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. Vic Stenger says:

    How about trying to predict it from no dynamics, no inherent laws of physics? The ones we use are are human inventions anyway. Randomness = perfect symmetry=laws of physics.

  2. Thomas Walsh says:

    A couple of simple questions that relate, in a broad sense, to cosmology.
    If gravity bends the pat of light and if it is still true that light always seeks the shortest path, does gravity then alter distance? (What does ‘warp space’ physically mean).

    Is the law of universal gravitation unqualified for any and all forms of mass? The questioning of the gravitational energy of anti-mater is seen as a valid question. Is it also valid to question if the gravitational energy of neutral Hydrogen is the same, in principal, as Hydrogen isotopes, Helium, Lithium etc. If the answer is absolutely Yes, what experiments create the absolute certainty?

  3. David Park says:

    You are an excellent and clear speaker, Sean, but I found the acoustics in these videos quite bad, and the blackboard was impossible to read.

  4. Vladimir Chang-Tanaka says:

    @Thomas Walsh
    “The questioning of the gravitational energy of anti-mater is seen as a valid question.”
    I’m sorry but you have this backwards: it’s not anti-mater; it’s anti-pater. It’s the father that’s the more important issue here, NOT the mother. QED.

  5. N. says:

    “If gravity bends the pat of light and if it is still true that light always seeks the shortest path, does gravity then alter distance?”

    In spacetime, gravity is geometry.

    The difference between ortodrome and locsodrome. 🙂

  6. Small says:

    How about a *small* universe with laws such that the initial conditions *have* to have low entropy? Wouldn’t that be preferable?

  7. Dr. Morbius says:

    The audio is much better if you turn down the bass. That seems to get rid of most of the echo. Headphones also help.

  8. Luke Barnes says:

    I was there, and I highly recommend this talk. Sean worked from a set of handwritten notes – scanned copy? I’ll ask around if one of the students thinks they took detailed enough notes to post on the website.

  9. Sean Carroll says:

    Luke, thanks! I might try to type up the notes — but some things I talked about were papers-not-yet-written, and I’ll probably try to get those done first.

  10. Torbjörn Larsson, OM says:

    Listening will be a weekend pleasure!

    Meanwhile it may be unfair to comment, but I have some reflections. [Mind, my interest is astrobiology founded – but the inflationary standard cosmology helped immensely, with its prediction of a consistent age, homogeneity and structure formation. So I’m trying to get to know the sharp edges of this useful tool from time to time.]

    – I wouldn’t ascribe thermodynamics and its arrow of time as the difference to predict future vs past. Rather it is an observation of a peculiar initial conditions. (More below.)

    – I’m not sure it is morally correct to elaborate over cosmological entropy if one is uncertain of cosmological energy and its conservation. Others accept it but point out its dubious usefulness. (I’m currently studying Susskind’s cosmological lectures.)

    Both points happen to converge, for me, in a paper on cosmological entropy [Lineweaver & Egan] The initial conditions of low entropy inflation is translated to initial conditions of unclumped, low entropy conditions of a universe which hasn’t yet much of large scale structures (LSS).

    So we have an arrow of time, heat death, free energy and internal energy, the whole enchilada. [L&E 2008] But, I note, an arrow of time only in universes where we happen to have observers at later times due to successful LSS formation. (Perhaps such a model is compatible with Stenger’s commentary too, in that sense.)

    Do I have to assume a more global dynamics of an arrow of time is not found in the dynamics of our peculiar universe but in a putative multiverse dynamics?

  11. Torbjörn Larsson, OM says:

    Shoot, I forgot about radiation [linked L&E fig 5]! So there is always an arrow of time. But that only moves the question back to initial conditions, and doesn’t entirely leave out the possibility of arrow of time being connected to a possibly larger dynamics. Why did inflation, with its low entropy, dominate at early times?

    Hopefully the videos will help me chew on this!

  12. John Duffield says:

    Low entropy? Surely the early universe had high entropy? The energy density was the same everywhere, so there was no available energy. Then when “inflation” occurred and the universe increased in size, you then had energy-density variations, and lots of available energy. When the energy-density is all evened out in the heat death of the universe, you’ve got high entropy and no available energy again.

  13. Carl says:

    “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.”

    Surely it follows from the 2nd law that the early universe had low entropy?

    Also, when thinking of possible “processes” that could create the universe, “specifying” a simple, low entropy initial state is simply easier than setting up a high entropy initial state with a very complicated description.

    Why should we not expect a simple, low entropy start of the universe regardless the 2nd law?

  14. Meh says:


    entropy is disorder. high entropy = lots of disorder. If the energy density is exactly the same everywhere, then nothing is different and there can’t be disorder if everything is exactly the same. In fact, that’s one of two ways that everything can be perfectly ordered with no disorder. low entropy = lots of order.

  15. John Duffield says:

    I know that’s what they say, Meh, but see . I take a “fundamental physics” view of this kind of thing rather than a statistical mechanics viewpoint. See the gif on the right at then lose the red particles and imagine the box is much smaller, and is a solid block of motionless blue.

  16. Gizelle Janine says:

    John: Agreed. But with 2 definitions of entropy, how can anyone ever be wrong? 😀

  17. Gizelle Janine says:

    John: I still think there needs to be a 4th law of thermodynamics that states all laws of thermodynamics are dependent and only work with quantum mechanical laws. I’m boundto get that one stolen.

  18. Meh says:

    Did you mean for your first link to be this part of that wikipedia page? :

    “Following on from the above, it is possible (in a thermal context) to regard entropy as an indicator or measure of the effectiveness or usefulness of a particular quantity of energy.[46] This is because energy supplied at a high temperature (i.e. with low entropy) tends to be more useful than the same amount of energy available at room temperature.”

    If so, then I don’t understand what it is that you are trying to communicate since that’s parallel to what I said. Do you mean that you are basing entropy on usefulness rather than energy availability? I don’t understand what you’re trying to say. (in clarifying, please don’t link to something else, just leave a comment in your own words)

    By the “fundamental physics” view, do you mean thermodynamics?

    If you’re relying solely on motion, then there are 2 ways to get to low entropy. By motion being at zero (the complete absence difference in values), or by motion being infinite (absolute motion with no difference in values). If the energy density is the same everywhere, then it is either infinite or nonexistent; if it wasn’t one of those 2, then it wouldn’t be the same everywhere. Your solid block of blue could be either the infinite view or the zero view.

  19. Gizelle Janine says:

    @John: Sorry. Bound to is what I meant, obviously.

  20. Doug says:

    If you want to have a privately held definition of entropy it’s going to make commenting on blogs very fruitless.

  21. Gizelle Janine says:

    Doug: I double agree!! 😀

  22. Gizelle Janine says:

    @Meh: Wow. I think a bird flew over my head…

  23. Gizelle Janine says:

    @Meh: My 4th law, I think, complements this article nicely. *starts laughing*

  24. David Stern says:

    Dear Prof Carroll,

    Your knowledge and conclusions about entropy as so wrong that it makes me question veracity of you your degree and your skills. I was baffled by some of your claims wrt entropy. May I suggest you pick up few books on stat thermodynamics and study so you don’t appear so clueless? I’d also love to see some peer review literature that validates your claims. I don’t think we’ll ever see those.