Sticking with Sean’s bedrock principle that all spontaneous, irreversible macroscopic evolution represents an increase in entropy, I would then conclude…

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The principle is not rock solid because it leaves out the observer. You could make it plausible by inserting this:

All spontaneous, irreversible macroscopic evolution seen by a single observer represents an increase in entropy as defined by that observer.

The definition of entropy has to do with how many microstates are indistinguishable to the observer and therefore constitute a single macrostate. Or is expressed in terms of the volume in phase-space of what the observer sees as a single macrostate. The observer’s MAP of phase space, in other words.

What you call Sean’s principle, otherwise known as the Second Law, can not be applied to a cosmological bounce simply because there is no observer who sees the Before and After universes and can apply a consistent map to phase space, or who can witness the bounce.

An observer Before will see increasingly chaotic geometry and (I would imagine measure increasing entropy) while an observer After will look back in time and measure a low entropy state. There is no contradiction and no violence to the Second Law because the two have different maps of phase space and measure entropy differently.

Thanks for continuing the discussion, Paul. I think it’s extremely interesting.

Watcher

I appreciate your homing in on my original question: what’s so special (ie low-entropy) about the way our Universe (probably) started, in a pretty-smooth, thermal radiation-dominated phase? If that’s really a special state, then it should be easy to say how you would change its characteristics so as to raise its entropy.

Your answer is quite straightforward: spatially smooth geometry is special, and so low-entropy; presumably, then, having a “bumpier” spatial geometry would be a higher-entropy state. At first glance this makes sense, since there are (presumably) more ways for space to be bumpy than there are for it to be smooth.

Thinking a little farther, though, I’m not so sure that bumpy space is necessarily higher entropy when that space is filled with radiation. We can see this by asking: in a radiation-dominated phase, will a non-smooth spatial geometry tend to grow bumpier or smoother over time? Now, mine is only a Little Brain but I can at least take a swing here.

Somewhat sloppily, we can divide spatial “bumps” into two kinds: (1) Volume-changing, which follow inhomogeneities in the mass-energy density and (2) Volume-preserving, which propagate on their own, ie gravity waves. The first types will tend to smooth out over time in a radiation-dominated phase, since we know that radiation does not clump gravitationally but instead tends to spread out more evenly in space — you can think of this as the effect of finite viscosity and/or heat conductivity in relativistic gases. The second type will, I think, also tend to damp out at long wavelengths, ie longer than the gas’ inter-particle spacing, as the gravity waves give up energy via dissipative/frictional/viscosity effects in the radiation gas. Short-wavelength gravity waves, ie with wavelengths comparable to the inter-particle spacing, may gain or lose energy randomly and so will tend to come to some sort of equilibrium; but this “graviton gas” does not (I think) represent a lot of entropy.

Sticking with Sean’s bedrock principle that all spontaneous, irreversible macroscopic evolution represents an increase in entropy, I would then conclude that bumpy space is actually _lower_ entropy than smooth space in a radiation-dominated phase, as in our Universe at early times. So, no: I disagree with your answer that smooth space in the early Universe is “special” or low-entropy, since this smoothness appears spontaneously during radiation domination.

Cheers,

Paul

PS If I can tempt anyone into a reply at this late date, I’ll venture a few words on my own opinion about special early states.

Let’s try it this way…When Einstein and Rosen developed the E-R Bridges, Einstein was definitely considering the ‘electron’ as the ‘base’ element. And was trying to show how that ‘base element’ could get here Via the Bridges from another universe.

BUT, of course he did NOT know about “Exotic Matter”/Point Particles even existing, NOT did he Know about SMBH’s. Nor did he really know about the Voids as we do today.

NOW, from there it is actually pretty simple, BUT, you won’t like the result!!! Why, because it will show that “Inadvertantly” science has defined certain things that wound up stacking the deck against finding the answer to how the universe is really working.

SO, quite simply…NOTHING can COME THROUGH a ‘Naked Singularity’…period, nada, zilch. (They simply cannot exist)

SO, the ‘base element’ is REALLY the “Point Particle”…BUT I am not going to name it, because as soon as I do, preconceived ideas about all that quantum ’stuff’comes into play.

So, the E-R Bridge(s), where ’something’ can come through, are the SMBH’s from the other universe.

SO, as Lee is suggesting/saying, the Second Law should NOT apply to ‘initial conditions’of the universe (Because we really don’t know the way it started to even be able to say!), which simply means that ’something’ CAN go ‘through black holes’. I know…blasphemy.

SO, whatever goes onto the event horizon of a SMBH in that ‘other universe’ spirals down to r=0=Ring Planck singularity, and comes through to our Voids.

That is simply where the “Point Particles” are being created. That comes to us as 96% just as Tim Thompson suggested above. AND, is the ‘gravity leaking’ to our universe just as Lisa Randall has shown. BUT, Lisa Randall CANNOT say that it is coming “through SMBH’s”, because that would be Career Suicide, and she may be many different things, BUT dumb is NOT one of them!

