MJackson.Wbst@Xerox.ARPA (07/16/85)
OK, as threatened here is the thought experiment from the article in the
April /Physics Today/. If this summary is unclear, it's my fault, not
Mermin's.
We have three boxes:
A E B
A and B are similar; each has two light bulbs, red (R) and green (G),
and a three position switch {1, 2, 3}. E has a button. Shortly after
the button is pressed (essentially, time-of-flight delay at close to
lightspeed) one of the lights flashes on A and on B.
One can do the following experiment: set the switches at A and B at
random to some values, press the button at E, and record the color of
the lights that flash. Do this many times, yielding long columns of
data that look like "13GR" (which means the A-switch was set to 1 and
the A-box flashed green, while the B-switch was set to 3 and the B-box
flashed red).
You may take whatever precautions you like to assure yourself that the
only "communication" in the system is from E to A and B. (For example,
if you put a brick between A and E and push the button, a light flashes
at B only; no lights flash if the button is not pushed, etc. It is even
possible to arrange matters so that the setting of each switch changes
randomly *during the interval* between the pressing of the button and
the flashing of the light.) We might as well say that when the button
is pushed E emits a pair of particles which are detected at A and B.
Now look at the data. Suppose it is found to have the following
characteristics:
(1) Taken as a whole, the flashing of the lights is completely random;
in particular, half the time the lights flashed the same color and half
the time different colors. Call this Fsame = 1/2.
(2) However, *every* time the switch settings at A and B were the same,
the lights flashed the same color.
Although it may not be immediately obvious, there is no possible "local
realistic" explanation for this outcome. Given the precautions taken,
any relationship between the flashing lights at A and B must be due to
something about the particles emitted from E. In particular, (2)
demonstrates that each particle pair shares some characteristic which
determines which light flashes depending on the switch settings. It's
fairly easy to see that this can be expressed in general by saying that
each pair has a set of "instructions" of the form (RRG), where the
example means "flash red if switch = {1, 2}, flash green if switch = 3."
(Note that *every* particle pair must carry instructions, since E has no
way of knowing for which pairs the settings at A and B will be the same,
and all instructions must be for *all three* switch settings, since E
has no way of knowing at what value the settings will agree. This is a
very powerful constraint.)
Now there are eight possible instruction sets: {RRG, RGR, GRR, GGR,
GRG, RGG, GGG, and RRR}, and we haven't said anything about how the
signals from E are divided among them. What we do know is that the
switch settings were random, so the cases 11, 12, 13, 21, 22, 23, 31,
32, and 33 each occurred close to 1/9 of the time. However, for each of
the first six instruction sets listed the *same* light will flash for
five of the nine setting combinations. (Example: for RRG the results
are S, S, D, S, S, D, D, D, S). And for GGG and RRR the same light
flashes *all* the time. So *whatever* the distribution of instruction
sets emitted from E, the same light must flash not less than 5/9 of the
time:
Fsame >= 5/9 (a form of Bell's inequality)
This contradicts (1). Thus, under very general conditions having
nothing to do with the "mechanism" by which information is transferred,
it is demonstrated that (1) and (2) cannot both occur.
Now the point of all this is that there is a very straightforward
quantum mechanical situation in which (1) and (2) *can* both occur.
Without going into details, A and B contain three spin-measuring devices
oriented 120 degrees apart, the switches select among them, the lights
are reversed (red is up for one box and down for the other), and E emits
spin 1/2 particle pairs from an s = 0 state (so that the spins are
opposite). Under these conditions, the outcomes (1) and (2) are
predicted to occur. Experimentally, they have been *found* to occur as
described.
The reason this is so profoundly disturbing is what it means about what
we usually think of as "objective reality." When we set the A-switch to
1 and get R, that is an unambiguous determination that the particle was
in the 1-R state, and so was the other particle (since on all occasions
that we also measured its 1-state it is found to be the
same--characteristic (2)). So when we obtain the outcome 12RG, we know
the 1- and 2-states of both particles. But the 3-state cannot have
existed! For if it had, it was either R or G, which would mean that the
particles were either carrying RGR or RGG, but particles cannot carry
instruction sets if Fsame < 5/9. So the states *exist only if we
measure them*; it is *not* sufficient to say that "we just don't know
what the value was."
In a (now-out-of-date but still worthwhile) article in the November,
1979 /Scientific American/, Bernard d'Espagnat points out that the
demonstration of the "impossibility" of (1) and (2) occuring together
depends only on three very general principles: realism ("observed
phenomena are caused by some physical reality. . .independent of human
observation"), induction ("legitimate conclusions can be drawn from
consistent observations"), and Einstein locality. Evidently Einstein
was wrong; spooky actions at a distance are unavoidable.
Mark