I am always a little amused by adamant statements about what QFT "is."  The topic is so formal and lacking in conceptual underpinnings that where to start of questions like the "mass gap" and so on typically involve only more ad hoc approaches.  No one can doubt the computational successes but even Feynman claimed not to understand it.  

There is an old CERN report on this topic I read a long time ago by Jackon. "All known intrinsic magnetic moments (of electron, muon, proton, neutron, nuclei) are shown to be caused, to a very high precision, by circulating electric currents and not by magnetic charges. http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/09/399/9399984.pdf

No, magnetic and electric fields are not made by different photons. As a matter of fact, magnetic and electric fields are really not different fields in the first place! What is seen as a magnetic field by one observer is seen as an electric field by another observer and vice versa. In other words, whereas the electromagnetic field is a generally covariant concept, the electric field or the magnetic field are not: they are observer-dependent manifestations. So when you construct a (relativistic) quantum field theory, it is necessarily the electromagnetic field, not the electric or magnetic fields, that would be interacting with charged sources.

I'd also like to take argument with the first paragraph in the question details. QFT does not "reduce fields to particles", nor are particles in QFT necessarily bosons. Particles in QFT are quantized excitations of the fields: this is true both for fermionic and bosonic fields. And interactions may exist between any and all types of fields: for instance, electrons (fermions) may interact with neutrinos (fermions), or photons (bosons) may interact with the charged W+/- vector bosons.

Dear Toth,

Thank you for your answer, but I think that you have avoided the question. Magnetic field exists and also the electric field. Take a compass in your hands, a solenoid for the magnetic field or a capacitor for an electric field.

I know that QFT do not take into account these details and also consider the electromagnetic field to be made by quantized oscillator (photons) in a certain gauge. But the question is if this point of view can be sustained when distinction of electricity and magnetism are necessary as in the case of Faraday law. What do you think? Can we distinguish e-e interaction exchanging magnetic field or is it always electromagnetic with any kind of distinction?

Dear Charles,

I think that it is too dangerous to define probability only as "knowledge". In fact if you ask to a mathematician perhaps is going to tell you that statistics is almost a phenomenological branch of mathematics.

In any case, this is not the corn of the question and it is more related with people that thinks that having only particles you can explain everything in physics. Perhaps this is true, but in such a case it would be interesting to go to details related with the reality. QFT appears always as pure theoretical context that assumes electrodynamics without going to distinctions as Faraday law with photons or even more basic things: how one photon can make make repulsion or attraction in the same Feynman diagram. Or what tricks as changing the direction of time in the diagrams if are sustained for these details.

Charles: In my view, quantized excitations follow once we accept that the field quantities in a quantum field theory are generally noncommuting. QFT is exact: considering a given set of initial and final conditions, it tells you exactly how the various modes (series expanded terms in a Schwinger integral or loops of varying order in a Feynman diagram) contribute. Probabilities only enter the picture once you consider different possible outcomes and interactions with classical measuring devices, which are actually not described by the theory. In other words, probabilities arise when we translate the exact predictions of a QFT into classical observables, they are not inherent in the QFT itself.

Daniel: A magnetic field that exists for one observer does not exist for another observer, who sees an electric field in its place. Whereas one observer attributes the force acting on a stationary compass to a static magnetic field, another observer sees the force acting on a moving compass due to a time-varying electric field. And most observers see a mixture of magnetic and electric fields, only special observers see a purely magnetic or purely electric field at a given location. This is how relativity works with electromagnetism. Faraday's law, in particular, is non-relativistic. If you replace it with the relativistic form of Maxwell's equations, there is no conflict between QFT and electromagnetism, and no need for "magnetic" or "electric" photons, only electromagnetic ones. Another way of putting this is that even if you somehow managed to invent, say, a "magnetic photon", it would be seen as an "electric photon" by some other observer, and vice versa; but most observers would really see it as a perfectly ordinary electromagnetic photon that is neither exclusively magnetic nor exclusively electric.

Dear Toth,

Thank you very much for your answer, but I think that you do not understand the question or I am explaining me very badly; perhaps both. Obviously I am always assuming that there an observer at rest measuring the field and no the relation with another with relative motion. This even could make the things more complex for interpreting how the magnetic fields exist and the electric ones too if their photons are equal and no distinguishable.

The question is very simple, you have a magnet acting on electrons moving through photons that cannot expend energy on them, and after that you have two electric charged plates, how the photons behave in each case? By the way, Faraday's law is relativistic and corresponds to spacelike component of a more general equation where the timelike component is the non existence of free magnetic sources.

Daniel: Take a magnetic field that is initially static. This field exists due to an electric current somewhere (e.g., the geodynamo, aligned electronic orbits in a ferromagnet, current in an electromagnet, etc.) Let an electron fly through this field. It will be deflected by the field. The deflection is perpendicular to the electron's trajectory (hence it's true that the field cannot be described as the gradient of a potential, and the electron does not gain any kinetic energy).

