How Does the Universe Use Temperature Differences to Create Structures?

[PeterDonis]

If the initial uniformity of matter is unstable because of gravity, why is it necessary for people to try to figure out initial temperature fluctuations to the nearest Kelvin. Wouldn't any fluctuation, however small, lead to the clumping of matter?

Not quite, because the universe is expanding. There needs to be enough of a fluctuation to concentrate matter enough to overcome the inertia of the expansion, so that it starts clumping.

Also, the increasing precision of measurement of the fluctuations is not just to show that they were there; it is to test actual quantitative predictions of how much clumping in today's universe should have been caused by a given level of fluctuation in the early universe, by comparing those predictions with how much clumping there actually is in today's universe, vs. the level of fluctuations in the early universe.

 

[Jimster41]

https://www.quantamagazine.org/20140122-a-new-physics-theory-of-life/

This popped up on a different featured thread. honestly until like yesterday it had never occurred to me that we did not have a complete technical theory of non-equilibrium thermodynamics. Seems like a major gap.

I do think it's a bit hard to categorize this topic, because it does cross disciplines. I wanted to mention this book to you @techmologist. It is one that is still changing the way I see things w/respect to structure and emergence. I'm not recommending any of these books out of a desire to persuade. I assume it wouldn't matter if I was. I've never found people that easy to persuade. But just to be clear, I'm just another fan in the stands man.

https://www.amazon.com/dp/0262600692/?tag=pfamazon01-20

I think Jablonka is also at the edge, and somewhat controversial (maybe Lamarck was seeing something real after all...) But I found her to be a thought provoking and lucid explainer.

 

[techmologist]

Okay, that makes sense.

Not quite, because the universe is expanding. There needs to be enough of a fluctuation to concentrate matter enough to overcome the inertia of the expansion, so that it starts clumping.

Ah. I hadn't considered the effects of expansion. Thanks.

Also, the increasing precision of measurement of the fluctuations is not just to show that they were there; it is to test actual quantitative predictions of how much clumping in today's universe should have been caused by a given level of fluctuation in the early universe, by comparing those predictions with how much clumping there actually is in today's universe, vs. the level of fluctuations in the early universe.

Okay, that makes more sense now.

Does the expansion of the universe somehow represent an increasing source of free energy? I read something to that effect in an article by Stephen Frautschi once.

 

[techmologist]

https://www.quantamagazine.org/20140122-a-new-physics-theory-of-life/

This popped up on a different featured thread. honestly until like yesterday it had never occurred to me that we did not have a complete technical theory of non-equilibrium thermodynamics. Seems like a major gap.

I do think it's a bit hard to categorize this topic, because it does cross disciplines. I wanted to mention this book to you @techmologist. It is one that is still changing the way I see things w/respect to structure and emergence. I'm not recommending any of these books out of a desire to persuade. I assume it wouldn't matter if I was. I've never found people that easy to persuade. But just to be clear, I'm just another fan in the stands man.

https://www.amazon.com/dp/0262600692/?tag=pfamazon01-20

I think Jablonka is also at the edge, and somewhat controversial (maybe Lamarck was seeing something real after all...) But I found her to be a thought provoking and lucid explainer.

That article looks very interesting. I only skimmed it just now, but it makes lots of interesting connections. I will print it out later and read it carefully. Also, the Jablonka book is the kind of book I would read. I am looking for ideas. Sifting through them and keeping what fits together.

I think the next book I read will be that Chaisson book you linked to. Right now I'm reading Per Bak's How Nature Works.

 

[PeterDonis]

Does the expansion of the universe somehow represent an increasing source of free energy?

It sort of does, in the sense that, as long as the universe keeps expanding, it can never reach thermal equilibrium. Another way to put it is, if the universe keeps expanding forever, there is no such thing as a state of "maximum entropy" for the universe as a whole.

 

[techmologist]

It sort of does, in the sense that, as long as the universe keeps expanding, it can never reach thermal equilibrium. Another way to put it is, if the universe keeps expanding forever, there is no such thing as a state of "maximum entropy" for the universe as a whole.

