There are NO examples of real, conservative forces that can be mapped as a two-body interaction (the foundation of Newtonian Physics = Classical Mechanics - CM). Math physics is a series of fictional 'Class Exercises' of unreal "Physics in a Box" (isolated, mental models unrelated to reality).
All real situations begin with the pre-existing situation of the initial condition, without describing the active agency for setting up this spatial separation with no relative motion between them. This agent (usually a human, brings biological energy to the situation, which is removed before Exercise begins.)
Try to bring a mass (object) to a given height above the Earth’s surface and keep it there without instantaneous subsequent motion or stretch a spring before letting go. In other words, we need a 3-Body system but Poincare showed these are unstable (as Newton, knew gravitationally). If PE is bogus, then so are Lagrangian and Hamiltonian CM. The only real energy (as Clifford pointed out) is the energy of relative motion i.e. kinetic energy.
Similarly, then QM is also without substance.
So, the question may be reformulated: have mathematicians conned the world since 1687 pretending they have a symbolic map of the world (aka physics)?
"Hydrogen atom is two-body system"
How about electromagnetic field, Eric?
The question whether or not the concept of "force", --considered as a function of "positions" or even velocities of (macroscopic) objects, and in conjunction with an "equation of motion" which includes this function or derivates thereof--, or "potential" makes sense for a mathematical description of motion of (macroscopic) objects is related to the question to what extent it makes sense that these objects can be characterized by the concept of "spatial distance" and, of course, by the concept of "time" at all.
If it turns out that there are some particular objects and some particular motions which can be mathematically and numerically described by a mathematical model in a reasonable approximate manner, then this model can be considered as a reasonable candidate for further investigations.
It seems to be typical for many physicists, not for mathematicians, of the past as well as of contemporary times to think or to claim that a mathematical model reflects a part of "reality" completely, if it agrees just with a finite number of some "experimental facts", without being aware that the mathematical models as well as the "experimental facts" are mostly based on (hidden) assumptions which have the character of hypotheses. With regard to CM,CFT,QM,QFT it seems that physicists mostly tacitly assume that "space" and "time" have the character of a continuum, but never give arguments which could justify such an assumption even for physical phenomenons below the microscopic scale. Physicists who try to look beyond the methods of theoretical physics are unfortunately outnumbered.
"Modern" general aspects concerning mathematical models and physical theories can be found in "Die Grundstrukturen einer physikalischen Theorie" by G.Ludwig, Springer, 1978/1990 ( French translation available too ).
https://web.archive.org/web/20100527061517/http://www.mathematik.tu-darmstadt.de/~ziegler/ludwig.html
Dear Herb,
the effort to bring about potential energy is something which begins with Leibnitz in 1700 and went on with Clapeiron and had its sinthesys in 1850 with Helmoltz who defined the conservations. Mathematicians usually hate conservations, most of the time they do not understand it... Without them we would not have much progress in Physics.
The last scientists who tried to overcome the idea of conservations was Bohr in Quantum Mechanics. In the attempt to justify a missing balance in a interaction he made the HP the conservations may not be respected in QM. The great Fermi was so sure of his knowledge of physics, that he affirmed that it was not possible to infringe such laws. He made the HP of a new particle in the balance as a pure "angular momentum balance" : what he called "il Neutrino".
Dear Herb: Very good question. I sometime say “The mathematics are a language that we use in many place and in physics too. But the physics is not a result of the mathematics.”
You say “Similarly, then QM is also without substance.” One aspect of the pre-existing situation of the initial condition of the QM is for example the periodic table. Its discovery is the very beginning of the QM. Then the transitions between to different levels have allowed to discover the different quantum numbers. But the measurement of the magnetic moments has led to forget that the quantification between the proton and the electron, for the hydrogen atom, concerns not only the two directions of the momentum but also the axe of the rotation. Forgetting this aspect we miss the two halve integers numbers which are not the spin, that is one for the momentum the second for the axe of rotation.
Your question generally seems to be about what is `real' in physics and what concepts are just `mathematical'. The problem is that meaningful concepts in physics tend to be mathematical concepts, or for sure have concrete mathematical formulations. So to me separating in a full way the `physical concept' from the `mathematical concept' is not really possible.
A better question you should ask is if a concept is useful or not. By useful I mean in extending conceptually our understanding, but also aided in practical issues. I argue that the concept of potential energy, the Lagrangian formulation and the Hamiltonian formulation of classical mechanics has proven useful. These classical ideas are essential in standard approaches to quantum mechanics and so these notions/concepts have proven their worth in the quantum context also,
So I am not sure if a Lagrangian is `real' in any deep metaphysical way, all I know is that it is a useful concept that helps us describe what we can see,
We are drifting toward Philosophy I think ...and opinion.
A pure mathematical fiction might be the Minkowski space-time for example, an "escamotage" found in the early days of high energy physics to give a framework to some non classical "effects".. whose predictions in most cases are still valid for electrodynamics but cannot host gravitation.
The role of mathematics in science, be it physics or chemistry is to present great many concepts in a concise mathematical formulation and to quantify concepts leading to a mathematical structure. Mathematics serves science to elegance and makes aesthetic.
Dear Stefano: Don't forget Joules, Thompson and Rankine (before Helmholtz) who all contributed to the invention and propagation of the 'generalized' view of 'Energy' that must then be "conserved".
PS I assume you meant Hamilton's Principle when you used 'HP' - always a good idea to use the full expression (e.g. FE) before reusing the abbreviation.
Dear Xavier: Bohr cheated when he over-extended his insights from the simple one-electron hydrogen atom to all multi-electron elements WITHOUT taking intra-electron repulsions into account to provide a "Theory of the Periodic Table". All he proved (as does wave mechanics) is that ANY restricted spatial motion can be represented by sets of Complete Functions (e.g. Fourier's trigonometric functions or Spherical Harmonics in 3D).
PS Exaggerating one's insights has a long tradition in math beginning with Pythagoras and his observation that a harp's note is related to its string length was extended to his claim that all of "reality" is number".
Dear Andrew James Bruce: Yes I am deliberately introducing a topic that is usually dismissed as 'metaphysics' because it challenges the assumptions that the science of physics is based on - easier to dismiss than to argue the case. I view physics as the study of MATERIAL REALITY and math is its representational tool - similar to a postcard of a holiday scene being only a sub-set representation of the real geography.
