Thermodynamics question

Some of you physicists out there can help me sharpen my understanding of some basic thermodynamics principles. To that end, here are a couple of questions I’m going to build up towards, or embed into some larger speculations for you to give me some clarity on.

I’ve been thinking about the internal energy of gases (a function of temperature), and how the particles in a gas are perfectly elastic in their collisions with each other or any container walls. Which makes sense, because a gas can’t just “lose heat” without losing it … to … somewhere. And heat is already the “lowest ocean” so-to-speak into which all energy drains. So an isolated system, so long as it is non-expanding (volume=constant), will forever stay at whatever temperature it happens to be at, right? And there is no “almost perfectly elasticity” - it has to be absolutely 100.000…% perfect elasticity, otherwise the 1st law is violated as heat energy would be lost to … nowhere. Am I correct so far?

But this brings me to a ‘heat-death’ question. The other way a gas can lose energy is from adiabatic expansion. That is, the gas does work, pushing outward, to expand its volume, causing its temperature (and internal energy) to fall by that corresponding energy of work done. But this is normally demonstrated as being against the walls of some container - though said container could be something so vague as surrounding atmospheric air masses being pushed aside. But on a cosmic scale, is it correct to think of our cooling universe as being largely due to its expansion; i.e. - cooling in an adiabatic sense? If it is space itself that is expanding, then are those somehow container “walls” being pushed outward? Or is it more in a straightforward sense of gas expanding out into pre-existing void already there (and itself expanding in advance of the gas)? I know that’s still a fairly Newtonian and therefore probably misguided sense of what is happening at such limits, but I don’t have any better sensibilities to go on here at the moment.

I’ve heard the cosmos described as a closed (even isolated?) system in the sense that even radiation doesn’t leave it, which if true, would preclude radiative heat loss. So all I’m imagining here is that heat loss would be due to unlimited expansion. If so, then everything asymptotically approaches absolute zero after vast eons of time, right? More like cold death than heat-death, I’m thinking, though I realize that concept has nothing to do with what we humans now characterize as pleasantly warm or hot.

That should be enough for some of you who really know something about this to bring me some needed education here.

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Your uncertainty about these questions is well-founded.

Short answer: Photons really do lose energy as the universe expands. Energy conservation, as taught in introductory physics, isn’t well-defined (and might not be strictly true) applied to an expanding universe.

Here are two articles written at a popular level which, I think, do a fairly good job.

Longer answer:
There are many forms of energy. Heat energy is the highest-entropy form. It’s particles and photons moving randomly in “thermal” distributions of energy. The “heat death” of the universe refers not to temperature, but to the eventual fate of all other forms of energy in the universe converting to heat energy, after which no more entropy-increasing processes (such as stars burning, or life) can occur. Since it looks right now that the universe will keep expanding forever, this will happen in our universe at a very cold tempreature.

Now regarding energy conservation and expansion:
Imagine a box full of particles elastically colliding with each other and the walls. Put that box inside an empty bigger box. If you knock a hole in one wall of the little box, the gas will eventually expand into the bigger box, increasing volume and increasing entropy of the gas without doing work, and the internal energy of the gas of particles will stay the same. If you, instead, let the walls of the little box expand to the size of the big box, the gas of particles will do work as the walls expand, and the internal energy of the gas will drop. You could tell a similar story with a box of perfect-mirror walls full of photons.

But if you have space full of photons, and space itself expands, the photons stretch in wavelength and lose energy. Does that mean that energy wasn’t conserved? Or did the energy go into the expansion of space itself somehow? We’re not sure. It seems we need a bigger, comprehensive theory that unites quantum field theory and general relativity (and, we hope, dark energy as well), and then maybe we’ll know the answer.

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The first part of your description has left out the consideration of thermal radiation. Even if the collisions are elastic the molecules still lose energy to radiation. Though in your isolated system it largely just means you need to add perfect reflectors to the boundaries in order to contain this radiation. But for the known universe which seems to be expanding without limit, radiation also contributes to the overall decrease in temperature.

That is correct. In a collapsing universe the opposite happens… which led to speculations about a bouncing universe, one which alternates between expansion and contraction. Though the evidence doesn’t seem to be agreeing with this.