Is the universe expanding at the expense of anything? The expansion means more gravitational potential, so is it coming from kinetic energy or something else? I am assuming that the total energy of the universe remains constant, if that is even relevant here.

The way Frautschi put it was that although entropy is still non-decreasing, as the second law requires, the maximum possible entropy is always increasing. That sounds wonderful but I don't really understand it. It also directly contradicts one of the formulations of the second law that I am accustomed to, namely that the energy available to do work is non-increasing. If what Frautschi says is true, you can have increasing entropy and increasing free energy, too.

Based on what you said above though, I do see that the universe will tend to a situation where there are many increasingly isolated systems that can't equilibrate with each other.

 

[PeterDonis]

Is the universe expanding at the expense of anything?

No.

I am assuming that the total energy of the universe remains constant

There isn't any well-defined "total energy of the universe". In general in a curved spacetime there is no way to define one; it can only be done in certain special cases. In the case of a spatially closed (i.e., finite) universe, there is a sense in which the total energy is zero (heuristically, positive energy due to matter and radiation is exactly canceled by negative gravitational potential energy); but for a spatially infinite universe, which ours is as best we can tell, even that doesn't work.

It also directly contradicts one of the formulations of the second law that I am accustomed to, namely that the energy available to do work is non-increasing.

That formulation only works in those special cases where a "total energy" can be defined.

I do see that the universe will tend to a situation where there are many increasingly isolated systems that can't equilibrate with each other.

If the universe's expansion continues to be dominated by dark energy, yes, that is what will happen.

 

[techmologist]

There isn't any well-defined "total energy of the universe". In general in a curved spacetime there is no way to define one; it can only be done in certain special cases. In the case of a spatially closed (i.e., finite) universe, there is a sense in which the total energy is zero (heuristically, positive energy due to matter and radiation is exactly canceled by negative gravitational potential energy); but for a spatially infinite universe, which ours is as best we can tell, even that doesn't work.

That is mind blowing. Why does any science based on the conservation of energy work? Is it somehow locally true that energy is conserved?

The expansion part even makes the other classical formulations of the 2nd law awkward. Can you have a cyclic process in an expanding universe?

 

[PeterDonis]

Is it somehow locally true that energy is conserved?

Yes, of course. The issue is purely with not having a well-defined notion of "total energy" for the universe.

Local energy conservation is just the law that, locally, energy cannot be created or destroyed. That is what prevents perpetual motion machines from working. But to translate this into a global law about "total energy", we have to add up the energy in all local regions of space at some instant of time. Hopefully you see the issue: "space" and "time" are relative. In a general curved spacetime, there is no well-defined, unique notion of "space" or "time". So there is no well-defined, unique way to add up all the energy in local regions to get a "total energy".

 

[techmologist]

Yes, of course. The issue is purely with not having a well-defined notion of "total energy" for the universe.

Local energy conservation is just the law that, locally, energy cannot be created or destroyed. That is what prevents perpetual motion machines from working. But to translate this into a global law about "total energy", we have to add up the energy in all local regions of space at some instant of time. Hopefully you see the issue: "space" and "time" are relative. In a general curved spacetime, there is no well-defined, unique notion of "space" or "time". So there is no well-defined, unique way to add up all the energy in local regions to get a "total energy".

Gotcha. I made an elementary logic error, transforming not (the total energy is conserved) into the total energy is not conserved without noticing it. Big difference. Heuristics work every time, except for when they don't.

So it is just because there is no way to talk about what is going on everywhere in the universe right now. Because whether or not things in different places happen at the same time depends on your reference frame.

Is it okay to talk about total energy at the galaxy level or is that too big? Then you could apply energy conservation to say that the energy of the galaxy is decreasing according to how bright it is.

 

[PeterDonis]

Is it okay to talk about total energy at the galaxy level or is that too big?

Any system that can be treated as an isolated system--a bunch of stuff surrounded by emptiness--can be given a well-defined total energy, at least as a good approximation. A planet, a star, a solar system, and a galaxy all can be treated reasonably well as isolated systems.

