Lee Smolin's molten gold analogy

[marcus]

Smolin used a really interesting analogy for the big bounce transition here:

http://cosmicvariance.com/2007/07/02/against-bounces/#comment-294116

the idea is a phase transition of the geometry of space which resets it to low entropy---and it looks like Bojowald's recent paper supports the possibility of this without violating the operational form of the Second Law.

The operational Second Law says that entropy is nondecreasing as defined and measured by an observer (who gives meaning to the idea of macrostates of the system, by what he or she is able to measure.)

Roger Penrose loves to point out that low entropy for gravity (i.e. geometry) is INTUITIVELY THE EXACT OPPOSITE of low entropy for matter. The more uniform spatial geometry is, and the less clumpy/lumpy, the lower entropy.

But with gas molecules, spread out uniform in the container is HIGH entropy. If the gas starts out clustered and bunched in one corner, that is low entropy and it will immediately start to spread out and get more and more uniformly distributed.

             geometry(gravity)       matter
low entropy     uniform spread       clumped
high entropy     clumped             uniform spread

So the universe starts out with very lowentropy gravitational field, totally uniform spread out, because the matter is just uniform cloud or wall-to-wall fire, however you picture it

and the first thing gravity starts doing is CURDLING AND CLUMPING and getting bumpier, as things begin to coagulate. It's how galaxies came to be.

and that is INCREASE OF ENTROPY in the gravitational field or overall geometry.
====================

Smolin didn't specify what metal. I will put the analogy in my own words to make it as graphically definite for myself as I can. In my version, it says Picture the cosmological bounce as going thru a Planck regime of extreme temperature and density during which "space melts" and actually the idea of macroscopic space is no longer meaningful.

It would be like say a statue or complicated goldsmith's artwork with all kinds of filegris and figleaves and grillwork and maybe some frogs or a figure of Adam and Eve and the Apple Tree or whatever----somebody paid Giovanni Bellini to produce all this clumping and clustering (like the galaxies of a used universe) and you MELT IT down to an ingot.

In terms of the gravitational field, you have reset the entropy back to "zero". It is a uniform block of metal with lowest possible entropy (thinking gravity)

although of course thinking matter, when you melt something you increase the entropy----but if you look at it that way you don't understand the analogy.

 

[marcus]

If that business about entropy in grav field being intuitively the direct opposite of matter entropy----if that seems strange, well it shouldn't. Roger Penrose has been going around making that point at just about every talk he gives for the past 3 years. Everybody should know this and understand it because it is the only way you can apply the Second Law to cosmology and make sense.

But i haven't come to the NEW part of the story!

the new part is really neat and it relates to Bojowald's piece in July 2007 Nature Physics.

First we have a kind of paradox where, at a bounce----say a black hole collapse leading to an inflation episode and a new universe (out the back door)---or any other kind of collapse-then-expansion bounce---IT SEEMS AS IF THE ENTROPY DEPENDS ON WHICH WAY YOU LOOK.

If you are in the Before universe, you see a black hole form and you see the Horizon with its huge cartload of entropy. and that's it. you are actually looking forwards along a branch of time at the backside of somebody else's "big bang" and it looks HIGH ENTROPY to you.

And that other person, in the After universe, looks BACK in time at the first three minutes of his universe and his CMB last scattering surface and it all looks reasonalby SMOOTH AND UNIFORM to him----a slightly mottled blank wall of fire. He is looking back at your black hole and it looks LOW ENTROPY to him!

That's a contradiction, or seems like one: Mr Before sees a huge truckload of entropy as he is looking at the event horizon and imagining the bounce beyond it and Mr After sees very low entropy as he looks back to the last scatter surface and imagines the bounce beyond it. Who is right?

It seems like if you could run your finger right along the raging "tube" of socalled Planck regime which connects from the collapse to the expansion that you MUST come across some point where there is a big drop in entropy.

That is the paradox.
==============

And we can even use Smolin's melting metal analogy to picture that point. It is where the golden geometry of a universe (or some region of it) melts to a puddle of Planck regime.
Or where the largescale illusion of space no longer happens and the fundamental degrees of freedom, from which space and matter are customarily built, become for a moment like a swarm of angry bees.

Lee cites some Fotini papers at this point, and says "phase transition". That is because it would sound overly dramatic to say reality MELTdown. heh heh.
we all know these moments heh heh. OK phase transition.

