At the beginning of the 1900's, a scientific revolution took place against the
traditional foundations of physics.
The usual ways, classical mechanics, appeared to be insufficient to explain
certain phenomena in the universe.
The most notable such problem was the blackbody-radiation conflict.
Imagine 
a hollowed out cavity with a tiny hole in the
side. Then a beam of light is shone
through the hole, and bounces off the sides until all the energy is eventually
absorbed
by the walls of the cavity. This blackbody will theoretically absorb
all the radiation that
enters into it, resulting in temperature increases in the walls. Experimenters
fiddled with close
models of blackbodies, and found the classical theories to disagree with the
obtained data. In classical physics,
thermal changes orginate from accelerated charged particles near the surface of
an object;
those charges emit radiation much like small antennae. Accordingly, the formula
applicable to a
blackbody was:
I(l,T) = 2pi * c * k * T/ l^4
where I(l,T) was defined as intensity of a region, k is Boltzmann's
constant, T is temperature,
l is the wavelength of the light (or radiation) that is used. Since
l is found
to be in the denominator, it is expected that as the wavelength becomes shorter,
the intensity should
approach infinity. Physically, an infinite energy in an electromagnetic field
is an impossible situation.
This contradiction was infeasible and was called the ultraviolet catastrophe..
Another baffling enigma for classical physicists was the photoelectric effect.
When light shines
on an evacuated-glass or quartz tube containing a metal plate connected to a
circuit. The photoelectric
plate acts as a resistor; when light shines on it, it allows current to pass
through more freely;
when it is dark, no electricity can pass through.
The incompatibilities of this effect
with classical thinkings include:
1. Below a cutoff frequency, the effect does
not occur
2. The maximum kinetic energy of photoelectrons increases with increasing light
frequency.
Hence, classical mechanics was found to be inadequate to explain a variety of
perplexities, not
limited only to those listed here. In resolving the problems, physicists found
a new realm they had
stumbled into.
This figure is from the page http://jersey.uoregon.edu/vlab/PlankRadiationFormula/
