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In the 19th century, most astronomers adopted an island universe model, in which our galaxy was the only object in an infinite space. They didn't know that the "spiral nebulae" were other galaxies. This model had the advantage of being dynamically stable (unlike Newton's infinite and uniform cosmology), and of avoiding the fact that Poisson's equation doesn't have unique solutions for an infinite and uniform universe. Ca. 1830, the geologist Lyell advocated a theory of uniformitarianism, in which the universe would have had uniform conditions going back infinitely far in time. There was some debate between Lyell and physicists such as Kelvin, who objected that the sun would have run out of energy, the earth would have lost its internal heat, and so on, but this was inconclusive because they didn't know enough thermodynamics and didn't know about the atomic nucleus.

But by 1850, the second law of thermodynamics had been formulated, and this would seem to have been solid proof that the universe could not possibly have existed for an infinite time in the past. (This level of understanding of thermodynamics would also, I'd imagine, allow them to show that stars would gradually evaporate out of the galaxy, since the velocity distribution would have a high-velocity tail.) Kelvin did attack Lyell with the second law, but it doesn't sound like people at the time appreciated that this was a decisive argument.

With the benefit of hindsight, we can say that it was decisive, and from 1850 to 1905, people should have been considering only cosmological models that used Newtonian mechanics and that stretched back a finite time into the past. Are such models possible?

For example, I suppose you could make a Newtonian big bang, in which, as many students today imagine, there was an explosion at a specific point in otherwise empty space. Extrapolating the motion of all particles back in time using the laws of physics, one would find their trajectories all converging on a point, then diverging from it again on the other side, i.e., it would look like a big crunch/big bang "singularity," -- it would be a singularity of the matter density, temperature, etc. Thermodynamically, it would look like an extreme thermodynamic fluctuation, which is no worse than the thermodynamic implausibility of the low-entropy big bang in modern GR-based theories. There would be an upper bound on ages of objects in today's universe, because everything was destroyed in the singularity.

Another possibility I can imagine is that you could start off with a universe containing an infinite amount of matter and an infinite amount of energy thermodynamically available to do work. After an infinite time, you would have expended an infinite amount of energy to do work, but you would still have an infinite amount left. The modern counterpart of this kind of thinking would be calculations of whether you can do an infinite calculation in various cosmological models (Dyson 1979, Krauss 1999).

Related: Why didn't Newton have a cosmological constant

References

Dyson, Time without end: Physics and biology in an open universe, Reviews of Modern Physics 51 (1979), pp. 447–460, doi:10.1103/RevModPhys.51.447; described in http://math.ucr.edu/home/baez/end.html

Krauss and Starkman, 1999, Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe, http://arxiv.org/abs/astro-ph/9902189

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  • $\begingroup$ I think there might be a problem of overestimating the capabilities of the people 1850-1905. Even if they had a model for the sun's energy source, it was certainly wrong (correct model was developed 1904-1939). Proposing that it could burn out seems like a jump they didn't have the background to make. $\endgroup$ – Alan Rominger Oct 21 '13 at 19:11
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    $\begingroup$ @AlanSE: I agree that there was a lack of knowledge on certain points such as the nucleus, and that it's not reasonable to blame them for not reaching certain specific conclusions that might seem obvious now. However, I still think it's interesting to figure out what they might conceivably have inferred, if they hadn't gone down various wrong paths. Proposing that it could burn out seems like a jump they didn't have the background to make. Kelvin did propose that it would burn out. He just got the time wrong because he thought the source of the sun's energy was gravitational PE. $\endgroup$ – Ben Crowell Oct 21 '13 at 20:49
  • $\begingroup$ I also seem to recall some reference to the sun using combustion reactions in A Short History of Nearly Everything, which falls on the same impossible conclusion that the solar system is only millions of years old. But that kind of observation also blocks the potential progress in cosmology you refer to. $\endgroup$ – Alan Rominger Oct 21 '13 at 21:04
  • $\begingroup$ @AlanSE: The line of thought I'm interested in is basically the hypothetical one where they don't inadvertently infer the wrong things from stuff they didn't actually know about. E.g., they say, "we don't know the source of the sun's energy." The thing about the second law of thermodynamics is that it's much more fundamental than any such consideration. $\endgroup$ – Ben Crowell Oct 21 '13 at 21:10
  • $\begingroup$ This seems like a good question to move to History of Science and Mathematics. $\endgroup$ – rob Mar 14 '16 at 20:42
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I don't have a direct answer about what cosmologists did with thermodynamics in the Victorian era. But to make a broader statement, cosmology was simply not a focus of research then. There is a nice summary in Vickers (2008), "Was Newtonian cosmology really inconsistent?" section 4.1 According to one book, in the 19th century "cosmology itself no longer existed" (Merleau-Ponty & Morando, The Rebirth of Cosmology, 1976)! Vickers explains there was much work in astronomy and celestial mechanics, just not in the big picture (i.e. cosmology). For history he recommends Jaki (1969), The Paradox of Olbers’ Paradox.

One book from 30 years ago says there were two detailed histories of modern cosmology: Merleau-Ponty, and North (1965). Maybe they will help. Update: I have requested North from the library and will update later.

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  • $\begingroup$ The downvote is mine and was purely accidental. I didn't even realize I'd done it until it was too late to retract it. My apologies. $\endgroup$ – WillO Feb 6 '18 at 6:50
  • $\begingroup$ haha, I'm grateful you shared this :) I'm new here, and suspected my answer properly belonged as a comment, but it was too long. $\endgroup$ – Colin MacLaurin Feb 6 '18 at 9:24
  • $\begingroup$ If the answer is edited then @WillO will be able to change his vote. $\endgroup$ – PM 2Ring Feb 6 '18 at 9:38
  • $\begingroup$ Vote changed. Apologies once again. $\endgroup$ – WillO Feb 6 '18 at 14:32

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