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Big Bang for beginners-14: Does the Big Bang theory violate the second law of thermodynamics?

Wednesday, 31 March 2010
by Mano Singham

In the previous post, I showed that the creation of the universe does not, as is sometimes thought, violate the law of conservation of energy, otherwise known as the first law of thermodynamics.

Another supposed problem 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.