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 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.

















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 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 darned 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 "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

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.





- Piz