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Big Bang theory and the second law of thermodynamics

Professor Mano Singham is a theoretical physicist. He is currently Director of UCITE (University Center for Innovation in Teaching and Education) at Case Western Reserve University in Cleveland, Ohio.

On his blog http://blog.case.edu/singham/big_bang_for_beginners/index he has written about the Big bang Theory and the laws of thermodynamics.

Big Bang for beginners-14:

Does the Big Bang theory violate the second law of thermodynamics?

Another supposed problem {with the Big Bang Theory} that disappears under close examination deals with entropy.

Entropy is a quantity that has a precise definition in science but whose meaning has not become as familiar to the layperson as other scientific terms like energy. It can be loosely related to what we call the level of disorder or the loss of information or the amount of ‘useless’ energy (i.e., energy that cannot be utilized to perform work).

So, for example, a system that is more disordered (a sock drawer in which the socks have been unceremoniously dumped) has a higher entropy than an ordered system (where the socks are neatly arranged in matching pairs.) Similarly a state in which information decreases or the amount of useless energy increases can be said to be a state in which entropy in increasing.

The second law of thermodynamics says that the entropy of a closed system must either increase or stay the same. It cannot decrease.

Any closed system (i.e., one in which no energy is allowed to enter or leave) that is left to itself will approach an equilibrium state, its entropy increasing until it levels out at the maximum value once equilibrium is reached.

So for example, if you take a closed container of (say) helium gas into a closed room and open the lid, the helium that was at that instant just in one region of the room (a state of partial order) will approach equilibrium by diffusing until it occupies the entire room, at which point the disorder is greatest and entropy is maximum.

The second law of thermodynamics is considered to be inviolate on a macroscopic scale and is what rules out the possibility of creating perpetual motion machines. As Arthur Eddington, famous for his experiment testing Einstein’s theory that light could be bent by gravitational fields, said in his 1927 Gifford Lectures (The Nature of the Physical World (1928), p. 74.)

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

The Big Bang seems, at first glance, to violate the second law. It starts off as a dense almost perfectly homogeneous gas (thus at almost maximum entropy) and then seems to separate into clumps that formed stars and galaxies.

Hasn’t order increased and thus the entropy decreased, and since the universe is a closed system, hasn’t this violated the second law?

The solution here is that because the universe is expanding it keeps getting shifted out of equilibrium, and in the drive to reach a new equilibrium state, you can get pockets of order occurring without violating the second law, because the maximum allowable entropy also keeps increasing.

Back to our helium example, even after the gas has completely occupied the room, if we now increase the volume of space available to it by opening the door that connects to an adjacent room, then the gas is now suddenly in partial order again because it is in only one part of the total space allowable to it. It is thus far from equilibrium and needs to start diffusing again to reach the new equilibrium where it uniformly occupies both rooms.

In other words, its entropy increases even though it was at maximum entropy before the door was opened. This happens because the increasing volume accessible to the gas also increases the maximum entropy available to it.

In more technical terms, if we consider the universe to be a sphere of radius R that is increasing, the maximum allowable entropy increases as the square of R, while the actual entropy of the universe increases less rapidly, only linearly with R.

Thus even if the initial universe was at maximum entropy for its size, as the universe expands its entropy can increase while still being easily able to accommodate the increasing order we see.

In fact, calculations done assuming that there exist ten planets per star, 100 billion stars for every galaxy and 100 billion galaxies (which are our best current estimates) show that the ordering of the planets produces changes in entropy of only one part in 1011 of the total current entropy.

Victor Stenger (Has Science Found God?, 2003, p. 152) summarizes the situation:

No violation of the second law of thermodynamics was required to produce the universe.

I don’t want to give the impression that these explanations are the last word on the subject and that all the problems are solved. Entropy is a tricky concept and there are disagreements (as is usually the case with research at the frontiers) on how to calculate it for the early universe. For example, some argue that the maximum allowable entropy of the universe remains constant even as the universe expands, and that the reason that the entropy can increase is because it started out with a small value at the Big Bang, well below the maximum. So the second law of thermodynamics is not violated in this case either.

The point is that blanket statements that the Big Bang violates the first and second laws of thermodynamics, and thus the only explanation is that it is due to the actions of a creator, are simply not true.

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