Why Quantum Mechanics Works

Quantum Mechanics is the theory of physics that is needed when working with anything that is very small. It’s notoriously abstract, mathematical and counter intuitive.

I must have about a dozen introductory books on the subject. They mostly follow a very similar pattern. First there are some examples of problems that can’t be solved by classical physics. Then they show how Einstein and Planck’s hypothesis about the particle nature of light helps to solve them. Finally, there are a set of postulates that are the basis of quantum mechanics.

It’s always been the last bit that gave me a problem. None of the textbooks do a particularly convincing job on making the postulates plausible. Their main justification is that they work. Yet it is perfectly possible to make them seem very plausible, almost inevitable.

I tried to illustrate this a few years ago with a series of pages on the old blog. I’ve now written a short paper that tries to expand on this.

The basic premise is that, if you take any random variable and map its possible values to a vector space, you get something that looks very much like quantum mechanics.

As well as making the postulates seem much less mysterious, this approach has the advantage that it distinguishes between those aspects of quantum mechanics that are genuinely novel physics, and the aspects that are simply consequences of the mathematical formalism.

Learning the Mathematics of Quantum Mechanics Using Simple Classical Analogies