The evolution of the wave function which is determined by Schrödinger’s equation, is said to evolve deterministically.
The wave function represents the probability distribution of potential measurements of a system. Each individual measurement is proposed to be truly random. Thus, it is proposed that the result of the measurement is occurring for no reason.
Now, probability is just related to frequencies. If X has a 5% probability, with enough trials, X will occur 5% of the time.
Now if an electron’s position has a certain probability distribution, shouldn’t there be something, some force, some reason, that is causing that probability distribution to materialize?
If the position at each measurement is truly occurring for no reason, then an amalgamation of things occurring for no reason shouldn’t create a probability distribution. For otherwise, without a guiding physical reason at each measurement that occurs, how would the electron have a “propensity” to be in a position such that over time, the positions agree with the probability distribution defined by the wave function?
An analogy would be coins. In each specific coin toss, we have a reason to prefer no side over another. Given the symmetry of the coin and the constant environmental conditions, we thus have a physical reason that gives each coin toss a “propensity” to land on heads 50% of the time. If the coin was biased, the coin would now have a “propensity” to land on the biased side more often.
Without this propensity which is governed by a physical reason, how could any probability distribution realize?