On 5/24/2025 9:50 PM, Alan Grayson wrote:
On Saturday, May 17, 2025 at 2:23:35 PM UTC-6 Brent Meeker wrote:
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
Is the classical singularity in the Coulomb force caused by the
assumption of point sized particles, that have zero volume?
Yes.
If particles were modeled as very smal but continuous regions of
charge,would the singularity go away
Yes.
when the distance to the center of the charge is less than its radius? AG
??
Brent
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