Lee, those “point particles” are the ‘Strings’/gravity and that is actually how String/”M” theory becomes “Background Independent”!

BUT, see, as soon as I indicated, that ‘those singularities’…ie, the ones in the E-R bridges, which are the SMBH’s rom the other universe to ours, and that there never has been a naked singularity, and therefore the universe started out cold, with the Gravity leaking to us ‘continually’ through the bridges to our Voids to create the expansion, everybody goes goofy…NO it HAD to start off HOT…we know that for sure!!!

There is another issue, which is whether generic states before the bounce result in near homogeneous cosmologies after the bounce, so that the specialness of the big bang is predicted. My understanding is that this is what Sean is querying and I believe it is an open question. It is interesting to note, as someone did, that a small period of inflation is generic in these models. Whether this is enough to set up iniitial conditions which will allow slow roll inflation in a model with an appropriate scalar potential is an interesting question, to my knowledge it is not resolved.

Besides this I would urge caution using thermodynamic arguments applied to the whole universe, for reasons I did mention above.

Thanks,

Lee/

Something we have NEVER ’seen’, measured, observed, understood in any sense of the word,……

Anti-Gravity………..wins the battle???

Lee Smolin…where is your response to #6 and especially # 7?

Let’s go back to your first question: “To put it another way, if you were observing the early, thermal radiation-dominated phase of the universe, what observation could you make that would lead you to say “Gee, this is a low-entropy state.”? ”

I guess I would answer: wow, look at how smooth the geometry of 3-d space is! How the heck did that happen?

In the early universe, essentially all forms of entropy were *high*, with the spectacular exception of the entropy associated with geometry. But just having low entropy in the geometry is not enough to ensure that entropy can increase — you need some way of *communicating* the low geometric entropy to other stuff. It seems that what you are saying is that low geometric entropy cannot be exported to a photon gas. In that case, the geometric entropy remains low, the photon gas goes its merry way, and there is no arrow of time of the kind we observe. The universe begins in a state which, *overall*, is extremely special, and it remains that special, in agreement with the second law. I don’t see anything strange in this, because as you admit your universe is nothing like ours anyway — and in what sense could time “pass” for a bunch of photons?

Now the hard question for me: am I agreeing with you or not?

Thanks very much for the clarifications; I really appreciate the help.

Now, just one more handful of lingering questions and then I promise I’ll let you go (at least on this thread); these are quick, the best one is last:

1. Reading this statement

” closed radiation-dominated universes …. are never able to reach their maximum-entropy configurations”

I don’t see this as particular to just radiation-filled closed universes; isn’t it also true of matter-dominated closed universes?

2. In the presence of a positive, non-zero cosmological constant open universes will, and closed universes may, end up as inflationary De Sitter spaces. De Sitter spaces are in many senses static and stable; they even have a temperature! Since it doesn’t appear to evolve, would you consider a De Sitter space to be a maximal entropy configuration?

3. I’m a bit puzzled by your preference for empty space as a maximum entropy/equilibrium state, ala

“That doesn’t mean that such an equilibrium doesn’t exist; it’s empty space.”

I’ll skip the obvious questions (what’s the entropy of empty space? and what’s the temperature of empty space? empty space has no macro evolution, but it also has no micro evolution; it’s only got one allowed state, classically, and so shouldn’t that count as zero, not maximum, entropy?) and ask instead what exactly you mean by “empty”.

Consider an open, forever-expanding universe with zero cosmological constant that’s filled with pure thermal radiation and no matter. You implied in an earlier comment that this kind of universe would evolve toward being an empty space, and hence (sensibly) toward equilibrium/maximum entropy. But I don’t see in what sense that’s true. Even after it stops self-interacting, a thermal photon gas retains its basic features as the universe expands. For example, thermal photons have a spatial density of (roughly) one per cubic wavelength, and if you think of them as having a size on the order of their wavelength then they’re packed “right next to each other.” This packing remains true even after an arbitrary amount of expansion, and so it is never the case that “empty space” opens up “between” the photons.

More concretely, we can observe that the entropy per co-moving volume is conserved during any amount of expansion, out to arbitrary scale factors, and so it’s hard to see how this qualifes as getting any closer to maximum entropy. And, while it is true that the energy per co-moving volume is always decreasing, there is no natural threshold scale below which you can declare space to be “empty” or even “relatively empty”. So in the radiation-only universe, even if it’s open, I can’t see how to make any sense of your statement that its true equilibrium is empty space.

A smattering of non-relativistic matter will complicate this picture, of course, and may lead to more sensible definitions of maximum entropy and empty space. But, do you really want to tell me that a universe has to have matter for the Second Law to be sensible/applicable? (Sir Roger said something like this last time I saw him.) If so, then that’ll be the weirdest thing I’ve heard this week, though it is only Wednesday.

OK, that’s it for now; thanks again,

Paul