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 ...''
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:
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.
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.
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)?