However, deflecting the electron requires a force, and Newton's third law tells us that there must be an equal and opposite reaction: the source of the magnetic field also experiences a force, and moves as a result. Now the motion of the whole Earth, for instance, may be imperceptible compared to the deflection of an electron in the geomagnetic field, but it is nonetheless there. Once the source starts to move, the magnetic field is no longer static: it is now time-varying. Moreover, a time-varying magnetic field implies an electric field. So even from the perspective of your privileged observer, who initially just saw a static magnetic field, once the electron enters the picture, that simplified view is no longer precisely valid.

Photons enter the picture if you describe the experiment microscopically using QED. Suppose we have a static magnetic field due to a stationary current in a conducting coil. The coil consists of positive atoms that are sitting still, and negatively charged electrons that move around and round, forming the static magnetic field. A free electron enters into the picture, flying by the coil. It would exchange virtual photons with both the moving electrons and stationary atoms inside the coil. If the electrons in the coil were also stationary, there would be no net force acting on the free electron as the force due to positive atoms and negative electrons would average out to zero. Because the electrons in the coil move, however, the equations become lopsided (to use a highly technical term) and the free electron experiences the magnetic Lorentz force. This lopsidedness is purely a consequence of the motion of the electrons in the coil and the fact that energy and momentum are conserved in every interaction (vertex) between electrons and virtual photons.

When it comes to the charged, conducting plates, it is the excess or deficit of electrons in those plates that results in a net force on the free electron, not the motion of charge carriers in the plates. But the individual exchanges of virtual photons are the same as in the magnetic case.

 Faraday's law, as you said it, corresponds to the spacelike component of a more general equation. A "spacelike component" is an observer-dependent thing, i.e., it is manifestly nonrelativistic.

Dear Toth,

I do not understand your answer, it seems that the state of motion of the electrons can change the state of the photons. That is obviously wrong, if I have understood you well. On the other hand what is fact is that the electrons move in very different form under a magnetic field than under an electric one. And finally the electromagnetic fields depends of the state of motion but no their invariants and the classification between electricity and magnetism is very clear. See my research gate contributions where I have the book:

D.Baldomir and P.Hammond, Geometry of Electromagnetic Systems, Clarendon-Press, 1996.

Daniel: Of course the electron's 4-momentum influences how it interacts with photons. This is basic QFT: 4-momentum is conserved at the vertices. You may have misunderstood something about my answer.

I am not certain what invariants you have in mind. The electromagnetic field tensor, as a physical quantity, is an invariant. Its components are not. The classification into electricity and magnetism is observer-dependent. This is elementary relativity theory.

   Dear  Toth,

   The electrons at different velocity can see different fields, but the photons cannot. The invariants that I said are the scalar and pseudoscalar ones which tells you that the electromagnetic radiation (photons) cannot be changed with respect to different inertial observers.

    Dear Charles,

    Thank you very much, but when you have an electric charge and you move it you obtain a magnetic field, of course, but an electric one remains always. That is to say, your fields invariants are going to tell you that the square of E minus the square of cB has to be positive for all the inertial observers.

    By the way, I do not know how the knowledge can be measured using the theory of probabilities.  This is exactly the theory which allows to measure the errors made with respect to what is assumed to be the good value ( or real?), i.e. the average using its standard variation.

Charles: Good point, re. probability theory, but I'd argue that there is a crucial difference: in QFT, it is the "probabilities" (i.e., the operator-valued fields) that interact, not the classical observables with which we associate these probabilities. So for instance, if I were to describe the behavior of a quantum computer, or indeed a network of quantum computers communicating via quantum communication channels, my description would be exact up to the point when we attempt to extract a classical observable.

Daniel: Photons have no perspective. There is no rest frame associated with a photon. So it's not very meaningful to speak of what photons "see". As to the scalar invariants, notice how they do not tell you that the field is electric or magnetic. For instance, E·B may be zero either because E (or B) is zero or because the two 3-vector fields are perpendicular to one another. (And this is exactly what happens when two observers look at the same field: they would agree on the value of E·B, but they would disagree on the values of the individual fields.)

    Dear Toth,

    If you have electric field for  a rest system and you transform it to another inertial observer, then you are always with this extra electric field. Or what is the same the part of the magnetic field cB must be balance with the new electric field because the difference E^2- (cB)^2 must be kept constant and independent of the state of motion.

   In any case Toth, I think that you know very well that the magnetic field exists and what is a Zeeman energy, etc... If you want we can leave this discussion and what is for me interesting is to know how the electric charges can "see" if the photons came from the magnetic field or from the electric one. Do you know it? It is clear that Lorentz formula gives different force at a classical frame while I do not know what QFT says since the particle point of view. This is all! Thank you in advance.

    Dear Remi,

    Thank you very much for your answer and help, but my problem is much more simple in principle, I was only thinking in the electromagnetic case. Say in abelian U(1) photons for one stationary magnetic field and for an static electric field. But you are right to go to non-abelian (quarks and gluons) for seeing how the photons are going to be polarized too.

    Dear Remi,

    My comment was reading your reference of the link about electroweak interaction. Sorry. What do you mean by near fields?

    Dear Remi,

    Now I understand you, but you are speaking about multipolar approaches of the field which is a good example. I suppose that you refers to the electric multipoles and the magnetic multipoles in the stationary zone.  This is true but this is not my example. My idea is to see that if we work only with particles instead of fields there are problems or what is the same, the fields are necessary in physics.

