The walking stick analogy

One of Bohr’s favorite analogies for the “new situation we face in quantum mechanics” is the case of the walking stick. He mentions this analogy in a couple of his written works (see below), and several of his acquaintances later recounted his using this analogy with them. (TO DO: reference these other articles.) In what follows we’ll first explain the analogy, and then we’ll raise some questions about what it’s supposed to show.

Before we put the analogy on the table, recall that Bohr said some — to many of us mysterious — things about there being a movable dividing line between subject and object. So please keep in mind the following picture.

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In the analogy, we have a person holding a walking stick, and two scenarios. In the first scenario, the person is holding the walking stick firmly and using it to feel (i.e. “measure”) the shape of some other objects (e.g. the furniture in a dark room). In the second scenario, the person is holding the walking stick quite loosely — in fact, it is more accurate to say that the person is not holding the walking stick, but feeling (i.e. “measuring”) it with his fingers.

Here is how Bohr describes the two scenarios:

In the first scenario, the human being and the stick together are the subject, and the atom is the object. In other words, the stick is part of the subject. While Bohr did not live long enough to follow discussions in analytic philosophy of science, his description of this first scenario is very much like Grover Maxwell’s argument against the observation-theory distinction (Maxwell 1962). The point, in short, is that what counts as observable depends on what we count as belonging to the subject, and there is no in principle reason to restrict “the subject” to the physical flesh of a human being. Think especially of eyeglasses, binoculars, or microscopes. A person with eyeglasses (to correct their vision) is no doubt a subject — the eyeglasses are part of the subject. So why wouldn’t we count a person with binoculars as a subject? That was Maxwell’s point, and we feel sure that Bohr would have agreed with him.

In the second scenario, the person is touching the stick — but the stick is no longer to be counted as part of the subject. Why not? If we were thinking in a purely metaphysical mode, we might be completely baffled at this point. What counts as a single entity? In both cases (first and second scenarios), the person is touching the stick. Why in the first scenario is the stick part of the subject, but not in the second scenario? Should we appeal to something like the strength of the binding forces between them?

No, that’s not how Bohr is thinking of the example. What constitutes a subject is not a fact about the subject-less ontology of the world: it is partly up to the subject him/herself to determine what is part of him/her. For example, if someone tells me that I’m just a certain bag of bones, then I could cut my pinky finger off — and then the subject has a different constitution. Or, less violently, I could put on a pair of gloves.

This is not very different from Kant’s problem of the unity of consciousness.¹ What makes a single subject? Nobody has a good answer to that question, but one thing that Bohr insists on is that the subject is not a transcendental, disembodied entity. The subject corresponds to some physical stuff, it’s just that the boundary of this stuff is determined by a unity of consciousness that all of us experience, and that nobody has been able to derive from physics or any other empirical science.

Sources

Bohr uses the walking stick analogy first in an article from 1929.

The relativity of our perception of motion, with which we become conversant as children when travelling by ship or by train, corresponds to common-place experiences on the reciprocal² character of the perception of touch. One need only remember here the sensation, often cited by psychologists, which every one has experienced when attempting to orient himself in a dark room by feeling with a stick. When the stick is held loosely, it appears to the sense of touch to be an object. When, however, it is held firmly, we lose the sensation that it is a foreign body, and the impression of touch becomes immediately localized at the point where the stick is touching the body under investigation. (Bohr 1934, p 99), a translation of (Bohr 1929)

Relativity theory

The measuring device is quantum

There’s a common misunderstanding of Bohr’s point of view: that he thought that the world can be divided up into a quantum part and a classical part. Well, there is a sense in which that is true, viz. Bohr thinks that the self-understanding of the subject is given in ordinary language supplemented by the terminology of classical physics. Bohr doesn’t have an argument for why that is true; he just says it happens to be the case for human beings.

However, the stick analogy shows, among other things, that Bohr believes that the “ontological type” of the subject is no different than the ontological type of atoms, viz. mostly correctly described by quantum physics. In the second scenario, the stick (read: measuring device in first scenario) belongs to the object that is being measured. But the object being measured is subject to the laws of quantum mechanics, hence the stick is subject to the laws of quantum mechanics. Or to put it in a different way: the object has states that can be superposed, and can be entangled with other objects. Hence the stick has states that can be superposed, and can be entangled with other objects.

Finally, what’s true about the stick is true about every part of the original subject, without remainder. Hence, the original subject is ontologically of the same type as atoms — it has states that can be superposed, and it can be entangled with other objects.