God doesn't play dice !

The probabilistic concept of the electron clouds was like an axe in the head for physicists, but it was a theory that is worth considering. In fact, they haven't been able to prove anything against it.

Erwin Schrodinger came up with a genuine equation that describes a particle's motion which is known as: 

it may seem complex but there is a more desirable way to write it and better comprehend it: 

 where

Depending on this equation we can notice that there are two states of 𝛙, a   𝛙0 and a 𝛙(t).

If 𝛙0 is the wave function of the start (t=0) then the term the time evolver.

What is physics? physics is the science of predicting the future like predicting where a projectile is going to land or how much time does an object in motion take to reach a certain location. This works the same for waves and by knowing their initial state and how they behave in time and space, we can predict the future variations. This is what Schroedinger equation is all about.

I am not going to explain how the derivation was established because it contains some +18 complex mathematics and I honestly hate math. 

The wave equation 𝛙 depends on two variables which are space and time and that's obvious because we can't imagine a wave the evolve independently of time or space. Schrodinger thought that the equation was meant to identify the exact location of an electron.The equation was 100% correct and it worked for every wave example but the thing he didn't know is that function allow us to determine the probability of finding an electron but not its exact location. So instead of asking where is the electron? we should ask, what is the likelihood of finding an electron in that specific place at that specific moments?

You should know that 𝛙 is a function that has a pure mathematical meaning and it is physically insignificant, On the other hand, |𝛙|² turns to have a logical physical sense, it represents the probability of presence of an electron according to the relation d(P)/d(V) = |𝛙|² where d(P) is the presence probability and d(V) is the little pack of space that surrounds the area where we want to verify if there is a probability of finding an electron. Thus, by determining the wave function at a certain coordinates x and t, we can calculate the electron's presence probability.

If the idea of probability and superposition is still foggy and unclear you may want to learn about something that might be even more famous than Schroedinger himself which is his cat. Well, it's not a  real cat but some kind of philosophically thoughted and never done experiment.

It suggests that we put a cat in a box that contains a radioactive device emitting radiations that have a 50% chance of killing the cat, then we close the box. The question is? What will we find if we open the box? A dead cat? Or maybe it's still alive?

So the theory wants to tell us is that while the cat is in the box it exist into two simultaneous states which are dead and alive, it's like two cats but each one has its own unique state. This unclear concept is resolved once we conduct an active measurement by lifting the cover from the box and finding one cat that's maybe dead or alive!! It's the superposition of the two images of the cat, it's like they collapsed on each other and form one unique but real image! And this is the same for electrons, during their active motion, an electron is able to be in every place at once it's not because it's speeding or something so it appears to be everywhere, it's really all over the place until we decide the moment and location to examine them to find whether it's there or not! This is the ultimate Incubus for physicists that they hoped it was wrong, but it's real. Einstein died trying to prove that wrong saying "God doesn't play dice" he thought everything in physics is based on certainty, nothing is random!! It's true until quantum mechanics came to say Hi.