     Dear Remi,

     Sorry because I have forgotten your reference to Toth and Francis. Perhaps it would be better that they answer you without my personal interpretation to their contribution.

 The wording of the question (Are magnetic and electric fields made by different photons?) implies that electric and magnetic forces are transferred by virtual photons. I am going to dispute this assumption and attempt to prove that neither electric fields not magnetic fields are made of virtual photons. A recently derived set of simple equations show that there is a close relationship between the electrostatic force and the gravitational force. http://onlyspacetime.com/QM-Foundation.pdf One of these equations is: FgFp = FE2N2 where Fg is the gravitational force between two of the same mass particles, Fp is Planck force (Fp = c4/G), FE is the magnitude of the electrostatic force between these two particles if we assume that both particles have Planck charge. "N" is the number of reduced Compton wavelengths separating the two particles; therefore N is dimensionless. This equation is one of a family of equations which together imply that both the electrostatic force and the gravitational force are wave phenomenon which scale with the particle’s Compton wavelength. Furthermore, the gravitational force can be expressed as the square of the electrostatic force if both forces are stated in dimensionless Planck units and separation is stated as the number of wavelengths. The implication is that gravity is a nonlinear effect which scales with wave amplitude squared while the electromagnetic force scales as wave amplitude to the first power. The reason for the vast difference between these two forces becomes obvious when viewed as a wave effect.

      The above referenced paper also proposes a new constant of nature which converts charge and electric field into a quantifiable distortion of spacetime. This concept is tested and found to make correct predictions about the maximum possible concentration of photons and the maximum possible voltage on a vacuum capacitor. These insights are all incompatible with the concept that virtual photons create electric and magnetic fields. This paper will be published next month.

Remi,    I did not think that it was too much of a stretch to make the argument that neither the electrostatic force not the magnetic force is transferred by virtual photons, While that is a conclusion, I am stating that the equations connecting the electrostatic force and gravity are absolutely correct and previously unknown, The vast difference in forces is the result of a simple square difference in exponents when the equations are stated using the particle's natural unit of length which is the particle's reduced Compton wavelength. Even the single polarity of gravity is easily explained by the fact that gravity involves an amplitude squared term which always produces a positive number.

      For a simple example, suppose that we assume two particles separated by their reduced Compton wavelength, therefore N = 1. At this special condition Fg/FE = FE/Fp. For example, if the two particles have the mass of an electron but Planck charge, then Fg = 3.7x10-46 N, FE = 0.21 N and Fp = 1.2x 1044 N and both ratios equal about 1.75x10-45. When these forces are expressed in dimensionless Planck units (c = G = ħ = 1) then the square is obvious because Fg = FE2 (bold used to indicate dimensionless units). I am claiming that virtual photons cannot explain these ratios but Compton wavelengths can.

   Dear Raptis,

   Thank you very my for your answer.

    Proca Lagrangian only introduce self-interaction of the photons making them massive or with a longitudinal component besides the transversal. No degrees of freedom are for this theory and therefore gauge choice.

    The Aharonov-Bohm effect or the Berry phase only takes into account of the photons associated to the potentials where the magnetic field doesn't exists. Thus it seems that this doesn't give insight to the simple question of answering in the photons associated to electric field are similar to the ones of the magnetic field. Obviously these fields couples in very different form to the electromagnetic sources.

    Dear Nilotpal,

    Thank you very much for your answer. You open a new perspective that we didn't touch so far: the magnetic field in matter doesn't come from the electric field by a relativistic transformation. In fact, it is obtained for exchange interaction among electronic spins.

    Dear Raptis,

    Thank you very much, it is very interesting but it is not the problem that I would like to know the opinion. How the fields get the macroscopic behaviour from the photon excitations or particles distinguishing "electric" from "magnetic". Provided this could be possible.

As I recall the masslessness of the photon (and supposed graviton) are what allows them to have sensible macroscopic limits as classical field theories.  In QED we can build coherent states that correspond to well defined macroscopic E and B fields.  I know there are formal approaches that introduce separate electric and magnetic vector potentials but haven't looked at them in a while.  I'm a big fan of using fictitious monopole currents for solving EM problems because they greatly simplify some problems and give universal results that don't depend on their existence.  This formulation allows E and B to enter in a more symmetrical fashion.  If one wants a gauge theory approach one then does need two vector potentials A_e and A_m.  

If I give a general distribution of photon fields with varying numbers of photons there are correlations that preclude any well defined E and B fields.  Is this at all in the direction of what you are asking? 

I didn't invent the practical use of magnetic monopoles for dielectric problems but I have a couple of examples in this paper (which I'm still trying to shorten enough for the editors).  

Article Beyond Quantum Fields: An Operator-Free Covering Theory for QED

See this Wikipedia infomation:

http://en.wikipedia.org/wiki/Magnetic_field

Regards

Dear Raptis,   

Perhaps you are right and I do not understand you. My question is very very simple. Have we the same photons for the magnetic and the electric fields? In Quantum Electrodynamics (QED) the photons appears as excited states of an underlying electromagnetic field, i..e. photons are field quanta devoted to couple mainly with the electrons producing the electromagnetic interaction. This picture is very rich because it allows interesting "landmarks" as the renormalization of the mass or charge, and to obtain the value of the spin with an unbelievably accurate value. This can induce to some people to think that the fields are only OLD objects employed in Maxwell equations, nowadays overcome, but this is not the reality. In fact the point of view of QED ( or QCD) is very restrict to a very small distances and high energies.

