How far back can the concept of "expanding space" be traced? Not only in a physical sense (e.g. cosmology), but also a mathematical one.
The trigger for this thread comes from a recent post by Charles Chandler:
He's certainly far from alone in thinking that the concept of "expanding space" is unintuitive, even apparently illogical; there must have been plenty of astronomers and physicists, in the second decade of the 20th century, who at least thought something similar.
But, as I understand it, the mathematical basis for Einstein's General Theory of Relativity (GR) - in which 'expanding space' is not at all illogical - hadn't been around for long, before Einstein (with help) worked it into GR; was Riemann the (sole) pioneer?
Non-Euclidean geometry had certainly been studied before Riemann, and the question of whether the universe is flat (Euclidean) was tackled by no less than Gauss (IIRC). But were there also concepts of 'expanding space' (or contracting) in the works of Gauss (and/or earlier mathematicians)? Ones not necessarily expressed in ways similar to Riemann?
The trigger for this thread comes from a recent post by Charles Chandler:
Quote:
Originally Posted by Charles Chandler (Post 10201066) Do you know of one where the BS is clearly labeled, so I don't have to waste my time with it? For example, I've seen in books, and in highly respected journals, that space itself is expanding. This is a self-defeating concept. To the critical thinker, for space to expand, there have to be 2 spaces: one that is expanding and one that is not. This is because the concept of expansion implies a ruler by which to measure it. Therefore, for space to expand, there has to be another space that is not expanding, in which there is a ruler by which to measure the expansion of the first space. But there can't be 2 different spaces, one expanding and one not -- all matter, and all rulers, are in only one universal space. Therefore, this is a meaningless concept, and only sounds intriguing to people who lack the capability to sort out such things. After running across a couple dozen of these in the mainstream literature, I became of the opinion that nothing in the mainstream can be taken on faith -- it all has to be double-checked. Excuse me for being skeptical, but no, you're not going to just cajole me into finally going along with the consensus -- at least not a consensus containing gibberish like that. I might be a long ways from understanding the Universe, and my lack of education shows through quite clearly. But at least I know that I'm lost!!! :) |
He's certainly far from alone in thinking that the concept of "expanding space" is unintuitive, even apparently illogical; there must have been plenty of astronomers and physicists, in the second decade of the 20th century, who at least thought something similar.
But, as I understand it, the mathematical basis for Einstein's General Theory of Relativity (GR) - in which 'expanding space' is not at all illogical - hadn't been around for long, before Einstein (with help) worked it into GR; was Riemann the (sole) pioneer?
Non-Euclidean geometry had certainly been studied before Riemann, and the question of whether the universe is flat (Euclidean) was tackled by no less than Gauss (IIRC). But were there also concepts of 'expanding space' (or contracting) in the works of Gauss (and/or earlier mathematicians)? Ones not necessarily expressed in ways similar to Riemann?
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