|MadSci Network: Physics|
What is energy? There is no dimensional dependence in the definition of energy (see Halliday & Resnick, Physics, Chapter 7). For mass, even though it is often computed as the product of a density and a volume, there is no dependency on dimension that would imply mass was somehow different in a one- or two-dimensional space. Sure, one could argue there is no volume in either of those spaces, but in that sense there would be no mass and therefore no energy definitions to be concerned with. The term explosion, though near and dear to the hearts of many physicists, is more of an engineering term. There is, for instance, no Newton's Law of Explosions. In that oversimplified sense, the term explosion is used to characterize observations made in this three-dimensional world. A computer code can be written to simulate a three-dimensional explosion in two or one dimensions, sacraficing a lot of detail in the process, but such a capability does not imply two- or one-dimensional explosions are real. Note the foregoing discussions has not reached the point explosion. But then, if neither two- nor one-dimensional explosions are real, why bother considering a zero-dimensional space. After Halliday & Resnick's Physics, the next reference you may want to look at is Taylor and Wheeler's Spacetime Physics, as it goes into energy in a relativistic sense but is not as difficult to read as more advanced relativity references. Maybe another topic area you would like to investigate, either on the web or in a library, is the work toward a Grand Unified Theory, including topics like Quantum Gravity and the use of Lie Algebras for some very intriguing multi-dimensional work. Unfortunately, I've just found a couple of titles that I haven't had a chance to look at. Those follow, though if you are interested in more than just a quick perusal it may take another degree or two to comprehend what these references are all about. The first one I have on my list of books to find is Foundations of Quantum Group Theory by Shahn Majid, Cambridge University Press, 1998, ISBN 0521648688. Assuming I survive the first, I would also like to find Abstract Lie Algebras by David J. Winter, MIT Press (I think that one is also 1998), ISBN 0262230518.
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