Could a physicist (or someone at least somewhat in the know) answer a simple question for me? Does the video below roughly approximate what went on at the Big Bang (a symmetry is broken, its granular debris entropically shattering and cascading through space and time)? I found this ad curious because it says, at the end, that it is modeling particle physics, and it just struck me, visually, as exactly what I imagine happening at the Big Bang (something containing a high degree of informational order and symmetry, decouples).
Is it useful to think of the Big Bang as the dropped block (or bunny rabbit!) at the beginning of time?
And the 1:24 mark in the above video, where (what looks to me like) a statue of Rodin’s “The Thinker” collapses, gave me a whimsical thought: what if we discovered, sometime in the 21st century, that the symmetry broken at the beginning of time was Leonardo’s man?
Prometheus Unbound 
The “particle physics” the ad indicates has nothing to do with the particle physics of quantum field theory, the standard model, supersymmetry, etc. Instead, the ad is referring to billiard ball physics (where the particles are just hard balls) or something similar (e.g. fluid mechanics).
As far as I know, the symmetries that were broken in the first few fractions of a second after the big bang refer to the “cooling” of the universe. That is, as the universe, which started out really hot, cooled down symmetries were broken. A decent analogy for this might be H20. When in a liquid and gas form, H20 has no preferred direction and is very symmetrical and has no structure. When cooled, it forms an ordered crystalline structure which has less symmetry, thus the original symmetry of vapor and water is broken as ice forms.
Grad Student:
Thanks for helping me out here. I may be trying to think about a topic that is way over my head (not the first time, as you know). But I do find something curious about your clarification: I thought quantum physics was characterized by graininess: the quanta as a discreet packet. Here, for example, is how the physicist Stephen Barr puts it:
“[T]he quantum world has a ‘graininess’ that a classical world would not have. However, this graininess is not apparent to the casual observer; in fact, it cannot be seen except with the help of very sophisticated instruments. This is why in many cases the classical description of reality is just as good, practically speaking, as the quantum description. In the real world, energy comes in little grains called ‘quanta.'”
So I guess I’m confused about how one would model quantum graininess (as opposed to Newtonian billiard balls).
Your ice example is clarifying. But aren’t you saying that nature, when it cools, makes walls that break symmetries? Put poetically, fences make good neighbors, but to make a wall you’ve got to expend energy and increase entropy.
And so ice, for all it’s crystalline beauty, is in a higher entropic state than the original symmetry, right? And when it melts back to a liquid symmetry the universe has lost still more information, and awaits its incarnation as a different ice crystal again. In other words, heat has been added to the system to set things into symmetry again (as you put work into setting a messy bedroom straight again). But when things cool down and are left to themselves, they get messy. Ice is the messiness of water, right?
Put another way, isn’t ice like the breakdown of the blocks and bunnies in the video: things once in symmetry are scattering and taking on a new pattern, but they end in an ultimate asymmetric dispersal of energy and a cold stop? To get the symmetric order of block and bunny back again, you would have to introduce it from the outside, with a new source of energy and purpose, right?
So here’s my question: where did the low entropy symmetry at the beginning come from in the first place? Who (or what) cleaned the bedroom?
—Santi
Those are all formidable questions so let me take them one by one:
1. “I thought quantum physics was characterized by graininess: the quanta as a discreet packet.”
In quantum mechanics the things that are quantized are momentum, energy levels, position…sometimes. Free particles (i.e. particles that aren’t confined to some region of space by external forces) can exist in any position, but electrons “orbiting” a nucleus tend to “inhabit” some areas around the nucleus and “avoid” others.
With billiard ball type particles the situation is different. *God* can always know where they are and how fast they are going simultaneously (contra the Heisenberg uncertainty principle). The particles have a finite extent and it’s well defined where they particle’s surface is (unlike fundamental particles like electrons and quarks, which are modeled as point-like, though they may be stringy if you believe Ed Witten and Brian Greene et al…). Finally, there are no long range forces in billiard ball physics or fluid mechanics. The billiard balls don’t attract or repel other balls at a distance, instead they only interact by bouncing off one another as in, well, billiards.
2. “But aren’t you saying that nature, when it cools, makes walls that break symmetries?”
Yes. If you mean talking about a fluid transitioning to a solid.
3. And so ice, for all it’s crystalline beauty, is in a higher entropic state than the original symmetry, right?
No. Usually hotter things have higher entropy then cooler things. So, as you cool water down from boiling to 0 Celsius, it’s entropy gradually decreases. When water turns to ice, the entropy takes a sudden and discontinuous drop. Crystalline structures have far more order than liquids, so solids generally have a lower entropy (for a given number of particles and volume).
3. The Universe.
The above logic would seem to contradict the standard Big Bang scenario: the universe starts out disordered and hot (high entropy right?) and cools off forming galaxies and stars (low entropy right?). Wrong. Gravity is a strange beast. With a certain number of particles and a particular volume of space, the highest entropy configuration is a black hole! That should sound weird as a black hole seems to be the most ordered state. Alas, with gravity the intuition that ordered = low entropy and disordered = high entropy is just wrong. Indeed, the universe actually started in a low entropy state and has evolved to a higher entropy state.
Oh, and physicists can’t count.
Grad Student:
Thanks for the clarification. The ice thing surprises me (concerning its entropy). And I read a piece by Stuart Kaufmann on symmetry that I’m trying to absorb. Hopefully, I’m not making the same ice error when I post about it.
Lastly, you said that “the universe actually started in a low entropy state and has evolved to a higher entropy state.”
That’s odd, isn’t it? How did all that low entropy and symmetry get there in the first place? Isn’t this Richard Dawkins’s instant 747? Where’s the climbing of Mount Improbable?
—Santi