You introduce the idea of 'usefulness' without the necessary linkage: "for whom". Newton's math was being discussed for well over 100 years before it impacted engineering (the British Industrial Revolution based on the Steam engine). Mental techniques, like concepts (which cannot be seen), were introduced about 2500 years ago by the Ionian philosophers, who realized they could generalize from the particular to the plurality. As intellectuals, they were too ready to dismiss the skills of tradesmen like builders and potters (for example) because they were the privileged smart sons of the aristocracy or rich merchants, who were not going to 'dirty their hands'. As I said before, the math techniques of LaGrange and Hamilton have provided dozens of class-exercises for thousands of students but what real examples have they described, apart from the 2-body planetary and hydrogen atom?
Dear Stefano: I am not 'drifting into philosophy' but steering there at full-speed. I will remind readers that these areas of investigation of reality were long called "Natural Philosophy' before they were professionalized into state-funded academic specialties. Today, few real philosophers are prepared to climb the huge mathematical walls erected around the now 'sacred' subject of physics so they can bring their analytical talents to bear.
Dear Herb,
You have asked the question and also provided inside the clue to its answer. You raised two basic old problems : 1. Is mathematics more than a symbolic language for describing the real world. 2. Do mathematical continuum concepts lead to a better cognition of the reality rather than the discrete Kronecker inspired method.
We include unawaringly arithmetics in mathematics as if they are one and the same concept. Arithmetic however is dealing only with numbers and is certainly needed only to quantify measurables in the physical world. Not so with the more abstract mathematical methods which are only a more systematic than the natural language of describing the physical laws. Fields theory of the continuum is indeed as you suggest an entirely abstract concept not more revealing than the direct action at a distance concept of the discrete methods. The great problem I see is that the entranced current Gravitational or EM fields theories for example rely on the artificial assumption that one needs additional travelling energy particles at c velocity or even virtual ones to explain the interaction between two or more material bodies at any distance or time-space interval. This is indeed an artificial construction as you hint in your articles.
These are my current rudimentary thoughts to your challenge for now. Lets see how is this thread going to evolve in more depth with time.
Dear Aaron: Thanks for your thoughtful reply. Yes, I too am zeroing in on the hidden assumptions underlying the human-scaled action of COUNTING discrete, stable objects. We simply assumed that this useful (business) technique has universal validity, even at the unobservable electron level (the basis of atomic physics). Too many people seem unaware of the hidden evolution of field theory, especially Maxwell's religious motivation to abolish Newton's atheistic particulate action-at-a-distance theory of gravity.
> I view physics as the study of MATERIAL REALITY and math is its representational >tool - similar to a postcard of a holiday scene being only a sub-set representation >of the real geography.
Physics is the construction of mathematical models of nature and the testing of said models. Because of this it is not easy or even possible to dismantle things clearly into `physics concepts' and `maths concepts'.
That said, taking a pragmatic view, the only things that are `real' are those that we can measure the properties of, so things we can observe.
We cannot directly observe a Lagrangian or Hamiltonian but we can use these concepts to build models of nature. I don't think one can say much more that this.
>You introduce the idea of 'usefulness' without the necessary linkage: "for whom".
For mankind as a whole.
>Newton's math was being discussed for well over 100 years before it impacted >engineering (the British Industrial Revolution based on the Steam engine).
So Newtonian mechanics is useful?
>As I said before, the math techniques of LaGrange and Hamilton have provided >dozens of class-exercises for thousands of students but what real examples have >they described, apart from the 2-body planetary and hydrogen atom?
Are you asking for more real world examples where classical mechanics has proved useful?
Classical mechanics as a whole is fundamental in lots of engineering applications. But, from your question I take it you are looking for applications of Hamiltonian and Lagrangian formulations specifically.
For example, we have applications in control theory, trajectory planning, image processing, computer graphics and so on.
--------
I will add that generally one has to get used to the idea that physics is a description of reality and not reality itself. There are plenty of things in physics that are not even observable, and so you have to wonder in what sense do they `exist'. Well, if they are not observable then I would say that they don't exist in any deep metaphysical way, even if these things are fundamental in the physics. At the end of the day you want to calculate things that can be observed and then pragmatically these things `exist' (or really the objects with these properties that we can define and measure). But then we are still stuck with mathematics as mathematics is needed to interpret what the `needles' on the output of your experiment are doing. Again, it seems to come back to the `mathematical concepts' agreeing with what we can measure. If they `exist' or not seems not to matter if they are in principle not observable.
Dear Herb: You write “Bohr cheated when he over-extended…..”, you are right as long as we just consider concept of Potential Energy without trying to propose an interpretation of the potential. But Einstein in 1905 with his study of relativity showed that there is no absolute space and that physical laws should be independent of the place of observation, which made a giant leap in physics. As a result it did not come to anybody the idea that there could be a lack in this analysis. Yet the difficulties encountered by the corpuscular approach of quantum mechanics are well related to the notion of space. Indeed there is no absolute space and one has to question how the space is built. On the macroscopic scale it is easy to define it in relation to the objects which occupy it, without forgetting the gas that fill volumes between objects, gases that transmit the sound for example. But what about the scale of the atom? Up to now electromagnetic field has allowed us to write the motion of the electron around the nucleus. But Einstein has also taught us that the mass is equivalent to an amount of energy by establishing the relationship E=mc2. This energy is huge so that it suggests that the electromagnetic field can be described by a discontinuous flow of grains of matter, constituting the mass, between the proton and the electron. More precisely through two fluxes: one from the proton to the electron the other from the electron to proton, these two fluxes not following everywhere the same route in such a way that the resulting action creates the movement. This allows at the scale of the grains to continuously respect the amount of action define per the number of quanta of the state of each electron and give a simple explanation of the fact that each element in the periodic table keeps the quantum properties of all its electrons. More details in “The Wave and the Quantum State” and in “Quantum State and Periodicity”
Dear Xavier:
As I said before the problem with Bohr's model of multi-electron atoms is that he used only his SINGLE electron model of the hydrogen atom while ignoring the expected huge INTRA-electron interactions in a multi-electron atom.
I do NOT view space as a SUBSTANCE - this is continuing to use the Old Greek method of reality analysis. I view space (like Leibniz) as a RELATIONSHIP, which is where Classic Philosophy falls down. I also dismiss all FIELD concepts as simplifying mathematical fictions. I support Feynman, Dirac, Newton, Demokritus in the particle model of reality.
I challenge the idea that SET-Theory is the basis of arithmetic. All objects in a set are considered to share a common defining property that justifies their set-membership.
