Some notes on Chapter 9: Our Skeleton in the Closet
This chapter is the one most often misunderstood. It’s easy to see why. First, Chapter 9 challenges our deepest intuition: that a physically real world exists independent of its observation. And, second, it presents material that is easily misinterpreted to unjustifiably extend the encounter with consciousness to magic. The purveyors of pseudo-science misappropriate this encounter to bolster their nonsense. And sometimes otherwise competent writers (intentionally?) unjustifiably extend these findings. Instructors should emphasize that the undisputed demonstrations say it all, at least everything we can be sure of.
Since Chapter 9 presents the unresolved enigma, we comment in these notes more about the material of this chapter than any other.
Chapter 9 presents our version of the 2-slit experiment. Feynman noted that the 2-slit experiment displays the entire mystery of quantum theory. (The EPR-Bell connectedness is implicit here in the collapse of the wavefunction, though it can only be displayed with multiple objects, as seen in our Chapter 13.)
Our use of “box-pairs” is a conceptual device. As we say in the book, there need not be actual boxes; a defined region of space is all that is needed to make the point. Thinking in terms of boxes allows us to (mentally) hold the object on the way to the detection screen for a long enough time for a person to make a free choice of whether to show thaat the object went on a single path or had been simultaneously on both paths (was wholly in a single box or was not wholly in a single box). The actually done “delayed choice” experiment (page 123) is essentially the box-pairs experiment, where the “free choice” is made rapidly by a random number generator.
To be clear that quantum mechanics applies not only to microscopic objects, we speak of the objects in our demonstration as “little green marbles.” And we say that if these “marbles” were as small as big molecules, that interference experiment has actually been demonstrated by Zeilinger with buckballs (C60 and C70 molecules). Forms of interference (quantum entanglement actually) is now being addressed for macroscopic objects, e.g., 1 mm^2 membranes, and now mirrors of several kilograms.
(Schrodingerís Drum, Physical Review Focus, 11 November 2008.
Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometery. Phys. Rev. Lett., 100, 013601, 11 Jan 2008.)
It’s worth strong emphasis that physicist’s demonstration of the quantum enigma is quantum-theory-neutral. The experimental facts themselves would display an enigma even if quantum theory were never invented. Therefore no mere interpretation of quantum theory can resolve the enigma. Even the development of a new theory is unlikely to resolve the enigma without revealing new (and, no doubt, amazing) physically observable facts.
The demonstration of the enigma is completely independent of the preparation of the box pairs. The enigma can be displayed by just presenting sets of box pairs without ever talking about their preparation. Just doing the experiments is enough.
It’s good to emphasize the contradictory nature of the result of either of the two free choices by noting that you can choose to demonstrate either that the object was wholly in a single box of its pair, or that it was not wholly in a single box of its pair, two clearly contradictory physical situations.
Even though it’s not the correct quantum mechanical picture, it sometimes can help to ask: “Is the object we sent into the box pairs something like a hard little marble or something like a fog ball that can separate at the semi-transparent mirror?”
The enigma depends on our assumption of free will, or what Bell calls the “free choice of the experimenter.” But abandoning that assumption in this case assumes a completely(!) deterministic universe. That is, we can’t evade the enigma by simply “denying free will” by saying the experimenter’s choice was determined by his brain electro-chemistry. To evade the enigma, we would have to assume that the experimenter’s apparently free choice of what to demonstrate strangely corresponds to what was actually in the particular set of box pairs, and everything related to that physical situation–essentially everything in the universe. A totally deterministic universe. Denial of this “free will” is a denial of what philosophers call “counterfactual definiteness.” It’s the meaningfulness of talking of what might have been done, but was not done, something we live our lives by. Chapter 15 has much more discussion of free will.
Since, by our choice of experiment, we can demonstrate that the object had been (randomly) in a particular single box of its pair, or that it had been distributed over both boxes, we create a history–backwards in time! We are more explicit about this with Schrodinger’s cat in Chapter 11, page 123.
When discussing in class the fact that the spacing in the (interference) pattern, “d,” depends on the spacing of the box pairs, “s,” (to establish that something came out of both boxes of each pair) we write d = f(s). We avoid this mathematical notation in the book.
This functional dependence, d = f(s), is all that is necessary to establish the enigma. The usual treatment of the 2-slit experiment talks of waves and interference (which we did in the previous chapter). But one actually just sees the relationship d = f(s). The wave idea is an extra theoretical construct, one not needed to establish the enigma. That is, we never see actual crests and troughs–either with the wavefunction, or with light waves.
However, a discussion of waves can relate the demonstration to the uncertainty principle and complementarity (discussed later). That is, establishing the object was in a single box essentially measures position. Establishing the interference pattern determines wavelength, therefore essentially momentum, the complementary variable. By choosing which experiment to do, we choose the basis, the Hilbert space.
To counter other possible objections to the object being totally inside the boxes, we note that nothing done in the region outside the box pairs (while the object is contained) affects any outcome.
We strongly emphasize in class what the demonstration does NOT establish. It does not say that “consciousness” (whatever that is) reaches out and does something physical (whatever that means)–even though we are admittedly left with an enigma that encounters consciousness (e.g., free will). We are not, for example, giving credence to “PK,” psychokinesis. Though we admit there is something here we don’t understand. (Feynman: “Nobody understands quantum mechanics.”)
Some pseudo-science treatments of quantum mechanics imply (some actually assert) that quantum theory tells us we can, by thought, bring about things we want. “Wealth and happiness,” for example. Maybe so. But the theory has a random aspect. (Which box, or which maximum of the interference pattern, the object appears in is random.) Therefore, according to quantum theory, that same kind of quantum thinking, instead of wealth and happiness, might bring about poverty and misery–or anything in between.
A student, who is a double major in both physics and film, is about to start producing a short movie based on the dialog sequence of Chapter 9. We expect it will be on YouTube and available on DVD for use in class.