After an early military career in signals analysis, I went back to college. I was astonished that the EE students, even many of the post-grads, had little idea what the equations they memorized actually meant. They had no intuition for how waves acted and interacted. The things they teach at school ...
"Shut up and calculate" isn't just a problem for physicists. It pervades engineering as well. It's that model-based intuition you mention that makes the difference between a journeyman and a maestro.
Imaginary test particles that respond to fields but do not affect them is the original sin of EM theory. (also the idea of uninvolved "observers")
Sometimes the potenial itself matters, not just the gradient - Aharonov-Bohm
David Hestenes' zitter model of the electron ( https://arxiv.org/abs/1910.11085 ) reconciles QM and visualizability while making novel verified predictions; his real-valued Dirac equation, using Geometric Algebra rather than matrices, endorsed by Dirac himself, discovers an unknown (phase?) field, beta, in the definition of psi, apparently related to a residue of multiparticle systems even in the single-particle case.
Father of chipmaking and Feynman colleague Carver Mead's short, clear book, Collective Electrodynamics, notes that there can be no single-charge photon emission or absorption, there must be an exact resonance between emitter and absorber, which though they may be separated by billions of years and an equal number of light-years have zero 4D distance. Though Mead is the most eminent figure in his field, and his theory is not only sound but gives true intuitive understanding of what was mysterious before, as with Hestenes, his most brilliant work has been ignored. https://www.google.com/books/edition/Collective_Electrodynamics/g9cGEAAAQBAJ?hl=en
"It is evident that this manner of handling problems in electrodynamics can be of only approximate validity. The motion of charged particles in external force fields necessarily involves the emission of radiation whenever the charges are accelerated. The emitted radiation carries off energy, momentum, and angular momentum and so must influence the subsequent motion of the charged particles. Consequently the motion of the sources of radiation is determined, in part, by the manner of emission of the radiation. A correct treatment must include the reaction of the radiation on the motion of the sources.
"Why is it that we have taken so long in our discussion of electrodynamics to face this fact? Why is it that many answers calculated in an apparently erroneous way agree so well with experiment? A partial answer to the first question lies in the second. There *are* many problems in electrodynamics which can be put with negligible error into one of the two categories described in the first paragraph. Hence it is worth while discussing them without the added and unnecessary complication of including reaction effects. The remaining answer to the first question is that a completely satisfactory treatment of the reactive effects of radiation does not exist."
-- J.D. Jackson, Chapter 17 [last chapter in the book]
Looking at my textbooks and notebooks also. Yes, see the fundamental flaw in optics, where so much is build on the premise of a plane wave. Easier to compute and convert with Fourier Transforms, than handling spherical waves (closed lines). The wavelengths for physical applications allow the small-angle and other approximations to work well enough, which is not the condition for EM applications up through millimeter wave.
About halfway through the section, the setting aside of Newton's Laws of motion clicked. Charge has to absorb energy for acceleration, to change velocity and momentum. Where does the energy come from, to act on a charge and accelerate it? It has to come from a field supplying energy.
That’s another reason I appreciate Whittaker's analysis of “Theories of Aether and Electricity.” Whittaker argued that “the expounders of the classical theory have been led astray by that artificial and (as we now know) physically impossible creation of mathematical analysis, the infinite plane-wave of light.”
"Consider a spherical cow" is apparently a warning, as much as it is a joke.
So many simplified of models may be geared to get as rapidly as possible to the calculation phase. But, we have to ask the question "can the model be linked directly back to the actual physical phenomenon under consideration, or via a more complex model of similar type and kind?"
How many of these models are Taylor Series expansions that are "epicycled" into a calculation mode, then set aside as good enough to grind out the necessary numbers?
Freeman Dyson introduced epicycles to save the day --er-- theory.
And with each Feynman diagram likely describing a less impactful component of the field, now iterating each term to be a correction to a modification is just Taylor Series expansion of a different type.
The horrible element here is the assumption that the form of Schwinger's g-value was correct. If g = 1 + [1/2](alpha/pi) is wrong, then the entire iterative process just hides the mistake while obfuscating the source.
Correct - radiation is the light or radio waves emitted by the electron as it is accelerated in the cathode ray tube.
As I understand the thinking of Assis, Ampere, and Weber, there is no such thing as light, just the accelerating electron in the cathode ray tub exerting forces on the electrons in the rods and cones of our eyes causing a physical stimulus we interpret as light.
In my thinking, fields do have an independent existence that does not depend on there being an eyeball or antenna to detect them.
The point I make about a single charge model of radiation is that physicists started from the cathode ray tube and modeled the radiation as a function of the single charge, ignoring the other charges and fields involved in repelling the electron from the cathode and attracting it to the anode. That leads to the problem of radiation reaction. A proper model of radiation has to include the charge or charges that interact to give rise to the radiation in the first place. The most simple model of that is a dipole.
No offense taken. Comments like yours helped get the Weberian Electrodynamic perspective on my radar, and I've learned a lot from you and other commenters.
After an early military career in signals analysis, I went back to college. I was astonished that the EE students, even many of the post-grads, had little idea what the equations they memorized actually meant. They had no intuition for how waves acted and interacted. The things they teach at school ...
"Shut up and calculate" isn't just a problem for physicists. It pervades engineering as well. It's that model-based intuition you mention that makes the difference between a journeyman and a maestro.