There is only one UNIVERSAL property of all objects - whether they EXIST or not. (Certainly during the human ACT of counting, which does NOT need any set ideas; this is why societies invented counting long before any higher math was ever conceived.)
Dear Herb,
The SET theory is a dangerous zone of discussion. Kronecker did not accept it and persecuted Cantor for it. The philosophical dealing with the infinite notion and its opposite number zero concept takes us time and again into a largely hotly disputed field, just like our lack of understanding the origins and constitution of space and time.
Dear Aaron: I am deep into researching these areas for an upcoming essay.
Their roots go right back before writing reached Greece and involve the Oral traditions of religion and early intuitions of the INFINITE (by looking Heavenward). Yes, they are contentious because people make these metaphysical assumptions about the foundations of all they believe in and resist ALL threats to them.
Dear Herb and Aaron: Thank for your clear position. Before to discuss the QM and propose an explanation of it I have given with Lochak a theoretical calculation of the magnetic momentum based on Dirac’ theory, see “Total angular momentum” where the coherency is better than 1% with the experimental results. In this work we make the assumption that the total angular momentum of each individual electron is still present in an atom and also in a crystal despite the strength of the perturbations.
I do not know if my approach is the best but you cannot refute it without a proposal for all these results.
Dear Xavier: A deep problem in philosophy is multi-theory mapping, where more than one theory fits with the numbers used to validate theories.
This is why I am raising the METHODOLOGICAL issue of introducing a space-based function as a mathematical technique for eliminating time from physics.
It's foundations that matter, not predicting how high are the waves on the pond. [Sorry for my mixed metaphors but as Lakoff has shown, we think very much via metaphors.]
Dear Herb: It is always enriching to discover new approach but I am a little disappointed, the time is the life. Without time you will lose your memory.
How will you describe the energy of a photon and its speed?
I got first two experimental theses and if I was good in mathematics, but I found that often the physic is lost with too much math.
Dear Herb,
I do not see how you expect to 'freeze' time in theoretical physics. There is indeed some isomorphism in time and space comparing the wavelength and period concepts in a plane EM wave but for time we cannot go experimentally in the negative direction. It also seems to be strictly a scalar rather than vector.
I am curious to see your space-time 'frozen' function concept.
Gentlemen: My apologies. People here seem to have totally misunderstood me.
I am IN FAVOUR of RESTORING TIME to center stage. I was raising the specter of mathematicians who have replaced time with spatial ideas, like potential energy.
Also, nowhere have I suggest that time might be "frozen'. This is again another human simplification: a photograph is "a spatial artifact that freezes time", giving us a false idea of the ever-changing nature of time.
Our personal memories do NOT work with a series of static images (not even 15 frames per second) but we uniquely reconstruct film strips in a creative manner that may bear some resemblance to PARTS of our experience.
How "There are NO examples of real, conservative forces that can be mapped as a two-body interaction"? The attraction/repulsion between two charges at rest is not a conservative field? And the attraction between two masses at rest is not a conservative field?
Herb says: "I do NOT view space as a SUBSTANCE - this is continuing to use the Old Greek method of reality analysis. I view space (like Leibniz) as a RELATIONSHIP, which is where Classic Philosophy falls down. I also dismiss all FIELD concepts as simplifying mathematical fictions. I support Feynman, Dirac, Newton, Demokritus in the particle model of reality"
Who says that a model of continuous field is correct? In QFT each field has a carrier, a particle, which carries a quantum of energy. The quantum of the electromagnetic energy is the photon. The question is what happens when two electric charges are separated by vacuum, i.e. where is the photon? And the answer is: the vacuum has to be held responsible for storing the energy.
That invites in continuation the question: what is vacuum? Don't take for granted that vacuum = "nothing".
Dear Herb,
To your question: "have mathematicians conned the world since 1687 pretending they have a symbolic map of the world (aka physics)? "
The answer can only be no. They did the best they could with the extent of knowledge then available. The same each time more complete theories were established over time. Nobody cheated. Everybody did what they could with what they had available.
To your quite appropriate and capital title question, my answer is that it was adequate (and still is) for issues of every day life at our macroscopic level, but that the answer can only be yes at the submicroscopic level where charged electromagnetic elementary particles rule.
The reason is that the current momentum / Lagrangian / Hamiltonian concept never was adapted to account for the possibility that kinetic energy could remain adiabatically induced in charged particles even when their translational motion is hindered.
Unfortunately, this antiquated concept still rules all currently useful physics theories.
If you have a look at this first tentative analysis of adiabatic processes at the sub-microscopic level since the Born-Fock theorem of 1928, you may connect with the hints I collected on this issue:
https://www.omicsonline.org/open-access/on-adiabatic-processes-at-the-elementary-particle-level-2090-0902-1000177.pdf
Time cannot be elliminated from our description of the universe - see the conservation of the relativistic interval when passing from an inertial frame of coordinates to the other: c2t2 - (x2 + y2 + z2) = const.
The time is connected with evolution (change). Systems which don't change in time are a particular case, and the stationarity in time holds only in a particular frame of coordinates.
Dear Sofia,
I agree with you that time obviously cannot be disconected from motion, but it can be disconnected from energy induction in charged particles, since such induction is strictly distance dependent between charged particles.
Dear André,
I have no idea what is "energy induction" in charged particles. I know what is magnetic induction. People use here all sort of words that I am not so sure whether they have a rigorous definition.
If in a conservative field one releases a charge to move freely, its variation in kinetic energy is proportional with the difference in potential between the initial and final equipotential surfaces. If the geometry does not change during the time of the experiment (which is rare) then ideed you don't need the time concept.
But in the general case time is inherent in physics. Without CHANGE, the Big-Bang and what followed, wouldn't have happened. As a very little consequence, life wouldn't have appeared (including us).
Dear Sofia,
In electromagnetism, the kinetic energy induced in two charged particles is inversely proportional to the distance separating them, as per the very definition of the Coulomb force in action between them, irrespective of the time elapsed if they are maintained at a fixed distance, and it adiabatically varies in both particles if they are in motion relative to each other, irrespective of their relative velocity, thus irrespective of the time elapsed during the corresponding motion sequence.
There are no surfaces at the sub-microscopic level. Only charged particles interacting.
Dear André,
Take a metallic ellipsoid positively charged. The equipotential surfaces around it are ellipsoidal. Therefore, at some distance from the ellipsoid center the potential is not inverse proportional with that distance, it is more complicated. A sphere around the center of the ellipsoid crosses a couple of equipotential surfaces.