I mean, like, WOWWWWWW! man. This is delicious. I will read and mull again.

I haven’t finished reading the linked articles yet, but meanwhile, thank you, Dr. Haarsma, for your response! And thank you too, Mitchell. I hope to get to more follow-up over the weekend.

Thanks again! While the 2nd article seems to embrace the simple answer that yes - photons lose energy due to the expansion of space, I appreciate how the first article holds even that conclusion somewhat loosely. As in - the amount of energy a photon has can also still be seen as a function of perspective (my peculiar motion as I encounter that photon). The sorting of motion into two varieties: “co-movement” vs. “peculiar” motion (the more traditional kind we think of) was new to me. At first glance, that seems to me suspiciously like breaking another one of the taboos of relativity: the attempt to identify an “at rest” state of the universe in defiance of all motion (or alleged non-motion) being merely relative. After all if we can think of distant galaxies as having mere “co-motion” with us due to expanding space, it would seem to imply the existence of a “co-motion” bubble from which all peculiar motion could then be identified as present or absent. But I think I see the answer to this, in the form of the “co-motion” also being relative to whatever set of matter (galaxies & such) one is choosing to consider.

I also appreciated the admission that we can’t strictly rule out the possibility of the infinite universe (infinite energy) which inspired the idea of selecting a large arbitrary region of it (the ‘membrane’) and just examining within that to see how conservation laws might fare - and knowing that what’s true of one region ought to be true of all.

But I guess the main take-away I have is a confirmation that these are very much open-ended questions, and that our high-school level physics can very much be held as tentative at the cosmological level, even while it still functions as a rock-solid understanding for us in our little corner of activity and observation.

-Merv

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I certainly considered the infinite universe possibility before I made my previous reply, but it changes nothing and so it wasn’t worth mentioning. The problem is that an infinite universe doesn’t alter the expansion of the universe, because this expansion of the universe is not a global effect but a local one. In other words, the space is expanding everywhere even in our corner of the universe and that still means the heat density is decreasing. I just wanted to make sure you understood that part.

Yes - and thanks for your responses too, Mitchell. I had read your first one too.

I don’t really think the universe is infinite, but was just making allowance for the fact that our telescopic eyes haven’t yet encountered anything we could call an ‘edge’ of it, right? Hence the open-ended nature of that query. But it seems to me that there are a lot of good reasons, mathematical, physical, theological or otherwise to rule it out. I probably can’t enumerate, much less explicate those as well as you could, but I’m just letting my intuition piggy back on my impressions gleaned from modern cosmology.

I’ve never understood how radiation could be prevented from leaving a finite universe, going out into … the void? Unless it be some transdimensional geometry that has “straight” lines just coming back over themselves (like a pacman just scrolling back onto the other side of the screen). I do like the oft-used image of the expanding surface of an inflating balloon. But it is just an analogy for something that my 3-D conditioned mind has not yet apprehended in any more direct form.

Yes, if the universe is finite then if the universe wasn’t expanding so fast we would be able to see ourselves in the distance. But the expansion is faster than light so that more and more of the universe passes outside the visible limits, rather than being able see more of the universe as time goes on (which is what you would expect if it wasn’t expanding so fast).

I know this is a long shot, but I thought I’d still ask a question. Awhile back I got into a long discussion with a person who claimed to have had a PhD in physics and that they earned a Nobel prize. I was skeptical. But they didn’t make a big deal about it and they seemed very knowledgeable about physics nonetheless.

At one point, as we wrangled about the impossibility for an infinite number of future events, they said something about the eventual heat death of the universe, to which I replied with the possibility of quantum particles coming into existence, to which they speculated on recombination. “But it’s still not an infinite number,” I said.

Are quantum fluctuations to be presumed upon in a dead universe?

That’s another very good question for which we don’t know the answer.

Suppose you ignore quantum fluctuations, and just imagine an eventual “heat death” universe with particles and photons in thermal equilibrium, with a more-or-less constant energy density. Some physicists have argued that if you wait a very very very very very long time, eventually, randomly, some large but finite region of that universe will become locally low-entropy, and allow for the evolution of interesting things for a finite amount of time. And the spontaneous formation of such regions could happen again and again, infinitely. However, even if this did happen, each such region would be finite in time before going back to high entropy. And there are some significant objections as to whether or not this would ever really happen. I don’t think there is consensus among physicists on this question. And then, if you add in an expanding universe due to dark energy, such events become increasingly unlikely, and might never happen.

