The discussion revolves around the mathematical representation of negative exponents, specifically the notation n^{-1} and its implications in various contexts, including dimensional analysis and physical equations.
The discussion is ongoing, with multiple interpretations being explored. Some participants provide clarifications on the definitions of negative exponents, while others express confusion and seek further explanation. There is no explicit consensus on the understanding of the notation.
Participants reference specific examples from physics, such as energy and the Dirac operator, to illustrate their points. There is a noted contradiction in the interpretation of dimensional analysis notation, which adds to the complexity of the discussion.
help1please said:Let's try this again. Let us say, E is energy.
What would be E^{-2} be?
help1please said:In fact let's do this another way. I was reading about the dirac operator
D(\psi) = \hbar^2 R^{-2} \psi(x)
How does R^{-2} read to you? Just 1/R^2 like you said before?
Yes, "divided by length squared" which contradicts what you wrote! MTl2= MT/l2, Not "MTl/2".help1please said:Because in Dimensional analysis, we tend to use the notation ie. MTl^{-2} which would mean that it is mass times time divided by length squared...
You are making this much too difficult- \epsilon\mu= \frac{1}{c^2} which again contradicts what you said originally.mmm... has it got something to do with things like
\epsilon \mu = c^{-2}
such that
\sqrt{\epsilon \mu} = \frac{1}{c}
I could be totally off, mind my ignorance.