Dear Sofia,
You are describing macroscopic set ups with macroscopic objects.
I am describing the behavior of elementary electromagnetic particles at the submicroscopic level, the foundation of physical reality, the only level where kinetic energy can be induced in the massive charged electromagnetic elemetary particles that make up all macroscopic masses.
This fundamental level needs to be clearly understood if we ever want to clearly extrapolate the properties of macroscopic setups emerging from the properties of these elementary electromagnetic particles.
Dear André,
I don't know what is SUB-microscopic level.
But I'd like to tell you something. The law 1/r of the electric potential has a quite strange turn at the quantum level. An electron can be absorbed by a proton producing a neutron, and a neutrino is emitted. But I never saw that in this process are involved infinite energies as the 1/r law implies if two elementary charges really fall on one another.
However, I am following this question because I am interested in the issue "where is stored the potential energy of static fields", not in side issues. People usually deviate with their comments from the question itself and the main question is abandoned. I wouldn't want to contribute to this custom.
Dear Sofia,
You would become cognisant of what gives at the submicroscopic level for the stable matter making up the univese if you were to analyze all past non desctructive scattering experiments carried out from the time the first cylotron came in service, followed by the Betatron, then the great SLAC accelerator before 1968, year at which destructive scattering began to be used at SLAC and other linear accelerators and cyclotrons, which irrecuperably muddled up the perspective of the following generations, who were badly informed with confusing information on the nature of scatterable charged point-like behaving elementary particles.
You would discover that all existing atoms can only be made of only 3 stable massive and charged elementary electromagnetic particles as building material, whose properties determine the properties of atoms and all macroscopic bodies.
You would eventually discover the function of the Coulomb force with respect to these charged point-lile behaving elementary particles.
At some point, you may also come to question the whole concept of kinetic energy morphing into potential energy and vice versa. I assure you that this is not a side issue.
@andre Michaud
Dear Andre:
You are simply extrapolating down to TWO electrons from macroscopic experiments with Gazillions of electrons. You are exhibiting my point of math exaggeration.
Coulomb may never have even conducted "his" original experiment as it cannot be replicated. [see ref# 92 of attached paper].
Dear André,
I am not a novice in physics. I disagree with the word "sub-microscopic", that's all.
The word "sub-microscopic" seems to me superfluous - even dangerous. The microscopic level is the quantum level, and there is no sub-quantal level. As to the 3 components of an atom, as you say, the atomic physics knows much more - see the Standard Model in QFT.
Dear Sofia,
You are free of course to disagree with the word.
I did not invent the term however. You can find it in any good dictionary.
The editors who invited me to publish found it quite appropriate also, so if you find it dangerous, I invite you to take up the issue with them, since I do not make policies in academia.
I personally find it quite appropriate to describe the level at which the point-like behavior of elementary electromagnetic particles can be measured during scattering experiments.
You say that there are much more components in atoms than the 3 I mention.
I invite you then to direct me to peer-reviewed experimental accounts of non-destructive scattering that confirm the presence of any other stable point-like behaving electromagnetic particles besides the electron, the up quark and the down quark inside atomic and nuclear structures.
I know the Standard Model and QFT, but there are more than one way to describe the submicroscopic level of physical reality. I prefer the infinitesimally progressive approach, coupled with experimentally confirmed non-destructive scattering experiments.
Dear André,
We waste time here. The true issue is where is stored the potential energy.
About terminology, it's not in dictionary that one should look for the words common in QM, but in the literature. In an atom one finds 3 stable particles, electron, and proton, and neutron in the nucleus, but it's not a sufficient description. You see, the beta decay involves neutrinos and at basic level the three bosons W+, W-, and Z. And the nucleons are formed from quarks and gluons.
These things are known, why should we waste time with them?
So, let me return to the question of Herb. let me say some thoughts of mine. It's obvious that the potential energy is stored in the vacuum, which is not just "nothing". However, these static fields have an interesting property: if two charges at rest are suddenly set in motion and then moved with uniform velocities, the electrostatic field goes with them unchanged. The same if instead of them we speak of two masses and gravitational field. You see, the vacuum is known as indicating no preferred frame.
In my mind, the static fields are stored in the vacuum due to some polarization of the vacuum, I repeat, I don't think the vacuum as emptiness. So, I compare the behavior of the vacuum with the behavior of a dielectric in which we place two electric charges. The dielectric between the charges gets polarized, s.t. each charge "feels" the presence of the other. As long as the charges are at rest, the polarization of the dielectric is static. But if the charges begin to move, as I said above, there are all sort of transients in the dielectric, because molecules in the dielectric that were polarized return to non-polarized state while other molecules, on the way of the charges, become polarized.
I don't know enough for being able to say whether such transients occur in the vacuum.
Dear Sofia,
You have the wrong information about protons and neutrons. They are not particles, but systems of particles. In the list you gave, only the electron is a confirmed elementary particle.
This was determined by deep non-destructive scattering at the SLAC facility in experiments carried out between 1966 and 1968. See paper below.
I already gave my info regarding potential energy. I have nothing else to add in this regard.
http://www.slac.stanford.edu/pubs/slacpubs/0500/slac-pub-0650.pdf
Dear André,
let's make some order. Protons are stable. Neutrons are building blocks of the nucleus, but not stable. As to quarks, their instability is so high that one cannot find them isolated.
The trouble is that what we thing today as elementary particle, tomorrow may appear as having a structure. This is also known to everybody.
Anyway, I am not willing to deal anymore on what I said several times that is not interesting for me.
By the way, I read what you said. However, all the experimental facts known to us show that in classical physics the energy conservation is respected. Never happened that the kinetic energy of a body in a conservative field differed from the difference in the potential energy between the initial and final level.
Well, since this thread, at least as it seems to me, doesn't deal anymore with the question itself, I am not interested anymore.
Dear Folks:
As the great mathematician, W. K. Clifford pointed out that one can always guarantee Conservation of Energy by redefining the terminology - this has been the case with Energy of (Spatial) Position aka Potential Energy. This has the added bonus of eliminating time from the physics situation; a process begun with smuggling in the controversial concept of "infinitesimals" (see attached) and completed with P.E. Time being replaced with spatial ideas has a very long history.
Dear Andre:
We know you said your piece; now show that you are mature enough to read the extensive answer I attached for you. Solipsism went out with Descartes.
Dear Herb,
I have read your extended answer.