Let me to try to show one place where is clearly seen the difficulty of translation of both scopes. If you have an electron in a magnetic field its "geodesic" is circular curve while in within an electric field it is one straight line. And things such Faraday law do, changing one electric field in one magnetic, by variations of space and time coordinates are almost inimaginable. The photon is an autist particle that cannot change its state of motion with respect to it and with respect to the other sources as are the electrons, which are the particles on we can act for changing the electromagnetic state. 

Dear Clifford,

You are very close to my worry. Let me read your paper and I agree that this goes in the direction to understand basic things which could help to find a quantum gravity theory. Thank you.

    Dear José,

    Thank you very much for your reference, although I think that everybody knows electrodynamics or have to do for entering in this discussion. In any case is good to remember it and to see the different behaviours even at classical level.

There is one sentence very appealing: "All equations in this article are in the classical approximation, which is less accurate than the quantum description mentioned here. However, under most everyday circumstances, the difference between the two theories is negligible". That I strongly do not agree. Most of the books of Quantum Field Theory starts with classical electrodynamics only for telling what it works in everyday life, but in the following chapters no relation is found.

Argh.  I posted the wrong paper.  The examples were in this one.

Data Abraham Minkowskii 4

Dear Clifford,

Your paper is very interesting for analyzing the electromagnetic propagation in a dielectric medium, but this is not the problem of the question. The question is related with the possibility that the photons can allow you to distinguish if they come of an electric field or from a magnetic field when both limit cases are assumed to exist is it happens with a magnet and charged electric body. Thank you!

     Dear Nilotpal,

     I am afraid that this problem is not related with a mathematical representation as can be the complex number or the Clifford algebras in general. The problem is that Quantum Mechanics have to work with particles or states associated to them and this is the scope chosen for QFT. This is good for small distances and high energies but not for the idea of field introduced by Faraday. This is obviously a subjective perspective of this issue and I would be very glad to see others. Thank you.

It is interesting that the magnetic field does no work on charges but that a charge in a pure magnetic field spirals and radiates away its energy until it is a rest due to the radiation reaction.  One can argue this is from the self electric field doing the work nevertheless the only external field is magnetic and the kinetic energy is not conserved. It is still unclear to me if by "magnetic photons" you mean those associated with a new and distinct vector potential A_m. 

Dear Dr. Daniel,

Please forgive me if I say that there is some confusion in the formulation of your question:

1. For one thing, QFT is not exactly what you say it is!  In simple terms, it regards the material universe as made up of (interacting) fields.  These fields manifest themselves through their quanta (photons in the em field; gravitons in the gravitational field; and so on ...).

2. For another thing, thanks to Maxwell's great (theoretical) synthesis, the electric and magnetic fields are mere components of the em field; they are two sides of the same coin, as it were.  In fact, it is sometimes remarked that magnetism is a relativistic phenemenon -- in the sense that if you sat on a charged particle shooting ahead, you would 'feel' only the electric field; whereas an observer at rest would 'feel' both electric and magnetic fields.  (In passing, one can remark that magnetism is a quantum phenomenon as well; classsically, it should decay in no time!)  Physics is fond of 'unification'.  Think of Newton's synthesis (1687); then came Einstein's (1905).  In between, there was Maxwell's (1850s).  I hope the electric and magnetic fields will never be broken asunder again!

Kindest regards.

Dear Humam,

Thank you very much for your email although I cannot understand it. Let me to respond you:

1. Obviously QFT is made by fields that can reduce to the interaction of particles. There are four fundamental interactions that three of them belongs to QFT electromagnetic, weak and strong interactions unified in the standard model. The sources of the interactions are always fermions while the fields are described by bosons(photons, gluons). The gravitational interaction doesn't belongs for the moment to QFT and gravitons are just one speculation without any kind of quantized gravitational field associated.

2. Besides the electromagnetic fields associated to the state of motion by Lorentz transformations, there are also static electric fields and magnetostatic fields. Every laboratory of electromagnetism is provided with magnets or charged spheres for producing them. It is true that one moving observer could be always electric and magnetic with respect to the observer in the lab, but the two invariants associated to the electromagnetic field keeps constant the amount of "electricity" or "magnetism".

Therefore, my question is very simple and direct, can we reduce the magnetic and electric fields to the same kind of photons due that the fields interact in a very different form with the electric charge?

Dear Clifford,

Let me to congratulate you due to have understood properly the question. Let me try to answer you in more detail:

1. "It is interesting that the magnetic field does no work on charges but that a charge in a pure magnetic field spirals and radiates away its energy until it is a rest due to the radiation reaction"

This is a good remark which clearly put in evidence that charges into strong magnetic fields behaves so differently than within electromagnetic or electric ones. They curl the electric charges and therefore produce acceleration as in the syncrotron. Obviously this radiation is made by photons which overlap to the ones of the original magnetic field. Notice that the radiation fields are independent of the sources and freely move on the spacetime.

