Cosmology and the Past Hypothesis

Greetings from sunny Santa Cruz, where we’re in week three of the Summer School on Philosophy of Cosmology. I gave two lectures yesterday afternoon, and in a technological miracle they’ve already appeared on YouTube. The audio and video aren’t perfect quality, but hopefully viewers can hear everything clearly.

These are closer to discussions than lectures, as I was intentionally pretty informal about the whole thing. Rather than trying to push any one specific model or idea, I gave an overview of what I take to be the relevant issues confronting someone who wants to build a cosmological model that naturally explains why the early universe had a low entropy. They are a little bit technical, as the intended audience is grad students in physics and philosophy who have already sat through two weeks of lecturing.

If there is one central idea, it’s the concept of a “cosmological realization measure” for statistical mechanics. Ordinarily, when we have some statistical system, we know some macroscopic facts about it but only have a probability distribution over the microscopic details. If our goal is to predict the future, it suffices to choose a distribution that is uniform in the Liouville measure given to us by classical mechanics (or its quantum analogue). If we want to reconstruct the past, in contrast, we need to conditionalize over trajectories that also started in a low-entropy past state — that the “Past Hypothesis” that is required to get stat mech off the ground in a world governed by time-symmetric fundamental laws.

The goal I am pursuing is to find cosmological scenarios in which the Past Hypothesis is predicted by the dynamics, not merely assumed. We imagine a “large universe,” one in which local macroscopic situations (like a box of gas or a lecture hall full of students) occur many times. Then we can define a measure over the microconditions corresponding to such situations by looking at the ways in which those situations actually appear in the cosmic history. The hope — still just a hope, really — is that familiar situations like observers or lecture halls or apple pies appear predominantly in the aftermath of low-entropy Big-Bang-like states. That would stand in marked contrast to the straightforward Boltzmannian expectation that any particular low-entropy state is both preceded by and followed by higher-entropy configurations. I don’t think any particular model completely succeeds in this ambition, but I’m optimistic that we can build theories of this type. We shall see.

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41 Responses to Cosmology and the Past Hypothesis

  1. Meh says:

    I sure hope David Stern is a fake name used to make douchebag comments so that nobody knows what a ignorant and over abundantly arrogant assclown you are.

  2. Fernando Paek-Nguyen says:

    Totally agree about this Stern idiot. In addition it appears that English is not his native language, looking at his fractured syntax. This is probably one of the reasons why he obviously didn’t understand anything in Prof. Carroll’s lectures.

  3. John Duffield says:

    Gizelle: yes, the definition of entropy is a bit of a problem.

    Meh: I’ll try to restate succinctly. I meant fundamental physics, not thermodynamics. Heat is just an emergent system property. A “hot” electron is merely a fast-moving electron. And an electron is in itself a concentration of energy. If you annihilate a 511keV electron at rest with a positron to obtain two 511keV gamma photons, each is another concentration of energy. If you then throw them into a black hole where we say the coordinate speed of light at the event horizon is zero, they aren’t fast-moving any more, they’re stopped. (I favour the original frozen-star black-hole interpretation as opposed to the point-singularity interpretation.) Energy exists, it’s real, it’s fundamental, matter is made of it, it’s the one thing you can neither create nor destroy. But entropy is emergent. It doesn’t actually exist at the fundamental level. It’s like “sameness”. Wind the universe back so the whole thing is like one big frozen-star black hole. Energy-density isn’t infinite, or zero. Just uniform, and very very high. But there’s no motion, so there is no heat. Clocks don’t tick because “gravitational” time dilation is total, so there’s no time. And there is no light moving, so it’s dark, and there’s no definable distance either. Take a tip from the gravastar and the whole universe is “a void in the fabric of space and time”. And black-hole entropy is said to be high.

  4. James Cross says:

    To borrow a phrase from von Neumann, nobody really knows what entropy is anyway so we can all have our ideas about it.

    Sometimes in trying to understand entropy, I feel a little bit like Tantalus. Every time I get close to grasping it the grape just moves away a little bit.

