My friends and I were discussing what we had read on the TalkOrigins site at school today. We were talking about how it said that the total entropy at the start of the universe was very low, and perhaps almost zero. If we understand right, this is because it was so compact, that the “stuff” that existed couldn’t be arranged in many more ways because of the tight space? Even if it was tight, couldn’t this molecule and that molecule just be in each other’s place?
Also, our English teacher told us that we were wrong and that entropy at the start would have to be huge, and this has something to do with equation for Gibbs free energy? I Googled “Gibbs free energy” and it is way over my head. Is he right?
One more thing:
The TalkOrigins site said that diamond crystals are the most ordered arrangement. What does it mean to be the most ordered arrangement? Thanks.
Entropy is the logarithm of the total number of possible states a system can be in. When there’s no room for stuff to move around in, and no stuff to do the moving, there’s only one state, so the entropy is 0.
I’m not a physicist, so I’ll leave your other questions for someone who is.
Nothing. This statement is completely meaningless. All crystals are, by definition, ordered arrangements of atoms and/or molecules; none can really be said to be either more or less “ordered” than another, however. The particular arrangement of atoms in diamond is called face-centered cubic. It is not unique to diamond and is, in fact, a very common crystal arrangement, because it’s the lowest-energy arrangement. Salt is one very common FCC crystal, for instance. Note that nowhere in this article on diamond is any mention made of the “orderliness” of the crystal arrangement.
Nah, in FCC, each fundamental cell has 12 nearest neighbors, but in diamond, each one only has 4. I’ve usually seen diamond’s crystal structure described as just “diamond”, or occasionally “tetrahedral”.
Referring to diamond as “most ordered” might mean “most ordered form of carbon”, or it might somehow be a reference to the fact that the tetrahedral arrangement is the lowest density three-dimensional crystal structure.
He’s right, but you’re not really wrong. The carbon atoms in the diamond lattice form two interpenetrating fcc lattices; each C in one lattice is connected tetrahedrally to four C in the other lattice. The diamond lattice is therefore not a Bravais lattice; there are two carbon atoms in each unit cell. (Find a picture of the diamond lattice, and ignore half of the carbon atoms, by counting off odd-even along each bond; the ones that are left form a simple fcc lattice, as do the ones you are ignoring. The two lattices are offset by one-quarter the body diagonal of the eponymous face-centered cube.)
When those links say that diamond forms an fcc lattice, what they’re talking about is the shape of the associated Bravais lattice: the lattice which by translation alone tiles space.
It seems that you’re saying that what TalkOrigins is claiming about entropy is that if nothing exists, entropy is zero. Isn’t this so obvious, that it would go without saying?
It seems that they must be saying more than this.
Here is the complete statement:
The author is not saying that there is nothing, since he’s saying that entropy was minimal or perhaps almost zero.
All I can come up with, is that he’s saying since such a small amount of “stuff” existed in such a small amount of space, the possibilities of different arrangements are relatively minimal. Is that it?
Or is it that all the stuff in the universe that existed then, exists now, but since it was in such a small amount of space, the possibilities of different arrangements are relatively minimal (compared to the amount of arrangements there could be in the much larger universe that we have now)?
But then, isn’t the same statement true for a simple cubic lattice? If I take atoms in a simple cubic lattice and count them off even-odd, I’ll get two FCC lattices. In fact, this is exactly what is happening in the afore-mentioned salt crystals.
Oh, and back to the Universe, entropy is constantly increasing, so as you look earlier and earlier in time, the entropy must have been less and less. The entropy can’t have been actually zero at any time after t=0, though, because then there’s no room for it to have been less at earlier times yet. And we also can’t say that the entropy was zero at exactly t=0, since we can’t really say anything meaningful about t=0.
I’ll also say that while folks often define “entropy” as “disorder”, this isn’t really exact, and can cause considerable confusion. Much better is the definition ultrafilter supplied, in terms of counting the number of possible states available to the system.
The stuff that was the universe then was in vastly different form than the particles that inhabit the universe today.
We live in a cool universe, where the overall average temperature is near zero degrees Kelvin. That’s why, according to consensus physics, we see the four forces that govern matter: the strong force, the weak force, electromagnetism, and gravity. In the first instant the temperature was so hot that all four forces were subsumed into one. (The appearance of these forces as temperatures cooled is known as broken symmetry.) Also because of the heat, no particles as we know them today could exist.
No particles, a single overriding force. One possible state. That’s why entropy was so low.
The talkorigins author is not saying that there was a small amount of stuff. He’s saying that everything was identical until the universe evolved. That’s the distinction that needs to be made. There wasn’t order or disorder. There certainly wasn’t any such entity as a molecule. There was just a thing, a single state.
P.S. Nobody has addressed the Gibbs free energy comment. I don’t see how this can possibly apply to the conditions before the Big Bang. Am I correct in this?
It depends on how the lattices interpenetrate. If the two fcc lattices are translated along a body diagonal of the cube by half the length of the diagonal, you get simple cubic (with a cube half the linear dimensions of the original cube); if by one-quarter the diagonal’s length, the diamond lattice.
Both fcc and simple cubic lattices are Bravais (all “atoms” lying on the integer lattice points). The diamond lattice, having two C atoms per unit cell, is not.
Gibbs free energy is a thermodynamic property, a thing of statistical ensembles. If the universe was a single thing back then, then classic Gibbs free energy would make no sense. There just wouldn’t be enough components for the generalization to hold.