 
This is a research project by Aditya
Mittal, a 12th grader, taking a Virtual
High School
course called Time, Space, and Other
Things...
The purpose of this web page is to discuss
why the superstrings theory
predicts ten dimensions when that seems so
odd a thing to predict.
The Theory of
EverythingSurely, we have heard
of gravity and electromagnetism, possibly even strong and weak nuclear
forces. These as we know it are the four fundamental forces of
nature.
Gravitational forces are attractive forces that
act between all objects in proportion to their masses. Gravitational
forces between atoms or subatomic particles are so small that they are of
no chemical significance. We all know the apple falling on Newton's
head story.
Electromagnetic forces are attractive or
repulsive forces that act between electrically charged or magnetic
objects.
Strong Nuclear Force is the force that keeps all
the protons in a positively charged nucleus together.
Weak Nuclear Force is weaker than the electric
force but stronger than gravity. We are aware of its existence only
because it shows itself in certain types of radioactivity.
For a very long time people have taken various
kinds of forces and tried to somehow group them together. For
example, electric force and magnetic force were once considered two
separate forces. Now we know they are very closely related and that
a magnetic field is generated by a wire carrying electricity. The
direction of the magnetic field is given by the right hand rule.
Similarly a wire in a magnetic field also generates electricity in
it. Now for a long time we have been trying to combine the remaining
four forces to get one or we have been trying to achieve a "Theory of
Everything." There is also a GUT theory that claims to combine the
two nuclear forces and electromagnetism but it is not quite fully
understood and accepted yet.
Finally, the Superstrings theory is attempting
to combine all four of the forces by using extradimensions which is what
this whole research project is about. The theory has excited many
physicists as we shall see. Clearly, it has a proposal on how to
combine the four fundamental forces. 
Basics on Why Extra
dimensions...One of the most
astonishing predictions of String Theory is that spacetime has ten
dimensions which seems odd as we apparently have only three dimensions of
space and one of time.
Yet, the Superstrings claims that six of these
dimensions are curled up very tightly and lost somewhere in the universe,
and so we may never be aware of their existence. But now let's look
at why it predicts so?
Well, having these socalled compact dimensions
is very beneficial to the String Theory in making the claim that it is a
"theory of everything." Why scientists are looking for this "theory
of everything" is discussed in the PURPLE SECTION you just read. The
idea is that degrees of freedom like the electric charge of an electron
will then arise simply as motion in the extra compact directions!
This has been said because dimension too, can be considered degrees of
freedom in which a certain object can move. For example, the ant
across the mountain analogy that Mr. Atlas made in one of the media center
documents, the ant had a two dimensional perspective of things in the
sense that it could only move in 2D across the mountain and not fly
across, as it may have been able to if it was looking and capable of
moving in 3D.
The principle that compact dimensions may lead
to unifying theories is not new, but dates back to the 1920's when the
theory of Kaluza and Klein came about. In a sense, String Theory is
the ultimate KaluzaKlein theory. What is KaluzaKlein theory in the
GREEN BOX.
Actually, to be truly honest, the idea of adding
dimensions to make things fit dates back even further to Hermann
Minkowski. Minkowski successfully used the fourth dimension to solve
the "spacetime continuum" that provided a framework for all later
mathematical work in Einstein's Theory of General
Relativity.
(http://wwwgroups.dcs.standrews.ac.uk/~history/Mathematicians/Minkowski.html)
For simplicity, it is usually assumed that the
extra dimensions are wrapped up on six circles. For realistic results they
are treated as being wrapped up on mathematical elaborations known as
CalabiYau Manifolds and Orbifolds discussed in the BLUE
BOX. 
What is KaluzaKlein theory
Antimatter vs. Matter
In order to understand the
KaluzaKlein theory I must first define what matter and antimatter
are.
Matter is the 109 elements we
have on the chemistry periodic table that we have all seen. It
is composed of particles and has mass.
Antimatter on the other hand
consists of antiparticles. These are subatomic particles
identical to the subatomic particles of matter in mass but opposite
to it in electric and magnetic properties (as sign of charge).
When these antimatter particles are brought together with the
counterpart particles of matter they produce mutual
annihilation. Thus there are also 109 antimatter elements
giving us a total of 218 elements on the matterantimatter periodic
table. The antimatter elements are named after their
respective matter elements; and their nuclear, physical, and
chemical properties are identified. The superscript ^{A
}before the element or symbol indicates that element is
antimatter. For example, hydrogen & oxygen are
^{A}hydrogen & ^{A}oxygen
respectively.
(http://www.matterantimatter.com/kaluzaklein_theory.htm)

