> Err, Einstein's static universe did not preclude the death of stars via exhaustion of their fuel.
Yes, by a process of radiating away massive amounts of energy.
> So, the entire universe would "heat up" to a uniform distribution (i.e. evolve according to the heat equation), with the future local heat being everywhere equal to the mean local heat at present.
No, not "at present" "At present" is the outcome of a combination of energy radiation and cosmological expansion leading to the present. Were it not for the factor of expansion, the universe would be much, much hotter than it is now.
> And, in general, the universe is overwhelmingly empty and cold.
Yes, it is -- because of cosmological expansion. Were this not the case, the universe's temperature would be equal to or or greater than it was at "recombination" time, i.e. when normal atoms formed and the universe first became transparent to radiation, at about 300,000 years and an average temperature of about 4000 kelvins.
> I'm not sure what the mean energy of the universe is ...
Don't you mean average temperature? One can speak of total energy, or average temperature, but "mean energy" doesn't make much sense.
> ... or what the minimal energy required to coax an electron to jump around and create visible light is ...
That's well-established. When the energy of an impinging photon is equal to that for a possible electron orbital transition, and ignoring for the moment a few other considerations, the electron will absorb the photon and move to a higher orbit. Conversely, if an electron should drop from its present orbit to a lower orbit, a photon will be emitted whose wavelength is proportional to the energy difference between the orbits.
> In other words, given a perhaps dubious mixing of temporally diverse understandings of physics ...
At any given time, there is one understanding of physics. It's obviously open to challenge as all scientific theories are, but each challenge must be accompanied by observational evidence. The point of science is not to have any number of theories, the point is to have one -- the one that best answers observation.
> the relevant homogeneously energetic universe would likely be nowhere energetic enough to cause light.
For a sufficiently comprehensive definition of "light" (meaning electromagnetic radiation), no, not possible. There will always be electromagnetic radiation, even for a universe at zero Kelvins, because of quantum effects.
> Thus, perhaps we should be more surprised that everywhere we look isn't dark?
Not in this universe, no -- not with stars converting mass into prodigious amounts of energy everywhere we look. Which leads, full circle, to Olbers' Paradox.
When I said "at present", I was operating in the context of your previous post, i.e. assuming a universe with static space-time geometry. In this context, the present empty coldness of the universe is relevant and the past crowded hotness is not. Certainly, when a full modern understanding of cosmology is brought into play, Olbers' paradox is quickly downgraded from paradoxical to merely non-intuitive.
As noted previously, I was mixing temporally diverse conceptions of physics. Obviously, at any point in time there is a physics representing the current scientific consensus. I meant that my construction of an argument using ideas sampled from non-contemporary points in the stream of evolving understandings of physics was potentially dubious. Or, metaphorically, I was mixing metaphors.
After I first put the focus on naked-human-eye-visible light, it was meant to be assumed that any use of the term "light", as opposed to, say, "electromagnetic radiation", was also intended to invoke the concept "naked-human-eye-visible light", and likewise for dark as the absence of "light".
I'm aware of the basic process underlying the emission/absorption of photons via orbital jumping. My precise point was that the incident energy required to invoke a jump of sufficient size to produce "light" may be greater than that which would be omnipresent in a homogeneously energetic universe with a space-time geometry equivalent to that of the universe in which we currently reside. Certainly, as you mentioned, the relative amounts of energy stored in mass versus motion would play an important role.
Anyhow, my entire line of argument was all just an exercise in Devil's advocacy, seeing as how satisfactory resolution of Olbers' paradox is readily available within our current best understanding of physical law.
> When I said "at present", I was operating in the context of your previous post, i.e. assuming a universe with static space-time geometry.
Yes, but for a static universe, we wouldn't have anything remotely like present temperatures, which is why Olbers' Paradox ultimately leads to universal expansion apart from any other issues.
> it was meant to be assumed that any use of the term "light", as opposed to, say, "electromagnetic radiation"
But they can't be opposed -- all light is electromagnetic radiation, and vice versa for a sufficiently large time frame. What was gamma rays at the time of the big Bang is now visible light. What was visible light at the time of the Big Bang is now microwaves. There's no reasonable way to talk about these issues without describing the electromagnetic field.
> seeing as how satisfactory resolution of Olbers' paradox is readily available within our current best understanding of physical law.
Yes, but not for a static universe, which was my point -- for a static universe, the assumption until 1929, Olbers' Paradox remained unresolved -- and without cosmological expansion, the issues are not "available within our current best understanding of physical law". Not remotely.
Yes, by a process of radiating away massive amounts of energy.
> So, the entire universe would "heat up" to a uniform distribution (i.e. evolve according to the heat equation), with the future local heat being everywhere equal to the mean local heat at present.
No, not "at present" "At present" is the outcome of a combination of energy radiation and cosmological expansion leading to the present. Were it not for the factor of expansion, the universe would be much, much hotter than it is now.
> And, in general, the universe is overwhelmingly empty and cold.
Yes, it is -- because of cosmological expansion. Were this not the case, the universe's temperature would be equal to or or greater than it was at "recombination" time, i.e. when normal atoms formed and the universe first became transparent to radiation, at about 300,000 years and an average temperature of about 4000 kelvins.
> I'm not sure what the mean energy of the universe is ...
Don't you mean average temperature? One can speak of total energy, or average temperature, but "mean energy" doesn't make much sense.
> ... or what the minimal energy required to coax an electron to jump around and create visible light is ...
That's well-established. When the energy of an impinging photon is equal to that for a possible electron orbital transition, and ignoring for the moment a few other considerations, the electron will absorb the photon and move to a higher orbit. Conversely, if an electron should drop from its present orbit to a lower orbit, a photon will be emitted whose wavelength is proportional to the energy difference between the orbits.
> In other words, given a perhaps dubious mixing of temporally diverse understandings of physics ...
At any given time, there is one understanding of physics. It's obviously open to challenge as all scientific theories are, but each challenge must be accompanied by observational evidence. The point of science is not to have any number of theories, the point is to have one -- the one that best answers observation.
> the relevant homogeneously energetic universe would likely be nowhere energetic enough to cause light.
For a sufficiently comprehensive definition of "light" (meaning electromagnetic radiation), no, not possible. There will always be electromagnetic radiation, even for a universe at zero Kelvins, because of quantum effects.
> Thus, perhaps we should be more surprised that everywhere we look isn't dark?
Not in this universe, no -- not with stars converting mass into prodigious amounts of energy everywhere we look. Which leads, full circle, to Olbers' Paradox.