**What is Quantum Physics?**

Quantum physics is a branch of
science that deals with discrete, indivisible units of energy called quanta as
described by the Quantum Theory. There are five main ideas represented in
Quantum Theory:

- Energy is not continuous, but comes in small but
discrete units.
^{1} - The elementary particles behave both like particles
*and*like waves.^{2} - The movement of these particles is inherently random.
^{3} - It is
*physically impossible*to know both the position and the momentum of a particle at the same time. The more precisely one is known, the less precise the measurement of the other is.^{4} - The atomic world is
*nothing*like the world we live in.^{5}

While at a glance this may seem like
just another strange theory, it contains many clues as to the fundamental
nature of the universe and is more important than even relativity in the grand
scheme of things (if any one thing at that level could be said to be more
important than anything else). Furthermore, it describes the nature of the
universe as being much different than the world we see. As Niels
Bohr said, "Anyone who is not shocked by quantum theory has not understood
it." ^{6}

**Particle/Wave Duality**

Particle/wave duality is perhaps the
easiest way to get aquatinted with quantum theory because it shows, in a few
simple experiments, how different the atomic world is from our world.

First let's set up a generic
situation to avoid repetition. In the center of the experiment is a wall with
two slits in it. To the right we have a detector. What exactly the detector is
varies from experiment to experiment, but its purpose stays the same: detect
how many of whatever we are sending through the experiment reaches each point.
To the left of the wall we have the originating point of whatever it is we are
going to send through the experiment. That's the experiment: send something
through two slits and see what happens. For simplicity, assume that nothing
bounces off of the walls in funny patterns to mess up the experiment.

First try the experiment with
bullets. Place a gun at the originating point and use a sandbar as the detector.
First try covering one slit and see what happens. You get more bullets near the
center of the slit and less as you get further away. When you cover the other
slit, you see the same thing with respect to the other slit. Now open both
slits. You get the sum of the result of opening each slit. ^{7} The most bullets are found in the middle of the
two slits with less being found the further you get from the center.

Well, that was fun. Let's try it on
something more interesting: water waves. Place a wave generator at the
originating point and detect using a wave detector that measures the height of
the waves that pass. Try it with one slit closed. You see a result just like
that of the bullets. With the other slit closed the result is the same. Now try
it with both slits open. Instead of getting the sum of the results of each slit
being open, you see a wavy pattern ^{8}; in the center there is a wave greater then the sum of what appeared there each time only one slit
was open. Next to that large wave was a wave much smaller then what appeared
there during either of the two single slit runs. Then the pattern repeats;
large wave, though not nearly as large as the center one, then small wave. This
makes sense; in some places the waves reinforced each other creating a larger
wave, in other places they canceled out. In the center there was the most
overlap, and therefore the largest wave. In mathematical terms, instead of the
resulting intensity being the sum of the squares of the heights of the waves,
it is the square of the sum.

While the result was different from
the bullets, there is still nothing unusual about it; everyone has seen this
effect when the waves from two stones that are dropped into a lake in different
places overlap. The difference between this experiment and the previous one is
easily explained by saying that while the bullets each went through only one
slit, the waves each went through both slits and were thus able to interfere
with themselves.

Now try the experiment with
electrons. Recall that electrons are negatively charged *particles* that
make up the outer layers of the atom. Certainly they could only go through one
slit at a time, so their pattern should look like that of the bullets, right?
Let's find out. (NOTE: to actually perform this exact experiment would take
detectors more advanced then any on earth at this
time. However, the experiments have been done with neutron beams ^{9} and the results were the same as those
presented here. A slightly different experiment was done to show that electrons
would behave the same way ^{10}. For reasons of familiarity, we speak of
electrons here instead of neutrons.) Place an electron gun at the originating
point and an electron detector in the detector place. First try opening only
one slit, then just the other. The results are just like those of the bullets
and the waves. Now open both slits. *The result is just like the waves!*^{11}

There must be some explanation.
After all, an electron couldn't go through both slits. Instead of a continuous
stream of electrons, let's turn the electron gun down so that at any one time
only one electron is in the experiment. Now the electrons won't be able to
cause trouble since there is no one else to interfere with. The result should
now look like the bullets. But it doesn't! ^{12} It would seem that the electrons do go through
both slits.

This is indeed a strange occurrence;
we should watch them ourselves to make sure that this is indeed what is
happening. So, we put a light behind the wall so that we can see a flash from
the slit that the electron went through, or a flash
from both slits if it went through both. Try the experiment again. As each
electron passes through, there is a flash in only one of the two slits. So they
do only go through one slit! But something else has happened too: *the result
now looks like the result of the bullets experiment!!* ^{13}

Obviously the light is causing
problems. Perhaps if we turned down the intensity of the light, we would be
able to see them without disturbing them. When we try this, we notice first
that the flashes we see are the same size. Also, some electrons now get by
without being detected. ^{14} This is because light is not continuous but
made up of particles called photons. Turning down the intensity only lowers the
number of photons given out by the light source.^{15} The particles that flash in one slit or the
other behave like the bullets, while those that go undetected behave like waves^{16}.

