On Philosophy

June 5, 2007

Materialism And The Bare Theory

Filed under: Metaphysics,Mind — Peter @ 12:00 am

The bare theory is the simplest no-collapse interpretation of quantum mechanics that makes all the correct predictions and is compatible with general relativity. Thus from the standpoint of physics the bare theory is attractive, since it solves all the major problems of quantum mechanics. However, it seems that the bare theory has unacceptable philosophical consequences, because it seemingly does away with the existence of determinate experiences, and thus with determinate measurements, and makes saying that we have a certain probability of experiencing a particular outcome without meaning. But I claim that with the addition of a relatively uncontroversial materialistic understanding of the mind the bare theory is converted into a many minds type interpretation, without altering any of the mathematics. This resolves the apparent philosophical problems, leaving us with a theory that has neither major physical nor philosophical difficulties. Thus the bare theory plus a little simple philosophy of mind seems like the best interpretation of quantum mechanics.

The relatively uncontroversial materialistic understanding of the mind that I will rely on here is simply the identification of consciousness with some functional properties of a system. Of course there is disagreement as to which functional properties are to be identified with consciousness, but it is fairly obvious that if the mind is material (some thing we have very good reason to believe due to causal closure) then it must be reducible to functional properties in some way. As far as we are concerned here all that this means is that if we notice that sate A, state B, and state C occur in sequence (what they are describing the state of doesn’t matter), A-B-C is a sequence that can be described as conscious, and the sequence occurs because of the functional properties of A B and C (A contributed to bringing about B and B contributed to bringing about C) then we have an A-B-C consciousness present.

As a first step let’s give this example a quantum formulation, but one in which there are no superpositions involved, and hence in which it is certain that experience and consciousness are determinate. So we have U1*|A>|…> = |B>|…> and U2*|B>|…> = |C>|…>. All this says is that the time evolution operators U1 and U2 transform a complex state that can be at least partly described by A into one that can be at least partly described by B and then into C. So here we have in quantum terms the classical case where the A-B-C consciousness is determinately present and has determinate experiences. Now let us consider what happens when a more complicated superposition obtains, α*|A>|…> + β*|…>. U1*(α*|A>|…> + β*|…>) = α*U1*|A>|…> + β*U1*|…> = α*|B>|…> + β*U1*|…>, because U1 is a linear operator. And to get to the next moment we take U2*(α*|B>|…> + β*U1*|…>) = α*U2*|B>|…> + β* U2*U1*|…> = α*|C>|…> + β* U2*U1*|…>. As you can see even when we are considering a superposition the A-B-C sequence still holds, and the sequence occurs because of the functional properties of the states. So even though the A-B-C sequence is part of a superposition the A-B-C consciousness still is present, with the same contents as it had before (because the content of consciousness is determined by the nature of A B and C, and those are unchanged). Just as part of a larger system may have the right functional properties for consciousness and thus be conscious, so may part of a larger superposition. When you think about it this isn’t a very surprising result at all.

Once we see that part of a superposition may be conscious independently of the rest of the superposition then the existence determinate experience and measurements is easily recovered. Since the same consciousness may be present both when it describes a feature of the entire quantum state or simply a part of it (as the A-B-C example above demonstrates) and since the content of that consciousness is dependant on the functional properties captured by the description then that consciousness is just as determinate when it exists because of functional properties of part of the quantum state as when it is determined to exist by the properties of the entire quantum state. Or, in other words, from the point of view of that consciousness it makes no difference whether it is part of a superposition or not, it experiences the same things in both cases. And if consciousness is determinate in this way (i.e. always experienced as determinate) then we can trivially recover what it means for a measurement to be determinate, relative to that consciousness.

That at least is the obvious part. The more difficult task is to explain why we perceive quantum probabilities as we do. As things stand we have accepted that in a superposition such as α*|A> + β*|B> the A part and the B part may contain one or more consciousnesses, which have determinate experiences and are basically independent (as far as their experiences are concerned) of the other terms of the superposition. How the coefficients of each term of the superposition, α and β come into play has so far been left out of the explanation, because in most cases they are irrelevant to conscious experience. Even if the coefficient of the term of the superposition that your consciousness supervenes on is very small it makes no difference to you, your experiences are the same no matter what the coefficient is, so long as it isn’t zero. But to explain the role that coefficients play we must first take a detour back to the way we think about ordinary consciousness and functional properties.

