The simplest two-particle system can be used to explain a quantum measurement. The core idea is all that counts. One particle, called the pointer, is used to establish the location of the other particle, called the object. Figure 43 shows things with which we are already familiar. At an initial time tset-up, the pointer (horizontal axis) and object (vertical axis) are not entangled. For any of the small range of possible pointer positions, the object has identical ranges of possible positions, shown schematically by points 1 to 6 on the left. Determination of the pointer position in this state would tell us nothing about the object. But the interactions of the particles are so arranged that by the later time tmeasurement the wave function, passing through the interaction region, has ‘swung round’ into the position shown on the right. Remembering how points in Q translate into positions in space, we see that the object still has its original range of positions 1 to 6, but that the new pointer positions are strongly correlated with them.
Figure 43. The initially unentangled state at tset-up, shown schematically at the bottom left by the vertical column of positions 1, 2, 3, 4, 5, 6, and the first probability density above it, evolves into the entangled state at tmeasurement, indicated on the right by the inclined numbers 1, 2, 3, 4, 5, 6 and the upper right probability density.
If we operate detectors at tmeasurement to find the pointer’s position (by letting it strike an emulsion or even, in principle, by acting ourselves as observers and placing our eyes at the appropriate places), the standard quantum rules immediately tell us the object’s position, for different pointer positions are now correlated with different object positions. Quantum measurement consists of two stages: the creation from an unentangled state of a strongly entangled state (creating the conditions of a so-called good measurement) followed by the exploitation of the correlations in that state (using the determination of the pointer position to deduce – measure – the object’s position). The existence of such correlations has now been wonderfully well confirmed by experiments. If detectors have been used to find the pointer and are then used to locate the object directly, the quantum correlations predicted are invariably confirmed. Measurement theory is really verification of the correlations associated with entanglement. Personally, I think that the term ‘measurement’ has generated misunderstanding, and that it would be better simply to speak of verification of correlations.
The measurement problem of quantum mechanics is this: how does the entangled state of many possibilities collapse down to just one, and when does it happen? Is it when the pointer strikes the emulsion, or when the human observer sees a mark on the emulsion? I won’t go into all the complications, which depend on how much of the world we wish to describe quantum mechanically. It leads to a vicious infinite regress. You can go on asking quantum mechanics again and again to say when collapse occurs, but it never gives an answer. The different possibilities already represented at tset-up in the different positions of the object system can never be eradicated, and simply ‘infect’ the rest of the world – first the pointer, then the emulsion, then the retina of the experimentalist’s eye, finally his or her conscious state. All that the Copenhagen interpretation can say is that collapse occurs at the latest in the perceptions of the experimentalist. When it happens no one can say – it can only be said that if collapse does not happen we cannot explain the observed phenomena.
But must it happen? Everett came up with a simple – with hindsight obvious – alternative. Collapse does not happen at alclass="underline" the multiple possibilities represented in the entangled state continue to coexist. In each possibility the observer, in different incarnations, sees something different, but what is seen is definite in each case. Each incarnation of the observer sees one of the possible outcomes that the Copenhagen interpretation assumes is created by collapse. The implications of this are startling. A single atomic particle – the object particle in Figure 43 – can, by becoming entangled with first the pointer and then the emulsion, and finally the conscious observer, split that observer (indeed the universe) into many different incarnations. In his paper in 1970 that at last brought Everett’s idea to wide notice, Bryce DeWitt wrote:
I still recall vividly the shock I experienced on first encountering this multiworld concept. The idea of 10100+ slightly imperfect copies of oneself all constantly splitting into further copies, which ultimately become unrecognizable, is not easy to reconcile with common sense. Here is schizophrenia with a vengeance.
Everett’s proposal raises two questions. If many worlds do exist, why do we see only one and not all? Why do we not feel the world splitting? Everett answered both by an important property of quantum mechanics called linearity, or the superposition principle. It means that two processes can take place simultaneously without affecting each other. Consider, for example, Young’s explanation of interference between two wave sources. Each source, when active alone, gives rise to a certain wave pattern. If both sources are active, the processes they generate could disturb each other drastically. But this does not happen. The wave pattern when both sources are active is found simply by adding the two wave patterns together. The total effect is very different from either of the individual processes, but in a real sense each continues unaffected by the presence of the other. This is by no means always the case; in so-called non-linear wave processes, the wave pattern from two or more sources cannot be found by simple addition of the patterns from the separate sources acting alone. However, quantum mechanics is linear, so the much simpler situation occurs.
As a result, quantum processes can be regarded as being made up of many individual subprocesses taking place independently of one another. In Figure 43 the total process of the wave function ‘swinging round’ and becoming entangled is represented symbolically by the arrows as six individual subprocesses (or branches, to use Everett’s terminology). In all of them, the pointer starts in the same position but ends in a different position. Everett makes the key assumption that conscious awareness is always associated with the branches, not the process as a whole. Each subprocess is, so to speak, aware only of itself. There is a beautiful logic to this, since each subprocess is fully described by the quantum laws. There is nothing within the branch as such to indicate that it alone does not constitute the entire history of the universe. It carries on in blithe ignorance of the other branches, which are ‘parallel worlds’ of which it sees nothing. The branches can nevertheless be very complicated. An impressive part of Everett’s paper demonstrates how an observer (modelled by an inanimate computer) within one such branch could well have the experience of being all alone in such a multiworld, doing quantum experiments and finding that the quantum statistical predictions are verified.