34
leaping from one allowed orbit to another, emitting a packet of light to
S35
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T H E B IG PIC T U R E
01
make up the difference in energy between them. The electron is doing
02
“quantum jumps.”
03
•
04
05
Okay. Electrons don’t orbit atomic nuclei with any energy they like, as clas-
06
sical mechanics would have it. For some reason, they stick to certain al-
07
lowed orbits, with fixed energies. That seems to be a fact of enormous
08
significance, apparently incompatible with the Newtonian worldview that
09
had been utterly entrenched in the structure of physics. But the data should
10
always overrule our expectations; if certain fixed electron orbits are what
11
we have to imagine in order to explain the stability of tables and other ob-
12
jects made of atoms, let’s go with it.
13
The next question is: What makes an electron skip from one allowed
14
orbit to another? When does it happen? How does it know that it’s time?
15
Does the state of the electron contain information other than simply what
16
orbit it’s in?
17
It took quite a bit of genius and hard work to figure out the answers to
18
these questions. Physicists were forced to throw out what we mean by the
19
“state” of a physical system— the complete description of its current
20
situation— and replace it with something utterly different. What is worse,
21
we had to reinvent an idea we thought was pretty straightforward: the con-
22
cept of a measurement or observation.
23
We all think we know what those terms mean, but in classical mechan-
24
ics there’s nothing all that special about them. We can measure anything
25
we want about the system, as accurately as we would like, at least in prin-
26
ciple. Not so in quantum mechanics. First off, there are only certain things
27
we can measure at any one experiment. We can measure the location of a
28
particle, for example, or we can measure its velocity; but we can’t measure
29
both at the same time. And when we do make those measurements, only
30
certain results are allowed, depending on the physical circumstances. If we
31
measure the location of an electron, for example, it could be anywhere; but
32
if we measure its energy when it is orbiting inside an atom, only certain
33
discrete values will ever be obtained. (That’s where the word “quantum”
34
comes from, since in the early days of the field, physicists were extremely
35S
interested in how electrons behaved in atoms; but not all observables have
36N
discrete possible outcomes, so the name is something of a misnomer.)
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t h E Q uA n t u M R E A l M
In classical mechanics, if you know the state of the system, you can pre-
01
dict with certainty what any measurement outcome will be. In quantum
02
mechanics, the state of a system is a superposition of all the possible mea-
03
surement outcomes, known as the “wave function” of the system. The wave
04
function is a combination of every result you could get by doing an observa-
05
tion, with different weights for each possibility. The state of an electron in
06
an atom, for example, will be a superposition of all the allowed orbits with
07
fixed energies. The superposition representing a given quantum state might
08
be heavily concentrated on one specific outcome— the electron might be
09
almost perfectly localized in an orbit with some particular energy— but
10
in principle every possible measurement outcome can be part of the quan-
11
tum state.
12
Quantum mechanics is a profound change from classical mechanics,
13
whereby the outcomes of experiments are not perfectly predictable, even if
14
we know the state exactly. Quantum mechanics tells us the probability that,
15
upon observing a quantum system with a specified wave function, we will
16
see any particular outcome. We don’t lack perfect predictability because we
17
have incomplete information about the system; it’s just the best quantum
18
mechanics allows us to do.
19
This quantum probability is very different from ordinary classical un-
20
certainty. Think once again of playing poker. At the end of a certain hand,
21
your opponent makes a big bet, and you need to decide whether your hand
22
can beat theirs. You don’t know what their hand is, but you know what the
23
possibilities are: nothing, a pair, three of a kind, and so forth. Given their
24
behavior so far in the hand, and the odds that they received certain cards to
25
start, you can be a good Bayesian and assign different probabilities to the
26
various hands they could have. Quantum states sound kind of like that, but
27
they are crucially different. In the (classical) game of poker, you don’t know
28
what your opponent has, but they have something definite. When we say
29
that a quantum state is a superposition, we don’t mean “it could be any one
30
of various possibilities, we’re not sure which.” We mean “it is a weighted
31
combination of all those possibilities at the same time.” If you could some-
32
how play “quantum poker,” your opponent would really have some combi-
33
nation of each of the possible hands all at once, and their hand would
34
become one specific alternative only once they turned over the cards for you
S35
to look at them.
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