Still Scandalous Heat

Me in ’09:

Physicists have long considered [thermodynamics] the physics area least likely to be overturned by future discoveries, in part because they understand it so well via “statistical mechanics.” Alas, not only are we far from understanding thermodynamics, the situation is much worse than most everyone admits! (more; related posts)

Many hope the theory of inflation can solve this, by predicting that a universe like ours would arise naturally out of “chaos.” But in the April Scientific American, Paul Steinhardt, a major contributor to inflationary theory, says:

Something peculiar has happened to inflationary theory in the 30 years since Guth introduced it. As the case for inflation has grown stronger, so has the case against. … Not only is bad inflation more likely than good inflation, but no inflation is more likely than either. University of Oxford physicist Roger Penrose first made this point in the 1980s. … Obtaining a flat universe without inflation is much more likely than with inflation — by a factor of 10 to the googol (10100) power! …

Many leading theorists argued that the problems with inflation are mere teething pains and should not shake our confidence in the basic idea. Others (including me) contended that the problems cut to the core of the theory, and it needs a major fix or must be replaced. (more)

Sean Carrol’s latest post reaffirms the point:

Imagine that you want to wait long enough to see something like the Big Bang fluctuate randomly out of empty space. How will it actually transpire? It will not be a sudden WHAM! in which nothingness turns into the Big Bang. Rather, it will be just like the observed history of our universe — just played backward. A collection of long-wavelength photons will gradually come together; radiation will focus on certain locations in space to create white holes; those white holes will spit out gas and dust that will form into stars and planets; radiation will focus on the stars, which will break down heavy elements into lighter ones; eventually all the matter will disperse as it contracts and smooths out to create a giant Big Crunch. Along the way people will un-die, grow younger, and be un-born; omelets will convert into eggs; artists will painstakingly remove paint from their canvases onto brushes. Now you might think: that’s really unlikely. And so it is! But that’s because fluctuating into the Big Bang is tremendously unlikely. (more)

We are not remotely close to having a reasonable account for the incredibly low entropy we seem to see in our past.

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  • Doug

    Robert Wald disagrees with Sean Carroll. I haven’t really read the arguments carefully but my money would be on Wald over Carroll.

    • That Wald paper doesn’t at all disagree with the Carroll paper described above.

      • Doug

        From the footnote on Page 4

        “Recently, Carroll and Chen [4] have proposed that “spontaneous inflation” can account for a locally observed arrow of time in a universe that is time symmetric on ultra-large scales. In their model, the universe has entropy growing unboundedly in both the past and future. The universe is “normally” (i.e., in most of the spacetime) a nearly empty deSitter spacetime, but, occassionally, thermal fluctuations produce regions of inflation that result in a large increase of entropy in that region, and a corresponding locally observed arrow of time. In their model, episodes of inflation would not be favored over episodes of “deflation” (i.e., eras of exponential contraction, in which the entropy decreases); indeed, episodes of inflation would dominate in the distant future, whereas episodes of deflation would dominate in the distant past. I do not find their proposal to be plausible, but, in essentially all other respects, the discussion of the issue of the origin of the thermodynamic arrow of time given in [4] is compatible with the viewpoints taken here.”

        The crux of the disagreement seems to be:

        “But in an infinite universe starting with “random” initial conditions,
        the probability of having a hugh patch that directly evolves—without inflation—to a region indistinguishable from the observed universe also is 1 (as is the probability of producing a universe indistinguishable from ours except that all elephants wear pink dresses), so it also is possible that the portion of the universe that we observe arose in this manner. In order for the chaotic inflationary scenario or other dynamical mechanisms to do better than this, it is necessary to argue that, within the context of the model, observers in the universe are likely to see a universe like the one we see; the presently observed universe should not merely be a (highly unlikely) possibility that is allowed in the model but rather should be a prediction of the model.”

      • That footnote responds to a very different Carroll paper. As the last sentence of the footnote makes clear, Wald agrees with Carroll’s basic view of the situation, which is the view I quote and refer to above.

      • Doug

        I see. Thanks for explaining Robin.

  • Buck Farmer

    Good topic, Robin, and one that is difficult to wrestle with.

    Maybe time across the whole universe has no arrow, and we’re just in an unusually consistently pointy section…

    …that said, I can’t in my sleep-deprived state think of:
    1. Argument for why we should be so lucky (Something anthropic, I presume)
    2. Why we should be so lucky in the future (Though I imagine reverse time will wreak havoc with us as observers, so maybe the only leg of the trousers of time is the increasingly unlikely one with a more or less consistent arrow)

    Yes, scandalous…

  • John

    There was a SciAm article maybe a year or two ago about how causality may be important in creating the universe that we see. So you’d start with a mess and then introduce causality. Pre-causality you might not have entropy in a meaningful sense.

    Not that I really know what I’m talking about, but I do remember thinking the article appeared to be thinking of the creation of the universe a little differently than the big bang as I understood it.