What if we include quantum fluctuations? I think (although I’m not sure) most physicists would agree that quanum vacuum fluctuations, creating (we imagine) virtual particle-antiparticle pairs for brief periods of times, could never lead to the creation of an interesting universe (or even an interesting sequence of real events) without the addition of some outside energy. So in a “heat death” universe, there might be an infinite sequence of such events, but none of them ever lead to anything interesting.

If you want to have an inifinite sequence of interesting things happening, you need some infinite source of orderly energy. The best candidate theory for that is something called “eternal inflation” – which has its own wikipedia page. There are observations in our own universe to suggest that some version of inflation theory might be true. There are several versions of inflation theory, and not all of them lead to multiple universes or eternal inflation. But some of the simplest versions of inflation theory describe an inflation field going forward in time eternally (but, interestingly enough, probably not backward in time indefinitely – this is still a subject of dispute), and this inflation field in turn gives rise to an infinite number of “bubble universes,” of which ours is one. Each bubble universe would be forever disconnected from the others, and each would have its own eventual heat death or in some other way be finite in time.

That, I believe, is the current thinking on those cosmological questions. Not a strong consensus on the answers.

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Thank you so much for the informative and interesting response

Gives rise to a number that may proceed to infinity without ever becoming actually infinite :wink:

Using the balloon as a three dimensional metaphor for four dimensional spacetime, and since the balloon expands with time, how would we be able see ourselves, regardless of the rate of expansion? The metaphor also says that the interior of the balloon does not exist, just the ‘fabric’, and we cannot ‘see through it’. It sounds like you’re saying we would be in two places at once.

After the initial cosmic inflation, it wasn’t always expanding faster than the speed of light. If it had been, we wouldn’t be able to see anything except our own galaxy, and maybe not even all of it.
 


So I was wondering when did cosmic expansion exceed the speed of light, and found this:

One of the most surprising facts about the Universe is that if you do the conversions and take the inverse of the expansion rate, you can calculate the “time” that you get out.

The answer? Approximately 13.8 billion years: the age of the Universe. There isn’t a fundamental reason for that fact; it’s just a fascinating cosmic coincidence.

Ask Ethan: How Does The Fabric Of Spacetime Expand Faster Than The Speed Of Light?

That may not be the answer to my question, but it looks like it might. Anyway, if it had been much sooner, we would be able to see way less.

It also fits nicely with these:

Have I ever mentioned that I like coincidences?

Because if the balloon isn’t expanding too fast then light would be able to travel all the way around the balloon back to where it began.

I think what you are alluding to is the acceleration of cosmic expansion in inflationary theory which is far from uniform – high positive then high negative rapidly going to zero, then slowly increasing to positive again. The visible edge of the universe is the point at which things are receding from us at the speed of light (anything beyond that is receding from us faster than light). When the acceleration is positive, things pass beyond that edge and when the acceleration is negative then things are passing back into the visible portion again. But this doesn’t mean nothing in the universe is receding from us faster than light. So the universe is still expanding faster than the speed of light even when the acceleration of that expansion is negative. Though if the acceleration remained negative long enough, then if the universe is finite, eventually all the universe would pass into visible portion (and it wouldn’t be expanding faster than light anymore) – long enough and we would see ourselves in the distance.

The universe is receding from us faster than the speed of light now, but it hasn’t always, is my point.

 
If that is true, then…

It appears that it will have been fairly recently, in a cosmological perspective.

Physicists, others, weigh in? @DeborahHaarsma, @pevaquark, @glipsnort?

Not my kind of physics, I’m afraid.

There’s more than one kind?! :flushed::grin: Oh yeah, astronomy, cosmology, astrophysics, elementary and high energy particle physics, planetary science, geology, geophysics, physical geography, oceanography, meteorology, hydrology, climatology, chemical physics, molecular physics… (How many did I leave out? ; - )

Thermodynamics

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