Argument From the 2nd Law of Thermodynamics

by Francois Tremblay

There are a few key concepts we must cover before explaining this argument. The first is the concept of entropy. Entropy (S), in its technical definition, is the measure of the amount of disorder in a system. It is measured in the units energy per temperature, traditionally ^Joules/_Kelvin. A system in which we measure S=10JK^-1 has more disorder than a system in which we measure S=5. We say that the system in which S=5 is “ordered” and the system in which S=10 is “chaos”.

Thermodynamics is the physics behind macroscopic systems based on the statistics of their particle (micro and nanoscopic) compositions. For example, temperature is a measure of the average kinetic energy of each of the particles that makes up a macroscopic object—and thus is part of thermodynamics. Thermodynamics has 3 laws (or 4 laws, depending on your definitions). The second law of thermodynamics states that the change in entropy is greater than 0. In math language:

dS > 0

This means that starting at point A and moving to point B, the overall trend of S will be increasing, and have a positive slope. Now, as for the heart of the matter, and what this argument is all about.

The Big Bang is a state of a extremely low entropy. Since the Big Bang, entropy has of course continually increased. But the 2nd Law of Thermodynamics does not only apply on the positive direction of the time axis within the block universe. The 2nd Law of Thermodynamics applies along any axis within the block universe. As such it is, statistically speaking, more probable that your half-melted ice cube came from a glass of warm water, rather than a fully formed ice cube. (Of course, we know that half-melted ice generally starts as fully formed ice, but this is due to the Big Bang—the initial state of low entropy.)

The reasoning behind this is simple to see. Imagine 2 H2O molecules bumping around. There is a pretty good chance that these 2 molecules will at one point come in close proximity, and form a half-melted (albeit microscopic) ice cube. In fact, this will happen every couple of seconds (the actual time varies depending on the substance). If we add more H2O molecules, the probability will drop, of course, but it still happens every so often for small numbers of molecules at a time. In any glass of water, there are always tiny pockets or duos of slow-moving (ice) molecules, and pockets of fast-moving (gaseous) molecules. There are many ways in which H2O molecules can combine to become a partial ice cube, but there are VERY few ways in which H2O molecules can combine to form a complete block of ice. Thus, given enough repetitions, H2O molecules will at some point form half-melted ice, and at another point (with a vastly increased number of repetitions) become a fully formed block of ice.

The same argument applies to the Big Bang, but with greater implications.

¹ First, however, we must briefly consider the god-concept. The god-concept, as it is usually defined, is an orderly entity (or system). If the god-concept is not orderly, then it is chaotic. But if god is chaotic, then he can not directly cause things to happen at his will. To even have a will means that god is ordered, and to willfully cause the Big Bang would mean that he has a lower entropy than the universe after the Big Bang. (Remember, dS > 0!) For more on a chaotic god-concept, read the Argument From Non-Cognitivism. If you’ve made it this far, and you are a believer, then you agree that your god-concept is orderly. Now we can get to the root of the problem:

Statistically speaking, as said before, pockets of low entropy within a high-entropy system are inevitable. They may be either offset by an increase in entropy elsewhere, or a statistical fluke that while improbable is certainly not impossible. As long as dS > 0 and entropy tends to be higher, the 2nd Law of Thermodynamics has not been broken. But, again, statistically speaking, these pockets of low entropy are most likely the result of simple probability. Consider that these low entropy systems were directly (or willfully) caused by another system with even lower entropy. Surely, we get into an impossible infinite regress (not to mention that a system with 0 entropy cannot exist!).

Thus, the Big Bang is, statistically, the result of an inevitable improbability that exists solely due to the 2nd Law of Thermodynamics, and is relevant throughout the block universe. We may picture it mathematically as such:

1. The Big Bang has entropy S.
2. A hypothetical god is either orderly or chaotic.
   1. Hypothetical gods have a personhood.
   2. Personhood implies orderliness.
1. A hypothetical god is orderly, and thus has low entropy. (See note¹ for more detail.)
3. In order for god to directly cause the Big Bang, he must have a lower entropy (S-a, where a is positive, real number).
4. The probability of the Big Bang coming from a higher state of entropy (S+b, where b is a positive, real number) approaches P=1, normalizing over the condition of many opportunities for the Big Bang to happen.
5. The probability of the Big Bang coming from an even lower state of entropy (god) approaches Q=0 (since Q=1-P).
6. The difference in probability is thus the limit of 1 divided by the limit of 0, which of course approaches infinity.
7. There is an infinitely greater chance that the Big Bang is the result of randomness than the result of even more order.

1. Thus, god does not exist.

   Possible Objections:

   Q: But God is not within the block universe, so how can you account for his entropy?

   A: Whether or not god exists within the block universe does not affect the necessity of his entropy. If god is in an ordered state, then he has low entropy. If god is not in an ordered state, and thus in a disordered state—he has high entropy. If he is neither ordered nor disordered, Non-Cognitivism takes hold. If you claim that god does not have an entropy, we here at strongatheism.net would certainly agree—for god has no properties—he does not exist!

   Last updated: March 28, 2005