I saw no new data that would bring a mechanical explanation of how the EM energy quantum that makes up the mass of localized EM particles can remain localized while their local electric and magnetic fields mutually induce each other in the self-sustaining manner that explains the existence of electromagnetic energy in Maxwell's equations.
I saw nothing either that would explain why their EM energy quanta made of self sustaining electric and magnetic fields remain localized to display the point-like behavior that we can observe when they scatter against each other.
If I missed it, then please point me to this explanation. I will definitely analyze further.
From the state of my analysis, this is what is missing in the current theories.
Lacking such further data to analyze, I can't see what could change my conclusions that do lead to such mechanical explanations, and reveals the inadequacy of the current concept of conservative momentum / Lagrangian / Hamiltonian.
Dear Sofia,
We have conclusive and confirmed evidence that up and down quarks are stable and are the only physically scatterable elementary and charged building blocks of protons and neutrons. I provided one of the seminal papers issued by the SLAC facility team at the time. The rest is in the SLAC archive.
Unless fundamental laws of nature change over the course of time, that was already the case billions of years ago when there was no one to observe and measure it, and it seems to me that it will still be the case in billions of years in the future, whether we believe it or not.
Repeatable confirmed experimental evidence is just that: confirmed experimental evidence.
Mr Spencer,
I first opposed this question as being too provocative. However some of the answers implicitely tell how it could have been put, and provide some essence on the proposed reduction.
Yesterday I heard something new that may relate to local spatial gradients and integration, but it is more applied and therefore cast in a new question.
Dear Herb
Potential energy as a purely fictitious continuous function of space does not exist physically indeed. In my view the potential energy is any locked up energy in a confined space from spring to mass excluding raw energy such as photons.
More precisely, a "concept" is always a man made "conclusion", with its possible need to be revised if new unaccounted for pertaining data requires it.
Dear Christian,
Indeed calling a physically measurable effect a conceptual name such as energy, force etc., does not reveal its true existence or meaning unless you can predict by using basic mathematics or other proper logical system its future measurable influence on masses in space and time.
Thus using the simplest example coming to my mind now , one can calculate from the 'potential energy' of a spring with a mass m attached to it , its behavior when released. The same you do when calculating the nuclear energy released from the nucleons in your Accelerators experiments.
Hence giving a name to something philosophically abstract is only a practical way to deal in reality with a measurable quantity.
Dear Aaron,
You write:
"Thus using the simplest example coming to my mind now , one can calculate from the 'potential energy' of a spring with a mass m attached to it , its behavior when released."
This will be true if you release it horizontally, that is, perpendicularly to spring-mass system axis with respect to the location of the center of mass of the Earth.
It cannot be true if you release it in the direction of the center of mass of the Earth.
The problem is that for masses large enough to carry out such experiments at Earth surface level, the adiabatic increase in energy in the charged massive elementary particles making up this mass is infinitesimal for the short distances that the mass is in motion into and impossible to measure. It can be calculated however.
At the lower end of its travel, the mass will systematically be slightly larger than when at the top of its run as this adiabatic energy synchroneously fluctuates, half of which is measurable electromagnetic mass.
As I mentioned previously, mathematicians in 1687 did the best job they could with what was available to them, aka macroscopic masses to experiment with.
We have been playing with charged submicroscopic masses since Kaufmann started deflecting electrons more than 100 years ago. We now have a huge pool of data to revisit concepts established from the "apparent" behavior of macroscopic masses.
Dear Christian: the art of the Conn is persuading the gullible that they are seeing reality, see that great movie "The Sting" with Paul Newman. The mathematicians have conned the world by claiming that the comparison of two numbers is a confirmation of truth; thus: mathematicians compute a number and experimentalists are convinced that their experiment fits the theory and finds the 'same' value of the number. Theory confirmed.
Pythagoras pioneered this game and was reinforced by Plato for his own theological reasons. Academics have been keeping the games going ever since - far more effectively than the Olympics.
Dear Chris: discover? still accepting the Platonic brainwashing?
Math is a simplistic analysis of the one/many division of the world.
Check out my essay to see how little progress has been made.
Dear Herb,
I scanned your essay. Quite thorough and factual I admit.
Progress has been made however, simply not integrated to enhance working theories.
For example, the fact that the very substance of which the electron invariant rest mass is made of is actually electromagnetic energy, as established by the repeatedly confirmed fact, initially discovered by Blackett and Occhialini in the early 1930's, that massless electromagnetic photons of 1.022 MeV or more can be destabilized into converting to massive electron-positron pairs and that the mass of a pair of electron and positron meta-stabilizing into positronium configuration will reconvert back to massless electromagnetic photon state as the final inward spiraling stage of the positronium decay process, which was also initially confirmed by Blackett and Occhialini in the same period.
This opens the door to clarifying electromagnetic theory with regards to localized charged and massive particles.
Also, the already mentioned discovery at SLAC in the 1960's that up and down quark behave during scattering experiments exactly like electrons, their slightly higher masses and lower electric signs of charges intensity notwithstanding.
This opens the door to clarifying what common characteristics they may have with the better understood electron.
From my analysis, once correctly put in perspective, I am even convinced that the methods of QM will be adaptable to describe their resonance volumes within nucleons in a much more satisfactory way than QCD does.
Sofia, you said, "As to quarks, their instability is so high that one cannot find them isolated." The reason quarks are never found isolated is because the quark system is asymptotically free in SU(3)/color-charge gauge, in part due to the need for color charge conservation, which makes the coupling constant variable with energy and distance between the quarks, such that the strong force that holds the quarks together paradoxically increases as the distance between them increases.
Dear Eric: Yes it is analogous to the planetary model with one moon. We don't 'measure' this system directly but introduce a third object to "pick up" the EM 'radiation that is assumed in transitions. One cannot 'look' directly at one electron.
We just assume that Newton's gravity law has its analog at the electron level.
Dear Herb,
You are a highly versed intelligent person and I adjusted for a better understanding of physics and science from just reading your articles.
But in two cases you are driven to extremes:
1. That Mathematics is a tool for CONN
2. That the Human race becomes a plague in the UNIVERSE
For point 1 just consider the simple explanation of negative integer numbers as a reflection of the real natural set of positive numbers in a mirror where the mirror interface symbolizes the zero concept and the number of reflections as infinite. Isn't that a beautiful image of our real world ? You surely can continue this journey further to obtain the whole continuum number set which gives us the irrationals, transcendentals and their usage in physical models.
