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

By starting with a closed universe, you’ve taken a certain set of degrees of freedom and put them on a trajectory for which they will hit a singularity before they reach equilibrium. That doesn’t mean that such an equilibrium doesn’t exist; it’s empty space. (There isn’t any stable and static configuration of a black hole in equilibrium with a radiation bath; the radiation necessarily back-reacts on the geometry, and the universe will expand or contract.)

Picking up from your main points

“the fact that something is evolving …. is evidence that you’re not in a maximal entropy state”

“he whole point, though, is that there is a state that is static, and remains so, without fine-tuning: empty space. That’s the honestly high-entropy state.”

you seem to be taking the hard line, that if any macroscopic evolution is taking place then the state of that universe is not the state of maximum entropy, and hence is a “special” state. This is not an unreasonable view, in my Little-Brained opinion. But, how are we to apply it to non-empty, closed universes?

Picture any non-empty, closed universe with some matter and no cosmological constant; this is perfectly reasonable, and not at all fine-tuned. Within the FRW description any such universe is _never_ macroscopically static and stable, and hence must _always_ be in a “special” state by your definition. So what is the honest maxium entropy state of a closed, non-empty universe?

Naturally we have to consider universes outside the family of Robertson-Walker spaces, ie globally non-isotropic/non-homogeneous geometries. I’m not well-versed enough in GR to discuss these geometries in any detail — perhaps after I’ve saved up enough money to buy your book I’ll know more. But what can you, the expert, tell me? Are there closed, non-empty, non-Robertson-Walker, non-fine-tuned, zero cosmological constant universes with a static geometry?

There’s one arrangement that suggests itself, just by considering what the matter in a static, closed universe would have to look like. As I see it, there is only one non-empty arrangement which could be forever macroscopically static: when all the matter is collected into one, single giant black hole which is in radiation/absorption equilibrium with a thin, cold gas of light particles. Such an arragement is clearly _not_ a Robertson-Walker universe; but could it exist in a static, non-RW geometry? If so, then it seems that that would be the honest maximum entropy state of a non-empty, closed universe.

If, on the other hand, there is no way to arrange a non-empty closed universe that is also static (and not fine-tuned), then I think your argument and Sir Roger’s loses traction: if all states of a closed universe must evolve macroscopically, then all states of its states are “special” by your definition. Clearly if all possible states are “special” then the word “special” has lost some of its meaning (remember that line from _The Incredibles_:”If everyone is special, then no one is.”) and we have to drop back to “relatively special”.

In this latter case, it is again fair to ask: is the intial, smooth radiation-dominated phase of a closed universe “relatively special”? How would we judge it to be so? As I see it, the main quality that makes it “relatively special” is the fact that it’s _not_ chock full of black holes. It’s the absence of black holes, not the simple fact of macroscopic evolution, that indicates you’re in a low-entropy state in that early phase. ["Where are all the black holes? The tour brochure specifically said there'd be black holes. I wonder if it's too late to get my money back..."]

In short, I think you have to do a little more work to apply your logic consistently to the case of non-empty, closed universes with zero cosmological constant; this is a perfectly respectable class of of universes (isn’t it?) and the Second Law must apply sensibly to them as it does to open universes.

Best regards,

Paul

http://arxiv.org/abs/0706.3379

By the way, I am certainly not merely postulating the phenomenon of Self-Replicating Space-Cells, nor am I a priori presuming that there should be any kind of replicators nor any other biological analogies. Instead I am arguing that the phenomenon of Self-Replicating Space-Cells must necessarily emerge from a discrete physics model, if it is to successfully model reality.

Let me know wether you think I am wrong, and why.

In cosmology, you can set up an evolution that is pretty darn adiabatic, if you are sufficiently careful. Any matter (nonrelativistic) degrees of freedom, for example, would ruin reversibility, as perturbations would grow. And you need to make sure you have a closed universe, not an open one.

But even then, it’s not perfect. At the nonlinear level, some of those photons are going to come together and make a black hole. And those black holes are just going to grow. The crunch is never going to be precisely as low-entropy as the bang was.

The whole point, though, is that there is a state that is static, and remains so, without fine-tuning: empty space. That’s the honestly high-entropy state.

Thanks for your quick reply; but I’m afraid I don’t buy it. Just because you see a gas expanding/diluting/cooling does _not_ mean that its entropy is increasing. If you move the walls of a gas-filled box to expand its volume, and do it (arbitrarily) slowly enough that the gas remains (arbitrarily) close to equilibrium throughout, then the expansion is isentropic and reversible. If you cycle the volume reversibly, then the entropy does not increase during expansion and neither does it decrease during contraction.

