MadSci Network: Physics

Re: Energy properties of Mass based on dimensions

Date: Mon Feb 14 14:50:07 2000
Posted By: Sidney Chivers, , Nuclear Engineering, retired
Area of science: Physics
ID: 949941250.Ph

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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