===============

So far I still have not told you the NEW part. The new part is How come this apparent violation of the Second Law is allowed?
==============

 

[marcus]

the Bojowald unmeasurability principle :-)

Martin Bojowald and a halfdozen co-workers have been slowly improving the LQC bounce model for the past 6 years or so, and it has been picking up lately.

a solvable model, mass-ful interacting matter---not just free massless matter,

working with inhomogeneities---not just simple homogeneous

the most recent paper you can download is
http://arxiv.org/abs/0706.1057

and the interesting thing is, in this paper, and also in the Nature Physics piece, he says he notices a kind of Heisenberg-like INDETERMINACY principle, or a kind of COMPLEMENTARITY between two measurments (one before and one after) where you have a tradeoff---and the better you know one the worse your knowledge is of the the other.

And this affects how much we can know about the BEFORE-world and the AFTER-world, and how much actual contradiction we can really experience.

You see we MIGHT have been able to make measurments HERE that would allow us to INFER AND KNOW something about before-the-bounce.
So then we would be having our knowledgecake and eating it too, because we would be nailing down information about BOTH sides of the bounce.

And then maybe you could run your finger along the tube of the bounce and find just that place where the entropy suddenly dropped!

But BOJO INDETERMINACY PREVENTS DOING THAT.

And so that violation of the Second Law can NEVER BE OBSERVED TO HAPPEN and therefore in a pragmatic operationally-defined sense it doesn't happen.

There is always just enough uncertainty about the prior universe to save the Second Law

Well anyway that's the idea

 

[marcus]

BTW if you count a physicist's PhD thesis advisor as his parent, then Bojowald is Heisenberg's grandson. So in an odd way it is appropriate he should come across this limit on before-and-after-bounce knowledge.

Bojowald's thesis advisor was Hans Kastrup, whose thesis advisor was Werner Heisenberg. Alejandro Rivero taught me that.
http://en.wikipedia.org/wiki/Genealogy_of_theoretical_physicists

 

[marcus]

it seems to be that (and all this is just speculation) there could be a huge controversy surrounding Martin Bojowald's "1057" paper and the July piece in Nature Physics.

I think it BREAKS UNITARITY at the point of "creation" of our branch of spacetime----the principle of unitary evolution of the quantum state is an entrenched assumption. sometimes it is referred to as "no loss of information"

Bojowald "1057" paper says, in effect, that there is a point in evolution such that

A) If you are AFTER that point, no amount of measuring you do of your universe will allow you to completely describe the quantum state of what was before.
You can describe some of it, but a kind of indeterminacy or "forgetfullness" principle prevents you, even in theory, from complete knowledge.

B) If you are BEFORE that point, no amount of measuring you do in your universe will allow you to determine the quantum state of what will come after that point.

I call it the "1057" paper because I have needed to refer to it a lot and this let's me get it on the internet----it came out in June 2007, which is "0706" so I can reconstruct the URL this way:

http://arxiv.org/abs/0706.1057

This paper also allows by-passing the SECOND LAW OF THERMODYNAMICS.
there is a cushion of uncertainty that prevents the second law from being confronted and possibly seen to fail.
Because at this point in evolution that I am talking about, the usual beautiful gradual constant increase in ENTROPY------as seen either by an observer after that point or an observer before that point, which is different cases---the two define and measure entropy differently----this familiar gradual increase of entropy with time STOPS at this point. (maybe time doesn't exist at this point or is not well defined)

In any case entropy is not defined at that point because you don't know which observer's view of it pertains----one sees it as high entropy and one sees it as low.
no observer can exist there, at the actual point
(it is the "planck regime" of extreme pressure, temperature, energy density---there is no reason to imagine that space and time actually exist there, since they are macroscopic manifestations of orderly arrangement, not fundamental degrees of freedom)
obviously no observer could survive in the "planck regime" conditions.

so it seems to me that basically the gauntlet has been thrown down by this "1057" paper and the choice pick of details from it that I assume went into the July 2007 Nature Physics piece.
It is somewhat as if two wrestlers have now "come to grips" and are locked into some kind of decisive engagement.