Well, we are not about to be
outsmarted by an electron, so instead of lowering the intensity of the light,
why don't we lower the frequency. The lower the frequency the less the electron
will be disturbed, so we can finally see what is actually going on. Lower the
frequency slightly and try the experiment again. We see the bullet curve ^{17}. After lowering it for a while, we finally see
a curve that looks somewhat like that of the waves! There is one problem,
though. Lowering the frequency of light is the same as increasing it's wavelength ^{18}, and by the time the frequency of the light is
low enough to detect the wave pattern the wavelength is longer then the distance between the slits so we can no longer see
which slit the electron went through ^{19}.

So have the electrons outsmarted us?
Perhaps, but they have also taught us one of the most fundamental lessons in
quantum physics - an observation is only valid in the context of the experiment
in which it was performed ^{20}. If you want to say that something behaves a
certain way or even exists, you must give the context of this behavior or
existence since in another context it may behave differently or not exist at
all. We can't just say that an electron is a particle, since we have already
seen proof that this is not always the case. We can only say that when we
observe the electron in the two slit experiment it behaves like a particle. To
see how it would behave under different conditions, we must perform a different
experiment.

**The Copenhagen Interpretation**

So sometimes a particle acts like a
particle and other times it acts like a wave. So which is it? According to Niels Bohr, who worked in Copenhagen when he presented what
is now known as the Copenhagen interpretation of quantum theory, the particle
is what you measure it to be. When it looks like a particle, it *is* a
particle. When it looks like a wave, it *is* a wave. Furthermore*, it is
meaningless to ascribe any properties or even existence to anything that has
not been measured*^{21}. Bohr is basically saying that *nothing is
real unless it is observed*.

While there are many other
interpretations of quantum physics, all based on the Copenhagen interpretation,
the Copenhagen interpretation is by far the most widely used because it
provides a "generic" interpretation that does not try to say any more
then can be proven. Even so, the Copenhagen
interpretation does have a flaw that we will discuss later. Still, since after
70 years no one has been able to come up with an interpretation that works
better then the Copenhagen interpretation, that is the
one we will use. We will discuss one of the alternatives later.

**The Wave Function**

In 1926, just weeks after several
other physicists had published equations describing quantum physics in terms of
matrices, Erwin Schrödinger created quantum equations based on wave mathematics^{22} , a mathematical system that corresponds to
the world we know much more then the matrices. After the initial shock, first
Schrödinger himself then others proved that the equations were mathematically
equivalent ^{23}. Bohr then invited Schrödinger to Copenhagen
where they found that Schrödinger's waves were in fact nothing like real waves. For one thing, each particle that was being
described as a wave required three dimensions ^{24}. Even worse, from Schrödinger's point of view,
particles still jumped from one quantum state to another; even expressed in terms
of waves space was still not continuous. Upon
discovering this, Schrödinger remarked to Bohr that "Had I known that we
were not going to get rid of this damned quantum jumping, I never would have
involved myself in this business." ^{25}

Unfortunately, even today people try
to imagine the atomic world as being a bunch of classical waves. As Schrödinger
found out, this could not be further from the truth. *The atomic world is nothing
like our world*, no matter how much we try to pretend it is. In many ways,
the success of Schrödinger's equations has prevented people from thinking more
deeply about the true nature of the atomic world

**The Collapse of the Wave Function**

So why bring up the wave function at
all if it hampers full appreciation of the atomic world? For one thing, the
equations are much more familiar to physicists, so Schrödinger's equations are
used much more often then the others. Also, it turns
out that Bohr liked the idea and used it in his Copenhagen interpretation.
Remember our experiment with electrons? Each possible route that the electron
could take, called a ghost, could be described by a wave function ^{27}. As we shall see later, the "damned
quantum jumping" insures that there are only a finite, though large,
number of possible routes. When no one is watching, the electron take every possible
route and therefore interferes with itself^{28}. However, when the electron is observed, it is
forced to choose one path. Bohr called this the "collapse of the wave
function"^{29}. The probability that a certain path will be
chosen when the wave function collapses is, essentially, the square of the
path's wave function ^{30}.

Bohr reasoned that nature likes to
keep it possibilities open, and therefore follows every possible path. Only
when observed is nature forced to choose only one path, so only then is just
one path taken ^{31}.

