## Saturday, June 16, 2012

### Spooky Action at a Distance

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 Spooky Action at a Distance

What is Spooky Action at a Distance?

The phrase “spooky action at a distance” comes from Einstein describing the idea, inspired by quantum mechanics, that in some cases measuring one particle can instantly (as in taking literally zero seconds) influence another particle regardless of how far away they are from each other, even if the two particles are light-years apart! The causal influence, if real, would be such that the cause is simultaneous with its effect. Stranger yet, one can’t exploit how this works to send an information signal faster than light. But how could the causal influence work this way and how is it we can have grounds for thinking this spooky action at a distance is real? In this article I’ll explain that, but to do that I’ll briefly introduce some simple quantum mechanics.

Introducing Some (Simple) Quantum Mechanics

Electrons have something called “spin,” a property that is not to be taken literally but in some ways electrons act as if they have spin. Along any given axis on which the spin of an electron is measured, an electron is either “spin up” or “spin down.” A Stern-Gerlach device is something that measures electron spin. This device can be rotated to measure an electron’s spin at any angle from 0 to 360 degrees, which allows for some interesting experiments. For example, suppose we have an electron passing through Stern-Gerlach devices which we can label #1 and #2. Suppose device #1 is titled at a 90 degree angle from device #2. If an electron measures “spin up” at Stern-Gerlach device #1, there is a 50% chance that this same electron will be measured as “spin up” by device #2 also. If we let Pr() symbolize “the probability that” we can let Pr(the measured spins are the same) represent “The probability that measured the spins are the same.” Given some angle A, the equation for how this works is given by the following:
Pr(the spins are the same) = cos2(0.5 × A)
That means we take cos(0.5 × A) and square it. In our case, the angle was 90°, and cos²(0.5 × 90°) = cos²(45°) = 0.5, and thus there’s a 50% chance that the measured spins will be the same between device #1 and device #2.

It’s possible to have a pair of electrons in a strongly correlated state so that when they fly apart from each other these two electrons have the interesting property such that if both have their first spin measurement be along the same axis, the spins will always be opposite of each other; these two electrons whose spins are correlated are “entangled.” If entangled electrons #1 and #2 have their spins measured on the same axis, then if #1 is measured as spin up then #2 will be measured as spin down. How is it that these spins are always opposite whenever the two electrons are measured on the same axis? One could say that the entangled electrons are in such a state that their spin measurements are in a sense “built-in” in advance. To help illustrate this I’ll symbolize three angles the Stern–Gerlach device can be used: let F represent an angle of 0°, L represent 120° (slanting upwards somewhat to the left), and R represent 240° (slanting upwards somewhat to the right). Let + represent spin up and – represent spin down. So an electron having a F+L–R– property means that if the electron were measured on the F axis the result would be spin up (+) and if the electron were measured on the R axis the result would be spin down (–).

Earlier I mentioned the probability of finding an electron’s spin being the same with a certain equation. Is this real randomness where identical physical conditions can produce different outcomes, or are there “hidden variables” that only make it look like it’s random? This is a matter of some controversy in philosophy of quantum mechanics that I won’t resolve here, but I can at least describe two (among many) different interpretations of quantum mechanics. The “hidden variable” theory says that the randomness is only apparent and that each electron has some property that deterministically determines the spin result before it enters the Stern-Gerlach device. For example, if an electron has a F+ property then it has the property that determines a “spin up” result if measured on the F axis. One version of hidden variable theory says that locality is true—which in this case means that a measurement on electron #1 has no physical effect on electron #2 (the denial of locality is called nonlocality). The conjunction of locality and hidden variable theory is called local hidden variable theory. So how does local hidden variable theory account for the electron spins always being opposite when the entangled electrons are measured on the same axis? By having the potential opposite spin results “built-in” in advance. So if electron #1 is F+L+R+, then electron #2 would be F–L–R– to guarantee that if the electrons were measured on the same axis the spin measurement results would be opposite. In contrast, something called the Copenhagen interpretation says (among other things) that the randomness is real and that when the two entangled electrons fly apart they don’t have a definite spin until measured, and the measurement randomly determines the spin of the electron. The Copenhagen interpretation also denies locality, unlike local hidden variable theory.

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