The world we live in is uncertain; that is, there are possibilities that might happen or be true but aren’t certain. Every possibility is attached to a probability, and while the possibility itself is something non-real, the probability of its existence usually comes from something that we have perceived or observed about it. As a simple example, you see talent or interest in music in your child, and becoming a musician in the future gets probable for him. Therefore, possibilities in our classical view of the world are objective because of the association between their probability and the objective world. Nearly all possibilities in the classical world have this indirect element of objectivity. That is why, in our common sense, possibilities often appear in the absence of limitations or overcoming them. We see those limitations in our environment, for example, family, social, geographical, political, and other statuses. However, beyond the surface of these limitations is the world’s potential energy, which dictates all the boundary conditions. The difference between the energies surrounding us and our own intrinsic energy defines the rules for how those boundary conditions can limit our lives and control our choices. In other words, we won’t consider any possibility of moving forward in front of a huge obstacle that we can’t overcome; Classical possibilities are connected with and defined by the objective world. As a result, possibilities get probable only through how the world’s potential energy appears to be from time to time. Nevertheless, we see that the same particle in the quantum world is less limited by the same potential energies because it can possibly penetrate into the classical forbidden areas. In fact, the very different way of defining “possibility” in the quantum world is why the particle could suddenly appear as a wave and overcome the barrier, even with intrinsic energy less than the potential energy of the obstacle.

In contrast to classical possibilities, quantum possibilities are subjective; that is, they essentially exist, not based on objective perception or observation. Their essential being makes the simultaneous existence of many possibilities feasible regardless of boundary conditions. This results from the nature of the wave function, a linear superposition of two or more states that the system can possess. This is known as the principle of superposition in quantum mechanics. Let’s assume a particle, the simplest quantum system, and its position as one obvious property. For simplicity, we ignore its other properties, so the wave function is simplified to a superposition of different places (states) the particle can occupy. In semi-classical language, the superposition principle means the particle is not limited to occupying position A or B; rather, it can be simultaneously found in both or even more positions (depending on the number of states in the superposition). All of these states are essential possibilities, that is to say, subjective, arising from the nature of the particle when it is no longer a particle but a wave, and existing essentially regardless of circumstance (or the objective world). The potential energies of the world can only change the probability, not the existence, of those possibilities. This is unlike the classical world, where an objective fact or observation gives birth to a possibility. Possibility in the quantum world essentially exists. The objective environment can interact with those possibilities without causing them to exist.

It seems, at least at first glance, that the superposition principle is simply a probabilistic view of the world. This also holds true in the classical view of the world, a dice, we might say, is in a superposition of six states (numbers). We know, when rolling the dice, that each of those numbers might occur with a probability attached to each state. So, how is the quantum superposition different? First of all, there is no evidence that the dice is in a superposition of six states before being rolled, as was the case for the particle in the double-slit experiment, where the pattern after the slits proved that the particle actually passed through both slits. We just assume that the dice was in a superposition of six states, but what we really say is that there is a probability for any of those numbers before rolling the dice, and the action of rolling defines which one will come true. Before taking the action, all we know is the probability attached to each one of those possibilities (in this case, the probability is the same for all possibilities and equal to ⅙). It’s like you have two different shoes and the probability of wearing any of them tomorrow is ½, but you are not wearing both now! It’s not actually a superposition but a hypothesis of different possibilities for the future, each with a probability that becomes certain after taking the action of decision-making (or experimentation in general). The uncertainty is in the fact that you don’t know yet which one you will pick tomorrow, which might depend on external conditions, for example, on the weather, showing the objectivity of those possibilities!

The superposition principle in quantum mechanics is fundamentally different; the particle can essentially be found in many states simultaneously, and now. In other words, quantum possibilities don’t belong to the future. They exist before taking any action. We might think that those states are equivalent to the possibilities in the classical world, but they are not the same; the quantum states are essential contingency in contrast to the hypothetical possibilities in the classical view. In other words, if we assume a magical boundary between the classical and quantum worlds, for us, standing in the classical world outside this boundary and watching the particle in the quantum world, those states might seem like different possibilities. We can define a probability for each of those possibilities because, statistically, we don’t see the state function itself but its squared form (or the amplitude of the wave). The state function in its pure quantum form is a superposition of different states, each associated with a complex number. Knowing that probability can be defined only as a ratio of two natural real numbers, the ratio of those states with their associated complex numbers gives us no clue about their probability. Only when we look at the particle closely, through experiment or measurement, does the probability appear as a real number, as if our action causes the particle to pass through that boundary, taking it out of the quantum world.

You might think the reality we live in daily is classical. So, what’s the point of knowing the quantum rules about possibilities when all we get in real life is a few of them, mostly on the other side of some huge obstacles over which we barely have any control! The answer is that quantum mechanics teaches us otherwise, that what we can observe and perceive is not the whole reality. Beneath our classical ordinary world, there is another layer of reality where quantum rules hold true. It’s no science fiction, it’s a fact that the tiniest building blocks of the universe are controlled by these rules. Understanding what is really there beyond what we can observe can change our whole perspective about our position in the world, our lives, and even decision-making! Despite objective possibilities in our classical understanding of the world, essential possibilities will take the pressure of boundary conditions off our minds. You might stop worrying about circumstances and focus more on your choices, when you know that every possibility is more than just a hypothesis, dictated by a probability, and already exists in another layer of reality.