  • Key point IMHO: “… we might think we know about the past via our memories and records, but this standard approach says our records are far more likely to result from random fluctuations than to actually be records of what we think they are.”

    Yes, if this basic approach to thinking about the origin of low-entropy states is right, then the past is with overwhelming probability fake.

    One question: why should a negentropic fluctuation produce a plausible ‘register’ of the past, rather than a bizarre and incoherent one (full of Lovecraftian anomalies, at the very least)? A fake past (projected low entropy origin and subsequent development path) would not be constrained by any real process of descent. Since a ‘good’ fake is vastly less probable than a ‘bad’ one, and there is no obvious probabilistic filter to provide us ‘anthropically’ with a good one, the economy and consistency of the cosmic record seems to suggest that there is something very wrong with this line of thinking.

    Has anyone coined ‘Azathothic young-universe creationism’ yet?

    • The past has to be “continuous” with the present. That imposes boundary conditions. The past of yesterday has to be continuous with today and with the day before yesterday.

      The most likely paths that are continuous are the paths where there seems to be cause and effect.

      For those paths to not be continuous requires violation of conservation laws, mass/energy, charge, momentum.

      • This holds only if ‘continuous’ is defined so broadly that it sacrifices almost everything that is normally, and scientifically, associated with the term. Fluctuation out of chaos is no more causally constrained to proceed from dinosaur to dinosaur fossil than from dinosaur to Cthulhu fossil (or rather, and crucially in this case, from ‘fossil’ to ‘fossilized’) — the mechanism that would ensure consistency with ‘normal’ (entropic) development simply does not exist. This is already granted as soon as it is conceded that recordings (e.g. memories) are causally dissociated from remembered facts, since there are far more economical paths to ‘memory’ formation in a contra-entropic flux than the process of remembering. Flux production of low-entropy states is already so contrary to conventional expectations that to assume it would neatly re-assemble ordinary causal sequences, just inversely, is nothing more than a huge leap of faith.

      • “Conservation laws [for] mass/energy, charge, momentum” exercise almost no constraint at all, at least relative to the constraints of ordinary, path-dependent (pro-entropic) causality.

      • Apologies for multiple posts, but one further point of clarification. IMHO Sean Carroll moves much too fast in suggesting that “the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium.”
        A negentropic flux would still be statistically constrained by principles of thermodynamic economy / probability, in that it would tend to minimize negentropy production at each step, in contrast to the ordinary tendency to maximize entropy production. The two processes are NOT symmetrical. In complex systems, especially, there are FAR more probable paths to entropy reduction than simple time-reversal, which means that the production of plausible ‘artificial memories’ (fake consistent fossil records, for e.g.) are an extremely unlikely case, even in the flux universe of inherently improbable processes.

      • I don’t think so. In the sense that I am using the term “continuous”, a time-reversed sequence that preserves local conservation of mass/energy exhibits continuity. A path where conservation of mass/energy is not locally conserved would be very much less likely, even than the very unlikely time-reversal case that does conserve it. Quantum tunneling over a Planck length is much more likely than quantum tunneling over macroscopic distances (meters).

        The scanning tunneling microscope uses the change in the tunneling rate of electrons with distance to measure distances. The rate changes exponentially with distance with ~10x change per Angstrom. A meter being 10^10 Angstroms, an electron tunneling the distance of a meter is 10^(10^10) less likely than tunneling the distance of an Angstrom.

        In other words, the paths where a single electron has to tunnel a meter are enormously less likely than paths where 10^100 electrons tunnel a few Angstroms. Paths where tunneling is confined to a few Planck lengths (and so mimics time reversal) will be common compared to paths where there is tunneling of meters.

      • Thinking like a physicist can be misleading when dealing with complex (path dependent) processes, because the continuity you are demanding is so easily met. Granting all your points, without reservation, doesn’t really get very close to the kind of ‘time-reversal’ Carroll is invoking, because the systems being examined are not in any strong sense historical. Consider the idea of paint spontaneously rehydrating and unmixing before being dipped off a canvas, deposited on a palette, and then (after more unmixing) sucked into a tube — what reason is there to assume this is the most thermodynamically efficient way of reversing the entropy production that the painting involved? For instance, why not discard the painter entirely? — it’s probably less of a physical stretch to have the paint particles drift spontaneously across space and back into the tubes, which is to say, there are no sufficiently constraining causal factors to impose symmetry (time-reversal). It seems to me your point about quantum tunneling would tend to lead to exactly this conclusion — numerous small increments of negative entropy production are vastly more probable than huge, bizarre — even miraculous — jumps in local order, of the kind that neat time-reversals of elaborate macro-systems inevitably require.

      • anon

        > what reason is there to assume this is the most thermodynamically efficient way of reversing the entropy production that the painting involved? For instance, why not discard the painter entirely? —

        This won’t work, because Carroll is implicitly invoking a universe in which a painter remembers having squeezed paint out of the tubes and placed it on the canvas. That memory cannot simply be erased without temporarily increasing entropy in the surrounding environment and making the whole fluctuation even more implausible. Instead, the physical process which might have created that memory must be reversed; stated another way, causality must be preserved: tbe painter must actually have “painted” the canvas in her perceptual past, i.e. she will clear the canvas in our future.