Pretty much the mass of the physics establishment believes in the UNIVERSAL APPLICABILITY of the ideas of no loss of information (unitary evolution in time) and the second-law (monotone increase of entropy in time).
but a number of individuals must nevertheless be ready for it, because Carlo Rovelli has often been asking what do you mean by something being conserved "in time". If there is a moment when time breaks, then what do you mean by unitary evolution in time, or increase of entropy in time. He is a nice person and would never intentionally offend anyone, he just pleasantly asks this question.
Certainly a lot of individual physicists must have heard this, and so are mentally prepared.
Bojowald must be ready because he decided it was time to say it and he seems to know what he is doing.
Lee Smolin has obviously been ready for a long time.
He is doing his job by communicating the idea of a phase transition, the instant when the METAL SCULPTURE MELTS.

Being ready doesn't mean you are going to "win". I believe in science the point is not to win, but to decide the issues. This is a tough one. The ideas of second-law and unitarity are deeply entrenched.
the nice thing, on the other hand, is that Bojowald has this MODEL that ticks along and shows you the place where the metal melts.

====
Fra, thanks for your comment. I am waiting to see if anyone else has a response or questions, so I will not reply quite yet.
BTW I put some comments from a blog discussion thread here:
https://www.physicsforums.com/showthread.php?t=175704
some of the blog comments, by Smolin, Aguirre, Carroll...are interesting. the first part of my thread is mostly press releases so you have to scroll down
if you are interested to see the copied blog comments. it is a potentially complex and exciting controversy that the Bojo articles and Nature Physics piece raise.

 

[Fra]

Hello Marcus, you do a nice job reporting various stuff on here! I am not one bit into any of the common approaches, and not cosmology specifically either, but on a first reading of the above it strikes me as close to dead on analogies that fits into my view very nicely. Those papers sounds like worth reading!

a) That disorder is relative, is clear in the subjective probability approach. Because any order needs to relate to something. This has been pointed out in many papers.

b) I always felt (at least the last few years) that unitary evolution somehow does not mix with a fundamentally evolutionary model. And non-unitary events are the challanging ones. In the general case of an information theoretic approach this is also natural, and unitary evolution seems to be a special case.

c) About entropy, and second law, and evolution, I think they will be united. The ultimate generalisation of the "second law" (to be seen) will ultimately (I think) explain dynamics as well. To separate dynamics from static entropy isn't quite consistent, I think unification should come with bettwe understanding.

I'm interested to see how he argued into this. Not that he needs to convince me as such, but the connection from a different starting point would be interesting.

/Fredrik

 

[marcus]

Hi Fra, thanks for your comment.

I've noticed a DISCONNECT in the controversy about the cosmic BOUNCE.

The kind of "ban-the-bounce" talk you can sample by going to cosmic variance does not seem to be based on an awareness of Bojowald's current work.

Here are the slides of the talk he gave in late June 2007 at Loops '07.

http://www.matmor.unam.mx/eventos/loops07/talks/PL4/Bojowald.pdf
Loop Quantum Gravity and Effective Theory

You could easily get the impression from listening to people giving "theoretical reasons" why a bojowald-type bounce could not possibly occur that they think the model he's using is a DIFFERENCE EQUATION with a couple of degrees of freedom. The radically reduced model of earlier Loop Quantum Cosmology. That is not quite true, some progress has been made in getting control of what I think is a more realistic model.

It looks to me as if he is using a system of DIFFERENTIAL equations---a considerable number of them in fact---and that current work involves PERTURBING around the symmetry reduced model in order to get more realistic and include inhomogeneous stuff and interacting matter etc.

The critics, such as they are, do not seem to know much about what is actually going on.

 

[marcus]

Something else I noticed. When you study what happens in classical Gen Rel as you approach a singularity a common thing to observe is CHAOTIC BEHAVIOR LIKE CRUMPLING A PIECE OF PAPER.

the geometry of space can get messed up in an almost "fractal" way.

My intuition is that one reason Mother Nature gives us quantum mechanics is so that such a crumpling CAN ONLY PROCEED DOWN TO A CERTAIN SCALE and when you start trying to fold wrinkles in something that are only Planck size then it just doesn't work and you can't fold it any more.

the trouble is these people that think in terms of CLASSICAL MANIFOLDS don't visualise a limit to crumpling, because a standard vintage 1850 differentiable manifold continuum has no microscopic limit to crumpling.

but if you are thinking along lines of quantum geometry, the degrees of freedom from which space and time arise, which give us familiar geometry at macro scale, are quantum critters at micro scale

and AFTER A WHILE FURTHER CRUMPLING JUST MAKES THEM SMOOTH.

that is the point at which Smolin's gold serving dish, with the frogs and turtles carved on it, melts.
=================

so for them it is a big issue "how do you get smoothness out the other end?" and for me that is not the issue at all.

for me there is a much much more serious problem---and this is something that you FRA have wondered about too, I expect. this is the problem of "how do you get the right number of DIMENSIONS out the other end?"

the dimensionality of space is, as Renate Loll pointed out, actually a quantum observable.

a fundamental theory of spacetime should explain why the basic degrees of freedom from which large scale geometry arises----why these basic degrees of freedom should produce space which is three dimensional.

fortunately Bojowald and friends, who are working on the level of an effective theory---with the possibility of being able to test things against CMB and galaxy survey observations---don't have to worry about that.
they just have to set up an effective theory and get predictions out of it.

