. They don't correspond to any physical notion of distance or time. Not always, at least, and surely not globally in a curved spacetime (unless distance and time are redefined accodingly). This is clear and not my question.

My question is more about the sociology of science perhaps: Why do we read so often statements formulated as if those "abstract" coordinates actually referred to something directly measurable? An example is the radius of the observable universe, or in general the descriptions of the expanding universe. If I think of how much gibberish I've read.... like "the galaxies are not actually getting farther from each other, rather thespace between themis expanding". It may well be shrinking, if you choose another coordinate system. The point is that the "space" in the "spacetime" of GR is not what you normally mean by "space". Or take the Schwarzschild radius of a black hole. Fair, it may be a useful quantity to compute, but it's not the radius of any sphere embedded in space: a radius measured along a timelike coordinate??

Am I right in finding that this fundamental aspect of GR is rarely emphasized? I started to study GR thinking of it as a theory of curved spacetime (right now with this: http://www.lightandmatter.com/genrel/ ) but I'm developping a somewhat different idea, a theory formulated on an abstract coordinate space which might locally correspond to space and time.

Ok this post is long enough, I'll wait for your comments!

And kudos for the wonderful site.

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# Coordinates in GR

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