Hey it's professor Dave, let's talk about
the ultraviolet catastrophe.
We know that the classical physics of
Newton and pals reigned supreme for a
few centuries, so what were the events
that finally exposed its limitations?
What was the first thing that suggested
there was more to the universe than we
had previously thought? This seismic
shift was initiated in 1901 when Max
Planck solved something called the
ultraviolet catastrophe. The problem went
like this. Certain objects are called
blackbodies because they emit
electromagnetic radiation of all
wavelengths. The sun is an example of
such an object, and we can take a look at
the distribution of the wavelengths of
light that we receive from the sun.
Most of it is in the visible spectrum, which
is why our eyesight evolved to pick up
this kind of light, but we also receive
light on either side, in the UV portion
as well as infrared and beyond. A hot
piece of metal will also do this, and
this was the way we studied blackbodies
at the time, noting that the distribution
depends not at all on the material but
only on temperature, with the particular
wavelength that is emitted with maximum
intensity shifting left as temperature
increases. This maximum will move into
the visible spectrum at around 4000
Kelvin and above. This is why very hot
objects appear to glow, like a hot oven,
light bulb filament, or the sun and other
stars, because objects at these
temperatures emit a lot of visible light,
as opposed to something like the human
body, which at around 310 Kelvin, emits
essentially no visible light, which is
why we can't see each other in the dark.
The problem with the blackbody spectrum
was that classical electromagnetism
could not account for it. Mathematical
models attempting to produce these
distributions were able to fit the data
for the longer wavelengths, but they did
not predict that the intensity would dip
down to the left
for the UV portion of the spectrum as
experimental data Illustrated. Instead,
the math predicted that the intensity
would continue to increase as the
wavelength decreased, and become
infinitely large as the wavelength
approached zero. Of course, we know that
this can't be true, otherwise every time
you use the oven you would get blasted
with UV radiation. This contradiction was
dubbed, somewhat dramatically, the
ultraviolet catastrophe. In science, if
a theory does not accurately align
with observations of reality, it must be
revised, and so we realized that
classical electromagnetism, as powerful
as it is, must have some kind of
limitations in its ability to describe
light and energy. As we said, Max Planck
solved this problem, and he did so by
introducing a concept called
quantization. We know from classical
physics that heat is just the transfer
of kinetic energy from one place to
another. In the case of a piece of solid
hot metal, that kinetic energy takes the
form of atomic vibrations or
oscillations. These vibrations are what
generate the light we see in the
blackbody spectrum. Planck proposed that
the vibrational energies of these atoms
and by extension the energies of the
electromagnetic waves emitted by these
atoms must be quantized, meaning that
rather than being able to take on any
value from a continuous series, they can
only possess specific discrete values
from a set of accepted values. In this
way he developed this expression for
blackbody radiation, where energy is
equal to n, which can be any integer,
times h, a term we call Planck's constant
equal to 6.626 times 10^-34
joules seconds, times f, the
frequency of radiation. The n value is
what results in quantization, as it can
only be an integer, and not any fraction
or decimal in between, meaning that the
resulting energies will also comprise a
set of allowed values, with anything in between
being forbidden. This application of
quantization and the accompanying
Planck's constant were developed in ad
hoc manner, meaning that they were simply
proposed for practical purposes, but they
allowed for the accurate prediction of
the true distribution of blackbody
radiation at all wavelengths, which meant
that this constant was more than a
mathematical fluke, but a clue as to the
fundamental nature of reality, and the
fact that Planck's constant is so
incredibly small explains why the notion
of quantization of energy had not
cropped up before, because it shows that
energy is quantized on such an
incredibly small scale that the
gradations between the allowed values
are utterly miniscule so as to appear
non-existent to any measuring apparatus.
Energy appears to be continuous to
macroscopic beings such as humans but on
the fundamental level it is indeed
quantized, even though this conclusion
was so strange that most scientists of
the time, including Planck, couldn't
believe that it had actual concrete
physical meaning. This was the first time
that quantization had solved such a big
problem in physics, but it wouldn't be
the last. It was the first in a series of
developments that would utterly
transform the field of physics, and by
extension, our perception of reality.
While Planck's work solved one problem it
created another. Why is there
quantization of energy? This marked the
beginning of the quantum revolution, so
let's continue and see what happened next.
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