Reality is fundamentally probabilistic

As a preliminary remark, I think it is useful to recall what science brings us in relation to the reality that is offered to us. My conviction is that science allows us to better understand the world. Given the size of the universe, we cannot be sure that it can provide a complete picture of it. Nevertheless, what it allows us to grasp, is already very vast and close enough to us to make it useful and to set limits on what discourse can or cannot assert with certainty. This will not prevent us from hearing erroneous claims. It’s just unfortunate because the laws of physics hold true, and hoping to prove them wrong can only lead to disappointment. That doesn’t mean everything is predetermined. So, what is the case?

Current understanding of quantum mechanics reveals a world governed by physical laws that describe reality not in deterministic terms but rather in probabilistic terms. Schrödinger’s equation provides the probability law that allows us to quantify the properties of a given physical system (the position, velocity, and energy of its constituent particles).

If a system’s properties are determined probabilistically, what about determinism? In reality, it seems to apply to average values—whether temporal or spatial—when a large number of similar events are taken into account. Thus, while luck may smile upon us by letting us win the lottery, the lottery operator is almost certain to make a profit, unlike the players, because they benefit from the deterministic laws that apply to averages when a sufficiently large number of players participate in the game.

The difficulty of understanding probabilities

It is from this observation that, in my opinion, the concept of entropy can be better understood. I still feel that this quantity remains somewhat mysterious. My main takeaway was that entropy is, in a way, a measure of disorder in a system containing a large number of particles. So, what does “measuring disorder” actually mean?

In practice, consider a system composed of a large number of identical particles. These particles can occupy several possible states characterized by physical quantities (position, velocity, angular momentum, etc.). The states of the particles are distributed according to a probability law whose origin is fundamentally quantum in nature.

The state of the overall system reflects the fact that the particles of which it is composed are subject to this law of probability. What is strange is that each individual state is unpredictable. We know only its probability. Nothing allows us to predict this state apart from this probability. In particular, the system’s past states cannot predict its future states. It is actually extremely unsettling to imagine that the state of an elementary system is unpredictable but that, on average, it will reach a specific value.

For example, in a coin toss, if heads come up ten times in a row, we tend to believe that tails are more likely to come up in the next tosses. This is false. Each toss is independent of the previous ones. This unpredictability gives the impression of total randomness and a system beyond control, which seems incompatible with the concept of probability theory. However, over a large number of tosses—whether using identical coins simultaneously or a single coin toss repeated multiple times—the law of probability dictates that the system will, on average, settle into a certain state, and that heads and tails will appear, on average, with equal frequency. As Einstein said, chance is God walking incognito.