Principles and Concepts
of Quantum Physics
of Quantum Physics
Implications of
Quantum Physics
Quantum Physics
16A. Details of Problems with Probability.
Summary
The limits on interpretations of quantum physics given by the probability law are considered in detail.
Attempts to put probability in QMA. One might be tempted to argue that the probability comes in the assignment of my perceptions to the perceptions of one of the versions; sometimes my perceptions correspond to those of version
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Correlation between the coefficients and our perceptions. By looking at a particular case, we can see the problem with probability in QMA from a different and perhaps more compelling perspective. Suppose we consider a two-state system,
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Now we know that each of these versions is equally valid (that is, of equal perceptual status) in the sense that (1) each has a valid version of the brain wave function and (2) each version is, within QMA, equally aware (see below). But we know experientially that my perceptions will (almost always) correspond to only one of them, the one with all ten outcomes 1. That is, one version from among all the 1,024 versions is (almost always) singled-out as the one corresponding to my experiential perceptions. Conversely, my perceptions never correspond to one of the 252 versions of the observer that perceives five outcomes 2.
Thus there is a correlation between the coefficients and my perceptions, a correlation which cannot be deduced from the tenets of QMA because perception has no coefficient-dependent or probabilistic characteristics in QMA. Something outside QMA must be responsible for this correlation.
Adding the probability law as an assumption? Suppose we try an interpretation, QMB, which consists of QMA plus the assumption that the probability law holds. This is an allowable interpretation, but it is, in my opinion, unsatisfactory. Why? Because the above argument (principle [P18]) implies there must be some ‘mechanism,’ outside QMA, which is responsible for the correlation, but the simple assumption says nothing about the mechanism. The assumption says, in effect, that the ‘my perception’-coefficient correlation is simply a law of nature.
It seems to me, however, that an interpretation is incomplete if it doesn’t specify the mechanism responsible for the correlation. It seems appropriate to require that a completely satisfactory interpretation explain why our perceptions never correspond to those states with very small amplitudes. Just saying it’s a law of nature leaves the central mystery unexplained. It’s like saying the wavelengths of light emitted by hydrogen atoms follow a regular pattern simply because it’s a law of nature, rather than looking for an underlying explanation.
So I view QMB as only a temporary, unsatisfying interpretation which we use until we understand the cause of the perception-amplitude correlation.
Singling out. The above reasoning shows that there is a correlation between the coefficients and my perceptions. This would almost certainly seem to imply that one version of the observer is singled out as the one whose perceptions correspond to mine. This in turn implies there is a unique me (instead of the many versions of me in QMA). Because no version is singled out in QMA, there must be some non-QMA ‘mechanism’ at work here (see the Probability Law and the Mind-MIND interpretation).
All Versions of the Observer Are Equally Aware.
When we perceive the results of an experiment with many potential outcomes, we are consciously aware (however you wish to define that) of one and only one outcome. So we might expect that one and only one version of the observer is aware in quantum physics. But we will show here that that is not the situation in the QMA (no particles, no collapse, no sentient beings) interpretive scheme; all versions are equally aware.
From the point of view of neuroscience or philosophy, what is meant by awareness or consciousness is not so easy to pin down. But we can define it in a general way that is suitable for our purposes here. The state vectors are all that exist in QMA, and so awareness can only correspond to some property—synchronous oscillations of many regions of the brain, for example—of the wave function of the observer’s brain or brain-body.
To see what happens to the observer’s awareness when a measurement results in several simultaneously existing versions of the observer, we consider an experiment on an atomic system with K states,
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But from our experience of awareness, that is not an allowable outcome; we are always aware of a result. So the only way the time evolution can be made consistent with the at-least-one-aware requirement is to suppose the observer state vector
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Comment: There is one way the above argument could fail and that is if the awareness-distinguishing feature is carried by the apparatus or the atomic system. Then the distinguishing feature could be transferred to the observer state vector in the transition from (16A-3) to (16A-4). But a singling-out of this sort amounts to a hidden variable theory (one version ‘physically’ distinguished from the others), and that is forbidden by hypothesis in this section.