  5. Eric Kemer says:

    Is it possible that the entropy of the Universe just after the Big Bang was at its maximum and that it was inflation that merely made this value small relative to what it could be in the newly expanded space? In other words, was the low entropy of the earliest universe not a matter of high order, but of a matter of a relatively small number of available microstates compared to the number created by expansion?

    Is this related to the “available energy” that John Duffield mentioned?

  6. Meh says:


    I don’t know where to start. Wait, yes I do; alt+space+c

  7. I have no reason(s) to think that CMBR is not evidence of entropy. Entropy is always increasing. Inflation goes together with a relative faster increase of entropy. Am I wrong?

  8. John Duffield says:

    I think so. For an analogy, imagine the early universe is a flat plain. Set down a ball, and it doesn’t roll. Then the universe expands and you realise that the plain is a plateau, which breaks up into mountains. Your ball now rolls. But eventually erosion wears down the mountains, and you end up with a flat plain again.

    Meh: mull it over. Imagine you’re a gedanken observer in the very early universe. The universe starts expanding at some sedate pace. But you’re subject to something akin to huge gravitational time dilation, so to you it happens very very quickly. You would call it inflation.

  9. Meh says:


    The only people to see the birth of the universe are the time lords, and only 1 exists now…theoretically anyway. I have my doubts about Dr. John Hurt’s theories on inflationary instabilities on a 7-space tardis manifold. Now, lets say you have a matter/antimatter engine powered by avatar fan fiction; would that be able to outrun the inflation paradox and give us an opportunity to check the entropy of the early universe?

  10. “low-entropy Big-Bang-like states”

    Pre Big Bang I guess. If so, do you mean systems in which the increase of entropy is relative slow?
    How relative slow given the thermodynamical effects in Black Holes?

  11. Luke Barnes says:

    Alas … I had a look at a few students notes and they were all a bit of a shambles. Shame – I wanted a set of notes for myself. From memory, what went on the board wasn’t essential to the general argument of the talk.

  12. Bob Zannelli says:

    I don’t understand Carroll’s arguments concerning the past hypothesis, I think I need to re-read his book again. Carroll’s own attempt to provide a solution to this problem, a model he developed with Chen , proposes a process where universes tunnel into existence from the low energy De Sitter space that our universe is expected to evolve to in the far future. The probability for this to happen is tiny but there is unlimited time available since even if the vacua state is unstable we would still very likely get an eternal De Sitter space. There are problems with this model as pointed out by Trodden but these problems may not be fatal. The model has inflation in both directions of time, so it evades the past boundary problem identified by Vilenkin , Guth and Bode, we get a future and past eternal Multiverse where time isn’t emergent but rather a persistent property of reality. However, it’s not clear to me why the “tunneling from Nothing” models don’t also provide a solution for the past hypothesis. Based on these models, universes with a high vacuum energy density and small volume are the most probable, it would seem that requires a relative low entropy at origin. Carols argues this is wrong. I don’t see why. The evolution of the universe is a decoherent history , I don’t see why unitarity is an issue, Carroll thinks it is. I don’t see it.

  13. John S. Hardy, M.D. says:

    From the “beginning” (pre-big bang), we surmise that the initial pre-big bang “environment” was “NON-existent” (i.e., a true vacuum) wherein there was NO extant space-time (and therefore no entropy nor chaos: I call this the null environment), which contrasted with a potential of infinite space-time with limits determined only as they have thus (now) become.
    The evolving universe was therefore a closed system (event horizon) of enormous potential.
    If Stephen Hawking is correct, a quantum fluctuation (a singularity) within that initial null environment “appeared” and, guided/driven by the Second law of thermodynamics (Entropy) and chaos (initially in their lowest possible states), acted to evolve space-time and thence drive the energy potential of that quantum fluctuation (singularity) into evolving space-time.
    The Current estimate of the total mass-energy of the observable universe[201]: is = 4×1069 Joules.

    Is it feasible that all mass-energy in the universe (including the Higgs and gravity) was/were in fact “created” or caused by entropy?