Then you could apply energy conservation to say that the energy of the galaxy is decreasing according to how bright it is.

Yes--the energy carried away by radiation would be equal to the decrease in energy of the galaxy.

 

[techmologist]

Any system that can be treated as an isolated system--a bunch of stuff surrounded by emptiness--can be given a well-defined total energy, at least as a good approximation. A planet, a star, a solar system, and a galaxy all can be treated reasonably well as isolated systems.

I am probably making that same logical error again, but is there a sense in which the universe is not isolated?

 

[rootone]

There is if you're inclined to take multiverses and colliding membranes in higher dimensions seriously.

 

[PeterDonis]

is there a sense in which the universe is not isolated?

More than that, there is no sense in which the universe is isolated; it is not a bunch of matter and energy surrounded by emptiness. Matter and energy is everywhere in the universe.

 

[PeterDonis]

There is if you're inclined to take multiverses and colliding memiranes in higher dimensions seriously.

This is not the sense of "isolated" I am talking about. The technical term for what I've been calling "isolated" is "asymptotically flat". The universe is not asymptotically flat. That is a statement about our 4-dimensional universe, which is valid regardless of whether or not there are multiverses, colliding branes, etc.

 

[techmologist]

More than that, there is no sense in which the universe is isolated; it is not a bunch of matter and energy surrounded by emptiness. Matter and energy is everywhere in the universe.

Ah, I was making the same error again. I need to name it so I will recognize it better. I'll call it the "Nothing-is-better-than-steak fallacy" (and hamburgers are better than nothing, so...).

 

[techmologist]

I'm going to go out on a limb and guess that the second law of thermodynamics is not directly applicable to the universe as a whole for the same reason, at least not when stated in a global form like "the total entropy is increasing". That version would only apply to parts of the universe that are approximately isolated. Perhaps the local, negative versions about what can't result from a cyclic process are the best, since they don't require that any extensive state function be defined for the universe.

 

[PeterDonis]

I'm going to go out on a limb and guess that the second law of thermodynamics is not directly applicable to the universe as a whole for the same reason, at least not when stated in a global form like "the total entropy is increasing".

Actually, it's not entirely clear that this is true. Entropy can be defined in a way that's more general than the usual way (where it's linked to the definition of energy); the more general definition is that the entropy of a given state is the logarithm of the number of states that have the same macroscopic properties as the given state. But those macroscopic properties don't have to be extensive; for example, heuristically, if we consider the universe as a whole to be homogeneous and isotropic (i.e., ignoring all local variations in energy density, etc.), then we can describe it by its energy density, pressure, and curvature, which are intensive quantities, and we could say that its entropy is just the logarithm of the number of possible universes that have the same energy density, pressure, and curvature. (This is heuristic because we don't currently have a way of counting the "possible universes", but it illustrates the sort of thing that could in principle be done.)

 

[techmologist]

for example, heuristically, if we consider the universe as a whole to be homogeneous and isotropic (i.e., ignoring all local variations in energy density, etc.), then we can describe it by its energy density, pressure, and curvature, which are intensive quantities, and we could say that its entropy is just the logarithm of the number of possible universes that have the same energy density, pressure, and curvature. (This is heuristic because we don't currently have a way of counting the "possible universes", but it illustrates the sort of thing that could in principle be done.)

That is an attractive idea. So these intensive quantities would effectively be averages over the 4-dimensional manifold, right? There would be no taking account of any gradients (and associated flows) in this picture.

Since you brought up possible universes, is there anything to the claims of fine-tuning of this particular universe? Some of the more extreme claims are obvious b.s., but the one that says some fundamental constants must be extremely precise in order for galaxies and stars to form got my attention. That is a very serious claim. Even a secular humanoid such as myself has a hard time imagining any life forms without stars and planets. But I don't know about cosmology and can't evaluate the claim.

 

[PeterDonis]

these intensive quantities would effectively be averages over the 4-dimensional manifold, right?