For point 2 it is clear that we cannot as a human race infect the universe before we become a 3rd civilization type as discussed by Michio Kaku.
https://futurism.com/the-kardashev-scale-type-i-ii-iii-iv-v-civilization/
But by then maybe some better more moral intelligence entities may appear.
there are many problems in mechanics that cannot be solved in the nice newtonian sense, we are especially aware since chaos theory.
but doing away with newton would not help philosophy or anything else
the concept of potential energy gradient as giving a conservative force is
essential yet.
electrostatic potential is not the same as gravitational potential,
the essential idea is the same.
There is no need to do away with Newton. Quite the contrary. Newton only needs to be adapted to take into account the energy adiabatically induced in charged massive elementary particles.
Newton smoothly integrates with Maxwell when this is done via correctly understood relativistic mechanics.
The potential energy gradient, valid transversally with respect to the perpendicularly oriented adiabatic energy induction process is totally invalid when applied axially and gives invalid results that have not been analyzed correctly, because the adiabatic gradient was undetectable during the macroscopic experiments carried out, due to the infinitesimal quantities at play in all experiments carried out axially with macroscopic masses, with the short axial distances involved at ground level.
This could be confirmed by new experiments specifically looking for such axial adiabatic mass variations.
In this regard, one glaring experiment that was completely misunderstood is the Hafele-Keating experiment. Misunderstood precisely due to this defect of the momentum concept with respect to axial adiabatic energy induction.
Your assertion that the electrostatic potential is not the same as the gravitational potential would make sense only if you could establish that the gravitational potential applying to the mass of the electron obeys an interaction law different from that of the charge of the electron since the electron is subject by definition to both interaction laws.
Otherwise, it becomes an illogical axiomatic assumption.
andre.
you are too nit picking, one acts on charge, the other on mass
that is why they are different.
sorry, could not understand your other remarks at all
potential, or potential energy is a scalar concept without direction.
only if you take a gradient is a direction associated.
Dear Juan,
I don't think I am nit-picking.
The electron is a single "object" possessing both a charge property and a mass property.
How do you suggest these two inverse square interaction laws operate if they are both present and acting at the same time on the same "object"?
By addition? In alternance at some frequency?
To my knowledge, the physically measurable interaction obeys only a single occurrence of the inverse square law.
From my analysis, there is no potential energy involved, only real adiabatic kinetic energy axially induced in electrons stabilized in atomic structures that may be hindered from being expressed otherwise than as a pressure towards atomic nuclei, which is where there is a disconnect with the current traditional concept of momentum / Lagrangian / Hamiltonian.
The only underlying physically existing gradient I see can only be made of the sum of each occurrence of such interaction between each pair of charges.
Each of these occurrences can then be seen as one unit occurrence in the multitude of such occurrences constituting a universal gradient made strictly of the addition of all such active occurrences between all existing charge pairs in the universe.
Contrary to QFT, where the presence of individual excited states affects the intensity of the local gradient, the presence of two electromagnetic particles is required for each discrete unit Coulomb force interaction occurrence to exist in the universal gradient, so the gradient is one of interactions intensity occurrences as a function of distance and not directly one of energy intensities, or density, as in QFT.
Although the gradient involves the Coulomb force, it does not involve the traditional representation as a potentially continuous electric field associated with this force, but uniquely the limited set of all really existing discrete interaction occurrences at play between the really existing charges in the universe as a discontinuous assembly of individual occurrences.
Since charged particles organize axially in atomic and nuclear structures, the intensity of the adiabatic energy induced in these charges can only vary axially in these structures.
Since the current concept of momentum that underlies all useful theories in their current state is strictly grounded on the Principle of energy conservation, I realize that this most probably will not make any sense to you either.
Sorry about this, but a complete change in paradigm is not easy to explain in a few sentences. I was at it for the best part of the past 20 years and the rationale is spread among 20 odd papers and then some.
Andre, another fundamental gradient does exist, and that is the time dilation gradient between inertial frames. Objects always accelerate in the direction of increasing time dilation, and the simple example of this is free fall towards a massive body (e.g. Earth), wherein the time dilation is greater at the surface of the earth than atop a mountain, for example. It is then possible to produce an accelerative force without the presence of a mass source, or without using conventional (combustion based) propellant, by imposing a time dilation gradient, using assymetric fields, across the length of a spacecraft, for example.
Dear Eric,
This interpretation of time comes from Einstein's relativity theories.
Time flow can certainly be visualized like this, but there are issues with his theories with regard to electromagnetism, as he himself mentioned in his last years, clearly mentioning that electromagnetism should be examined in relation to gravitation.
Masses are treated as having no internal structures, so the charges and motion of individual masses of the elementary particles whose masses add up to make their total macroscopic masses are not individually taken account of. Neither is the Coulomb adiabatic energy inducing force.
Event the mass of the electron is treated as having no internal electromagnetic structure.
From the electromagnetism perspective, the flow of time, actually the progression of the "present moment", appears constant across the universe.
I personally don't see curved spacetime in the picture.
Dear Christian,
You write:
"almost any system in physics is treated as if it had no internal structure"
You must take into consideration that our theories are manmade "representations" of the really existing systems. In other words they are "maps" that we built to represent the real "country".
Like maps, they will be no more detailed than we make them.
The map must not be confused with the real country, about which some details may not appear on our map, that we may not have noticed. If it is a mile wide chasm that doesn't appear on the map, we will fall into it if we reach it,even if it is not on the map.
The maps of the world that were made 500 years ago now appear strangely warped, but they were appropriate for maritime navigation, but would have caused any airplane to irretrievably lose its way.
You say that treating bodies as if they had no internal structure is fine as long as this internal structure has no influence on its external properties.
I'll give you just one example of the warping that the principle of conservation does and that prevents further exploration.
In traditional classical and relativistic mechanics, this difficulty is made particularly obvious with respect to the rotating motion of massive bodies, whose angular momentum is deemed to be conservative, which is a conclusion that disregards the fact that in physical reality, all macroscopic rotating masses can only be made of the sum of the masses of a number of captive elementary massive particles translating on circular orbits about the body’s axis of rotation, all of which are individually subject to the 2nd principle of thermodynamics, that mandates that the constant change in direction imposed on them de facto involves an expenditure of energy as work, which comes in contradiction of the definition of rotation as being conservative.
There is no way that the individual massive atoms captive in circular motion inside these bodies can be exempted from the 2nd principle of thermo. If you think so, please explain to me why. My conclusion is that rotation cannot be conservative except when the rotating body is captive of a natural least action equilibrium state that renews its lost energy due to an underlying factor that maintains its least action equilibrium state, such as astronomical bodies stabilized on their orbits.