Is the early thermal universe any different? Recall that we’ve had some of this conversation before, back at #60 and #61 in the “Latest Declamations” thread (see http://blogs.discovermagazine.com/cosmicvariance/2007/06/11/latest-declamations-about-the-arrow-of-time/#comment-286711 ). I consider the history of a closed Friedmann universe in which only radiation can exist (not our universe, clearly, but I don’t see it as an unreasonable postulate). This universe expands and then re-contracts, and in the absence of matter the two phases should mirror each other (very nearly) perfectly. So a claim that entropy is greatly increasing during the expansion phase must imply that entropy is greatly _decreasing_ during the re-contraction phase, which would be a big violation of the Second Law. The only reasonable conclusion that respects the Second Law is that the expansion of a radiation-only universe is reversible and so isentropic in all phases. Hence, someone observing the early, radiation-dominated expanding phase would _not_ be correct in concluding that entropy is increasing just because there’s a spontaneous expansion in progress.

In short, spontaneous macroscopic evolution can often be a _sign_ that entropy is increasing, but it is _not_ a sufficient criterion by itself. Some spontaneous macroscopic evolutions are reversible and isentropic, and an expanding radiation-dominated universe is one example.

What am I missing?

Thanks,

Paul

High-entropy states are in thermal equilibrium; they’re static, not evolving. The early universe is rapidly expanding, diluting, and cooling off — as you would expect from a low-entropy state.

Don’t despair completely. If you want a little more action, you Big Brains can try gearing down to reply to my Little Brain comment at #56, which asks some basic second law questions before addressing bounce models.

To make scrolling back up worth your while, here’s a short form of the same question. I’ve seen Penrose’s presentation as well (video of his recent appearance at BNL can be found here http://www.bnl.gov/video/lectures.asp ), and recognized many of the diagrams from _The Emperors’s New Mind_ in its outstanding chapter on entropy. Sir Roger starts from the same observation as Sean, namely that since entropy is increasing through the evolution of the universe it must have been very low in the early phases, ie that the universe must have been in a “very special” state at early times. But if the early (post-inflationary) universe was (essentially) dominated by highly relativistic gas spread very smoothly, then how is that state in any way “special”? 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.”?

Let ‘er rip; regards,

Paul

is the same slides as what I saw him give in March 2006 at Berkeley MSRI and with help from that Penrose talk, I think a good overview is that there are
THREE reproductive cosmology scenarios that people are offering and they differ in the detail of the imagined reproductive mechanism and all three are covered by the same Second Law insurance policy.

there’s Penrose’s, there’s Smolin’s, there’s Sean’s.

in each case when you hop over to the baby universe, the map of macrostates in phase space changes abruptly—–from the new perspective different combinations of fundamental degrees of freedom are significant and measurable.

So there is a discontinuity in the definition of entropy when you jump to the new point of observation. A new map of phasespace resets the Second Law. There is one absolute correct map of regions in phasespace. So evolution, in terms of fundamental degrees of freedom, can be continuous. But there is this discontinuity in entropy which by definition cannot be observed.

Schematically all three reproductive cosmology scenarios are so similar that, if we were playing by traditional scholar etiquette, each of the three would be CITING the other two in their references. Maybe they do. Penrose does cite SMOLIN in any case, prominently on one of his early slides. He actually cites it more as “Wheeler-Smolin” because apparently Wheeler had the branching baby universe picture first (or at least the blackhole-to-bigbang part of it). Penrose style here is casual and informal. I like the way he presents the issues visually very much.

At the end, Penrose makes the point that a large region in one observer’s phasespace can correspond to a small region in another observer’s phasespace
(so entropy can be reset). He doent acknowledge that the same reconciliation covers the bounce invoked by Wheeler and later by Smolin, but that’s OK it is IMHO just normal scholar tunnelvision when you find a solution you like then you are temporarily blind to other people’s

what he says in the November 2005 talk is very relevant. he draws phasespace, and different size blob regions on it representing the macrostates from perspective of some observer—-the coarse grains of phase space

then he draws a squiggly line in phasespace and shows how it likely wanders into everlarger blobs (that is entropy likely increases)

then he goes out to near “time-infinity” and, at the next to last slide, he takes the Reproductive Cosmology step of imagining a new big bang

and there he says the coarsegraining map of the phase space TOTALLY CHANGES so that we dont have to worry about entropy—-there is a new perspective, as if a new observer with different significant measurments—so basically he assumes a radical discontinuity in entropy

even though the squiggly line wandering in phapsespace is continuous, because that is moving in a space of fundamental degrees of freedom, which do not change (only the coarsegraining changes, at the moment of reproduction).

Sean’s scenario seems like an alternative version of Penrose story, except that the detail of reproduction is different. Same argument can basically support both—in rough outline, I think. Have to go, talk more about this later!