In today’s society, and especially in academia, it seems like believing in God is thought to be only for the delusional. It some ways it is justified. Religion in general has had a less than stellar track record. Also, invoking a higher power seems to be cheating when investigating nature. You are somehow jumping over this idea of causality. This leads me into my diatribe on God and Quantum Mechanics. In a lot of ways I’m a novice, I only have an undergraduate degree in physics and have no formal training in philosophy. Keep this in mind as you read this article. I am just spitting out my thought process from several conversations that I had with friends. Please leave your thoughts as comments and please correct me if I misunderstand some of the elementary concepts.
When most people think about science, they think about determinism. By this I mean that the universe is controlled by precise laws that determine the exact behavior of all objects in them. Therefore, if we knew the state of the universe
, we would be able to predict the state of the universe at another time. Therefore, we could express the universe as function
where
is a deterministic function that dictates how the universe evolves.
To clarify this point, I would like you to consider a pool table. If one knew the exact locations of all the balls, a deterministic universe would allow you to predict the motion of all the balls if you were to hit one of them. In short, it maintains this idea of causality. That is, every event that occurs was caused by another event. In the case of the pool table, a particular ball will move with a certain speed and direction because another ball hit it with a certain force. When one thinks about the universe in this way, it is easy to dismiss the idea of God. The idea that someone can mystically interfere with the chain of causality is unnerving at best. And if something outside the universe could interfere, the universe would cease to be deterministic because the evolution of the universe would no longer solely depend on the previous state of the universe. Instead, we would have to add some God parameter
which would change our deterministic function to

If one were to have a predisposition to keep this idea of causality, we could easily dismiss the idea of God.
Before I talk about Quantum Mechanics, I want to make a small detour. Just because the world is deterministic, does not mean we are capable of determining it. In order to explain this, I need to introduce chaos theory. In a lot of ways, this theory has been widely misunderstood by the general public. A system is considered to be chaotic if small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes rendering long-term prediction impossible in general [Wikipedia]. Unfortunately, the universe is definitely considered a chaotic system. This leads to the idea that a butterfly flapping its wings in Brazil could cause a tornado in Texas. The common fallacy is to think that randomness/probability is the cause of the unpredictable behavior. However, this is not the case, the unpredictable behavior comes from not being able to obtain the initial conditions perfectly. If we consider a deterministic universe, we are saying that a small error when measuring the initial state of the universe
will result in a really bad estimate on how the universe will evolve. This can be said more precisely that

where
is a really small number/vector. Even with chaos, the universe that I described remains deterministic and preserves causality. The problem is that, even if we knew
, we would never be able to create accurate predictions because of measurement limitations.
A deterministic universe is not the only way of viewing the universe. The universe could perhaps be stochastic. Therefore, the universe could be defined as

where
is a function that returns a probability distribution instead of an exact value. The universe state
would be determined by taking a single sample from the distribution
. This is exactly how Quantum Mechanics describes the universe. To illustrate this concept, let’s go back to the pool table example. If we shrink the pool table to the size of an electron, we will enter into the realm dominated by Quantum Mechanics. If we hit one of the balls, it is impossible to predict exactly how this ball will collide with all the other balls. Instead, for the sake of simplicity, Quantum Mechanics might predict 10 different options. Out of these 10 options, the universe will randomly select one of them and that is what we will observe. If this description of reality is true and we live in a stochastic universe, then we have to accept that not everything has a cause. In the case of the pool balls, there are 10 possible states, however, nothing causes it to collapse to one of these states. In the quite literal meaning, we can have events occurring without any causes.
The next question that I would like to pose is whether or not we live in a stochastic or deterministic universe. Quantum Mechanics claims that we live in a stochastic universe, but how do we know that reality is actually stochastic? The universe could actually be just chaotic. We could have arrived with a probabilistic model just because it is impossible to gain the precision needed to create a deterministic model. At first glance, there seems to be no good way of determining whether an observed system is chaotic or stochastic. In the end, they are both unpredictable.
After thinking about the matter, I came up with a good example that strongly suggest that the world is actually stochastic. In the early universe, seconds after the big bang the universe was in an extremely hot uniform dense state. As the universe expanded quantum thermal fluctuations broke the uniformity of the universe. This uniformity could only have been broken if the universe was stochastic. A chaotic system would require a small perturbation to break the uniformity of the universe. However, since the universe is hypothetically deterministic, this perturbation could never exist. The universe required something intrinsically random to create the fluctuation. As the universe grew, these fluctuations allowed the universe to create the structures we observe today (galaxy, stars, etc). If it weren’t for these fluctuations, the observed universe should still be uniform. Of course, there is plenty of room to argue for determinism. However, the evidence does seem to lean towards a stochastic universe.
How does this relate to God? Well, if we live in a stochastic universe, we have to admit that some events may have no direct cause. If this is the case, there is no rational reason not to concede the possibility that an event was caused by God. In the end, the universe is still determined by something outside the universe. For this reason, you can not exclude the idea of God on scientific ground while letting go of causality.