Disconnected thoughts:
Imaginary test particles that respond to fields but do not affect them is the original sin of EM theory. (also the idea of uninvolved "observers")
Sometimes the potenial itself matters, not just the gradient - Aharonov-Bohm
David Hestenes' zitter model of the electron ( https://arxiv.org/abs/1910.11085 ) reconciles QM and visualizability while making novel verified predictions; his real-valued Dirac equation, using Geometric Algebra rather than matrices, endorsed by Dirac himself, discovers an unknown (phase?) field, beta, in the definition of psi, apparently related to a residue of multiparticle systems even in the single-particle case.
https://davidhestenes.net/misc/Hestenes_2016_-_The_Genesis_of_Geometric_Algebra,_A_Personal_Retrospective.pdf (eq. 14)
Father of chipmaking and Feynman colleague Carver Mead's short, clear book, Collective Electrodynamics, notes that there can be no single-charge photon emission or absorption, there must be an exact resonance between emitter and absorber, which though they may be separated by billions of years and an equal number of light-years have zero 4D distance. Though Mead is the most eminent figure in his field, and his theory is not only sound but gives true intuitive understanding of what was mysterious before, as with Hestenes, his most brilliant work has been ignored. https://www.google.com/books/edition/Collective_Electrodynamics/g9cGEAAAQBAJ?hl=en
This fellow applies conformal geometric algebra to transmission lines and publishes about antennas: https://www.researchgate.net/profile/A-Arsenovic
Excellent snippet. Well written and thoughtful.
Ah, if only scientists were taught to think instead of merely memorize and compute.
Copenhagen interpretation delenda est!
"It is evident that this manner of handling problems in electrodynamics can be of only approximate validity. The motion of charged particles in external force fields necessarily involves the emission of radiation whenever the charges are accelerated. The emitted radiation carries off energy, momentum, and angular momentum and so must influence the subsequent motion of the charged particles. Consequently the motion of the sources of radiation is determined, in part, by the manner of emission of the radiation. A correct treatment must include the reaction of the radiation on the motion of the sources.
"Why is it that we have taken so long in our discussion of electrodynamics to face this fact? Why is it that many answers calculated in an apparently erroneous way agree so well with experiment? A partial answer to the first question lies in the second. There *are* many problems in electrodynamics which can be put with negligible error into one of the two categories described in the first paragraph. Hence it is worth while discussing them without the added and unnecessary complication of including reaction effects. The remaining answer to the first question is that a completely satisfactory treatment of the reactive effects of radiation does not exist."
-- J.D. Jackson, Chapter 17 [last chapter in the book]
I am very grateful for your comment, and I have incorporated it into my summary for Chapter 4, publishing tomorrow morning.
You're welcome.
That passage above bothered me bigly when I read it three and a half decades ago. Greatly looking forward to your resolution.
Which edition of Jackson is that?
Second Edition. Pages 780-781.
Looking at my textbooks and notebooks also. Yes, see the fundamental flaw in optics, where so much is build on the premise of a plane wave. Easier to compute and convert with Fourier Transforms, than handling spherical waves (closed lines). The wavelengths for physical applications allow the small-angle and other approximations to work well enough, which is not the condition for EM applications up through millimeter wave.
About halfway through the section, the setting aside of Newton's Laws of motion clicked. Charge has to absorb energy for acceleration, to change velocity and momentum. Where does the energy come from, to act on a charge and accelerate it? It has to come from a field supplying energy.
Re unphysical plane waves: Throw in QED and solid state physics.
That’s another reason I appreciate Whittaker's analysis of “Theories of Aether and Electricity.” Whittaker argued that “the expounders of the classical theory have been led astray by that artificial and (as we now know) physically impossible creation of mathematical analysis, the infinite plane-wave of light.”
"The model's the thing, wherein I'll catch the conscience of the king."
"Consider a spherical cow" is apparently a warning, as much as it is a joke.
So many simplified of models may be geared to get as rapidly as possible to the calculation phase. But, we have to ask the question "can the model be linked directly back to the actual physical phenomenon under consideration, or via a more complex model of similar type and kind?"
How many of these models are Taylor Series expansions that are "epicycled" into a calculation mode, then set aside as good enough to grind out the necessary numbers?
Grief, now I am thumbing through old textbooks.
This video is a more accessible introduction to what's wrong with QED.
https://www.youtube.com/watch?v=xaC_aKqjCXU
Freeman Dyson introduced epicycles to save the day --er-- theory.
And with each Feynman diagram likely describing a less impactful component of the field, now iterating each term to be a correction to a modification is just Taylor Series expansion of a different type.
The horrible element here is the assumption that the form of Schwinger's g-value was correct. If g = 1 + [1/2](alpha/pi) is wrong, then the entire iterative process just hides the mistake while obfuscating the source.
Lord, have mercy.
Indeed.
Just wait until we get into this: https://www.researchgate.net/publication/338980602_Something_is_rotten_in_the_state_of_QED
Oh, most certainly QED. I read the linked paper some time ago. Thanks for the video link.
Pet theories have to be the first ones to go under the microscope.
I don't want to do the experiment where I turn into a supernova, if that's OK with you? Just want to be clear about that before we get to Chapter 8.
Jus don't reach for your mouse or touch screen and we'll all be fine.
Correct - radiation is the light or radio waves emitted by the electron as it is accelerated in the cathode ray tube.
As I understand the thinking of Assis, Ampere, and Weber, there is no such thing as light, just the accelerating electron in the cathode ray tub exerting forces on the electrons in the rods and cones of our eyes causing a physical stimulus we interpret as light.
In my thinking, fields do have an independent existence that does not depend on there being an eyeball or antenna to detect them.
The point I make about a single charge model of radiation is that physicists started from the cathode ray tube and modeled the radiation as a function of the single charge, ignoring the other charges and fields involved in repelling the electron from the cathode and attracting it to the anode. That leads to the problem of radiation reaction. A proper model of radiation has to include the charge or charges that interact to give rise to the radiation in the first place. The most simple model of that is a dipole.
No offense taken. Comments like yours helped get the Weberian Electrodynamic perspective on my radar, and I've learned a lot from you and other commenters.