Is the position of a quantum particle truly random or does it depends upon uncontrollable factors?

Question

When you roll a dice or flip a coin, the result depends upon the way you roll/flip it, where it lands, etc. So practically, the dice or coin are not actually random. Does this apply to quantum particles, like electrons? Does their position depend upon any factors which affect their position due to their small size, or are their movements truly random?

Answer 1

The short answer is that nobody knows for sure. But we do know (thanks to Bell's Theorem) that if the results are due to "hidden" factors that we don't know about, then those factors are not "local", which means they act in a peculiar way that has no analog in classical mechanics. The randomness of quantum mechanics cannot only be due to our ignorance of some underlying variables; those variables must also be unusual in particular ways.

Answer 2

At the moment the theory we have to model elementary particles and their composites, as atoms, molecules, lattices, is quantum mechanics. This theory has postulates and laws and principles that are used in order to pick up the solutions of the wave differential equations that can model data, and predict new values.

A fundamental postulate is that the theory predicts probability distributions, and not exact measurements.One has to do many measurements with the exact boundary conditions and input energy values in order to validate the theory. For the scattering of particles and their products quantum field theory, based on quantum mechanics, is used and has been very successful in modeling the data and predictions.

This means that the probability distributions are not random, but weighted with the values given by the calculation. Thus in the double slit experiment for electrons, even with one electron at a time, the probability of finding the electron is weighted towards the wave pattern seen, and not the random pattern expected from tiny billiard balls.

This does not preclude the possibility of some type of deterministic underlying level to be affecting these probabilities, and a number of good physicists have been trying to create such a theoretical model, with no success at this time. See for example this discussion.