P & P, commentary P.

Mon Feb 24 22:30 PST 1997 Particles and Paradoxes, a commentary

``Since ontology and epistemology are obviously the two most interesting questions of Philosophy, we shall engage both of them ...''

Introduction

Peter Gibbins' text Particles and Paradoxes, the Limits of Quantum Logic focuses on issues in the philosophy of physics, particularly the challenges presented by quantum mechanics. The book seems a bit unsure of its focus, sometimes appearing to be an introduction to physics for philosophers and sometimes an introduction to philosophical issues for physicists. In general, it assumes that the reader already has a fairly solid grounding in the ideas and formalisms of quantum mechanics, and thus can be fairly heavy going.

There are two general questions (and an intermediate sub-question) at which I am hoping to get in our reading and discussion:

What is the character of existence (of fundamental particles)? I am sure we are all at least vaguely familiar with the quantum mechanical notion of wave/particle duality. Fundamental particles (electrons, protons, neutrons, photons) sometimes behave as waves, and sometimes as particles. One might ask, ``Well, what is their real nature, as opposed to their occasional appearance/behavior?'' Implicit in this question is the covert assumption that there actually is a `real nature' to which we have only partial access, which is sometimes revealed to us in wave-like form and sometimes particle-like. This general approach to understanding the paradoxical mysteries of quantum mechanics is frequently called the hidden variable interpretation (whose greatest champion was Albert Einstein). A primary alternative view (which actually seems to be the most widely accepted view by physicists today) is generally termed the Copenhagen interpretation (developed and championed by Niels Bohr and his colleagues at the Institute for Theoretical Physics in Copenhagen from about the mid 1920's). The Copenhagen interpretation in essence says that there is nothing more to be known about a quantum system than what quantum mechanics itself can tell us (not just that we have trouble getting the information, but that it isn't there to get!).

(Sub-question) What about the Heisenberg uncertainty principle? In its most familiar and accessible form, the Heisenberg uncertainty principle asserts that we cannot simultaneously know precisely the position and velocity of a particle. The `popular science' explanation of this impossibility of knowledge (which is consistent with, and often covertly evokes, the hidden variables notion) is that in order to `read off' the position or velocity we must disturb the system by some experimental procedure (e.g., shoot a photon, which imparts energy and leaves the particle in a new, unknown, state). Physicists (and Gibbins) talk instead of the indeterminacy relations and, following the Copenhagen interpretation, suggest that the particle simply has neither a precise position nor precise velocity, and that the imprecisions of the two are related to each other. This sub-question, for me, floats in the middle ground between between the first and third, having to do both with what there is to know (about particles) and how (or how much) we can know it.

What about quantum logic? Quantum mechanics seems to come equipped with a `logic' which has strange and disturbing characteristics. As an heuristic example to evoke some of the difficulties, consider the classically `true' assertion . Now suppose we ask the question ``Is an electron a particle or not?'' Quantum mechanics refuses to answer the question (under the Copenhagen interpretation, denies that there is an answer!). This naive (but still troubling) example expresses some of the paradoxical feeling of quantum mechanics, but really does little more than point the way towards the rigorous formal quantum logic which is the primary subject of Gibbins' book.

Let me proceed with some discussion of these issues, and try to do some brief annotation of the portions of Gibbins' book which you have.

Existence

It is (seems?) obvious that the yellow car in my driveway exists, whether or not I (or anyone else) am there to observe it. It collects the dust stirred up when the fields are plowed, and is still there in the morning. We live and act under a realist worldview. Things are there. They have properties, which we can discover or detect, and they have those properties whether or not we engage in an experiment to detect them. Quantum mechanics (under the Copenhagen interpretation of Bohr), on the other hand, presents a very different picture. The Copenhagen interpretation is, in Gibbins' word, antirealist. Our experience of the world consists of phenomena where, in Gibbins' interpretation of Bohr,

The `phenomenon', in this usage, means the whole experimental arrangement. The individual quantum system on which a measurement is performed is, in Bohr's view, an abstraction. We cannot assign properties to it as such. We can only assign properties to it in the context of a measurement. This is not to say that the measurement `creates the property' (say, of having a position). Nor is it to say that the position of the electron is a logical construction from, or is reducible to, statements about the measuring apparatus. Rather, talk of the position of an electron has sense only in the context of an experimental arrangement for making a position measurement.