**The Uncertainty Principle**

Wait a minute… *probability???*
If we are going to destroy the wave pattern by observing the experiment, then
we should at least be able to determine exactly where the electron goes. Newton
figured that much out back in the early eighteenth century; just observe the
position and momentum of the electron as it leaves the electron gun and we can
determine exactly where it goes.

Well, fine. But how exactly are we
to determine the position and the momentum of the electron? If we disturb the
electrons just in seeing if they are there or not, how are we possibly going to
determine both their position and momentum? Still, a clever enough person, say Albert Einstein, should be able to come up with
something, right?

Unfortunately
not. Einstein did actually spend a good
deal of his life trying to do just that and failed ^{32}. Furthermore, it turns out that if it were
possible to determine both the position and the momentum at the same time,
Quantum Physics would collapse ^{33}. Because of the latter, Werner Heisenberg
proposed in 1925 that it is in fact *physically impossible* to do so. As
he stated it in what now is called the Heisenberg Uncertainty Principle, if you
determine an object's position with uncertainty x, there must be an uncertainty
in momentum, p, such that xp > *h*/4pi, where
*h* is Planck's constant ^{34} (which we will discuss shortly). In other words,
you can determine *either* the position *or *the momentum of an
object as accurately as you like, but the act of doing so makes your
measurement of the other property that much less. Human beings may someday
build a device capable of transporting objects across the galaxy, but no one
will *ever* be able to measure both the momentum and the position of an
object at the same time. This applies not only to electrons but also to objects
such as tennis balls and toasters, though for these objects the amount of uncertainty
is so small compared to there size that it can safely
be ignored under most circumstances.

**The EPR Experiment**

"God does not play dice"
was Albert Einstein's reply to the Uncertainty Principle. ^{35} Thus being his belief, he spent a good deal of
his life after 1925 trying to determine both the position and the momentum of a
particle. In 1935, Einstein and two other physicists, Podolski
and Rosen, presented what is now known as the EPR paper in which they suggested
a way to do just that. The idea is this: set up an interaction such that two
particles are go off in opposite directions and do not interact with anything
else. Wait until they are far apart, then measure the
momentum of one and the position of the other. Because of conservation of
momentum, you can determine the momentum of the particle not measured, so when
you measure it's position you know both it's momentum and position ^{36}. The only way quantum physics could be true is
if the particles could communicate faster then the
speed of light, which Einstein reasoned would be impossible because of his
Theory of Relativity.

In 1982, Alain Aspect, a French
physicist, carried out the EPR experiment ^{37}. He found that *even if information needed
to be communicated faster then light to prevent it,
it was not possible to determine both the position and the momentum of a
particle at the same time* ^{38}. This does not mean that it is possible to
send a message faster then light, since viewing either
one of the two particles gives no information about the other^{39}. It is only when both are seen that we find
that quantum physics has agreed with the experiment. So does this mean relativity
is wrong? No, it just means that the particles do not communicate by any means
we know about. All we know is that every particle knows what every other
particle it has ever interacted with is doing.

**The Quantum and Planck's Constant**

So what is that *h *that was so
important in the Uncertainty Principle? Well, technically speaking, it's 6.63 X
10^{-34 }joule-seconds ^{40}. It's call Planck's
constant after Max Planck who, in 1900, introduced it in the equation E=*hv* where E is the energy of each quantum of
radiation and *v *is it's frequency^{41}. What this says is that energy is not
continuous as everyone had assumed but only comes in certain finite sizes based
on Planck's constant.

At first physicists thought that
this was just a neat mathematical trick Planck used to explain experimental
results that did not agree with classical physics. Then, in 1904, Einstein used
this idea to explain certain properties of light--he said that light was in
fact a particle with energy E=*hv* ^{42}. After that the idea that energy isn't
continuous was taken as a fact of nature - and with amazing results. There was
now a reason why electrons were only found in certain energy levels around the
nucleus of an atom ^{43}. Ironically, Einstein gave quantum theory the
push it needed to become the valid theory it is today, though he would spend
the rest of his lift trying to prove that it was not a true description of
nature.

Also, by combining Planck's
constant, the constant of gravity, and the speed of light, it is possible to
create a quantum of length (about 10^{-35} meter) and a quantum of time
(about 10^{-43} sec), called, respectively, Planck's length and
Planck's time ^{44}. While saying that energy is not continuous
might not be too startling to the average person, since what we commonly think
of as energy is not all that well defined anyway, it is startling to say that
there are quantities of space and time that cannot be broken up into smaller
pieces. Yet it is exactly this that gives nature a finite number of routes to
take when an electron interferes with itself.

