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Ana Kata Dimension

You Wrote:
One day I was sitting in my living room, reading a book on physics, an idea occurred to me. (This idea probably may be unscientific and unreasonable, but read the rest of this letter anyway.)

This is, specifically, a question about dimensional physics (that's probably not the real term for this branch of physics). From now-on, I will refer to the ana/kata dimension (the fourth spatial) dimension as the fourth dimension rather than the fifth dimension, even though time is really the fourth dimension.

One popular theory, if I understand it correctly, holds that, rather than being on some kind of "plane" (by plane, I mean 3-dimensional space), we are on a hypersphere (the 4-dimensional equivalent of a sphere).

Let's look at this in a 2-dimensional analogy. The theory holds that, rather than being on a flat, 2-dimensional plane, the 2-dimensional people are on a 3-dimensional sphere.

If this is the case, then doesn't it follow that the 2-dimensional beings must be held to the sphere somehow? Perhaps they are held by gravity. But if they are truly 2-dimensional, they must be perfectly flat, and thus have no mass in the third dimension. In their own terms, they have mass, but to a higher-dimensional being like you or me, they are without mass. If they possess no mass in the third dimension, then how can a 3-dimensional body - the sphere - attract them. Thus, if 2-dimensional beings are on a hyperphere, and they are held by gravity, they must have some thickness in the third dimension. This is supporting evidence for the theory that all 2-dimensional bodies have some thickness in the 3rd dimension and 3-dimensional bodies have some thickness in the 4th dimension.

Another possibility I have thought of however, is that the sphere that the 2-dimensional beings are stuck on is, in fact, hollow. The thickness of the outer edge of the sphere is 0, as would be, in my theory, the thickness of 2-dimensional creatures. The creatures are somehow held to the boundary of the hollow sphere. This brings up the question of how they are held to the boundary. Perhaps there is some force other than the basic four (gravity, electromagnetic, weak nuclear, and strong nuclear force). This force would cause all n-dimensional objects to be attracted to spheres of dimension (n+1). Thus it would cause lines to be attracted to circles, circles to spheres, spheres to hyperspheres, and so on.

All of these principles can be applied to our dimension. If this letter seems unreasonable and unintelligent, just remember that a 12-year-old, not a physics professor, wrote it.

Sincerely,

Jeffrey Barnes, 12 years old
Cedar Rapids, IA, USA

Dear Jeffrey,

Thank you for writing to Fermilab about your ideas about dimensional physics. Your ideas are well thought out, and in fact are closely related to some of the pioneering work in mathematical physics. You should continue to think about these concepts. I have enclosed references and extra information that may be useful as yo carry on with these ideas.

To start with, I thought I would begin by telling you some background about myself. I am a physics professor at Southern Methodist University in Dallas, but am visiting Fermilab this year to work with some of the people here at the lab. My research is in high energy physics theory; we study the fundamental properties of the "strong interaction" that holds the proton together. Specifically, I work with experimentalists to learn about the latest data (sometimes called facts), and then work with theorists to learn about the latest theories (soemtimes called fiction). Finally, I try to match the data with the theory to prove and disprove theories, and to discover new phenomena.

As it turns out, the ideas of dimensional physics that you mention are in fact the foundations of a number of very important theories in the field of mathematics and physics. The properties you describe in your letter where "the creatures are somehow held to the boundary of a hollow sphere" is very similar to what we postulate happens in superstring theories -- sometimes known as the Theory of Everything (TOE).

Rather than have me attempt to describe some of these topics, I think it is best for me to suggest a few sources where you can get more detailed information about these ideas. First, there are three books that discuss on this material in a manner that I think you will find understandable and enlightening. I have attached information below on these books, with short reviews where available. Your library should have most of these available.

Flatland: A Romance of Many Dimensions. This is written in the form of a story, yet is very thought provoking. It describes a 2-dimensional world embedded in a 3-dimensional space. This serves as a useful analogy as we try to imagine our 3+1 dimensional world embedded in a higher dimensional space.

Mr. Tompkins in Paperback. This is a collection of essays (also in short story form) written by the eminent physicist, George Gamow. Among the interesting physics topics that Gamow uses in his stories is the structure (and ultimate fate) of the universe.

One Two Three... Infinity: Facts and Speculations of Science. Also by George Gamow. He discusses a wide range of science topics including an N-dimensional world embedded in a higher dimensional space.

Although these books were written some years ago, the information is still relevant and the presentation is excellent.

  • For something a little more up to date, I have enclosed a copy of a Scientific American Article on Superstrings from 1986. There was tremendous progress (and excitement) in the superstring field during this period, and this article discusses some of the important advances.

  • I have also attached a brief description from my on-line encyclopedia that describes the Theory of Everything.

  • Finally, there is a rather interesting web address that provides an excellent interactive account of superstring theory.

    http://photon.kyunghee.ac.kr/~nam/intro.html

I hope this information is useful to you; please feel free to contact me with any more questiond or ideas that you might have. I should also mention that you can reach me via e-mail: olness@mail.physics.smu.edu, or you can get to my homepage via WWW at:

http://www.physics.smu.edu/~olness

Best regards,

Frederick I. Olness,
Theoretical Physics Department,
Fermilab

and

Department of Physics,
Southern Methodist University

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