The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [85]
This process of calculating the clock (known in the jargon as the ‘amplitude’) for each Feynman diagram, adding all the clocks together and squaring the final clock to get a probability that the process will happen is the bread and butter of modern particle physics. But there is a fascinating issue hiding away beneath the surface of all that we have been saying – an issue that bothers some physicists a lot and others not at all.
The Quantum Measurement Problem
When we add the clocks corresponding to the different Feynman diagrams together, we are allowing for the orgy of quantum interference to happen. Just as for the case of the double-slit experiment, where we had to consider every possible route that the particle could take on its journey to the screen, we must consider every possible way that a pair of particles can get from their starting positions to their final positions. This allows us to compute the right answer because it allows for interference between the different diagrams. Only at the end of the process, when all of the clocks have been added together and all the interference is accounted for, should we square up the size of the final clock to calculate the probability that the process will happen. Simple. But look at Figure 10.2.
What happens if we attempt to identify what the electrons are doing as they hop to X and Y? The only way we can examine what is going on is to interact with the system according to the rules of the game. In QED, this means that we must stick to the electron–photon branching rule, because there is nothing else. So let’s interact with one of the photons that can be emitted from one or other of the electrons, by detecting it using our own personal photon detector; our eye. Notice that we are now asking a different question of the theory: ‘What is the chance to find an electron at X and another at Y and also a photon in my eye?’ We know what to do to get the answer – we should add together all of the clocks associated with the different diagrams that start out with two electrons and end up with an electron at X, another at Y, and also a photon ‘in my eye’. More precisely, we should talk about how the photon interacts with my eye. Although that might start out simple enough, it soon gets out of hand. For example, the photon will scatter off an electron sitting in an atom in my eye, and that will trigger a chain of events leading ultimately to my perception of the photon as I become consciously aware of a flash of light in my eye. So to describe fully what is happening involves specifying the positions of every particle in my brain as they respond to the arrival of the photon. We are sailing close to something called the quantum measurement problem.
Figure 10.2. A human eye taking a look at what is going on.
So far in the book we have described in some detail how to compute probabilities in quantum physics. By that, we mean that quantum theory allows us to calculate the chances of measuring some particular outcome if we conduct an experiment. There is no ambiguity in this process, provided we follow the rules of the game and stick to computing the probabilities of something happening. There is, however, something to feel uneasy about. Imagine an experimenter conducting an experiment for which there are only two outcomes, ‘yes’ and ‘no’. Now imagine actually doing the experiment. The experimenter will record either ‘yes’ or ‘no’, and obviously not both at the same time. So far, so good.
Now imagine some future measurement of something else (it doesn’t matter what) made by a second experimenter. Again, we’ll assume it is a simple experiment whose outcome is to make a ‘click’ or ‘no click’. The rules of quantum physics dictate that we must compute the probability that the second experiment goes ‘click’ by summing clocks associated with all of the possibilities that lead to this outcome. Now this may include