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13 June 2003
E-Bulletin Backscatter
Radiation Hormesis
Sheldon,
With respect to the comments about radiation hormesis in the June 6 issue of "E-Bulletin Backscatter", here are two websites that may be of interest:
http://cnts.wpi.edu/RSH/Docs/TR_6-97_FOF.html
http://www.sepp.org/NewSEPP/case_for_nuclear_radiation.htm
Obviously, these two references present the other side of the coin, including certain economic effects.
Jim Rowland
Toroidal Coil Magnetic Fields
In the June 6 Feedback column, Charles Burgess responded to Lee White's question about magnetic fields external to a toroidal coil: "Rather than simply give you the answers directly, I wish to refer you to a book by Richard Feynman, QED: The Strange Theory of Light and Matter. This will provide a good jumping off point for your quest."
Readers of this response might be led to image that Charles knows the answer to Lee's question and that Feynman's book will help him find the answer. I'm skeptical on both counts. On page 9 of the referenced book, Richard Feynman makes the following statements about the book's central topic (quantum electrodynamics): "You see, my physics students don't understand it either. That is because I don't understand it. Nobody does."
Peter Baum
Einstein's Erroneous Algebra?
Hi George,
Even Einstein was found to have made a few algebraic errors in his Theory of Relativity." Where? Which theory of relativity?
Albert Einstein experienced some mathematical difficulties in getting his Special Theory of Relativity to work out satisfactorily with Euclidean geometry and is generally paraphrased by biographers as the complexities being beyond his mathematical abilities. It wasn't until the compilation of Rhinman geometry that the Special Theory of Relativity was mathematically workable. At least that is what the biogarphers have written. One gets the feeling that biographers may have taken Einstein's comments out of context, as he seemed to be prone to joking around in a self-abasing manner.
There are two other individuals who assisted in the effort, one being Minkowski and the other a gentleman from India whose name escapes me at this moment. The principle issue is that the mathematical tools at that time, namely Euclidean geometry, did not lend itself to curved space time calculations.
Regards,
Charles Burgess
As it turns out Special Relativity was never intended to work with Euclidean geometry. The space for special relativity is Minkowski space, not Euclidean space. Euclidean space has absolute time, Minkowski space does not. Not that this matters, Einstein had no algebraic difficulties in applying curved spacetime into Minkoswski space, or any other for that matter, because special relativity does not live in curved spacetime; you are thinking of general relativity. As I portrayed in recent theory columns there are no algebraic difficulties in deriving special relativity, I did it with just some simple algebra, pretty much the way Einstein did it himself.
The biographers are referring to the fact that it took Einstein the next ten years to work out general relativity which require the use of tensor analysis (by the great mathematician Levi-Civita) and Riemannian geometry (due to Georgi Riemann). This is where curved spacetime comes into play.
Things break down like this:
1. Galilean relativity applies to make Newton's laws invariant from inertial frame to inertial frame, but fails to do the same for Maxwell's equations (describing electromagnetism). It allows absolute velocity and acceleration. It lives in Euclidean space and time is a separate thing that lives on the real line.
2. Einstein's special relativity continues to have Newton's laws invariant with respect to inertial frames, but also allows Maxwell's equations to be invariant. It still allows for absolute acceleration (the reason that Einstein developed general relativity). It lives in Minkwski spacetime (this uses complex numbers, rather than real numbers).
3. Einstein's general relativity has all of the above invariances. Nothing is absolute. It lives in Riemannian spacetime.
Hope this helps clear things up.
George Hrabovsky
