5 The Incredible Quantum Mechanics
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and there is zero probability that it is located elsewhere. Our act of measurement has resulted in the wave function of the electron shrinking to the size
of the detector. In QM this is known as the collapse of the wave function.
To reiterate, up until the moment of detection we had no idea exactly
where the electron was located; instead our knowledge was confined to a
probability distribution that we obtained from the electron’s wave function,
showing the statistical likelihood of it arriving in each of the various detectors. After the moment of detection, we are now certain where the electron
is, and also, simultaneously, we are certain of where it is not, even if the other
detectors are far away from the first one. In the next Chapter, however, we
will learn that such a simultaneity is in conflict with Einstein’s Theory of
Relativity. This conflict remains one of the outstanding problems of modern
physics. We will discuss it in more detail in Chap. 6.
The issue of the collapse of the wave function caused by observation is
itself a controversial topic, and has been debated at length by philosophers
and physicists alike. The impression that the observer triggers the collapse by
the act of measurement attaches an anthropomorphic element to QM. An
extreme of this approach is the Many Worlds Interpretation of Hugh Everett,
who proposed in a Ph.D. thesis at Princeton in 1973 that the universe splits
into parallel divergent universes whenever a measurement is taken, each of
them bound to the choice of detector made by the arriving particle. This
proliferation of universes continues as time progresses, until essentially, somewhere at some time, there exists a universe where anything we can imagine is
possible. (Where is Occam’s Razor when you most need it?).
Part of the difficulty may lie with the tendency to interpret the wave
function as possessing a physical reality. Rather, it should be viewed as a
mathematical artifice that enables the calculation of the probable location
of the electron. If the electron is suddenly localised because of an experiment providing extra information (e.g. that the electron has been found in
detector No. 1), then clearly the probability distribution of the electron’s location needs to be updated (as there is now no probability of the electron
being located in other detectors). This is what we mean when we say that
the electron’s wave function has collapsed.
An intriguing puzzle that has been known to fool even professional mathematicians may cast a little light on the above situation. Known as the Monty
Hall problem after an American TV games show host, it runs like this: Contestants stand before three closed doors. Behind one of the doors is a car, while the
other two conceal booby prizes. The contestants choose one of the doors, hoping to
win themselves the car. The show host, who knows where the car is, does not open
the contestant’s choice, but opens instead one of the two other doors, revealing a
91
and there is zero probability that it is located elsewhere. Our act of measurement has resulted in the wave function of the electron shrinking to the size
of the detector. In QM this is known as the collapse of the wave function.
To reiterate, up until the moment of detection we had no idea exactly
where the electron was located; instead our knowledge was confined to a
probability distribution that we obtained from the electron’s wave function,
showing the statistical likelihood of it arriving in each of the various detectors. After the moment of detection, we are now certain where the electron
is, and also, simultaneously, we are certain of where it is not, even if the other
detectors are far away from the first one. In the next Chapter, however, we
will learn that such a simultaneity is in conflict with Einstein’s Theory of
Relativity. This conflict remains one of the outstanding problems of modern
physics. We will discuss it in more detail in Chap. 6.
The issue of the collapse of the wave function caused by observation is
itself a controversial topic, and has been debated at length by philosophers
and physicists alike. The impression that the observer triggers the collapse by
the act of measurement attaches an anthropomorphic element to QM. An
extreme of this approach is the Many Worlds Interpretation of Hugh Everett,
who proposed in a Ph.D. thesis at Princeton in 1973 that the universe splits
into parallel divergent universes whenever a measurement is taken, each of
them bound to the choice of detector made by the arriving particle. This
proliferation of universes continues as time progresses, until essentially, somewhere at some time, there exists a universe where anything we can imagine is
possible. (Where is Occam’s Razor when you most need it?).
Part of the difficulty may lie with the tendency to interpret the wave
function as possessing a physical reality. Rather, it should be viewed as a
mathematical artifice that enables the calculation of the probable location
of the electron. If the electron is suddenly localised because of an experiment providing extra information (e.g. that the electron has been found in
detector No. 1), then clearly the probability distribution of the electron’s location needs to be updated (as there is now no probability of the electron
being located in other detectors). This is what we mean when we say that
the electron’s wave function has collapsed.
An intriguing puzzle that has been known to fool even professional mathematicians may cast a little light on the above situation. Known as the Monty
Hall problem after an American TV games show host, it runs like this: Contestants stand before three closed doors. Behind one of the doors is a car, while the
other two conceal booby prizes. The contestants choose one of the doors, hoping to
win themselves the car. The show host, who knows where the car is, does not open
the contestant’s choice, but opens instead one of the two other doors, revealing a