 

[Micha]

Very interesting stuff, Marcus.

Regarding dimensions: Who says, that baby universes always have the same number of dimensions? Maybe there is an argument, why 4d spacetime maximizes the number of black holes. Or is this stupid?

 

[marcus]

Or is this stupid?

No way is it stupid! It sounds like a good idea for somebody to explore.

BTW ALEJANDRO SATZ who has an excellent blog (including quantum gravity with good book reviews and intriguing philosophical discussions) called
RealityConditions, http://realityconditions.blogspot.com/ this Alejandro has ventured a comment in the cosmicvariance.com BOUNCE thread
http://cosmicvariance.com/2007/07/02/against-bounces/#comment-294402
and an anonymous observer has replied

==quote cosmicvariance==
58. Alejandro on Jul 7th, 2007 at 2:22 pm

This is a question that has been worrrying me for years about bounce models. I asked Ashtekar about it at a coffee break in Loops 07, and as far as I understood his answer, he seems to think that the quantum regime has intrinsically low entropy for some reason, so in the collapsing phase entropy is decreasing (Sean´s option 2).

However, I didn´t press to ask the following natural question: would a generic collapsing spacetime (which has growing entropy, in the classical regime) also become low-entropy as it enters the Planckian regime? This would be very difficult to believe…

69. Watcher on Jul 7th, 2007 at 4:22 pm

this is the phase transition that Smolin was talking about
he used the analogy of a piece of elaborately worked metal becoming more uniform when it melts.

gravity is different from matter in the sense that a smooth uniform state of the grav. field corresponds to LOW entropy, with lots of potential to evolve structure by clumping.

so if you think of the grav. field as a chaotically structured piece of metal, that suddenly “melts”, it is a moment when the entropy is set back to zero—the field was elaborately clumped and even crumpled, when it goes into Planck regime it is returned to a uniform condition

the question, Alejandro, (BTW I like your BLOG very much!) is how can this sudden reduction of entropy be allowed?

the answer is that nobody can see it happen. there are only two possible observers one in the region before the bounce and one in the region after the bounce. the before man (B) just sees e.g. a black hole event horizon with a lot of entropy, he cannot see into where it goes Planck regime and bounces

the after man (A) looks back towards the beginning of his universe and observes the CMB and so on, but he also cannot see the Planck regime and the moment when the entropy goes from very high (chaotic crumpled geometry) to low

Alejandro I have to go, will get back to this later

60. Watcher on Jul 7th, 2007 at 5:32 pm

Alejandro,
Just to finish what I was writing when interrupted, I think an operationally defined version of the Second Law is that one should likely never be able to measure a decrease of the entropy.

BTW it is interesting to imagine how things might conspire to protect the Second Law or to conceal its possible failings.

AFAIK in Bojowald’s Nature Physics paper he talks about a kind of indeterminacy that limits the ability to measure certain pairs of quantities—to know certain things both about the before and after states. I think there is not a complete “forgetfulness”, that would be too dramatic, but some modest limitation of knowlege. In any case, Bojowald’s paper refers to a principle of forgetfulness.
One might conjecture that this uncertainty about conditions in the other region would also serve to protect the Second Law.

I think I could agree with what Ashtekar told you about Planck regime being a low entropy state of the gravitational field.
==endquote==

WHAT NO ONE HAS POINTED OUT IS WHERE ALEJANDRO MADE A MISTAKE BY ASSUMING CONTINUITY. Ashtekar simply said that the entropy in the Planck regime is low. He did not say that the entropy was DECREASING during the collapse! As long as the collapse is classical it is going to increase increase increase! Then suddenly, with the phase transition, right near bounce, it abruptly decreases. But Alejandro says that it is "decreasing during collapse" and this is wrong, so he was right to be puzzled by it.