2. "It is still unclear to me if by "magnetic photons" you mean those associated with a new and distinct vector potential A_m."

This could be if we think in the duality rotations of the electromagnetic fields. But this is not my idea. Notice that if we think in a pure magnetic feld it is difficult to introduce the "magnetic moment" using Poynting vector, but this can be done by its equivalent form of the vector potential, which at the same time is the usual physical magnitud to be quantized in QED.

For me the problem is that the people who takes, without thinking enough, QED as containing everything which is in Classical Electrodynamics using is wrong and I think that if we want to quantize one interaction as gravitation we need to understand properly these basic things.

     Dear Nilotpal,

     Thank you very much for your answer but I do not think that the problem is related with mathematics. On the other hand, QFT can have criticisms, but not for the use of mathematics which are deeply developed.

@Nicotpal:

From your answer posted to the Daniel BaIdomir commentary at ResearchGate - it is evident that you are focused on the real problem: “...the only means by which we can realize the topic is by some...mathematical calculations (that) could predict the Quantum Mechanical properties but I feel the link is missing right from the beginning...when we analyse polarized light with quantum concepts one of the component is with 'i' which I personally could not interpret to the physical meaning...so far found no solid explanation for the same other than mathematical comfort....The use of the imaginary number (i or j ) starts with electromagnetism but only for mathematical comfort... we didn't analyse the exact physical aspect of this mathematical tool. I might be unaware of the explanation and expect some clarification from all.”

For the past hundred and fifty years - the ‘Riemann Hypothesis’ has been useful as a ‘mathematical comfort’ in theoretical analysis - but the Riemann conjecture derives from algebraic approximations and abstract imaginary numbers deficient in the mathematical calculation of real numbers or accurately defining the real natural numerical and harmonic order - of the exact sequence and how prime roots actually function in the calibration of precise quantum frequencies in the great spectrum of vibration that arises from the Universal Number System that governs the Cosmos.

The Riemann conjecture originated from a brilliant harmonic deduction and it has served a useful purpose as an abstract placeholder - but the Riemann formula  now represents an imprecise and archaic mathematical device in terms of quantum computation.

A significant mathematical discovery has been made that will have a unifying effect on all fields of scientific research - recently deciphered ‘The Prime Root Matrix’ and this discovery is in effect the solution to the dilemma of approximations by the Riemann conjecture.

Alwyn

Dear Clifford,

Although you suggest a new possibility that it is far of my initial idea, perhaps it would be interesting to analyse with you the possibility to use the duality transformations symmetries of Maxwell's equations for seeing how the photons could change.

For defining A_m instead of A, we need to transform the field in such a form that we have only magnetic sources (no magnetic monopoles as the Dirac's ones) and in such a form that now div B=ro_m instead of zero having radial lines from the magnetic poles and H= time derivative of A_m if the whole magnetic poles are zero as the source of a given this magnetic field.

Say it seems that we have exchange just the words electric by magnetic without having any action on the photons as being the particles devoted to exchange energy and momentum between the electromagnetic sources. Isn't? Do you find any important difference? Notice the radial fields are changed names but they can be interpreted in the same form physically speaking.

I am always a little amused by adamant statements about what QFT "is."  The topic is so formal and lacking in conceptual underpinnings that where to start of questions like the "mass gap" and so on typically involve only more ad hoc approaches.  No one can doubt the computational successes but even Feynman claimed not to understand it.  

There is an old CERN report on this topic I read a long time ago by Jackon. "All known intrinsic magnetic moments (of electron, muon, proton, neutron, nuclei) are shown to be caused, to a very high precision, by circulating electric currents and not by magnetic charges. http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/09/399/9399984.pdf

@Theo, I'm not sure the connection of these papers to the thread.  These topological optics results are interesting but I've never been able to decide how important they are versus just flashy uses of math that generates another paper.  I'm still mulling them over.  EM is just another linear theory.  Topology is interesting to physicists usually because of how some obstruction restricts dynamics.  Maybe there is more in here.  

Dear Clifford,

Thank you for your answer. You have entered a new point of view, or at least I didn't realize in the reading of the previous posts, when the multipolar approaches are considered. Jackson study the magnetic dipolar interaction considering the Zeeman energy shift between a hyperfine field with respect to an electron moving in an orbital s or l=0. Making the assumption of having magnetic charges joined in bound pairs he obtain a different value than if he, instead, assumed a circular current as origin of the magnetic dipole. And experimentally it is seen that the currents are the realistic approach or what is the same no magnetic sources exist even grouped in pairs.

This is very far of the monopole magnetic (isolated) that I was thinking for obtaining a magnetic A potential instead of the electric one. But for our question of if the photons associated to the magnetic fields is different to the electric ones could follow to be valid.

Dear Raptis,

Thank you very much for your contribution. In your first link is studied what could happen to the polarization of the fields in non-trivial topological background and it is found something obvious: they keep invariant as Classical Electrodynamics says. It is true that they refer only to zero electromagnetic fields, i.e. radiation, but I can advance that even more difficult to prove, it happens for a general configuration. The reason is that they represent the two Casimir of the Lorentz group which is not changed under such topological transformations if I have understood it properly.

