The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [22]
Here is the correct answer: the particle can be anywhere else in the Universe at the later time. That means we have to draw an infinite number of clocks, one at every conceivable point in space. That sentence is worth reading lots of times. Probably we need to say more.
Allowing the particle to be anywhere at all is equivalent to assuming nothing about the motion of the particle. This is the most unbiased thing we can do, and that does have a certain ascetic appeal to it,1 although admittedly it does seem to violate the laws of common sense, and perhaps the laws of physics as well.
A clock is a representation of something definite – the likelihood that a particle will be found at the position of the clock. If we know that a particle is at one particular place at a particular time, we represent it by a single clock at that point. The proposal is that if we start with a particle sitting at a definite position at time zero, then at ‘time zero plus a little bit’ we should draw a vast, indeed infinite, array of new clocks, filling the entire Universe. This admits the possibility that the particle hops off to anywhere and everywhere else in an instant. Our particle will simultaneously be both a nanometre away and also a billion light years away in the heart of a star in a distant galaxy. This sounds, to use our native northern vernacular, daft. But let’s be very clear: the theory must be capable of explaining the double-slit experiment and, just as a wave spreads out if we dip a toe into still water, so an electron initially located somewhere must spread out as time passes. What we need to establish is exactly how it spreads.
Unlike a water wave, we are proposing that the electron wave spreads out to fill the Universe in an instant. Technically speaking, we’d say that the rule for particle propagation is different from the rule for water wave propagation, although both propagate according to a ‘wave equation’. The equation for water waves is different from the equation for particle waves (which is the famous Schrödinger equation we mentioned in the last chapter), but both encode wavy physics. The differences are in the details of how things propagate from place to place. Incidentally, if you know a little about Einstein’s theory of relativity you might be getting nervous when we speak of a particle hopping across the Universe in an instant, because that would seem to correspond to something travelling faster than the speed of light. Actually, the idea that a particle can be here and, an instant later, somewhere else very far away is not in itself in contradiction with Einstein’s theories, because the real statement is that information cannot travel faster than the speed of light, and it turns out that quantum theory remains constrained by that. As we shall learn, the dynamics corresponding to a particle leaping across the Universe are the very opposite of information transfer, because we cannot know where the particle will leap to beforehand. It seems we are building a theory on complete anarchy, and you might naturally be concerned that Nature surely cannot behave like this. But, as we shall see as the book unfolds, the order we see in the everyday world really does emerge out of this fantastically absurd behaviour.
If you are having trouble swallowing this anarchic proposal – that we have to fill the entire Universe with little clocks in order to describe the behaviour of a single subatomic particle from one moment to the next – then you are in good company. Lifting the veil on quantum theory and attempting to interpret its inner workings is baffling to everyone. Niels Bohr famously wrote that ‘Those who are not shocked when they first come across quantum mechanics cannot possibly have understood it’, and Richard Feynman introduced