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21 19
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h .eysics majors taking their first college courses
2422
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2523
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2624
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2725
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2826
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mödinger, who later became
2927
famous for torturing cats in thought experiments. (Not real cats, it should
3028
be emphasized.) Here i i
t is, i t Ψ
n it
s mos Ĥ
t ge Ψ
ne r . al form:
31 29
3230
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33 31
stsattaet. Th
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The left
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3432
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35S33
ereartasito
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sft at‑ taheta i
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36N
34
over time?” The right‑ hand side provides an answer, by doing a certain op‑
35S
eration on the state itself. It’s parallel to Newton’s famous “force equals
36N
16
1 4
6 4
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t h E Q uA n t u M R E A l M
mass times acceleration,” in which forces determine how the system changes
01
through time.
02
Evolution according to the Schrödinger equation is very much like the
03
evolution of a state in classical mechanics. It is smooth, reversible, and com-
04
pletely deterministic; Laplace’s Demon would have no problem predicting
05
what the state would be in the past and future. If that were all we had to the
06
stor
y, quantum mechanics wouldn’t be problematic.
07
But there is also an entirely different way the quantum state can evolve,
08
according to the textbook treatment: namely, when it is observed. In that
09
case, we teach our undergraduates, the wave function “collapses,” and we
10
obtain some particular measurement outcome. The collapse is sudden, and
11
the evolution is nondeterministic— knowing what the state was before, you
12
can’t perfectly predict what the state will be afterward. All you have are
13
probabilities.
14
Despite the appearance of probabilities, the predictions of quantum me-
15
chanics can be extraordinarily precise. For example, we can measure the
16
strength of the electromagnetic interaction by one kind of experiment, such
17
as how an atom recoils when it emits a photon. Then we can use that mea-
18
surement to predict the outcome of a different experiment, such as how
19
fast electrons precess in a magnetic field. Finally, we can compare that
20
prediction to an actual observation. The resulting agreement is breathtak-
21
ingly good:
22
23
Observation/ Prediction = 1.000000002.
24
25
The observed and predicted values aren’t exactly the same, both because
26
of experimental error and because of theoretical approximations. But the
27
lesson is clear: quantum mechanics isn’t some loosey- goosey, anything- goes
28
kind of operation. It is relentlessly specific and unforgiving.
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30
31
32
33
34
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02
03
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04
05
Interpreting Quantum Mechanics
06
07
08
09
10
11
12
13
14
15
16
17
W hat really bothers us about quantum mechanics is that the
word “observer” appears in the theory at all.
What counts as an “observer” or an “observation” anyway?
Does a microscope count, or does a conscious human being have to be using
18
it? What about a squirrel, or a video camera? What if I just glance at the
19
thing rather than observing it closely? When exactly does the “wave func-
20
tion collapse” take place? (So you’re not kept in suspense, almost no modern
21
physicist thinks that “consciousness” has anything whatsoever to do with
22
quantum mechanics. There are an iconoclastic few who do, but it’s a tiny
23
minority, unrepresentative of the mainstream.)
24
Together these issues are known as the measurement problem of quan-
25
tum mechanics. After fretting about it for decades, physicists still don’t
26
agree on how to address it.
27
They have ideas. One approach is to suggest that while the wave func-
28
tion plays an important role in predicting experimental outcomes, it doesn’t
29
actually represent physical reality. It might be that there is a deeper way of
30
describing the world, in addition to the wave function, in terms of which
31
the evolution would be in principle completely predictable. This possibility
32
is sometimes called the “hidden variables” approach, since it suggests that
33
we just haven’t yet pinpointed the real way to best describe the state of a
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