    Also: given the above, what was the probable minimal amount of energy confined in the initial quantum fluctuation (singularity), now expanded via the second law of thermodynamics (entropy), interacting with increasing chaos to create the present dimension of the universe?

  14. Torbjörn Larsson, OM says:

    Well, *that* took a while (nearly 4 h). But I learned a lot. For example yet another way that flat space is a natural result.

    Also that this is, as so many times when there is conflict, a competition between 2 major work strategies. The frame would be that we have moved on to pre-inflation, analogous to how inflation moved on to pre-Big Bang (if you define it as after thermalization).

    In that sense inflation has no “low-entropy problem”. Or at least, it doesn’t have to predict the entropic arrow of time any more than previous big bang models.

    As an analogy, classical gravity had no prediction for masses. General relativity could predict that there was a transformation pathway for masses out of energy, but had no concept of inflationary thermalization. So when inflation (or at least inflationary physicists) now can predict that there is a fluctuation pathway for inflationary patches out of high-entropy ones, it does no worse or no better than GR.

    The question is if selection over the environment, selection bias, anthropic selection, whatever it is called, works in parts or as a whole. I think one should take into account that same as naturalness earlier seemed, well, natural, selection now seems to pop up all the time. Maybe there is a reason, even if ultimately selection doesn’t work.

    [I didn’t think much of BB’s before, but when they can tighten the earlier selection prediction on Higgs masses to be (perhaps) quasistable, I have to rethink.]

  15. Torbjörn Larsson, OM says:

    Some of the questions on entropy asked here can be answered by looking at the paper I linked to (2nd link).

    @Meh: “entropy is disorder”.

    Except when it isn’t of course. In highly confined systems the high entropy states are, arguably from theory and from model experiments, the most ordered ones.

    In cosmology this is no problem, if one accepts for example holographic entropy, entropy increases regardless. (But there are IIRC other ways, see my earlier link to L&E.)

    @John S. Hardy: “Is it feasible that all mass-energy in the universe (including the Higgs and gravity) was/were in fact “created” or caused by entropy?

    Also: given the above, what was the probable minimal amount of energy confined in the initial quantum fluctuation (singularity), now expanded via the second law of thermodynamics (entropy), interacting with increasing chaos to create the present dimension of the universe?”

    Yes on 1st question, the internal state of a system decides its free energy (1st question), and is not to be confused with its total energy (2nd question), see my earlier link to L&E.

    2nd question: Thermodynamics rarely interests itself in the total energy and how to derive it. Here however we are lucky: since the universe is flat, its total internal energy is zero.

    Carroll’s and other’s (see the 3d quantization links above) description of the quantum void seems to say these fluctuations are more like particle pair creation than large scale BB thermal fluctuations out of vacuum fields. (So I guess it is lucky inflation, or whatever, separates the universes. =D)

    In QFT those fluctuations sum to zero energy under allowance for uncertainty. It all (Q1 & 2) looks consistent to me.

  16. Isko Velagic says:

    Imagine completely empty rum. There is absolutely nothing, just vacuum or dark energy. Each cubic centimeter of vacuum has energy equal to 1, and we can say that there is maximum energy a cubic vacuum may have. You can compare it with salt water that is completely saturated with salt.
    Now something happens (big bang) that allows energy released from the vacuum. The energy we can see now. It appears as ordinary matter. Protons, neutrons, electrons, etc..
    Now cubic centimeter of vacuum, “near” the big bang has no energy 1, but almost 0, and everywhere else, the energy of cubic centimeters of vacuum is less than 1.
    Now we can invent a rules:
    1) If cubic centimeter of vacuum is less than 1, no new big bang may occur. Events like the big bang can happen, but as cubic centimeters of vacuum now have energy that is less than 1, the big bang has no consequences.
    2) Vakuums nature is to return to the energy level 1

    The consequences of this rules is that there is only one universe. Several universe can not exist simultaneously. Universe will be adsorbed by the vacuum with time and the vacuum energy becomes 1 when the last gram of matter disappears.
    Now that cubic centimeter of vacuum has energy 1, big bang can trigger new universe.