The two last references generalize these invariants to have instanton solutions in a kind of Yang-Mills non-abelian fields. The topological solutions are much more sofisticated but my argument is exactly the same because Lorentz group is the responsable of this invariance of the fields and it is not touched in any case studied.

Dear Daniel,

I think your question formulated as it is has important pedagogical value, as far as it is addressed to intuitive understanding of QFT.

The brief answer is yes, there are electric and magnetic photons. They are simply photons wich differ by certain property , namely electric photons are those with Parity=(-1)^J, while magnetic are with Parity=(-1)^(J+1), where J is total angular momentum of a photon. Not comming into details of what is Parity and Total angular momentum (Im sure you know), one can proove that in classical field limit the first type photons are responsible for manifestation of electric field effects , while the second type photons are responsible for magnetic field effects. Thus, if  your question consists in derivation of such transition from QFT to classicalfield theory, where the difference between electric and magnetic photons would be evident, you can find it in Landau Lifshitz, Qunatum Electrodymanics, vol. 4, the relation between parity-angular momentum properties and  magnetic/ electric "classical field" properties is established there in explicit form.  

    Dear Alexei,

    Thank you very much for your answer. That it true, magnetic photons and electric photons are with different parity, i.e. they respond differently under the spacelike inversion of coordinates. But this doesn't explain why the magnetic photons coupled to the electric charge without expending energy while do with respect to the electric. Or how the variation of time of one of them produce the space variation of the other in certain direction. What do you think about? 

3.17.15@Nilotpal Bhattacharjee:

The ‘Prime Root Matrix’ is based on numerical and harmonic systems that are not ‘theoretical’ in their functions - on the contrary - the fundamental properties and primary attributes of the ‘Photon’ are precisely governed by a unified numerical and harmonic system that integrates the quantum processes of gravity, electricity, magnetism and all electronic functions of energy and matter.

It is a ‘Harmonic Universe’ based on a greater ‘Unified Number System’ that includes ‘The Quantum Gravity Matrix’ and the ‘Atomic and Molecular Matrix’ (which defines the exact numerical and harmonic composition of the ‘Periodic Table of Chemical Elements’ and the electronic orbital configuration of the ‘Janet Left-Step Table’ and ‘The Harmonic Code of The Chromatic Spectrum’). The function of these harmonic systems are naturally integrated in a common numerical interface based on the architecture of the ‘Prime Root Matrix’.

The precise order that prime roots are distributed, and more important - how Primes mathematically function in terms of a greater ‘Unified Number System’ - has been for many centuries an ancient mystery to scientists unable to decipher ‘The Code’ by means of a maze of algebraic expressions and numerical approximations - in place of real numbers which actually represent the basic laws of primary harmonic functions. Specifically, the orderly vibrations and quantum frequencies of the Photon, the Electrons, and all the Atoms are entirely numerical and harmonic functions.

These are new discoveries - you may with skepticism doubt their existence and require proof  - but any major scientist will intuitively sense that the computational means is available, and the circumstances and time have arrived that these Universal numerical and harmonic laws are on the verge of intellectual and scientific discovery.  This is the path into the enlightened future...at the moment when mankind needs a technological breakthrough - instead of chaos.

The fact that I publicly claim priority - to be the first scientist to decipher ‘The Code’ - is a sensible deduction, which will no doubt suggest to other astute scientists that this discovery is possible, and probable - thereby motivated to independently research the matter by individually thinking outside the cavity of the academic and industrial box.

What to you may seem like a diversion on this platform - is in fact a new direction toward understanding the numerical and harmonic nature of the Photon - as it relates to the wave functions of gravity, electricity and magnetism.

However, to explore in greater depth the specifics of these original discoveries - starting with the construction of the ‘Prime Root Matrix’ and how it relates to the Photon - your advice is well taken that the subject requires a new dimension of discussion. And I suggest that you consider the ramifications of that scientific disclosure in terms of copyright and patents - and the danger posed by the military industrial complex.

Dear Daniel,

If you are looking for brief arguments they could be the following:

The parity-orbital momentum properties of electric and magnetic photons are related to the fact, that electric type photons can be associated with 4-vector-potential of the type (F,0) where F is scalar potential, while magnetic photons with (0,A), where A is 3-vector potential. In its turn this means that coupling of electric photons with charge current is via scalar product, while coupling of magnetic photons is via cross-product. In static field limit this means that electric photons produce potential force, while magnetic photons produce force of Lorentz type, i.e. orthogonal to charge velocity and thus such force does not produce job. 

These brief answers do not cover all tricky things that are often hidden in limiting transitions, but they give a path for intuitive understanding. For detailed answers I can again recommend Landau, Lifshitz Quantum Electrodynamics. 

Dear Alexei,

You are right, you have the coupling energy between field and density of current. And if you calculate its derivative changing the sign, you obtain the Lorentz equation of motion. This is classical electrodynamics and I do not see where the photons play any role there.

