Eddington’s Selective Subjectivism (Part 5: Quantum Theory)

It might be useful at this point for me to reiterate Eddington’s view of post-classical physics.

He though that modern physics was not merely another step in the empirical program – an attempt to find universal patterns that are closer to the truth. No, he consider it to also herald the abandonment of the naïve presumption that we are studying the objective world. Instead, he supposes that quantum mechanics and general relativity have Kantian perspectives, whereby they admit we are merely studying our perception of the objective world.

According to the classical conception of microscopic physics, our task was to discover a system of equations which connects the positions, motions, etc. of the particles at one instant, with the positions, motions,etc. at a later instant. This problem has proved altogether baffling; we have no reason to believe that any determinate solution exists, and the search has been frankly abandoned. Modern quantum theory has substituted another task, namely to discover the equations which connect knowledge of the positions, motions, etc. at one instant with knowledge of the positions, motions, etc. at a later instant. The solution of this problem appears to be well within our power. (p 48)

From this perspective, the epistemological status of quantum mechanical probability becomes far less mysterious.

The mathematical symbolism describes our knowledge, and the mathematical equations trace the change of this knowledge with time. Our knowledge of physical quantities is always more or less inexact; but the theory of probability enables us to give an exact specification of inexact knowledge, including a specification of its inexactitude. The introduction of probability into physical theories emphasizes the fact that it is knowledge that is being treated. For probability is an attribute of our knowledge of an event; it does not belong to the event itself, which must certainly occur or not occur. (p 48)

Thus, for Eddington, the probabilities of quantum mechanics are not speaking about the physical world, but are speaking about our knowledge of this world. For, what is probability other than a self-aware and quantified declaration of ignorance?

Therefore, the ‘indeterminacy‘ of quantum mechanics is not an abandonment of methodological naturalism, nor a claim that the future is yet to be written. No, this admission of ignorance merely recognizes that we are afforded imperfect glimpses of the objective world. We can still seek to find patterns between our perceptions, but are limited, in some way, by how our sensory equipment interacts with the world.

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This view is rather different from my own. I have always thought of quantum mechanical probabilities as intrinsic probabilities, insofar as they are not a matter of ‘ignorance’, in the classical sense. If we knew everything there was to know about the a radioactive atom, there is still no way to tell exactly when it will undergo decay.

However, now I consider Eddington’s perspective, I realize that I have been confusing claims about knowledge with claims about the objective world. Surely I wasn’t claiming that the objective world decides at the last moment when the radioactive atom will decay!? No, it’s merely that the there is a limit to our knowledge of what will happen, and we are prevented from fully predicting the future.

…knowledge, however expressed, is inadequate to predict quantities which, independently of our frame of conception, can be directly observed when the time comes. (p 84-85)

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Eddington continues:

Wave mechanics investigates the way in which probability redistributes itself as time elapses; it analyses it into waves and determines the laws of propagation of those waves. Generally the waves tend to diffuse; that is to say, our knowledge of the position (or of any other characteristic) of a system becomes vaguer the longer the time elapsed since an observation was made. A sudden accession to knowledge – our becoming aware of the result of a new observation – is a discontinuity in the “world” of probability-waves; the probability is reconcentrated, and the propagation starts again from the new distribution. (p 48)

In this view, our theories of quantum mechanics predict the patterns between perceptions (what Eddington calls ‘knowledge’). And our ability to predict future perceptions tends to degrade with time. Therefore:

The statement often made, that in modern theory the electron is not a particle but a wave, is misleading. The “wave” represents our knowledge of the electron. The statement is, however, an inexact way of emphasizing that the knowledge, not the entity itself, is the direct object of our study (p 49)

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As for the role of observation, Eddington says that:

A “good” observation of a quantity, although it does not determine the quantity precisely, narrows down the range in which it is likely to lie. It creates a condensation in the probability distribution of the quantity or, as we usually say, forms a wave packet in it. The method of wave mechanics is to investigate the wave equations which govern the propagation of waves from such a source. (p 49)

And, there can only be ‘good’ observations; not ‘perfect’ ones. Our slicing of the objective world into variables has the consequence that it disqualifies us from making perfect observations. For whenever we try to measure such a variable, our apparatus disturbs the measurement.

It is well known that the interference of different kinds of measurement is the source of Heisenberg’s uncertainty principle, which is the epistemological gateway by which the probability conception enters quantum theory. (p 92)

Therefore, one should speak unashamedly about probabilistic physical theories – they are the only sort of theories that are possible.

Probability is commonly regarded as the antithesis of fact; we say “This is only a probability, and must not be taken as a fact”. But, if the answer of quantum theory is right, the “hard facts of observation” are probabilities. What we mean is that the result of an observation, though undoubtedly a fact in itself, is only valuable scientifically because it informs us of the probability of some other fact. These secondary facts, known to us only through probability, form the material to which the generalizations of physics refer. (p 83)

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Eddington then takes some time to demonstrate that it is not possible to rescue determinism from this new probabilistic physics. We might suppose, as many have before, that there is some way to find determinism by formulating a new perspective. So Eddington has his interlocutor say:

The results of observational measurement can be construed as a hazy and uncertain knowledge of the entities of classical physics; but does not that mean that we should abandon the classical entities, and introduce more fundamental entities of which observation gives us precise and certain knowledge? (p 83)

Here’s the trouble:

The result of an observation determines definitely a probability distribution of some quantity, or a modification of a previously existing probability distribution; but the connection is not reversible, and a probability distribution does not determine definitely the result of an observation. For an ordinary physical quantity there is no difference between making a new determination and verifying a predicted value; but for a probability the procedures are distinct. (p 85)

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Next, Eddington promises us a full exposition of his ‘selective subjectivism‘, and an argument that all of physics can be derived a priori. I look forward to more thought-provoking material in this second half of his book.