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 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. (http://www-groups.dcs.st-andrews.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 Calabi-Yau Manifolds and Orbifolds discussed in the BLUE BOX. |
What is Kaluza-Klein theory
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Calabi-Yau Manifolds and OrbifoldsThese 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 - 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)
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ConclusionAfter 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. |