Correct.

There would be no taking account of any gradients (and associated flows) in this picture.

More precisely, differences in gradients/flows would be different "microstates" (detailed states of the universe) that correspond to the same "macrostate" (average values of the intensive quantities).

is there anything to the claims of fine-tuning of this particular universe?

This is still an open question, because, as I said before, we don't know how to count the "possible universes", so we don't know how to quantitatively estimate how "fine-tuned" our universe really is.

 

[techmologist]

More precisely, differences in gradients/flows would be different "microstates" (detailed states of the universe) that correspond to the same "macrostate" (average values of the intensive quantities).

That makes sense.

This is still an open question, because, as I said before, we don't know how to count the "possible universes", so we don't know how to quantitatively estimate how "fine-tuned" our universe really is.

Thanks. Just knowing that it is a real question helps. I couldn't tell if I was being conned. Some of the more vocal proponents of fine-tuning have motivations that are at best unrelated to scientific understanding.

In your opinion, is the question "why are there heat engines" a real question?

 

[PeterDonis]

In your opinion, is the question "why are there heat engines" a real question?

Well, it's led to a real thread.

I think the answer is "sort of". It's certainly true that our local observation that there are heat engines must be consistent with what we know of the universe as a whole, so in that sense it's a real question.

But our concept of a "heat engine" is based on our concept of "useful work", and that's not really a physics concept; it depends on what we find to be "useful", so it's more of a subjective concept. Physically, something we call a "heat engine" is no different from any other system; it obeys all the same laws. It just happens to have an output that we consider "useful". So in that sense, "why are there heat engines" isn't a real question, or at least not a real physics question; it's a question about how we choose to describe certain portions of reality, not a question about the laws that govern reality.

 

[Jimster41]

Thanks for making it a real thread Peter! I'm trying to read G.Crooks paper from 1999 talking about the fluctuation theorem. This after realizing J. England is sort of starting with that. Very interesting. He is generalizing the work done by a heat bath coupled classical system in transitioning over a path in configuration space, whether the path exchanges heat with the bath or is isothermal but selects between microstates (I may be botching that) - so I got to think about your statement that "useful work" is observer dependent.

 

[techmologist]

But our concept of a "heat engine" is based on our concept of "useful work", and that's not really a physics concept; it depends on what we find to be "useful", so it's more of a subjective concept. Physically, something we call a "heat engine" is no different from any other system; it obeys all the same laws. It just happens to have an output that we consider "useful". So in that sense, "why are there heat engines" isn't a real question, or at least not a real physics question; it's a question about how we choose to describe certain portions of reality, not a question about the laws that govern reality.

I think you're right that the "useful" in "useful" work is not strictly a physics concept. But what I have in mind is not completely subjective, either. I definitely do not mean only useful to humans. I would say "usefulness" has a certain objectivity in the context of organization. The "purpose" of any organization is simply to persist, to keep producing itself. How it does this depends on how it fits into a larger network of relations among organizations. This larger network of relations is itself a higher-order organization. Within the context of that higher-order organization, the organization performs a "function". But it is only performing this "function" because by doing so, it directs resources to itself and persists--produces itself, renews itself, repairs itself. So to an organization, "useful work" is self-repair.

As an economic example, a steel-producing firm performs an essential function as part of a larger economy. But the owners of the firm aren't doing it out of the goodness of their hearts, or patriotism, or whatever. To the extent they have an interest in the continuation of that business, they will consider "useful" any action that tends to grow the business, or at least maintain it. Actually it is more complicated than that, because in any modern firm of that type management and labor also have their own interests, all pulling in somewhat different directions. So the organization, the firm, ends up "acting" as if it had a personality of its own, not identical to that of any of its constituents. It's actions are useful the extent that they tend to keep that organization going.

At the physics level, useful work performed by a Benard cell is work that overcomes viscous drag, keeping the Benard cell from fizzling out. Similar things can be said of a thunderstorm or hurricane. These may or may not have some direct use to humans, but the usefulness referred to here is from the perspective of the organization itself.

