|
We are all familiar with the motion of particles
from our every-day experience with solid objects. Like balls on a billiards
table, when two particles run into each other, they bounce apart. In contrast,
when two waves meet, they pass right through each other!
|
As the animation shows, when two waves overlap
they add up to form a larger wave (reinforcement). They can also cancel
out to form nothing at all (cancellation), or partially cancel to make
a more complex waveform. This is called interference.
When moving particles hit a gap in a barrier
they will generally trickle out in a thin stream, but waves will spread out
in every direction to form a circle. This is called dispersion.
|
|
|
If there are two gaps in the barrier, the two waves
will interfere to create an interference pattern. The pattern is formed
by alternating bands of wave reinforcement and cancellation. According to classical
laws, particles do not create an interference pattern. This setup is called
a double-slit experiment.
|
For all these reasons, at the beginning
of the 20th century everybody thought particles and waves were
totally separate phenomena. But that view had to change.
|
Photons: the Particle Nature of Light
|
|
At the beginning of the 20th century everyone thought
light was a wave. For most purposes physicists still think of light as an
electromagnetic wave traveling at 186,282 miles per second! The different colors
are just waves of different frequencies (most frequencies are invisible to our eyes).
|
However, one experiment could not be explained
by the wave model of light. When light is shined onto a metal plate, its energy is
transferred to electrons in the material, giving them enough velocity to
fly off of the plate. This is called the photoelectric effect.
|
|
|
According
to the wave model of light, the speed of the electrons should be related to
the intensity of the light. But that's not what happens. In reality
the speed of the electrons depends only on the frequency of light, and the light
intensity determines the number of electrons that fly off.
|
|
Einstein explained the photoelectric effect by showing that light came
in discreet particles called photons.
The energy of each photon depends on its frequency, and therefore when an electron absorbs a photon, the frequency
determines the electron's speed. Higher intensity means more photons, which means more electrons get to
absorb photons and fly off the plate. This was the birth of quantum theory.
|
|
|
When Einstein introduced the concept of photons,
he showed that waves could have particle aspects. 18 years later
Prince Louis de Broglie showed that every particle had wave aspects.
Combining the energy-frequency relation for photons
with Einstein's famous equation E=mc2, where "E" is energy,
"m" is mass and "c" is the speed of light, de Broglie argued that every particle had
a frequency, something only waves have.
|
|
This was hard to explain since particles are supposed to have an exact location, whereas
waves are spread over a range of locations. But remember that two waves can interfere to form another,
more complex wave. If we add enough waves together, we can make a wave packet
with a range of locations that's as small as we want.
This doesn't give a particle an exact location,
but it looks like an exact location and so explains why we see it that way.
|
|
The trick is that whenever we measure the position of the particle,
the range of locations narrows just enough so that we never see the wave, a process
called wave collapse. The reason we know the wave exists is because it determines the
possible range over which we might see the particle.
If this seems far fetched to you, you're in good company: what exactly happens
when a particle-wave collapses is still debated by physicists today. But it works,
so let's put off discussing wave collapse for a bit.
|
Recall the double-slit experiment from above, but this time let's do it with electrons,
which are one of the fundamental particles. On the other side of the barrier we put a screen
that emits light when an electron hits it. Now, the electron hitting the screen amounts
to a measurement of its position, so the electron-wave collapses and we only see a tiny speck.
But repeating this process many times creates an interference pattern! The
electron-wave is determining the possible range of locations: an electron is very likely
to appear at points of reinforcement, and has zero chance of appearing at points of cancellation.
|
|
|
|
Another phenomenon explained by the particle-wave is tunneling, which occurs when
a particle actually passes through a seemingly impenetrable barrier. When a particle
hits a barrier, it either has enough energy to break through or it doesn't and bounces back.
But with a wave, part of it can pass through while part of it is reflected, making it
possible for the particle to appear on the other side.
|
Since a particle is a wave, it simultaneously exists over a range
of locations. This range is called the uncertainty of the particle's position.
In the picture to the right,
the triangle in front of the "x" is the Greek letter delta. If "x"
stands for the particle's position,
then "delta x"
represents the range of possible locations for the particle, or the uncertainty of "x".
|
|
|
The narrower you want to make the range of positions,
the more waves you have to add together. This creates a wider range of wavelengths for
the wave packet. According to de Broglie, a particle's momentum (its speed times its mass)
is related to its wavelength. Therefore a narrow range, or small uncertainty, in position means a wide range,
or large uncertainty, in momentum.
|
Werner Heisenberg derived these uncertainty relations,
between position and momentum, and between
energy and time. The "h" is a number called "Planks constant"
(the line through it means divide by twice the number "Pi"). They put an absolute
limit on how much we can know about a particle.
|
|
|
de Broglie's wave also predicts the orbits of electrons in atoms. The radius of
an electron's orbit must be a multiple of its wavelength. Since its wavelength is
related to its energy, the electron can only have certain discreet values of energy.
We say that its energy is quantized.
|
To the right is shown the difference between the quantum and classical electron in an atom.
Classically the electron has a definite position, but in the quantum picture
the electron is in many places at once, spread out like a cloud.
The left picture shows several different configurations of electron-waves in a hydrogen atom.
The darker the area in the plot, the more likely it is that an electron will be there.
If a photon has enough energy, it can annihilate and create an electron
(e-) and its antiparticle,
the positron (e+), in its stead. The photon's energy is
converted into the mass of the
two particles according to E=mc2, and whatever energy is
left over goes into their speed.
This is called pair production. The positron, which is identical to the electron
but with positive charge, quickly collides with another electron and annihilates, creating
another photon.
|
|
|
You can interpret a positron as an electron traveling
backwards in time! In this picture, with time on the vertical axis, an electron comes in from the left
and reverses its direction in time, emitting a photon. soon afterwards
it emits a photon backwards in time (absorbs a photon) and resumes traveling forward in time.
To our eyes it looks like a photon comes in from the right, creates an electron and a positron by
pair production, and then the positron annihilates with an electron from the left, creating a photon.
|
|
|
We know that the de Broglie wave of a particle
exists because particles can form interference patterns. But we can never see the
wave because whenever we measure its position the wave collapses.
The most common interpretation is that
the particle doesn't have a definite position until we measure it.
|
Many physicists, including Einstein and
de Broglie,
found this interpretation unacceptable.
Erwin Schrodinger reasoned that if a particle can exist at both A and B in the picture above,
then a cat whose life depends on the particle being at A could be both dead and
alive until we look at it!
|
|
Physicists still don't agree
on how to interpret wave collapse.
Some claim that answering this question is a job for philosophers, not physicists.
Others insist that quantum theory is incomplete and are searching
for a deeper explanation of the world.
Still, everyone agrees that quantum theory works. We're just not quite sure what it means.
