The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [15]
Before we do this, it might be worth reading the above paragraph again because it is very important. It’s not supposed to be obvious and it is certainly not intuitive. The ‘electron wave’ proposal has all the necessary properties to explain the appearance of the experimentally observed interference pattern, but it is something of a guess as to how things might work out. As good physicists we should work out the consequences and see if they correspond to Nature.
Returning to Figure 3.1, we have proposed that at each instant in time the electron is described by a wave, just as in the case of water waves. At an early time, the electron wave is to the left of the slits. This means that the electron is in some sense located somewhere within the wave. At a later time, the wave will advance towards the slits just as the water wave did, and the electron will now be somewhere in the new wave. We are saying that the electron ‘could be first at A and then at C’, or it ‘could be first at B and then at D’, or it ‘could be at A and then at D’, and so on. Hold that thought for a minute, and think about an even later time, after the wave has passed through the slits and reached the screen. The electron could now be found at E or perhaps at F. The curves that we have drawn on the diagram represent two possible paths that the electron could have taken from the source, through the slits and onto the screen. It could have gone from A to C to E, and it could have gone from B to D to F. These are just two out of an infinite number of possible paths that the electron could have taken.
The crucial point is that it makes no sense to say that ‘the electron could have ventured along each of these routes, but really it went along only one of them’. To say that the electron really ventured along one particular path would be to give ourselves no more of a chance of explaining the interference pattern than if we had blocked up one of the slits in the water wave experiment. We need to allow the wave to go through both slits in order to get an interference pattern, and this means that we must allow all the possible paths for the electron to travel from source to screen. Put another way, when we said that the electron is ‘somewhere within the wave’ we really meant to say that it is simultaneously everywhere in the wave! This is how we must think because if we suppose the electron is actually located at some specific point, then the wave is no longer spread out and we lose the water wave analogy. As a result, we cannot explain the interference pattern.
Again, it might be worth rereading the above piece of reasoning because it motivates much of what follows. There is no sleight of hand: what we are saying is that we need to describe a spread-out wave that is also a point-like electron, and one possible way to achieve this is to say that the electron sweeps from source to screen following all possible paths at once.
This suggests that we should interpret an electron wave as describing a single electron that travels from source to screen by an infinity of different routes. In other words, the correct answer to the question ‘how did that electron get to the screen’ is ‘it travelled by an infinity of possible routes, some of which went through the upper slit and some of which went though the lower one’. Clearly the ‘it’ that is the electron is not an ordinary, everyday particle. This is what it means to be a quantum particle.
Having decided to seek a description of an electron that mimics in many ways the behaviour of waves, we need to develop a more precise way to talk about waves. We shall begin