I realize that the second law of thermodynamics doesn't explicitly refer to "engines" in the sense of "useful to somebody"--to power their car. It just says that if you have a system and two heat baths at different temperatures, it is possible to arrange a cyclic process with the result that thermal energy is absorbed from the hotter bath, some of which energy is used by the system to do work on its environment, and some of which is passed on as thermal energy to the colder bath. The second law is completely agnostic about whether such a work-producing cyclic process will ever happen. It only puts limits on what such a process could achieve, should it happen. That's where my question is coming from. Is it just a case of anything that can happen will happen?

Thanks for making it a real thread Peter!

Seconded. :)

 

[techmologist]

Thanks for making it a real thread Peter! I'm trying to read G.Crooks paper from 1999 talking about the fluctuation theorem. This after realizing J. England is sort of starting with that. Very interesting. He is generalizing the work done by a heat bath coupled classical system in transitioning over a path in configuration space, whether the path exchanges heat with the bath or is isothermal but selects between microstates (I may be botching that) - so I got to think about your statement that "useful work" is observer dependent.

Everything in those papers seems to hinge on the condition of microscopic reversibility relating the probability of a forward process to the probability of its reverse process.

P(A->B)/P(B->A) = e^(beta*Q)

where Q is the heat delivered to the surrounding bath during the forward process.

This idea is new to me. I am familiar with detailed balance, which applies at equilibrium, but this microscopic reversibility condition is claimed to apply away from equilibrium. How do they know that? Is there some way to see why it must be so?

 

[PeterDonis]

I would say "usefulness" has a certain objectivity in the context of organization.

But what counts as an "organization" is subjective. There's no law of physics that says what an "organization" is; it's just a particular piece of reality that someone picks out as being of interest.

At the physics level, useful work performed by a Benard cell is work that overcomes viscous drag, keeping the Benard cell from fizzling out. Similar things can be said of a thunderstorm or hurricane.

True, but again, it is not physics that picks out the Benard cell or the thunderstorm or hurricane; it's us. True, these systems are usually thought of as being "natural", whereas a refrigerator or an engine is thought of as "artificial"; but even those are distinctions made by us, not physics.

The second law is completely agnostic about whether such a work-producing cyclic process will ever happen. It only puts limits on what such a process could achieve, should it happen. That's where my question is coming from. Is it just a case of anything that can happen will happen?

Not every possible work-producing process that could happen, actually does happen. Since the underlying microscopic physics is chaotic (i.e., it has a sensitive dependence on initial conditions), we really have no way of knowing what picks out which work-producing processes actually happen (except in the obvious cases where somebody deliberately arranged for a particular process to happen).

 

[techmologist]

But what counts as an "organization" is subjective. There's no law of physics that says what an "organization" is; it's just a particular piece of reality that someone picks out as being of interest.

Right, there's no law of physics that says so. But who says physics is all there is? Everything that happens is founded in physics, in the sense that the underlying laws of physics provide the background for everything. But most things aren't objects of physics. Like algorithms, for example. At some level, it's physics that makes your graphing calculator work. But it isn't physics that makes it give you the right answer. The same physics governs a calculator that gives you the wrong answer.

And while it's true that we do pick out things of interest, we aren't totally at liberty to pick out just anything, or ignore just anything. Our minds organize around a real world that we find ourselves in. They have to or we wouldn't be here.

 

[PeterDonis]

who says physics is all there is?

It isn't, but it's all that's on topic for this forum. If your question "why are there heat engines" wasn't a question about physics, then it's off topic. I was assuming it was a question about physics.

 

[PeterDonis]

Our minds organize around a real world that we find ourselves in.

Quite true. But there's still a difference between our models of reality, and the reality that is being modeled.

 

[Jimster41]

But what counts as an "organization" is subjective. There's no law of physics that says what an "organization" is; it's just a particular piece of reality that someone picks out as being of intetest.

Chaisson's breakdown of "complexity" as "energy flux density" is pretty objective isn't it?