Let’s say that system X has functional properties Q. And suppose that X is a macroscopic system, meaning that Q is determined by the large scale operation of X (this is true of the human brain, consciousness is determined by the functional properties of the neurons, not individual atoms and electrons). So consider the system made up of half the particles of X, evenly distributed throughout it, called X1, and another composed of the remainder called X2. It is likely that both X1 and X2 have the functional properties Q. And we can also consider systems Xa, Xb, and so on, each of which is X minus a few atoms. Each of these systems is distinct and each has functional properties Q. How many copies of Q are present, and if Q makes X conscious what is that like? Such questions are based on faulty intuitions, namely that functional properties are like countable things, they are not, they are a kind of abstraction. As a analogy consider a red ball. Clearly each half of the ball is red, as is any arbitrary part of it, but asking how many reds are present in the ball is an ill-conceived question. In terms of the content of consciousness the number of ways in which the functional properties can be said to be instantiated is irrelevant, the content of consciousness is determined by the functional properties themselves, not how much redundancy there is in them.

So such considerations have no bearing on the content of consciousness, what it is like to be such a system, etc. But suppose that X1 and X2 somehow diverged, so while they agree up until some time, there is a later time where X1 is thinking about A and X2 is thinking about B, and in this case let us suppose that X1 is 80% of the particles that make up X and X2 is the remaining 20%. Suppose that you are such a system before such a divergence occurs. What is the chance that you will find yourself to be thinking about A in the future? It is best to reason as follows: if the right kind of functional properties holds for some division of the world for a period of time we can consider that division of the world to have a consciousness for that period of time determined by those functional properties. Each division can be said to be a separate consciousness even though different divisions may have the same functional properties and thus be in another sense the same consciousness (the are different instances of the same consciousness). Now as far as personal identity goes it usually makes sense to identify with the abstract consciousness, which may have more than one instance (in fact usually does, as the reasoning here shows). But in this case it is best to identify with one particular instance, although you know not which one, since each instance does have its own viewpoint, its just that the viewpoint of the instances are identical in every way except in which particles they supervene one. We then estimate that 80% of the instances will follow the X1 path. Since we don’t know the particular instance that we are, and can’t even determine it in principle, we thus estimate that there is an 80% probability that we will end up experiencing A.

Now what we have said about this non-quantum case we can carry directly over to the quantum case. Let’s say that |A> is a quantum state which contains a consciousness, and let us further say that it will later evolve into the quantum state α*|B> + β*|C>. What is the probability that the consciousnesses at A will later find themselves experiencing being in the |B> part of the superposition rather than the |C> part? Well, like before we have to consider how many ways in which the functional properties we are interested in are present in |A>. Here things are a bit more complicated since |A> can also be expressed as ε*|A> + ε*|A> + …, and each of these 1/ε parts will have the same functional properties (because the time evolution operator is linear) and hence each will instantiate the relevant consciousness. And ε can be as small as we like. But we can do away with this complexity simply by realizing that the quantum state is a vector, and so the number of ways in which consciousness is instantiated in part of a superposition is proportional to how much that part of the superposition contributes to the total quantum state vector. In the case of |B> that would mean that it is proportional to |α|2 and in the case of |C> it is proportional to |β|2. Given that |A> is the entire quantum state, and thus the ways in which the relevant functional properties can apply is proportional to 1, this gives us the correct probabilities by the same reasoning we used above in the non-quantum case.

So, to put a finish on this rambling exposition, simply adding a well thought out, but generic, doctrine of mental materialism to the bare theory resolves its philosophical problems. As demonstrated it recovers determinate experience and measurements, and we can see that the probability that we will experience a particular event occurring agrees with the predictions made by the standard collapse theory and confirmed experimentally.

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