that is, by the Doppler Effect for light, they must be moving away from us. This is
evidence that the universe is expanding, because within an expanding universe, all
galaxies would appear to moving away from each other. Astrophysicists have
attempted to use the equations of general relativity to explain this. Larger and larger
telescopes, which work by collecting more and more light in order to see distant
objects better, among other advances in telescope technology, have allowed for
more precise measurements that have continued to refine the science of astronomy.
After the development of general relativity, which described the very large, the
quantum mechanics of the 1920s came to describe the very small. After working on
the Bohr model of the atom, which accurately describes the emission spectra of the
hydrogen atom but seemed to be based on arbitrary postulates, Niels Bohr
continued to develop models of the atom. Louis de Broglie proposed that, since
light could be treated both as a stream of particles and as a wave, perhaps matter
could as well, so electrons might be able to be described by wave theory, and he
gave the equation for the wavelength of such waves. One practical application of
this is the electron microscope. Electron microscopes bombard very tiny objects
with magnetically-focused electrons (instead of the usual photons by which we
normally see things) and can get extremely high resolution because of the very
small wavelengths of such electrons. Erwin Schrödinger introduced the equation
that described the way the waves propagated in space and time. Werner
Heisenberg, who also developed an equivalent formulation of quantum mechanics
using matrix algebra, showed that the new quantum mechanics predicted that the
degree to which one knew the position of a particle was inversely proportional to
the degree to which one could, even in principle, know the momentum of a particle.
In other words, Heisenberg’s principle, called the Uncertainty Principle, says that
one cannot simultaneously know both where a particle is and where it is going to
arbitrary accuracy. Many others worked on quantum mechanics, including Wolfgang
Pauli, who stated the Pauli Exclusion Principle, that certain types of particles, such
as electrons, cannot be in the same quantum states.
One great success of quantum mechanics was in explaining superconductivity. The
resistivity of a material is slightly temperature dependent: An object will conduct
better at lower temperatures, and at very low temperatures (often only 20 or 30
degrees above absolute zero), the resistivity of some substances will drop to zero.
A material with zero resistivity and therefore zero resistance to electric current is a
superconductor. With quantum mechanics (and, frankly, a great deal of math),
superconductivity can be explained, a feat that classical electromagnetic theory
cannot duplicate.
Despite the tremendous successes of general relativity and quantum mechanics, the
history of physics is not over, since these two theories have not been successfully
united. Almost immediately after quantum mechanics was proposed, attempts began