On 5/16/2025 8:34 PM, Alan Grayson wrote:
On Friday, May 16, 2025 at 2:14:57 AM UTC-6 Alan Grayson wrote:
On Thursday, May 15, 2025 at 2:13:53 PM UTC-6 John Clark wrote:
On Wed, May 14, 2025 at 4:39 PM Alan Grayson
<[email protected]> wrote:
/> The Coulomb field of a point charge diverages as the
distance to the charge decreases to zero. Is this
singularity resolved in the classical or quantum theory of
E&M?/
*In classical physics the amount of energy in a point
electrical charge such as an electron is infinite, quantum
electrodynamics avoids infinity in a process called
"renormalization". The point charge interacts with a cloud a
virtual particles that pop in and out of existence with each
having their own Feynman diagram; the infinity from one part
of the calculation is canceled out by another infinity in
another part of the calculation, so you're left with a finite
charge that agrees with experimental results better than one
part in a billion. It has been called the most accurate
prediction in the entire history of science.*
*Richard Feynman had more to do with developing
renormalization than anyone and received the Nobel prize for
it, but he was never satisfied with it because, although it
worked wonderfully well, this canceling out inconsistencies
business is not mathematically rigorous and so it cannot be
proven to contain no inconsistencies. Feynman said this:*
*"/The shell game that we play is technically called
'renormalization'. But no matter how clever the word, it is
still what I would call a dippy process! It's a way of
sweeping the problems under the rug/."*
*
*
*A few years later during his Nobel Prize acceptance speech he
said:*
/*"It has not yet become obvious to me that there's no real
problem. I cannot define the real problem; therefore, I
suspect there's no real problem, but I'm not sure there's no
real problem."*/
*/
/*
*John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
Do point charges exist in quantum field theory? Is it the electric
field which is quantized? If not that, then what? TY, AG
What I am asking is whether Feynman's renormalization procedure is
specifically applied to a single point charge in quantum E&M? AG
You mean, "Is the electron assumed a point particle?". Yes, but you
exchange photons not charge. At each photon-electron vertex you get a
coupling constant of /g=sqrt(4pi alpha)/ where alpha is the
fine-structure constant /e^2/(hbar*c^2)=1/137/ So that's the only way
that the electron charge, /e/, enters and it's the experimental charge
value. No renormalization is needed since /g<<1/ and the terms don't
blow up.
For the strong force, even the vacuum propagator term blows up, so you
subtract it off from all the higher order terms to get a finite remainder.
Brent
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