Was the Big Bang a Low Entropy State in the Universe?

[johne1618]

I understand that the standard cosmological model says that as one goes back in time towards the big bang the Universe is radiation-dominated. This means that the mass/energy density, rho, in the universe is given by the Stephan Boltzmann law:

rho = T^4

where T is the temperature of radiation in the Universe and "=" means proportional.

Now the temperature T is inversely proportional to the size of the Universe R so we have:

T = R^-1

Thus

rho = R^-4

Now the total energy of the Universe, E, is the energy density times R^3:

Therefore:

E = R^-1

Now the entropy of the Universe S is given by its total energy E divided by its temperature T:

S = E / T

S = R^-1 / R^-1 = 1

Thus as you go back to the beginning of the Universe the standard cosmology says the entropy is constant.

But this must be wrong.

Surely we expect the entropy to go to zero as we go back to the big bang?

 

[Vanadium 50]

Why would you expect that?

 

[Chalnoth]

Thus as you go back to the beginning of the Universe the standard cosmology says the entropy is constant.

But this must be wrong.

Surely we expect the entropy to go to zero as we go back to the big bang?

No, the early radiation-dominated expansion was indeed adiabatic.

 

[johne1618]

I understand that Roger Penrose for example likes the idea that the Big Bang was a low entropy state. The fact that the Universe is so uniform and isotropic now could be due to it starting in a very ordered state. You can't get more ordered than zero entropy!

Also if entropy is constant we would not have a direction for time. We need a direction for time in the radiation-dominated era as much as the present matter-dominated era.

 

[Chalnoth]

I understand that Roger Penrose for example likes the idea that the Big Bang was a low entropy state. The fact that the Universe is so uniform and isotropic now could be due to it starting in a very ordered state. You can't get more ordered than zero entropy!

Also if entropy is constant we would not have a direction for time. We need a direction for time in the radiation-dominated era as much as the present matter-dominated era.

It's not just Penrose. That our universe started in a low-entropy state is a necessary truth because of what we say when we mean "entropy": overall, entropy always increases into the future. Therefore it must have been much lower in the past.

As for the direction of time, if your universe is actually made of pure radiation, there is no direction of time, because the expansion is meaningless. It is only the existence of other forms of matter that makes the expansion meaningful.