When forced to explain quantum superposition in plain English, physicists have an unfortunate tendency to equivocate. They will utter variations on ” a quantum superposition means a particle is in two different STATES at the same time”, or even worse “a quantum superposition means a particle is in two PLACES at the same time”. No experiment in any lab has ever seen this. A particle is always detected at the same location as the particle detector.

Why is this equivocation? It is trading on the ambiguity of the word STATE. In physics, the state of a physical system is a list of numbers that enables you to predict, with little error,  the results of any measurement you wish to make upon it. No measurement is ever perfect so this list does not determine the result of measurement (see my earlier post).

In classical mechanics (CM) this list is the position and velocity of every particle in the system. Given this, Newton’s equations predict the position and velocity of every particle into the future (and the past).  The position and velocity are real numbers and we cannot give them arbitrary precision. In many case finite precision will suffice for predictions a few time steps at a time without too great an effect on error.  Anything you can measure is a real valued function of the numbers in this list. Classical physicists tend to think the state is ‘out there’ waiting to be discovered in greater and greater accuracy. They think that a physical state  has an objective status that is discovered by measurement.

In quantum mechanics (QM) the physical state is a list of complex numbers. (Each complex number is actually comprised of a sub-list of  two real numbers.) Together with Schroedinger’s equation, this list of complex  numbers (or list of pairsof real numbers)  determine the probability to obtain a result for any kind of measurement you care to make upon the system. This is a very different kind of state  to the classical state.  We use the same word ‘state’ to refer to both lists as they determine the statistics of outcomes for anything you care to measure.

Physicists, if  forced to explain quantum superposition,  equivocate over the precise meaning of `state’ they are using. In both classical and quantum physics a carefully prepared physical system is only ever in a one state at a time. It is the meaning of the word state that is different in the two theories.

Now here is a curious fact. In CM, if you know the state  with perfect accuracy,  you can predict with certainty the results of every measurement you may care to make. In QM however if you know with perfect accuracy the list of numbers for the quantum state, there is always one measurement  for which the results are completely random. This is the most general statement of the Heisenberg uncertainty principle. In CM, if you know the state perfectly, all measurement results are determinate. Knowledge of the whole is knowledge of the parts. This is never the case  in QM. Knowledge of the whole can coexist with total ignorance of  the parts.

Is the quantum state out there? Is it an ontological fact about the world?  Or is it something else, perhaps simply a way to encapsulate all we have learned about our interventions in the quantum world. Physicists are still arguing about this, but the argument is moribund. We have been arguing about it for almost a century yet this has not slowed the discovery of new physics.

The concept of learning machines gives an alternative response: neither CM or QM make ontological claims. They make claims about the kinds of functions physical learning machines like us can learn in order to intervene effectively in the world. Kant said sometime similar long before the quantum world was discovered. It is time to heed the message. The problem is not the interpretation of quantum mechanics, the problem is the interpretation of classical mechanics.