12.5. PROBABILITY WAVES: QUANTUM PHYSICS 187
Gravity is the key that makes the dynamics of a galaxy fundamentally different from the
kind of action that occurs in, say, a wave on a vibrating violin string. For the string, one small
piece can directly affect only its immediate neighbors. But each individual star in a galaxy, al-
though it most strongly affects that which is closest to it, puts gravitational forces on distant
stars as well. And so gravity allows distant parts of a galaxy to affect each other directly on a
global as well as local scale.
is long-distance action of gravity fundamentally changes the nature of wave phenom-
ena, and allows for the possibility of a spiral density wave. As orbiting stars and nebulae approach
the density wave, they slow down, and so bunch up slightly, making a denser region. is denser
region triggers star formation, and that part of the galaxy lights up. It is the most massive and
luminous of these newly-formed stars that provides the most light; a single O star can out-
shine a million Suns. Since these stars don’t live long, they are only found in regions of ongoing
star formation. And so the slight increase of density in the spiral wave pattern creates the very
high-luminosity stars that make the spiral arms visible.
12.5 PROBABILITY WAVES: QUANTUM PHYSICS
e view of light as an electromagnetic wave is wildly successful, able to predict and explain
a wide range of phenomena in precise detail. But by the end of the 19th century, it became
increasingly clear that some experiments defied explanation with Maxwell’s equations alone.
e blackbody spectrum of Section 12.2.3 is a good example.
e solid black line in Figure 12.12 shows the spectrum of a 5000 K blackbody as predicted
by the electromagnetic theory of the late 19th century, and it is a catastrophic failure of agreement
between theory and experiment. At the dawn of the 20th century Max Planck demonstrated
that the observed shape of the blackbody spectrum could be explained only if one assumed that
energy came in discrete clumps, or quanta. is Planck quantum hypothesis was the first step in
the development of quantum physics, and the idea was extended by Einstein and others to form
the modern concept of the photon—a particle of light. And so although we observe the spectrum
emitted by a blackbody as a wave phenomenon, the fact that light can act as individual particles
is essential to its creation.
e particle and wave descriptions of light are connected by Equation (12.13):
E D hf D
hc
: (12.13)
Here c is the speed of light and E represents the energy of an individual photon when the light
is acting as a stream of particles. When the same source of light is acting instead like a wave, it
has a frequency, f , and a wavelength, . Put another way, a source of light of wavelength can
be seen as made of individual photons, each of which has energy, E, given by Equation (12.13).
is particle model of light is necessary in order to provide a physical basis for the non-
thermal spectra described in Section 12.2.5. And so physicists of the early 20th century were
188 12. WAVES
UV VISIBLE INFRARED
0
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0 0.5 1 1.5 2 2.5 3
5000 K
4000 K
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Spectral radiance (kW · sr
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Classical Theory (5000 K)
Figure 12.12: e curved marked “classical theory” shows how badly theory fit the data before
the development of quantum physics. (Graphic by 4C, CC BY-SA 3.0.)
faced with a dilemma. On the one hand, light clearly does the things that waves do—and so in
that sense it is a wave. On the other hand, there are many experiments for which a strictly wave
explanation fails miserably, but that are explained quite naturally when light is instead assumed
to be comprised of discrete photons. And so in these circumstances there is an important sense
in which light is a stream of particles.
Later evidence showed that this wave-particle duality extends to ordinary matter as well as
light. We want to think of electrons, for example, as discrete particles of matter. But sometimes
their actions can be explained only if they are assumed to act like waves. One of the first suc-
cessful theoretical explanations for these rather odd observations is the wave mechanics of Erwin
Schrödinger, published in 1926.
In Schrödinger’s theory, even when light (or matter) acts as a stream of particles, there
still is a wave. is abstract wave function is not directly observable. But for any particular well-
defined system, it evolves with time in a determined way, governed by the Schrödinger equation.
e trick is that although the wave function is not observable, it is related to the proba-
bility—the likelihood—of a particular observation being made at some place and time. And so
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