Penrose (2004: 512-4):
This point can be made even more forcefully in a somewhat different experimental situation. This has the additional advantage of making quite clear to us that the wave-packet picture of a wave/particle is, by itself, quite inadequate for explaining particle-like quantum behaviour. Let us imagine that there is a particle source, just as before, and we are going to suppose that it only emits a single particle. Instead of using a barrier with a pair of slits, we are going to suppose that there is what is called a beamsplitter in the particle’s path.
It will help our imaginations if we think of our particle as a photon, and we can imagine that the beam-splitter is a kind of ‘half-silvered mirror’ which is to split our photon wave packet into two widely separated parts. For clarity of our conceptions, let us envisage our ‘experiment’ being carried out in interstellar space (and the reader should be warned that I am not proposing anything remotely practical here — our example will serve merely to exhibit some very basic predictions of quantum mechanics under extreme circumstances).
If we choose, we can imagine the photon’s wavefunction to start out from the source in the form of a neat little wave packet, but, after encountering the beam-splitter, it will divide itself in two, with one wave-packet part reflected from the beam-splitter and the other wave-packet part transmitted through it, say in perpendicular directions (Fig. 21.8).
The entire wavefunction is the sum of these two parts. We could wait for a year, if we like, before choosing to intercept the photon’s wavefunction with a photographic plate or other kind of detector. The two parts will be a very long way away from each other by now, but we can imagine that I have two colleagues (in two different space laboratories), more than 1.4 light years separated from one another. Each of my colleagues has a separate detector, and although each of the two wave-packet parts may individually have dispersed considerably by now, each colleague has a large paraboidal reflecting mirror which collects the dispersed wave packet, focusing it on that particular colleague’s detector.
What does quantum mechanics say will happen? It says that one or other of my colleagues will indeed detect the photon, but that they cannot both detect the photon. This is not the kind of thing that a classical wave does. Remember that my two colleagues are over 1.4 light years apart. Relativity insists that no signal can pass between them in less than 1.4 years; yet the fact that one wavepacket part yields up a photon prevents the other one, 1.4 light years away, from doing so, and vice versa. In only a year’s time, I learn from each of them what has happened, and I find that only one of them has received a photon. The part of the wavefunction that each colleague has access to seems to ‘know’ what the other part of the wavefunction is up to!
Every time I perform this experiment, I find that one or other of them receives the photon, but not both. No classical type of wave effect could achieve this apparently ‘instantaneous communication’ between the two parts of the wavefunction. Quantum wavefunctions are just different from classical waves.
Blogger Comments:
From the perspective of Systemic Functional Linguistic Theory, this misconstrues potential as actual. It is a particle that either passes through the beam-splitter or is reflected by it, not the wavefunction in the form of a wavepacket. The 'splitting of the wave packet' is the superposition of two wavefunctions, one for each possible trajectory of the particle after it encounters the beam-splitter. It is this superposition of potential that constitutes the 'entire wavefunction'.
The reason why only one colleague detects the photon is that only one photon is emitted. There is no 'instantaneous communication' between the 'two parts of the wavefunction' because their superposition represents potential events, not actual events.
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