I would define quantum theory as a set of rules governing how the universe works on a microscopic scale. By microscopic I mean on the scale of electrons and atoms. We know that the universe works in a very different way at that scale than it does on the scale we’re used to in our everyday lives – footballs and aeroplanes and all these objects we can hold and feel obey what are called Newton’s laws or Newtonian physics. In Newtonian physics, each object has a well-defined set of attributes, so a velocity, a position, a momentum, and if you know all of these exactly you can predict what’s going to happen in the future.
So if you have, say, a football and you know the mass of the football and how much force is imparted on the football, you can calculate with certainty whether it’s going to go in the net or not. That’s the behaviour we’re comfortable dealing with. If instead we had a ‘quantum football’ that obeyed the rules of quantum theory, it would act very strangely indeed. If we measured its velocity and position very accurately, and then turned our backs, we would find that a certain percentage of the time the football made it into the net, but a certain percentage of the time it would be found on the other side of the stadium, or very rarely, on the moon. At best in the quantum world we can know the likelihood of a particular outcome of an experiment, but we can never predict with complete certainty what the outcome of an individual experiment will be.
If you take a whole bunch of tiny little quantum objects and you add them together – for instance you put together all the atoms inside of a normal football – the strange quantum behaviour of the individual atoms averages out, so what you’re left with is this giant football that behaves like an everyday object. So people understand why the universe works differently on different scales, but they don’t understand at a fundamental level why quantum physics is the way it is – it’s just an intrinsic property of the universe originating perhaps with The Big Bang. Trying to understand how the laws of physics evolved from The Big Bang gets back to the idea of a Theory of Everything, which would combine the ideas from quantum theory with gravity and other aspects of physics. People like Einstein have spent years looking for this – but we’re still far away from such a theory.