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 Everything

Surely, 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 extra-dimensions 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 space-time 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 so-called 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 Kaluza-Klein theory.  What is Kaluza-Klein 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 "space-time continuum" that provided a framework for all later mathematical work in Einstein's Theory of General Relativity.  


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 Calabi-Yau Manifolds and Orbifolds discussed in the BLUE BOX.



What is Kaluza-Klein theory

Antimatter vs. Matter

In order to understand the Kaluza-Klein 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 matter-antimatter 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 Ahydrogen & Aoxygen respectively. 



The Theory and its Usage

In 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. 


The Modern Kaluza-Klein 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 Kaluza-Klein 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. 


Three distinct approaches to explain the extra-dimensions are identified and contrasted: compactified, projective and noncompactified.  I talked about the idea that for simplicity it is generally assumed that the extra-dimensions 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 Space-Time-Matter Continuum by eliminating the cylindrical assumption from Kaluza-Klein Theory.  In Wesson's book,  "Space-Time-Matter, Modern Kaluza-Klein Theory," there are numerous examples that correlate Modern Kaluza-Klein Theory to the physical reality including general relativity and elementary particle physics.  



Calabi-Yau 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 Calabi-Yau 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 M-Theory.  To read more about why this theory is called the M-Theory 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.


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 -, 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)




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 extra-dimensions 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.


Bibliography: (discusses the Kaluza-Klein theory in which extra-dimension was added in an attempt to unify gravity and electromagnetism) (attached as link earlier) (The work on 5D Space-Time-Matter consortium where the scientists do not "compactify" the extra dimension as Kaluza and Klein did.) (is a page about Minkowski)  (contains Einstein's Theory of Relativity) (Orbifold explaination) (attached as link earlier) (has some good specific ideas about dimension and contains the Kaluza-Klein Theory) (contains many of the basic ideas) (also dimension specific things)