On 5/25/2025 7:30 PM, Alan Grayson wrote:
They're resolved by quantum field theory, which I suppose could the thought of as a drastic change in the model of particles.On Sunday, May 25, 2025 at 5:20:08 PM UTC-6 Brent Meeker wrote: On 5/25/2025 2:17 PM, Alan Grayson wrote:On Saturday, May 24, 2025 at 11:31:27 PM UTC-6 Brent Meeker wrote: 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? AGYou 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 awayYes.when the distance to the center of the charge is less than its radius? AG?? I was referring to the situation where the test charge is within the boundary of the source charge, assuming the latter has a finite radius. If the singularity is resolved by modifying the model of the source charge, can we conclude that a quantum theory of the EM field is NOT necessary to resolve this particular singularity? If so, what's the motivation of developing a quantum theory of EM? AGThe notional singularity isn't the only reason for wanting a quantum theory of gravity. It's a also a matter of consistency in interactions and what goes on the right-hand side of Einstein's equation. BrentI was referring to a quantum theory of EM, not GR. Are all the singularities in the classical theory of EM resolved by changing the model of particles? AG
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