The Theory and its UsageIn 1919, Theodore Kaluza attempted to unify Maxwell's
Electromagnetism and Einstein's Gravitation Theory by adding a fifth
dimension. Kaluza found that adding the fifth dimension, which
was independent of the other dimensions, would unify gravity
and electromagnetism. In 1921, Kaluza published his theory,
with Albert Einstein's support.
(http://www.matterantimatter.com/kaluzaklein_theory.htm)
The Modern KaluzaKlein Theory
can be used to model galaxies. Supermassive Blackholes at the
center of the galaxy constantly take in everything around them as
the matter spirals at high speeds around them. The spinning
matter, called a spiral arm, contains billions of stars, planets,
galactic dust and plasma. Due to this high velocity, as laws
of physics predict some of the outer matter and antimatter is able
to escape the gravitational pull (somehow electromagnetism is also
involved and that is why matter and antimatter are both predicted)
of the blackhole in the middle. Thus, a "bulge" is formed
around the black hole. This matter escaping at high velocities
is said to be "ejected by the blackhole" although it's not really
ejected from inside the blackhole. When this galactic and
stellar antimatter dust enters our solar system, it is called
"comets." Astronomers have identified hundreds comets,
composed of antimatter, orbiting the sun. Yes, this is comets
as we know them, although it is not the only way to get
comets. I know they come from a belt near Pluto (the planet in
our solar system) also from Astronomy Class. A few years ago,
if any of you remember in our lifetime, some scientists attempted to
claim there was another planet after Pluto and wanted to call it
"Zeus." I am guessing that too, may be a large comet because
comets are common on that belt.

Others Who Based things Upon this Theory
In 1926, Oskar Klein applied Kaluza's
Theory to quantum theory, which is the basis of modern string
theory. Over the past eighty years, mathematicians and
scientists have had a difficulty correlating the KaluzaKlein Theory
to the physical reality. They have modified the
assumptions, evaluated, compactified, and used extra
dimensions. The String & Super String Theories, which have
resulted, do not give acceptable solutions.
(http://www.matterantimatter.com/kaluzaklein_theory.htm)
Three distinct approaches to explain the
extradimensions are identified and contrasted: compactified,
projective and noncompactified. I talked about the idea that
for simplicity it is generally assumed that the extradimensions are
wrapped around six circles and lost in space and that was the idea
of compactified dimensions.
After a discussion of the cosmological and
astrophysical implications of extra dimensions it has been concluded
that none of the three approaches can be ruled out on current
observational grounds. This conclusion was made by Overduin
and Wesson in 1998. They demonstrated that the fifth dimension
can solve the SpaceTimeMatter Continuum by eliminating the
cylindrical assumption from KaluzaKlein Theory. In Wesson's
book, "SpaceTimeMatter, Modern KaluzaKlein Theory," there
are numerous examples that correlate Modern KaluzaKlein Theory to
the physical reality including general relativity and elementary
particle physics.
(http://www.matterantimatter.com/kaluzaklein_theory.htm)  
CalabiYau Manifolds and Orbifolds
These concepts are very complex,
especially when related to how various dimensions may be wrapped around
them in some part of the universe. However, considering these things
in small bite size pieces can help us as VHS students understand the
concepts better although with limitations. Let me begin by
explaining what an Orbifold is.
An orbifold is in the simplest
terms a type of fold on which something can be folded. Huh? Let me
explain. Take for example a sphere. Now take a bunch of triangles and
paste them around the sphere. What you have is an orbifold
of triangles on a sphere. So what these scientists are saying
is that the "missing dimensions" might simply be folded up on a really
small orbifold and lost somewhere in the universe. Similar idea with
CalabiYau Manifolds. The scientists and mathematicians are doing
intensive calculation to figure out the shapes and forms of these
Manifolds and Orbifolds.
WHAT
IS AN ORBIFOLD Check out this
link for more examples of Orbifolds. It is very easy to
read.
OK, so now we can see what an Orbifold is and
how a particular design is wrapped around something repeatedly, and that's
what we are trying to say has happened to the dimensions. It is what
mathematicians and physicists are studying in detail. Now there is a
theory called the SUPERSTRINGS that has excited modern physicists with
it's high degree of freedom. This theory is also known as the
MTheory. To read more about why this theory is called the MTheory
and what the string theory is try the following link. This page is
also easy to read and understand and will provide a good understanding of
the theory itself. You'll also see some ideas already discussed
about dimensions, which is what this page (the one you are reading)
focuses on, in reappear.
MTHEORY
Finally, try the following link which basically
claims that the dimensions may not be curled up after all, and we have
wasted our time doing so many calculations with the assumption that they
are curled up. But, as I said earlier, none of the three approaches,
compactified (folded on an orbifold or manifold), projected (spread around
us throughout), and noncompactified (check out this link for more on this
type  http://astro.uwaterloo.ca/~wesson/home.html), have been disproved or proven correct with surety.
All three are simply logical explanations.
The
Dimensions may not be Curled Up
(navigate around to other postings
on this site  some of the comments are very interesting  and give
various views about these ideas)

Conclusion
After all this research, it is evident that the
idea of extra dimensions has been introduced because there is a strong
notion amongst scientists that this addition of dimensions may help
explain how the four fundamental forces are related. The idea is to
get "a theory of everything" when that may or may not be
possible.
Therefore, now there is a frenetic collaboration
of ideas in an attempt to define or "find" those extradimensions if they
exist and that's what this is all about. Yet, like everything else
that is abstract in science this too, must be explored if we are to
develop some final conclusion. 