The thesis of the essential indivisibility of the quantum phenomenon is not a piece of idle holistic metaphysics in Bohr's philosophy, though metaphysics it certainly is. It is a piece of working metaphysics. It plays a decisive role in Bohr's response to EPR. [Gibbins, 59]

More explicitly, Bohr says

...any observation of atomic phenomena will involve an interaction with the agency of observation not to be neglected. Accordingly, an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation. [Gibbins, 55, from ...]

But where does this leave us? Suppose, for argument, that atomic phenomena do not have `an independent reality' (do not actually exist, in the traditional sense?). What does that imply about the existence of my car? Is my car not made of atoms? Does quantum mechanics only apply in physics labs to isolated simple atomic phenomena? Does physics (qua quantum mechanics) have nothing to say about real-world things like cars? Perhaps in some obscure way subatomic particles do not have an independent reality, but as we go up in scale to atoms to molecules to cars the property of `existence' mysteriously appears ...

There is also the second half of Bohr's assertion: that an independent reality cannot be ascribed to the `agencies of observation' - to us. How does it all get started? From whence the original `experimental arrangement'?

One might argue that these objections show that quantum mechanics is just wrong, but it does have the redeeming characteristic of making the best experimental predictions of any physical theories at hand.

Logic

Perhaps more disturbing than the doubts about existence hinted at above are the doubts raised about logic. As philosophers, we habitually take classical logic, with its propositions, connectives, truth functions, quantifiers and deductions, completely for granted. When confronted with a new idea, we apply logic to evaluate it. We test it for (logical) consistency. We accept it if it can be proven, reject it if it can be disproven.

What then happens if the new idea is a new `logic'? Quantum logic seems to be incompatible with classical logic, but it also seems to be the logic of the `real' world, at least to the extent that quantum mechanics is about and reflects the real world. Is the incompatibility just apparent, or is it real?

Consider, for comparison, the relationship between (classical) newtonian mechanics and relativity theory. In conception, the two are incompatible (they can't both be `true'), but in practice they are compatible since in slow-moving (non-relativistic) situations, the predictions of the two theories agree. Similarly, quantum mechanics and everyday observations seem to be (physically) compatible, since the statistical experimental predictions of quantum mechanics for large scale systems agree with what we observe in everyday life. There is a `limiting process' in each case which allows compatibility.

On the other hand, as Gibbins says:

There is nothing like the correspondence principle in logic. This is a point worth emphasizing. Logic cannot `go over to distributivity' in the limit of large quantum numbers. The failure of the distributive law in quantum logic does not depend on size, it depends only on Planck's constant being nonzero, and between zero and nonzero there is an absolute discontinuity. [Gibbins, 143]

Gibbins also notes that (using arguments couched in classical logic!):

We could try comparing the corresponding truth tables, if it were agreed what these should be in the case of quantum logic, which it is not. (...) But if we do compare truth tables we can say that, given reasonable assumptions, the quantum logical connectives cannot be truth functional, whereas the classical connectives of course are. (...) quantum logical disjunction and negation cannot both be truth functional and two-valued. [Gibbins, 155]

This raises the specter that logic itself, `truth' and `falsity', is not analytic or a priori, but rather empirical, to be found in the world. If that is the case, though, what methods do we have for evaluating rival `logics'? If quantum logic (or something else?) is the `real' logic of the world, why do we feel so comfortable with classical logic? Is the world `inconsistent', with several different and incompatible logics applicable in different contexts (and how would we know which logic to apply when)?

Tom Carter

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