You have given a great step saying that there are electric and magnetic photons as Landau did, but this only using the concept of parity or the spacial inversion symmetry. What I am looking for is to go with these photons to the usual classical electrodynamics and do not know the way of doing it. I must say that I have been studing QFT and the philosophy of most of texts is that QFT contain the classical fields as a limit, what is not true for me. It is only true that you can find QFT when you reduce the scale but not the inverse. Perhaps it is because there is something that I do not know!

At the risk of incurring another flurry of downvotes (you'd think I wrote some really outlandish crackpot nonsense; or have I offended someone?), let me respond to comments regarding the appearance of "electric" and "magnetic" photons in Landau-Lifshitz Vol. 4.

Here is the actual text in question: "The following terminology is customary to denote the various states [emphasis mine] of the photon. A photon with angular momentum j and parity (−1)j is called an electric 2j-pole (or Ej) photon; one with parity (−1)j+1 is called a magnetic 2j-pole (or Mj) photon. For example, an odd state with j = 1 corresponds to an electric dipole photon, an even state with j = 2 to an electric quadrupole photon, and an even state with j = 1 to a magnetic dipole photon."

I emphasized the word state, because it makes it clear that being "electric" or "magnetic" is not an intrinsic property of the photon. This is just another way of stating the obvious, namely that in QED, there are no separate electric and magnetic fields with their corresponding quanta of excitations. There is only the one electromagnetic field and its excitation quanta, photons that, being elementary particles, are indistinguishable from each other. The state (which is not Lorentz-invariant) that these photons are in can be characterized as electric or magnetic as suggested by LL.

However, the question to which we are responding in this thread concerned the possibility that the electric or magnetic fields could be thought as being made up of different kinds of photons. This is not the case! While it may be convenient to characterize the states of individual photons as electric or magnetic, in a relativistic field theory (quantum or otherwise) this distinction is necessarily dependent on the observer.

The terminology is ambiguous, by the way. For another, very different definition of a "magnetic photon", see https://en.wikipedia.org/wiki/Magnetic_photon.

@Theo

I believe these exotic "non diffracting" solutions have no square integrable energy density in their cross section so are not entirely physical.  This sort of problem is often the case with fancy exotic solutions and results in EM.  My maxim is that if it is totally amazing then there is probably some evil at the boundaries that hides the truth. This is not to say that such solutions don't matter or are good approximations for a while but I am always skeptical about something totally amazing arising out of a linear field theory. Pretty much everything you expect from such a theory holds without any extra fanciness.  As far as topological knotted fields, I want to know why they are interesting. Are we going to use them as atom traps to some end with topological phase implications?  To fuse thermosetting resins in some interesting pattern?  The fields are still just boring old linear fields.  

If you can wow some editor enough to get on a roll of publishing these results then you become the expert and get the papers to review thus keep the gravy train going.  It is not that I think this stuff doesn't matter and shouldn't be done but I'm tired of all the over hype of everything in this field.  Theory is kind of in the doldrums.  

Dear Daniel,

 I understood your question as what are the properties of photons which are responsible for difference between electric and magnetic fields in classical field limit. The answer is- the spatial inversion transformation properties of photons, characterized by given total angular momentum. If you are looking for phenomenon, in which such transition from quantum field  limit (few photons) to classical field limit (many photons) could be studied in most evident way, this is perhaps emmision of photons by systems of charges, which spatial size is much less than corresponding wave-length. 

   Dear Toth,

   Thank you very much for your answer that I am not sure to have understood it. Let me to separate the main points on discussion:

   1. Magnetic photons and electric photons exist in QED, at least defined in LL, as Alexei has told us and also I recommend you to go to the sections 46, 47 and 48 for seeing how they work in radiation emission. They are defined taking into account the angular momentum that they can carry.

   2. If the electric and magnetic photons could not be distinguished, and also no the electric to the magnetic fields within QED, then would it be realistic to claim that QED generalizes Maxwell Electrodynamics at microscopic scale?

    3. Let me to tell you that Maxwell Electrodynamics is also relativistic in spite to distinguish electricity of magnetism. Being QED a relativistic theory this cannot be a justification for avoiding this separation.

Dear Daniel: Of course classical electrodynamics is relativistic. That is precisely my point! The electromagnetic field tensor is Lorentz invariant. Its components are not. So what one observer sees as an electric component, another sees as a magnetic component and vice versa. This also remains the case in QED.

Case in question: you mentioned §§ 46-48 in Landau-Lifshitz Vol. 4. §46 begins with the words, "Instead of considering the emission of a photon in a given direction (i.e. with a given momentum), let us now consider the emission of a photon with definite values of the angular momentum j and its component m in some chosen direction z." I emphasized the last phrase, because the choice of the z-axis is observer dependent! So yes, with respect to a chosen direction, a photon can be said to be in an electric or magnetic state (again: it's not the photon that is electric or magnetic, but its current state) but this is not an intrinsic property of the photon, but a consequence of choosing a preferred direction. So what you see as an "electric photon", I may see as a "magnetic photon" and vice versa.

   Dear Alexei,

   Thank you very much and I am absolutely sure that you are understanding me very well. My worry, and also my ignorance, is if QFT which describes the particles as excited states of the fields and in the case of QED we have the photons as excited states of the electromagnetic field or electrons as excited states of Dirac one, they work very well at very low scale and high energies. But what I do not know is if they are so successful at a macroscopic point of view.

