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." 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 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.
Generic Experiment Setup
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.
Bullets Experiment
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.
Water Experiment
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
Electron Experiment
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
Electron Experiment with Light
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 waves16.
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 measured21. 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
mathematics22 , 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 26.
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 itself28. 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
other39. 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 frequency41.
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
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."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 charge50. 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 be51. 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 interpretation54.
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 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.
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