Measurement is theory-laden part 3
August 26, 2013 Leave a comment
In my two previous posts in this series I pointed out that measurement is theory laden: you need an explanation of what is happening to bring about the results. Without such an explanation you can’t work out what the results of a measurement mean.
One example where I think naive ideas about measurement have caused problems is in quantum mechanics. Many physicists seem to think that when you do a measurement the measurement has to reveal a complete picture of the state of the system being measured and otherwise it just doesn’t count. So if I see my toothbrush sitting in a plastic tumbler on my right then that measurement has the outcome it does because that’s where the toothbrush is and that’s all there is to it. In quantum mechanics measurement just doesn’t work that way.
According to quantum mechanics, there are multiple versions of the toothbrush and of everything else. Those multiple versions form layers that are approximately dynamically isolated from one another – they act like parallel universes. The whole of physical reality, which includes those parallel universes, but also has richer structure, is called the multiverse. A lot of physicists seem to think that they don’t actually see multiple versions of the brush, only one version exists and quantum mechanics must be modified to take account of this. However, quantum mechanics accounts for the fact that I only see one version of the brush without eliminating the other versions. What happens is that when I see the brush different versions of the brush produce different versions of me and those different versions of me can’t interact with one another directly. So there is no conflict between the existence of multiple versions of the brush and the fact that I only ever see one version of the brush.
The next thing physicists often say when they hear this explanation is that if I can only ever see one version of the toothbrush then the existence of the multiverse makes no difference to anything. One problem with this idea is single particle interference. That is, we can do experiments in which a single particle behaves as if there are multiple versions of it going along all of the possible paths through an experiment and those different versions interact with one another but we only ever see one of them at the end of the experiment. Are we supposed to think that all the versions we didn’t see just vanish at the end of the experiment, even when quantum mechanics implies that they don’t?
There are also experiments with macroscopic systems that can’t be explained without the multiverse, such as the EPR experiment. In one version of the EPR experiment, two photons are produced by the same source at the same time and head in different directions. Let’s call one of the photons photon A and the other photon B. A photon has a property called polarisation that has some similarities to angular momentum. In particular we can measure the polarisation along different directions. We measure the polarisation along a particular direction with a filter that only lets through photons polarised in that direction. For each photon, regardless of the direction in which we measure the polarisation the probability of it going through the filter is 50%. If we measure the polarisations of A and B along the same direction then we find that they match. If we measure the polarisations along different directions we find that they don’t match with a probability that depends on the angle between the directions in which we measure the polarisations. So whether the polarisations are later found to match or not depends on whether two detectors happen to have the same setting. We can put the detectors far enough apart so that no signal can travel at or below the speed of light from one to the other during the detection process. Some physicists have decided that this means the photons influence one another by some faster than light means during the detection process. Since the probability of any given measurement result on a single photon doesn’t depend on what happens to the other photon, there is no way to use this supposed link to send messages but nevertheless many physicists seem to think the link exists. This leads to a lot of confusion about how quantum mechanics can be consistent with relativity. This confusion is entirely unnecessary because the EPR experiment can be explained without any nonlocality.
The two photons are generated in the same process at the start of the experiment t = 1 and so the multiversal description of photon A at t=1 depends on the multiversal description of photon B at t=1. After they part the photons fly apart and evolve independently of one another. They then get measured. This, too, is an entirely local process with no funny business involving photons magically influencing one another. I’ll start by discussing photon A: everything I say about photon A applies to photon B with the photons labels switched around. What happens is this: the multiversal description of the measuring device for photon A comes to depend on the multiversal description of photon A. Since the multiversal description of photon A depends on that of photon B at t = 1, the multiversal description of the measuring device for photon A also depends on the multiversal description of photon B at t=1. Exactly what information about photon B is transmitted by photon A to the measuring device depends on what happens to photon A between the t=1 and when the measurement process is over. Now regardless of exactly what polarisation observable we choose to measure in 50% of the universes the photon goes through and in 50% it doesn’t. However, the multiverse doesn’t just consist of parallel universes and some of the multiversal information contained in photon A, including the information it contains about photon B, isn’t revealed by the measurement on photon A alone, i.e. – it isn’t reflected in the way the multiverse locally differentiates into non-interacting parallel universes. What happens instead is that hidden information is transmitted to the measuring device and then to other systems that interact with the measuring device and at some point in the future the information from photon A is transmitted to some system that contains information from measurements on photon B and the measuring results from photons A and B become correlated due to the hidden multiversal information the two photons contained about one another. The precise pattern of the correlation depends on what multiversal information was transmitted by each photon to the measuring devices and so depends on what happened to them between t=1 and when they were measured.
For more technical detail see Information Flow in Entangled Quantum Systems and Does Quantum Nonlocality Exist? Bell’s Theorem and the Many-Worlds Interpretation.
What is needed to understand measurement in quantum mechanics is a more subtle idea about the role measurement plays in our understanding of the world. A measurement is an interaction whose results are relevant to whether we should accept or reject a theory. This doesn’t require that there is only one version of me after the measurement. A theory should be judged by whether it is a good explanation and whether it successfully predicts the results of experiments, not by whether it matches a naive and parochial intuition about how measurement should work.