I see a direct connection with the unexplained observed rotation slowing down of all bodies left to rotate in deep vacuum for extended periods of time after having been set in rotation from an initial impulse, such as both spacecrafts Pioneer 10 and 11, or the ball bearing of J.C. Keith’s experiment in 1963, that was made to rotate frictionlessly at high velocities in deep vacuum while suspended in magnetic fields, or the ball bearing in a similar confirming experiment conducted by J.K. Fremerey in 1973? Or even of individual electrons being made to translate on perfectly circular orbits in the Betatron during J.P. Blewett’s experiments in 1946?
Except in the case of the Blewett experiment which was left hanging without an answer when the Betatron was decommissioned, and that everybody lost interest into, very reassuring patches were applied that did not endanger the assumed "conservative" nature of rotating motion.
The concept is so deeply rooted into the thinking processes of everybody that even the electron is assumed to have a volume simply by finding no fault with the concept of spin as corresponding to an angular momentum.
This disregards the fact that no scattering experiment ever detected any unbreachable limit at some distance from their center that would have related them to a measurable volume, as was the case for protons and neutrons.
Nothing that has no volume can rotate. The then only logically possible cyclic process resoves to some reciprocating internal motion.
I could go on and on, but surely you see the point.
With our technology, it wouldn't be difficult to carry out many of the experiments I suggest to double check, just in case.
If I am wrong, so be it. Nothing has been lost.
If the Coulomb force really is not an attractive and repulsive force as it has been defined from comparison with the apparent behavior that was the only possible interpretation in Newton's time, but just an underlying adiabatic-kinetic-energy-inducing-(yet-to-be-correctly-understood-agent-that-we-name-the-Coulomb-force), then there will be work for everybody for decades to come rectifying theories and exploring new ground, and maybe provide us with powered space travel, who knows.
My analysis is now complete. The rest is out of my hands.
It is available for the community to act on or not.
dear andre
there are two forces acting at the same time. but the gravitational one is very much weaker, it is usually discarded in calculations.
I cannot believe it, already two persons wanting to do away with potential
energy. Any more?
It is true that any aritrary energy can be added to energy, it has no
fundamental zero, but the utility arises when you take the gradient. So even if in a sense undefined it is still a usefull concept. Cannot buy your alternative vision. Never heard of it before,
best regards, juan
herb
ther are some nanocircuits where they detect one electron at a time
going through.
the scanning electron microscope detects one atom at a time on a surface.
you dont see with your eyes directly, but you detect.
saludos, juan
Dear Juan,
You would have a valid counter argument only if you can provide a coherent mechanics of mutual induction of the electric and magnetic fields of the self sustaining energy quantum making up the invariant rest mass of the electron grounded on your conclusions, that explains why electrons behave point-like during scattering events.
Failing that, your conclusions can only be grounded on beliefs not completely synchronized with physical reality.
I was not trying to "sell" you my alternative vision. I was just answering your comments from the perspective I have.
You are entirely free to disregard all I have said and ignore my analysis.
It is entirely normal that you never heard of it before, because it was not explored before. It is now published and will remain available for those interested.
Dear Christian,
I stated the case as straightforward as I could.
I have great respect for your analyzing abilities.
Unless you can give me a reason that I can coherently relate to the 2nd principle of thermodynamics that explains why elementary massive particles captive on circular orbits about the axis of rotation of a macroscopic mass of which they are the building blocks, can avoid expending energy as work according to the 2nd principle of thermo on account of their constant change in direction, I can't see how I could draw any other conclusion than that induced rotation of macroscopic masses cannot be conservative since the tranlation motion of their constituting massive subcomponents cannot be conservative.
If all of the constituting massive subcomponents lose translational energy as work, there is no way that the whole mass will not synchroneously lose rotational energy.
That's my conclusion.
Dear Juan: "Taking the gradient" is exactly my target. This is a spatial operation {of the imagination} since infinitesimals are "beyond measure".
I am cheer-leading for our focus to return to Time without all these spatial 'crutches'.
Dear Christian,
To your item a), the answer is no.
I am telling you that unless you can give me a reason that I can coherently relate to the 2nd principle of thermodynamics that explains why elementary massive particles captive on circular orbits about the axis of rotation of a macroscopic mass of which they are the building blocks, can avoid expending energy as work according to the 2nd principle of thermo on account of their constant change in direction, I can't see how I could draw any other conclusion than that induced rotation of macroscopic masses cannot be conservative since the tranlational motion of their constituting massive subcomponents cannot be conservative.
If all of the constituting massive subcomponents lose translational energy as work, there is no way that the whole mass will not synchroneously lose rotational energy.
To your item b) My answer is that since the 2nd principle of thermo states that the state of motion of massive bodies cannot be changed without energy being expended as work, then I do see a relation that considering rotating macroscopic masses as having no internal structure is failing to take acount of, because the state of motion of the internal subcomponent masses is constantly changing.
These submicroscopic masses are the real massive components of the macroscopic body system of massive particles.
A rotating macroscopic body is a closed system.
Dear Christian,
You write: "Then what do you predict for a massive rotating object? That it radiates some kind of energy and slows down?"
I do not "predict". I "conclude" that some amount of kinetic energy must be "expended" to sustain the constant change in direction that the elementary massive particles that make up the mass of a rotating body are submitted to, on their forced circular orbits about the macroscopic body's rotation axis, which can only result in the macroscopic body's rotation to slow down.
Not radiated. Adiabatically expended, wasted, not there anymore, in exchange for the net change in direction (the change in state of motion).
From the conclusion that kinetic energy is adiabatically induced in accelerating charges, it can also be adiabatically expended, just like the 27.2 eV adiabatically induced at the hydrogen ground state orbital reduces to nothing without being emitted after an incoming 13.6 eV photon is provided to cause it to escape the atom.
I explain processes from the perspective that kinetic energy is a really existing substance whose amounts can be adiabatically increased and decreased as a function of the distance separating charged particles. I would be very surprised if my explanations made any sense from the assumption that energy is always conserved and that kinetic energy can miraculously morph into so-called potential energy when motion is hindered and then just as miraculously morph back into kinetic energy when motion is resumed.
My statement is that kinetic energy does not morph into any potential energy, but is a really existing substance that behaves accordingly (no miraculously morphing into some ethereal characteristicsless potential when the motion that it sustains is hindered, but remains present in a manner that the current concept of momentum / Lagrangian / Hamiltonian is unable to account for).
