How Math Explains the World.pdf

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base coaching box (or the third-base coaching box, it doesn’t matter). A
coach can always tell when a runner has run past him—or whether no
runner has gone by. Similarly, a photon detector can determine whether a
photon has passed. This has a dramatic effect on the light pattern behind
second base; it now consists of two bright patches, indicating that the
photons have behaved as particles.

How Do Photons Know?
When obser ved (v ia a photon detec tor), photons behave as par t ic les. When
not observed (when there is no photon detector), photons behave as waves.
This is strange enough—how does a photon know whether it is being
observed or not? This is one of the riddles at the core of quantum me-
chanics, and it is a riddle that pops up in different guises.
Things get even stranger. In the 1970s, John Wheeler proposed a bril-
liant experiment, now known as a delayed-choice experiment. Position a
photon detector far away from “home plate,” and equip it with an on-off
switch. If the photon detector is on, the photons behave as particles, if it
is off, the photons behave as waves. This is essentially a combination of
the two previous experiments.
Wheeler’s suggestion was to turn the photon detector on or off after the
photon has left home plate. This is known as a delayed-choice experi-
ment, because the choice of whether to turn the detector on or off is de-
layed until after the photon has, presumably, already made its choice as to
whether to behave as a wave or a particle. There appear to be two possibil-
ities—the behavior of the photon is determined the instant it leaves home
plate (but if so, how does it know whether the photon detector is on or
off?), or the behavior of the photon is determined by the final state of
photon detector. If the latter is the case (as experiments conclusively
showed), the photon must simultaneously be in both states when it leaves
home plate, or is in an ambiguous state that is resolved when either it
passes the photon detector and learns it is being observed, or gets to sec-
ond base without having been observed.
As has been previously mentioned, the mathematical description of
quantum phenomena is done by means of probability. An electron, before
it is observed, does not have a definite position in space; its location is de-
fined by a probability wave, which gives the probability that the electron is
located in a certain portion of space. Before it is observed, the electron
is everywhere—although it is more likely to be in some places than oth-
ers. Additionally, in going from here to there, it goes via all possible routes
available in going from here to there! However, the observation process


All Things Great and Small 51 
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