# B Why is the low entropic state of the early universe a puzzle

1. Jun 11, 2017

### bland

I often find that in books or lectures discussing the arrow of time and entropy and trying to explain how we have such complexity that the explanation is that when the universe was in it's early stage and was just a relatively small ball of apparently high entropy gas that it was in fact very low entropy because of gravity. But that is not what I'm concerned about. What I find confusing is that in books or lectures discussing time, or Boltzman or entropy for example Brian Green's The Fabric of the Cosmos or Sean Carroll's From Eternity to Here, that we do not understand how it is that the Universe began in a relatively low entropic state, compared to now.

The thing is I don't understand why it's a puzzle, because if the Universe began as something that was very much smaller than the size of a proton, then that would mean that all the mass and all the energy was contained in that tiny area at one point, so wouldn't it necessarily follow that if that were the case how could it be anything but a low entropic state? For example of you got a big box of gas as big as a house the gas would be in a high state of entropy, but if you then squashed that box down to the size of a pea, it would have to be in a much much lower state of entropy? So what is puzzling about the low entropy of the early Universe how could it not be low if it was all crammed into such a small space?

My knowledge of this comes from books and lectures like the ones I've quoted and other similar books.

2. Jun 11, 2017

### Staff: Mentor

Not if the size of the proton is all that exists. The distribution of matter within the existing space matters - this distribution was very uniform, and we don't know why.

3. Jun 11, 2017

### bland

Exactly, that's my point. Ok so say a millionth of a second after the creation event, I'm guessing the Universe is still very small, whether it's as big as a grapefruit or the Sun, I don't know but let's say the distribution of matter within that size was not uniform, OK so now we keep going back in time further and further and eventually we must come to a small enough volume that whatever is there cannot but be uniform. That's a question btw. If we go back far enough in time so that the universe is only as large as the Planck length, or if things can be smaller than that then back far enough in time until all that exists has to be uniform because there's no room for non uniformity. Doesn't that have to be the case? Doesn't that mean that if we go back to as close to the instant of the creation event as is physically possible even given that it will be physics that we don't understand, that there must be a time when absolute uniformity must exist. Therefore why should that uniformity not manifest as it expands?

Or are you saying that whether the early distribution of matter was very uniform or not uniform at all, we don't understand it either way, they'd both be equally puzzling because we simply are puzzled by everything that happened then because everything we know breaks down. That I could understand. Except that would be like saying 'everything I don't understand is puzzling', while that may be true, it's trivial and an oxymoron..

4. Jun 11, 2017

### Staff: Mentor

Our laws of physics don't make sense at this point, we don't know what happened at the Planck temperature, or if that even happened at all - many models avoid reaching these densities and temperatures.

Keep in mind that size values always refer to the observable universe, not the overall universe - which is probably much larger, or even infinite.
No.
There are many ways to have a non-uniform distribution but only a few ways to have a uniform distribution. Why do we observe this unlikely case of a uniform distribution if there is no known reason why it has to be uniform?

Throw 1000 pieces of paper on the ground. It is possible that they all arrange in a perfect square pattern where every piece of paper has its own space of the same size. But if that actually happens, I think you would be very surprised.

5. Jun 11, 2017

### bland

OK but I'm really struggling with this. What if we throw a thousand pieces of paper into a funnel whose small end is as big as these pieces of paper. Then they could only pile up in to a relatively uniform pile. They'll be on top of each other so that's better than being spread out all over the place, so all they can now be is in a random order. BUT if these pieces of paper are quantum objects that are all identical then the order that they can pile up can only be one way. Like if you have three boxes each with an pea in them, and ask how many ways can we arrange these peas you would say 123, 132, 213, 231, 312, 321, so you'd say 6 ways. But if these peas were quantum objects like electrons then we could not tell them apart so they could only be arranged one way... eee, eee, eee, eee, eee, eee, because the other five ways would all be the same way because we could not tell which electron was which? These are all questions btw, I'm not stating anything as a fact.

6. Jun 11, 2017

### rumborak

My 2 cents: I think the key here is that, while we have a good idea of what happened very close to time 0, our laws of physics fall apart in the realm of time that you are asking about, @bland. So, while there *may* be a mechanism that enforces uniformity at t=0, we don't know that mechanism. In the time realm after, normal laws of thermodynamics say that it should *not* be uniform.

That said, and I might be mixing up things here, hasn't acceleration of expansion in the early universe been suggested for the uniformity?

7. Jun 11, 2017

### bland

@rumborak, no, the rapid early inflation only explains the uniformity of the temperature so at the end we end up with a football sized box of gas which if it was in my room would have a high entropy but that's because gravity doesn't enter into it and it's the immense gravity of the original box of gas that makes it low entropy. I address that in the first sentence of my first post.

I'm saying that at T=0 and a bit, that bit being the smallest bit possible, that even disregarding gravity, everything that is or will ever be must somehow reside in the tiny bit if only in an unmanifest form. I just don't see how at the smallest bit of possible size that there's any wiggle room for something to not be anything other than perfectly ordered because there's only one of anything. Like for example lets blow up that infinitesimally small bit and represent it as a circle on the blackboard, and then you draw a whole bunch of random dots to represent different parts of it, then you'd immediately run into the problem that it can't have any 'parts' by the very way that this tiny bit has been defined. If it could have parts or be divided then it couldn't be the smallest bit possible.

8. Jun 12, 2017

### Staff: Mentor

You don't.

9. Jun 12, 2017

### Stephen Tashi

Are we (and those articles) talking about "low entropic state" as a scientific concept or just as the popular notion of "not very disorderly"?

If we are speaking of a scientific concept, how is the entropy "of the universe" to be defined?

Thermodynamic entropy is defined, in classical physics, as property of an ensemble of things. Are we conceptualizing an ensemble of universes when we talk about the entropy of "the" universe?

Thermodynamic entropy is defined for an ensemble of systems in an equilibrium state. How is the entropy of the universe to be defined in situations when the universe is not in an equilibrium state?

The phrase "distribution of matter" and the phrase "probability distribution" have different meanings. Shannon entropy is defined for probability distributions. If we want to talk about a "distribution of matter" having a Shannon entropy, then we have the problem of saying what probability distribution we will associate with a given distribution of matter. In particular, what is the co-domain for the associated probability distribution? In we are talking about a distribution of all matter in "the universe", then is the co-domain of the associated probability distribution going to be "all of space"? Is "all of space" going to be constant with respect to time or is "all of space" expanding with respect to time?

10. Jun 15, 2017

### bland

11. Jun 19, 2017

### Khashishi

Volume (for a comoving space) is smaller in the earlier universe, but temperature is also larger. The effects of volume and temperature cancel out in the entropy. Entropy for a photon gas scales like
$S \propto \frac{V}{T^3}$
(from https://en.wikipedia.org/wiki/Photon_gas)
but $V$ also scales like $T^{-3}$. So you need a better explanation for low entropy than low volume.