Dear Christian and Aaron,
The answer is in the paper I referred Herb to in my first contribution to this thread on page 3 of this conversation.
Looks like the Coulomb force has become invisible in the background of QED. It is still in action however in every virtual photon, but cut into too many little pieces to be obvious.
QED makes us observe every individual pixel in the 4K screen. If we pull back sufficiently, we can see the completely smooth picture.
Sorry Andre for not reading your article to the end.
The introduction seemed rather lengthy.
Apologies
Aaron
Dear Aaron,
Quite understandable, I know I am a tad wordy.
But the whole issue requires so much material to be put in acute perspective before the related analyses can be set in motion that this can hardly be avoided in some of the papers.
Coulomb 'forces' are a fiction unless their source is so massive that they cannot move (actually, even then they must conserve momentum, so it's just that the movement is too small to be observed). This is not the case in atomic systems, even the hydrogen nucleus is only 1840 times more massive than the electron, so why does EVERYONE assume that this is the interaction mechanism at the atomic scale?
Simply because it is the only known interaction force between elementary charged particles.
The interaction is not between the electron and the proton. It is between the electron and the charged up and down quarks.
The electron is an elementary charged particle.
The proton is not a particle, just like the solar system is not a star.
The solar system, is a system made of planets stabilized on orbits about a central star.
The proton is a system of elementary charged particles whose internal structure is made of electromagnetically stabilized interacting elementary charged particles named up and down quarks.
So the interaction is between the electron and the up and down quarks that are captive inside the proton structure, the only 3 elementary charged particle that are the building blocks of all atoms in the universe.
But Andre, from an electrostatic standpoint and Gauss' law, the proton can be considered a central point charge of +1. The movement, spin, and momentum of the quarks are not felt by the electron, or else if they were the electron orbit would (probably) not be stable.
Dear Eric,
The charge associated to the proton is a combination of the charges of its inner charged particles +2/3 +2/3 -1/3 =1
Its spin is a combination of the 3 half spins of its inner quarks.
Since the proton is not a charged particle it cannot interact with the electron. The stability of the electron orbital can only be due to an electromagnetic equilibrium state established between the electromagnetically oscillating energy of the electron and of its carrying energy on one hand and the electromagnetically oscillating energy of the individual up and down quarks and of their induced carrying energy on the other hand.
The properties of the proton are emergent from the properties and electromagnetic structure of its constituting electromagnetic elementary subcomponents.
If the hydrogen atom was upsized so that the proton would have the diameter of the sun, the electron would be stabilized as far as the orbit of Neptune, at which distance the parallax angle due to the sun's diameter woud reveal not much more than a highly luminus point.
The same for the hydrogen atom. This is why treating the proton as a point-like particle for electric interaction works fine. But the real interaction can only be with the inner charged quarks, since only them have a charge.
Herb
"coulomb forces are a fiction"
a whole series of serious misunderstanding
In the presence of external force linear momentum is not conserved, angular momentum conserved for central forces(no torque)
achieved by newton;Two body problem solvable even if the masses are close to each other
then what force holds the atom together, ie. eletrons to the nucleous, if not Coulomb?
topics i suggest,, two body problem, effective mass, hydrogen atom, kepler laws.
central forces, conservation of momentum and of angular momentum, conservative force.
to build up "scientific culture"
regards, j,w.
I'm trying to respond to Andre, and the system won't accept my post, it keeps saying, "Identify yourself as an expert in the field by providing high-quality answers"...?
Hi Eric
Your message beginning with "I'm trying to respond ..." has appeared in the thread. So this method seems to be working.
Maybe just refreshing your screen right before copying your text in the window would work. You may be stuck with the buffer copy of the screen.
andre
in the abscence of torque and friction, pay attention to conservation of angular
momentum.
regards, j.w.
Dear Juan,
I clearly understand how well the principle of conservation of angular momentum has been experimentally verified with all past experiments, and I don't dispute the results.
I also clearly understand that all of these experiments have been carried out with macroscopic bodies each made of countless billions of massive submicroscopic elementary particles, each single one of them captive on a circular orbit about the rotation axis of the macroscopic body and that cannot escape being individually submitted to the 2nd principle of thermodynamics.
I found that their energy loss as they constantly change direction can only be infinitesimal at each rotation cycle with respect to the energy provided as initial impulse to set macroscopic bodies in rotation.
They all are translating on macroscopic scale perfectly circular orbits identical to the isolated electrons observed by Blewett in the Betatron experiments, the only accelerator type that allows perfectly circular orbits for isolated charged electrons. The still to be investigated unexplained slowdown of the Betatron electrons needs to be studied in depth and correlated with the circular orbits that elementary charged particles are forced into within macroscopic bodies.
From my perspective these electrons cannot escape the 2nd principle of thermo either.
I concluded that the related energy loss has not been observed in experiments meant to confirm conservation of angular momentum for rotating bodies for the same reason that it was impossible in Newton's time to even imagine that the mass of bodies could increase as velocities progress towards the relativistic range, because they could not even observe the infinitesimal increases that occur at the asymptotic low velocities range that were then observable for macroscopic masses.
I concluded that we are in the same situation with rotating bodies. We cannot observe the asymptotically infinitesimal losses involved that no short term macroscopic experiment can easily reveal even in deep vacuum.
We have clues however for such bodies left for years in deep vacuum where no friction occurs and for which we have decades worth of data: Both Pioneer 10 and 11 crafts, for which the rotation loss is explained by ad hoc "most probable according to current theories" reasons. The same for the ball bearing experiments.
From my conclusions, it simply is impossible that massive elementary particles could be forced to constantly change direction without some energy being expended in the process.
Dear Juan:
You ask "what force holds the electron to the atom?".
This is the inherent periodic intra-electron impulse (not continuous EM 'force).
This mechanism is as intrinsic as its partner's resistance to change (aka 'mass').
Dear Herb,
I correlate your "its partner's resistance to change (aka 'mass')" with the omnidirectional inertia of electrons.
But can you elaborate on what you call "the inherent periodic intra-electron impulse"?
Please read the attached paper: (UET6.pdf) in the above response or my research program on my profile page at Academia.edu.
It is well accepted that the properly interpreted fundamental
principles of conservation of energy, linear momentum and angular momentum also carry over to the microscopic domain.
will not say anything more.
regards, j. w.
Accepted is not the issue.
Conformity with objective physical reality is the issue.
The Earth orbited the Sun even when it was accepted that the Sun orbited the Earth.
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