22 August 1934
I just received Nathan’s latest results, and needless to say, I am dismayed. He suggests we publish now, as “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” The Physical Review will take it for Spring. But I am not ready to give up just yet.
The non-local effects remain deeply worrysome. Again and again, it comes down to this: Either the result of a measurement performed on one part A of a quantum system has a non-local effect on the physical reality of another distant part B, in the sense that quantum mechanics can predict outcomes of some measurements carried out at B; or QM is incomplete. There’s no way out of it. Two horns of a dilemma.
Speaking of horns – I have one more thought experiment, based on recent readings in the Babylonian Talmud. (Did Elsa mention I was studying? A pleasant diversion.) On the Day of Atonement, the High Priest performs a lottery to choose two he-goats, one of which is designated to be sacrificed as a sin offering, and one of which is sent off to the wilderness as a form of collective communal expiation. The goats must be qualitatively identical – of the same appearance and size, and purchased simultaneously. (Again simultaneity! – Minkowski would be pleased.) They are distinguished from one another only from the moment that the High Priest performs a lottery—playing dice, again–to determine which one will be for the sin offering (let’s call it A), and which one will be sent off to the wilderness (B).
Until the instant the lots are drawn, A is both A and B; and B is both A and B. Or, as E.S. would have it, the goat is both alive and dead. The wave (“tenufah”) function does not collapse until the instant the lottery is performed in the Inner Innermost.
If, following the lottery, one goat dies, the other goat automatically loses its status. A is not A if not for B. They exist thus in quantum entanglement. The consequences are manifold. For instance, if A dies, we must perform another lottery to yield an A’ and B’. (The no-cloning theorem, like the rabbinic principle known as “sh’vut,” does not exist in the Temple.) By virtue of the existence of B’, A is restored as A. (Others say A’ replaces A – an unresolved dispute.)
The goats remain in this state of quantum entanglement until death, though they are separated far from each other and all effects are non-local. B is sent to the wilderness, accompanied by a special messenger. The messenger’s job is to push B off a cliff, where it is smashed to the rocks below.
At the moment that B is torn limb from limb, A also loses its spin singlet; it is, at that very instant, slaughtered by the High Priest. But how does he know the exact moment in which to slaughter? Several of the rabbis resist the possibility of a hidden variable, claiming, for instance, that the other priests in the temple would time the distance traveled by B by the speed of their own pacing. (This is the opinion of Rabbi Yehuda.) But Rabbi Yishmael maintains that there is spooky action-at-distance in the form of a crimson thread hung from the door of the sanctuary. At the moment that B tumbles to its death, the thread turns white and the goat is slaughtered. As it is written: “Though your sins be as scarlet, they shall whiten like snow” (Isaiah 1:18).
What to make of this spooky action-at-a-distance? Have we no choice but to resist the conclusions of special relativity, allowing for the travel of information from B to A faster than the speed of light? Can the quantum-mechanical description of reality only thus be considered complete?
Boris, my friend, I cannot abide by Nathan’s decision. The Physical Review may have its submission deadlines, but I insist we wait. Elijah will come from a distance and resolve the quantum quandaries.
Cordial greetings, yours,