This Quantum World

Meaning of "both"

Discussion, first conclusions, interpretational strategy

In rejecting Bohm's story, we reject the first of two assumptions that, together, are inconsistent with both quantum mechanics and the empirical data. (Bohmians reject the second.) Under the conditions stipulated by Rule B, it is not the case that each electron goes through a single slit — either L or R. In some sense, each electron goes through both slits.

In which sense?

Let us be clear that saying that the electron went through both slits cannot be the same as saying that the electron went through L and that it went through R. If we use a setup by which we learn (i) whether the electron went through L and (ii) whether the electron went through R, then we invariably obtain one positive and one negative answer (given that the electron passed the slit plate). We never get two positive answers.

Here is what saying that the electron goes through both slits can mean:

The electron goes through L&R — the regions defined by the slits considered as a single whole — without going through L, without going through R, and without getting divided in the process.

In other words, the proposition "the electron goes through L&R" is true while the propositions "the electron goes through L" and "the electron goes through R" lack truth values; they are neither true nor false but meaningless.

Without getting divided? Could it not be that one part of the electron goes through L while another goes through R?

Much the same interference pattern has been observed with C₆₀, a fullerene made of sixty carbon nuclei arranged like the 60 corners of an old-fashioned soccer ball. (Interference experiments with such "heavyweights" are done using diffraction gratings that contain a large number of slits. The larger the particles' mass, the closer the interference fringes. The effect of using a diffraction grating instead of a plate with just two slits is to sharpen the interference maxima, so they remain resolvable in spite of being closer.)

A bucky ball (inset: a soccer ball)

This answers our question. We don't picture parts of a C₆₀ molecule getting separated by many times the distance between slits (hundreds of nanometers) and then reassemble into a ball less than a nanometer across! Each molecule goes through a large number of slits as a single, undivided whole.

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