The Science Book

205

law of thermodynamics remained
valid, Boltzmann’s reading gave
it a probabilistic, rather than an
absolute, truth. Thus, we observe
entropy simply because it is
overwhelmingly more likely than
the alternative. A plate breaks but
does not remake itself, but there
is no absolute law preventing a
plate from putting itself back
together—it is just exceedingly
unlikely to happen.

Quantum of action
Planck used Boltzmann’s statistical
interpretation of entropy to arrive at
a new expression for the radiation
law. Imagining thermal radiation as
being produced by individual
“oscillators,” he needed to count the
ways in which a given energy could
be distributed between them.
To do this, he divided the total
energy into a finite number of
discrete energy chunks—a process
called “quantization.” Planck was a
gifted cellist and pianist and might
have imagined these “quanta” in
the same way that a fixed number
of harmonics is available to the
vibrating string of an instrument.
The resulting equation was simple,
and it fit the experimental data.

Introducing “quanta” of energy

reduced the number of states of

energy available to the system,

and in doing this (although it

wasn’t his goal), Planck solved the

ultraviolet catastrophe. He thought

of his quanta as a mathematical

necessity—as a “trick”—rather

than something that was real. But

when Albert Einstein used the

concept to explain the photoelectric

effect in 1905, he insisted that

quanta were a real property of light.

As with many of the pioneers

of quantum mechanics, Planck

spent the rest of his life struggling

A PARADIGM SHIFT

Max Planck Born in Kiel in northern Germany

in 1858, Planck was an able pupil

at school and graduated early,

at 17. He chose to study physics at

the University of Munich, where

he soon became a pioneer of

quantum physics. He received

the Nobel Prize in Physics in 1918

for his discovery of energy quanta,

although he never was able to

satisfactorily describe the

phenomena as a physical reality.

Planck’s personal life was

beset by tragedy. His first wife

died in 1909, and his eldest

son was killed in World War I.

Both of his twin daughters died

giving birth to their children.

During World War II, an Allied

bomb destroyed his house in

Berlin and his papers, and in the

closing stages of the war, his

remaining son was caught up in

the plot to assassinate Hitler

and was executed. Planck

himself died soon after the war.

Key works

1900 Entropy and Temperature

of Radiant Heat

1901 On the Law of Distribution

of Energy in the Normal

Spectrum

to come to terms with the

consequences of his own work.

While he was never in any doubt

about the revolutionary impact

of what he had done, he was—

according to historian James

Franck—“a revolutionary against

his own will.” He found the

consequences of his equations

not to his taste since they often

gave descriptions of physical reality

that clashed with our everyday

experience of the world. But for

better or worse, after Max Planck,

the world of physics has never

been the same. ■

The ultraviolet catastrophe was a

nonsense result predicted by classical

physics (shown here as the Raleigh–

Jeans Law) in which black-body radiation

increased exponentially as its wavelength

shortened. By quantizing radiation,

Planck produced a formula that fit the

experimental data.

1000

Rayleigh–

Planck Jeans Law

Radiation

Formula

Wavelength of radiation (nm)

Radiation intensityVisible light

2000 3000