Although it may seem like the idea
that energy is quantized is a minor part of quantum physics when compared with
ghost electrons and the uncertainty principle, it really is a fundamental
statement about nature that caused everything else we've talked about to be
discovered. And it is always true. In the strange world of the atom, anything
that can be taken for granted is a major step towards an "atomic world
view".

**Schrödinger's Cat**

Remember a while ago I said there
was a problem with the Copenhagen interpretation? Well, you now know enough of
what quantum physics *is* to be able to discuss what it *isn't*, and
by far the biggest thing it isn't is complete. Sure, the math seems to be
complete, but the theory includes absolutely nothing that would tie the math to
any physical reality we could imagine. Furthermore, quantum physics leaves us
with a rather large open question: *what is reality?* The Copenhagen
interpretation attempts to solve this problem by saying that reality is what is
measured. However, the measuring device itself is then not real until *it*
is measured. The problem, which is known as the measurement problem, is when
does the cycle stop?

Remember that when we last left
Schrödinger he was muttering about the "damned quantum jumping." He
never did get used to quantum physics, but, unlike Einstein, he was able to
come up with a very real demonstration of just how incomplete the physical view
of our world given by quantum physics really is. Imagine a box in which there
is a radioactive source, a Geiger counter (or anything that records the
presence of radioactive particles), a bottle of cyanide, and a cat. The
detector is turned on for just long enough that there is a fifty-fifty chance
that the radioactive material will decay. If the material does decay, the
Geiger counter detects the particle and crushes the bottle of cyanide, killing
the cat. If the material does not decay, the cat lives. To us outside the box,
the time of detection is when the box is open. At that point, the wave function
collapses and the cat either dies or lives. However,
until the box is opened, the cat is both dead and alive ^{45}.

On one hand, the cat itself could be
considered the detector; it's presence is enough to
collapse the wave function ^{46}. But in that case, would the presence of a rat
be enough? Or an ameba? Where is the line drawn ^{47}? On the other hand, what if
you replace the cat with a human (named "Wigner's friend" after
Eugene Wigner, the physicist who developed many derivations of the
Schrödinger's cat experiment). The human is certainly able to collapse
the wave function, yet to us outside the box the measurement is not taken until
the box is opened ^{48}. If we try to develop some sort of
"quantum relativity" where each individual has his own view of the
world, then what is to prevent the world from getting "out of sync"
between observers?

While there are many different
interpretations that solve the problem of Schrödinger’s Cat, one of which we
will discuss shortly, none of them are satisfactory enough to have convinced a
majority of physicists that the consequences of these interpretation s are
better then the half dead cat. Furthermore, while
these interpretations do prevent a half dead cat, they do not solve the
underlying measurement problem. Until a better interpretation surfaces, we are
left with the Copenhagen interpretation and it's half
dead cat. We can certainly understand how Schrödinger feels when he says,
"I don't like it, and I'm sorry I ever had anything to do with it."^{49} Yet the problem doesn't go away; it is just
left for the great thinkers of tomorrow.

**The Infinity Problem**

There is one last problem that we
will discuss before moving on to the alternative interpretation. Unlike the
others, this problem lies primarily in the mathematics of a certain part of
quantum physics called quantum electrodynamics, or QED. This branch of quantum
physics explains the electromagnetic interaction in quantum terms. The problem
is, when you add the interaction particles and try to solve Schrödinger's wave
equation, you get an electron with infinite mass, infinite energy, and infinite
charge^{50}. There is no way to get rid of the infinities
using valid mathematics, so, the theorists simply divide infinity by infinity
and get whatever result the guys in the lab say the mass, energy, and charge
should be^{51}. Even fudging the math, the other results of
QED are so powerful that most physicists ignore the infinities and use the
theory anyway ^{52}. As Paul Dirac, who was one of the physicists
who published quantum equations before Schrödinger, said, "Sensible
mathematics involves neglecting a quantity when it turns out to be small - not
neglecting it just because it is infinitely great and you do not want it!". ^{53}

**Many Worlds**

One other interpretation, presented
first by Hugh Everett III in 1957, is the many worlds or branching universe
interpretation^{54}. In this theory, whenever a measurement takes
place, the entire universe divides as many times as there are possible outcomes
of the measurement. All universes are identical except for the outcome of that
measurement ^{55}. Unlike the science fiction view of
"parallel universes", it is not possible for any of these worlds to
interact with each other ^{56}.

While this creates an unthinkable
number of different worlds, it does solve the problem of Schrödinger's cat.
Instead of one cat, we now have two; one is dead, the other alive. However, it
has still not solved the measurement problem ^{57}! If the universe split every time there was
more than one possibility, then we would not see the interference pattern in
the electron experiment. So when does it split? No alternative interpretation
has yet answered this question in a satisfactory way. And so the search
continues…