X-Message-Number: 22082
From: 
Date: Thu, 26 Jun 2003 20:41:49 EDT
Subject: physical infinities & infinitesimals

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A few thoughts, doubtless of infinitesimal interest except to those who may 
want to repair my brain when the time comes.

1. To say that an accelerated charge produces an infinite number of real 

photons is really just a manner of speaking. At best it is a statement 
consistent 
with a particular theory or a particular interpretation of a theory. It 

reminds me of the Ptolemaic theory of the solar system--the math was fine, 
better 
than the initial Copernican math, but the ontology was highly suspect.

2. If a lab event produces an infinite number of real photons, with total 
energy still finite, then 100% of them (not all, but still 100%) must have 

infinitesimal energy (less than any preassigned number) and infinite wave length
(greater than any preassigned number). Thus the time required to observe them 

will be greater than any preassigned interval, such as the age of the universe.
(I think Yvan Bozzonetti may have said something similar.)

3. Levy-Leblond and Balibar, in their book QUANTICS, stress that a quanton 

(any physical object, although especially things like "photons" or "electrons")
is neither a particle nor a wave nor combination, but a different animal, and 
such terms as "de Broglie wavelength," h/p, are misnomers, even though 
sometimes useful.

4. I now have Kaku's QUANTUM FIELD THEORY to go with my older books on QED. 
It would take me several years to master all the details, if I could live that 
long and had nothing else to do, but he has some things to say about the state 
of the theory that leave a good deal of room for speculation. For example, he 
says:

"One of the most remarkable properties of supersymmetry is that 

supersymmetric field theories can be finite to all orders in perturbation 
theory, which was 
once thought to be impossible. In some sense, these theories answer Dirac's 

old objections to quantum field theory, that renormalization theory was in some
sense contrived and artificial."

Robert Ettinger



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