How Math Explains the World.pdf

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and he and physicists Boris Podolsky and Nathan Rosen devised, in 1935,
a thought experiment, known as the EPR experiment,^10 that challenges
the idea. Einstein, Podolsky, and Rosen objected to the concept that be-
fore the measurements, neither spin is known. Suppose two groups of
experimenters, light-years apart, set out to measure the spins of these
photons. If the spin of photon A is measured, and seconds later the spin
of photon B is measured, quantum mechanics predicts that photon B
would “know” the result of the measurement on photon A, even though
there would not be enough time for a signal from photon A to reach pho-
ton B and tell photon B what its spin should be!
According to Einstein, this left two choices. One could accept the so-
called Copenhagen interpretation of quantum mechanics, due primarily
to Niels Bohr, that photon B knows what happened to photon A even with-
out a signal passing between them. This possibility, corresponding to
“intuition” in Lower Wobegon, is doubtless the reason that quantum me-
chanics seems to open the door to mysticism in the real world. After all,
what could be more mystical than knowledge of what happens to another
body without a measurable transmission of information? Alternatively,
one could believe that there is a deeper reality, manifested in some physi-
cal property as yet unfound and unmeasured, which would account for
this phenomenon—this corresponds to “rehearsed answers” in Lower
Wobegon. Einstein died holding f irmly to this latter view, which is known
in the physics community as “hidden variables.”


Bell’s Theorem
More than a hundred papers were written between 1935 and 1964 dis-
cussing the pros and cons of the hidden variables explanation, but these
were just discussions and arguments—until the Irish physicist John Bell
came up with a highly ingenious experiment that would subject the hid-
den variables theory to an actual test. Bell suggested that the experiment
should consist of an apparatus that could measure the spin of each pho-
ton around one of three axes. The axis for each photon would be randomly
selected, and the spins of the two photons recorded. These measurements
would be recorded as pairs: the pair (2,L) indicates that axis 2 was selected
for measurement and the photon was spinning left around this axis.
Suppose that the two entangled photons are each imprinted with the
following program: if axis 1 or axis 2 is selected, spin to the left; if axis 3
is selected, spin to the right. Assuming the axis for each photon is ran-
domly selected, there are nine possible choices of axes, just as there
were nine possible choices of questions for the two pollsters in Lower


All Things Great and Small 61 
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