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:
<OL>
Energy is not continuous, but comes in small but discrete units.
<SUP>1 (#1)</SUP>
The elementary particles behave both like particles and like waves.
<SUP>2 (#2)</SUP>
The movement of these particles is inherently random.
<SUP>3 (#3)</SUP>
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.<SUP>4 (#4)</SUP>
The atomic world is nothing like the world we live in.
<SUP>5 (#5)</SUP>
</OL>
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 then even relativity in
the grand scheme of things (if any one thing at that level could
be said to be more important then anything else). Furthermore,
it describes the nature of the universe as being much different
then the world we see. As Niels Bohr said, "Anyone who is
not shocked by quantum theory has not understood it."
<SUP>6 (#6)</SUP>
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 it's 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.
http://tqd.advanced.org/3487/media/generic.gif
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.
<SUP>7 (#7)</SUP>
The most bullets are found in the middle of the two slits with
less being found the further you get from the center.
http://tqd.advanced.org/3487/media/bullets.gif
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
<SUP>8 (#8)</SUP>; 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.
http://tqd.advanced.org/3487/media/water.gif
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
<SUP>9 (#9)</SUP>
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
<SUP>10 (#10)</SUP>. 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!<SUP>11 (#11)</SUP>
http://tqd.advanced.org/3487/media/electrons.gif
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! <SUP>12 (#12)</SUP>
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!!
<SUP>13 (#13)</SUP>
http://tqd.advanced.org/3487/media/electrons2.gif
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.
<SUP>14 (#14)</SUP>
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.<SUP>15 (#15)</SUP>
The particles that flash in one slit or the other
behave like the bullets, while those that go undetected behave
like waves<SUP>16 (#16)</SUP>.
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
<SUP>17 (#17)</SUP>. 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
<SUP>18 (#18)</SUP>, 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
<SUP>19 (#19)</SUP>.
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
<SUP>20 (#20)</SUP>. 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<SUP>21 (#21)</SUP>.
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<SUP>22 (#22)</SUP>
, 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
<SUP>23 (#23)</SUP>. 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
<SUP>24 (#24)</SUP>.
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 darned quantum jumping,
I never would have involved myself in this business."
<SUP>25 (#25)</SUP>
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
<SUP>26 (#26)</SUP>.
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
<SUP>27 (#27)</SUP>.
As we shall see later, the "darned
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<SUP>28 (#28)</SUP>.
However, when the electron is observed, it is forced
to choose one path. Bohr called this the "collapse of the
wave function"<SUP>29 (#29)</SUP>.
The probability that a certain path will
be chosen when the wave function collapses is, essentially, the
square of the path's wave function
<SUP>30 (#30)</SUP>.
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
<SUP>31 (#31)</SUP>.
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
<SUP>32 (#32)</SUP>. 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
<SUP>33 (#33)</SUP>.
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
<SUP>34 (#34)</SUP>
(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.
<SUP>35 (#35)</SUP> 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
<SUP>36 (#36)</SUP>.
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
<SUP>37 (#37)</SUP>.
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
<SUP>38 (#38)</SUP>.
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<SUP>39 (#39)</SUP>.
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<SUP>-34 </SUP> joule-seconds
<SUP>40 (#40)</SUP>.
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<SUP>41 (#41)</SUP>.
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
<SUP>42 (#42)</SUP>.
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
<SUP>43 (#43)</SUP>.
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<SUP>-35</SUP> meter) and
a quantum of time (about 10<SUP>-43</SUP> sec), called, respectively,
Planck's length and Planck's time
<SUP>44 (#44)</SUP>.
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
<SUP>45 (#45)</SUP>.
On one hand, the cat itself could be considered
the detector; it's presence is enough to collapse the wave function
<SUP>46 (#46)</SUP>.
But in that case, would the presence of a rat be enough? Or
an ameba? Where is the line drawn
<SUP>47 (#47)</SUP>?
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
<SUP>48 (#48)</SUP>. 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 intrepretation 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."<SUP>49 (#49)</SUP>
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<SUP>50 (#50)</SUP>.
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<SUP>51 (#51)</SUP>.
Even fudging the math, the other results
of QED are so powerful that most physicists ignore the infinities
and use the theory anyway
<SUP>52 (#52)</SUP>.
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!".
<SUP>53 (#53)</SUP>
Many Worlds
One other interpretation, presented first by
Hugh Everett III in 1957, is the many worlds or branching universe
interpretation<SUP>54 (#54)</SUP>.
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
<SUP>55 (#55)</SUP>. Unlike the science
fiction view of "parallel universes", it is not possible
for any of these worlds to interact with each other
<SUP>56 (#56)</SUP>.
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
<SUP>57 (#57)</SUP>!
If the universe split every time there was more then 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…
Further Reading
If you are interested in learning more about
quantum physics, here are some books that you could try (check
the bibliography for more specific information on the books you
are interested in):
Richard Feynman's Lectures on Physics
deals with the math associated with quantum physics. If you can
understand basic calculus, then this book is for you. Otherwise,
while Lectures still provides some valuable information,
you may find yourself lost before you get too far.
John Gribbin's In Search of Schrödinger's
Cat is an excellent non-mathematical treatment of quantum
physics. If you've been watching the footnotes you've seen that
much of the data for this paper came from this book. It includes
a good history of quantum physics. Be advised that the sections
on supergravity and supersymmetry at the end are outdated.
Alastair Rae's Quantum Physics: Illusion
or Reality presents the basics of quantum physics in terms
of the polarization of light. It's 118 pages, half of which are
devoted to a discussion of the alternate interpretations of quantum
physics, can easily be read in an afternoon. It spends more time
on alternate interpretations then Gribbin's book, but is less
detailed in almost every other respect. I suggest reading Gribbin's
book first then this book.
- Piz