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  • תמונת הסופר/תNoa Feldman

1 - Quantum Mechanics: The Very Basics

Hi! Welcome. I guess that you’re here since you are interested in quantum mechanics for some reason. Perhaps because it sounds special or peculiar, or maybe because you’ve heard about it in a movie or a TV show. Personally, I am interested in quantum mechanics, and physics in general, because I want to understand how the world works. Specifically - how do the most basic building blocks of our universe work, and what are the most general and basic rules of nature. I hope this blog will open a door for you to understand more as well.

So what is quantum mechanics? We sometimes hear in movies or even in the newspaper that quantum mechanics is described as a set of mysterious, even magical rules of nature. They are never really clear, but they are always different than the world we live in, and it is unclear how our world and the quantum world connect.

The quantum universe and our day-to-day universe are indeed the same one (the only universe we’ve got, as far as I know), but for now, let’s set this fact aside and leave our day-to-day world behind. We can imagine the quantum world as a separate, fantasy parallel world, and understand its rules and how they are different from ours. Later on, we will see how the two worlds connect.

We start by looking at the world from the point of view of a physicist: The world is composed of many objects, which physicists usually denote as ‘bodies’, which are affected by forces, that is, by interaction with other bodies. This interaction can make bodies change their behavior: move around or stop in place, connect into one big, heavy body or fall apart into smaller ones. In physics, we try to observe this behavior and describe it using mathematics. For example, the ball’s position is x=6cm:

The ball can just stay in this position, but it can also move, say, with a velocity (speed) of 15 cm/s. Then, its position would be something like this:

The state of the ball can be described by some more properties other than position and velocity, like energy, for example. For now, we will focus only on the position of the ball, and go back to a non-moving ball at x=6cm.

In the classical world (which is our day-to-day world) physical bodies have a well-defined position. For example, our ball is at x=6cm in relation to the ruler next to it (in a three-dimensional world we will need two more axes in order to describe the ball’s position, but we stick to one dimension for now). If we hide the ball's location with a curtain, it will still have a definite position - the ball did not move just because we hid it.

Maybe after the curtain was set up, someone moved the ball to a different position behind the screen. In this case, for us, the ball can be at any point behind the screen, with equal probability. This probability manifests our lack of knowledge, and it has nothing to do with the ball. The ball has a definite position, we just don’t know what it is. It might even sound weird to you that I am saying this - of course the ball is in a single, definite position, even if I don’t know where it is.

However, in the quantum world, a different and peculiar phenomenon occurs: assume our ball was a quantum body. In this case, probabilities have a different meaning. The probability of the ball’s position does not mean that I don’t know where the ball is, but instead, that the ball really is, with equal probability, in all possible positions behind the screen. The ball itself hasn’t ‘decided’ where it is. Even if we know everything there is to know about the ball, we would still only know that it could be anywhere behind the screen with equal probability. The probability does not manifest *our* lack of knowledge, but instead, the non-definite position of *the ball*.

This is the first main difference between the quantum world and the classical world: In the classical world, bodies always have a definite position, although we may sometimes not know it and therefore have to use probabilities in order to describe them. In the quantum world, bodies may have a non-definite position, defined only by some probability distribution. Perhaps you have heard before that quantum particles can be in several places at the same time - this is what it means. This property is called in the (somewhat) justified name, super-position.

There is an important point to note regarding superposition - we *do* know something about the ball’s position. We can know, with confidence, what is the probability distribution that describes the ball’s position. In the case described above, it has an equal chance to be anywhere behind the screen, and zero chance to be anywhere else.

We could also think of a different state of the ball’s position, described by a different probability distribution. For example, the position of the ball could look like a bell curve centered in the middle of the screen, like in the drawing:

This distribution is definite regarding the position of the body. This is a little puzzling point, but a very important one. This is in fact the definite state of the ball - its distribution of all possible positions.

So when will the ball ‘decide’ where it is? That is, when will it acquire a definite position? Here we arrive at the second important difference between the quantum and classical world. Say I move the screen and check the ball’s position. I am performing a measurement of the ball: There is some outside body, which is me, that observes the ball at some certain position.

In the classical world, if I move the screen without touching the ball, then I do not affect the ball at all - it will stay exactly where it was right before the measurement. The only effect my measurement has is on *my* personal knowledge. Before moving the screen, my knowledge was that the ball has an equal probability to be at any point behind the screen, and after moving it, my knowledge is that it is exactly at x=21.5cm. In the quantum world, however, something interesting happens: Once I measure the ball’s position, it must have such a position - I cannot ‘see’ a distribution but only definite positions. At the moment I performed the measurement, the ball ‘chooses’ a position. We in fact do not attribute choice or free will to the ball, so instead, we say that the ball collapses into some definite position.

Here the distribution plays a role - the ball will collapse into some position, based on the probability distribution it had before. In our case, it will definitely be in a point formerly hidden by the screen, with an equal chance to be in any of these points. Where exactly will it collapse? There is no way to know, and no way to predict. No matter how much information we have regarding the state of the ball or the way the measurement was performed, we will still not be able to tell exactly what will the position of the ball be, only the chances it collapses into each point. This is a second important property of quantum mechanics - the quantum world is not deterministic, and the behavior of quantum bodies is somewhat at the hand of chance.

In fact, the measurement of the position has affected the position itself! By observing the ball, we made it collapse into one of its possible positions. The really special thing is, that after the measurement the former position distribution is forgotten, and the ball has a definite position: x=21.5cm.

This means that the ball is definitely where we measured it. This is the last important difference between quantum and classical worlds that we will see today: observing a body is interacting with the measured body, and therefore observing a body changes its state. What exactly is observing a particle? A person looking at the ball, but also light beams reflecting from it, or some sensor that feels the heat that the body emits. There is a lot more to say about what observation, or measurement, actually is, but we will get to it further on.

So to summarize: quantum bodies do not have a definite position, but instead, some position distribution. By the way, they also don’t have a definite velocity or definite energy - only distributions of these properties. When we perform a measurement of one of these properties, the body collapses into one of the possible options based on the probability distribution it had before, and there is no way of knowing for sure which option will be chosen. After the measurement, the distribution is changed - the body now has only one possible position (or velocity, or energy), based on the measurement’s result.

This indeed sounds like a fantasy world, completely different from the one we live in. But at least now we understand a little how this world works. In the next post, I will show how this weird world can relate to the one we live our lives in. Hopefully, it will also help you understand the points made in this point better as well. I hope I meet you there!

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