        You might ask why an entropy transition of this kind should involve painters and canvases at all, but that’s a different matter.

      • Thermodynamics only deals with equilibrium processes. Thermodynamics is the wrong tool to use to try and decide which paths a non-equilibrium process will take. By thermodynamics, everything should spontaneously convert to nickel-62 because Ni62 has the highest binding energy per nucleon. But that can only happen via a path, and there are not many paths that lead to Ni62 even though it is the most stable nucleus. Formation of Ni62 is kinetically unfavored (and so it is rare) even though it is thermodynamically the most favored.

        The reason Ni62 is kinetically unfavored is because it takes a lot of energy to enter the transition state between other compounds and Ni62. The high energy of the transition state to Ni62 makes transitions to Ni62 unlikely.

        The transitions states where paint particles spontaneously tunnel out into the air are extremely unlikely. A transition state where a molecules of solvent diffuse into the solid paint, cross linked molecules decompose and release O2, the paint softens and is then picked up by a brush wielded by a painter is much more likely than paint particles spontaneously tunneling from the canvas back into the paint tube.

        At equilibrium, the rate of forward and reverse reactions is the same. The degree to which a system is out of equilibrium can be characterized by differences between the forward and reverse reactions. Reactions with a low activation energy are closer to equilibrium than reactions with a very high activation energy. The spontaneous formation of Ni62 is extremely low. The spontaneous decomposition of Ni62 would be even lower.

        The deposition of paint on a canvas by a painter has a pretty low activation energy. The removal of paint from a canvas by a painter also has a pretty low activation energy and is of the same order of magnitude. The spontaneous tunneling of paint from a canvas to a tube has an extremely high activation energy as does the spontaneous tunneling of paint from a tube onto a canvas, so high that we should expect to never observe it on the time scale where we do observe removal of paint from a canvas by a painter.

  • mjgeddes

    Let’s consult my ontology…it shows a fundamental three-fold division in physics…symmetries are level one (the basic building blocks), forces are level two (the active transforms), and fields (space-time) are level three (fields are the self-representations of the universe, they mediate all communication)

    The observable universe is defintely an RPOP …just very poorly optimized at present. But definitely a goal directed system with universal terminal values. Field-theory is most fundamental in physics, answers should be found there, is linked to priors (complexity measures/information theory) and aesthetics…as I said in earlier postings on the topic, look for universal complexity measures. Also category theory….so fields are closely analogous to both complexity measures and categories. If high-entropy states can be simply specified, this is indicates a problem with current defintions of ‘complexity’.

    • > If high-entropy states can be simply specified, this is indicates a problem with current defintions of ‘complexity’.

      Not really. Think: PRNG. High thermodynamic entropy, low information-theoretic entropy. The answer is probably not Occam’s razor – since high-thermodynamic entropy states can be made simply.

      • mjgeddes

        Shannon entropy is only one particular definition of entropy (from information theory), which fails to take into account the actual *semantic* content of data, which is a product of the work that went into producing that data.

        It’s clear that fields (in physics) are closely analogous to a mind’s representational system (since they carry information to mediate communciation exchanges), and they are also far in influence. This provides (weak) support for my claim that the universe is in fact a poorly optimized (broken, malfunctioning) RPOP.

        If the universe is in fact a goal-directed system analogous to a mind, it’s important we find out what ‘priors’ the universe is using. And that needs a more generalized definition of entropy.

  • The universe is becoming more informationally complex by becoming more textured, with the information becoming densified in local regions. One has to take into consideration the relationship between information and entropy. I (I think) solve the problem in my book Diaphysics.

  • Anthropic explanation: entropy only increases, universe takes a long time to evolve intelligent agents, therefore, entropy started off being much smaller.

  • Has it occurred to anyone that less complex things look more entropic to more complex things and that, therefore, the less complex elements of the universe look entropic to humans, while more complex elements look negentropic? But do we know how to recognize negetropy?

  • jim object

    I blame Greenspan amd Bernanke.

    I’m sorry, okay. I had to. Its a compulsion.

  • Ian

    Actually, as it turns out, the universe didn’t start with low entropy; in fact, it started with maximum entropy. The universe started out as a sphere of Planck dimensions (whether inflation happened or not), and then expanded. A sphere of Planck dimensions, however, is necessarily a black hole, and thus has maximum entropy. How, then, can the Second Law of Thermodynamics hold? Well, it’s because the expanding universe increases the maximum entropy. Because of the 2nd LOT, entropy increases approximately polynomially with the radius of the universe, but the maximum entropy increases exponentially with radius. Since any exponential function increases faster than any polynomial function, there is an increasing room for order in the universe, despite the entropy constantly increasing.