As an introductory post, I want to put forward one of the essentials of quantum mechanics (from now on, QM).

When you begin reading a textbook about QM, one of the first things you usually encounter is the comparison with classical mechanics (CM), that theory enunciated by the apple guy some centuries ago.

Alas -they tell you- CM and QM differences are not simply due to slight adjustments to a couple of parameters, but affect profoundly the essence of both.

Maybe the flashiest differences between QM and CM are:

- Quantum randomness
- Uncertainty principle
- Energy quantization

Let’s forget about uncertainty and quantization (they’ll show up in another post exclusive for each). What about quantum randomness? Why should you care at all?

Physical laws are good to predict what a system does, what it did, and what it will do (by “system” you can imagine a collection of any number of particles, moving or not).

The laws of CM allow us to predict the motion of a system, literally at any time, as long as we know some fundamental information about it at *one single time* (positions and momenta of the particles of the system). That is, just having the right info on a single instant, we know everything. We can know that much, according to CM!

But QM has an element of randomness. Oops. How can we predict something which is random? We can’t. Shit.

We can know everything that we can about a quantum system, and still we may not be able to predict what it will do. In QM, most of the times we can only predict *probabilities* of an event to happen. Think throwing a dice or a coin.

I like to illustrate this in the following way. This is what happens with CM:

1, 2, 3, 4, 5… are different states of a system. Our physical law tells us here that the probability of “jumping” from one state to the other in the order shown above is 100%. This is typical CM behavior.

What happens with QM? Something a bit fancier. Look at this:

There are “jumps” between states which are similar to the CM case. The system jumps from one state to another state with 100% probability. These we can predict. But other jumps show *divergence*. For instance, 2 may jump to 3 or to 3′ (whatever they represent) with a 50% chance for each case to happen, and *this is all that we can know*. There’s no way to know for sure if 2 will go to 3 or to 3′, no matter how much millions we spend on measuring devices…

If we throw a (perfectly made) coin, we simply know that we have a 50% chance of obtaining heads. QM is conceptually similar. Probabilities, probabilities…

So maybe the most fundamental difference between CM and QM is that, while CM is a *deterministic* *theory*, QM is a *probabilistic* *theory*.