   Let me to put a simple example. You have a sample with negative magnetoresistance, then you apply an external magnetic field on it but nothing changes, while if you apply one magnetic external field the electronic resistance changes drastically. The same could happen with Hall effect, etc..., then how the electrons distinguish the "photons" if we represent the electromagnetic field by them? What is clear is that the fields are well distinguished? Therefore could you go a little bit further in this direction for telling us how QED could help to interpret these issues using their particles as the photons?

Dear Daniel: In another one of your comments, you write, "The sources of the interactions are always fermions". This is not true even for electromagnetism: the charged W+/W- bosons are also sources for the EM field. Gluons (bosons) carry color charge and are thus sources themselves of the strong interaction; and Z/W bosons have nonlinear self-interactions so they themselves can be sources of Z/W bosons. Hope you don't mind that I offer this correction.

   Dear Toth,

   If I look a car in a given direction (for instance z) and you in another for example y, this doesn't forget that there is only a real car. The electric photons and magnetic photons are not different due to the choice of the z direction but for their j angular momentum and parity associated. These are the physical magnitudes that distinguish them.

   Respect to electricity and magnetism it seems that you are wrong, sorry, because you repeat this argument many times. You cannot substitute an electric field for a magnetic field for an observer in the kind of motion that you want. What happens is that one electric field for a rest observer can be seen as electric and also magnetic for another in relative motion, but the electric one never disappears. In fact, due to the two electromagnetic invariants associated to the electromagnetic field you conserve the electricity character or the magnetic one. This is a very popular mistake that it seems that the electricity can be substituted by the magnetism or vice verse without any problem, what is wrong.

     Dear Tohr,

     In all that I know the source of electromagnetism are the leptons which are fermions, while for the weak and strong are the quarks which also are fermions.

Dear Daniel,

If I understand correctly you aim at macroscopic effect (whatever it means) where qunatum nature of EM field is important. (Otherwise classical field gives correct description without any need in photons). Could it be stimulated emmision of light by electrons ( like in laser), where you have coherent state of very large number of photons and the consept of photon with given quantum numbers is essential for understanding such an effect? 

      Dear Alexei,

     I had two aims when I thought this question:

     1. Purely conceptual of understanding the limits between classical and quantum fields. Pedagogical if you want.

     2. Practical because if I could understand exactly how change the possibilities of being an "electric" phonons or "magnetic" photons then there are many phenomena, not only optical ones, that could be applied within this physical context. I am thinking in spin quantum Hall effect or topological insulators.

    Dear Toth,

   Sorry that it seems that I have made a mistake with your name. Sorry.

Dear Daniel: Please don't worry about my name :-) (It's Viktor, by the way.)

I think I see your point. Lorentz transformations amount to hyperbolic rotations of the complex 3-vector F = E + iB. These rotations leave the four quadrants (defined by the two diagonal asymptotes) invariant. Specifically, they leave E2 − B2 invariant; if this invariant is positive, then E, otherwise B cannot be eliminated by a Lorentz transformation. Would it be fair to say that this is what you are alluding to as "electric" vs. "magnetic" fields?

Nonetheless, the actual magnitudes of E and B are observer dependent, not intrinsic to the field, and at least one of them can always be eliminated by a Lorentz transformation. So where one observer sees a combination of electric and magnetic fields, another observer may only see a purely electric (or magnetic) field.

Regarding sources, at the risk of repeating myself allow me to re-iterate: W+/W− bosons have the same electric charge as a positron or electron; gluons carry the same kind of color charge as quarks; and the massive vector bosons have nonlinear self-interactions. So all three fundamental fields have bosonic sources in addition to the usual fermionic sources. (As for gravity, it is of course sourced by all fields, including gravity itself.)

@Theo, I'm sure you can get such results with some nonlinearity.  That's how solitons arise and do so in such a universal fashion for many nonlinear equations.  I think a nonlinear medium would be far more interesting than pulling out the big boy of GR.  It is more likely to lead to a practical result as well.  Maybe these linear solutions can then be tweaked into something nonlinear and persistent that I find interesting.  I was annoyed at the implication of soliton behavior from linear fields.  

    Dear Viktor,

    You said "I think I see your point. Lorentz transformations amount to hyperbolic rotations of the complex 3-vector F = E + iB. These rotations leave the four quadrants (defined by the two diagonal asymptotes) invariant. Specifically, they leave E2 − B2 invariant; if this invariant is positive, then E, otherwise B cannot be eliminated by a Lorentz transformation. Would it be fair to say that this is what you are alluding to as "electric" vs. "magnetic" fields?"

   The invariants in this C3 representation came from F.F, say, E2-B2 and E.B. If the first invariant is positive then a given observer cannot avoid to have electricity while it is negative it happens the same with the magnetism. But never you can exchange electricity by magnetism or vice verse. This is the point!

  Nonetheless, the actual magnitudes of E and B are observer dependent, not intrinsic to the field, and at least one of them can always be eliminated by a Lorentz transformation. So where one observer sees a combination of electric and magnetic fields, another observer may only see a purely electric (or magnetic) field.

  The observer cannot decide if it can see electricity or magnetism, this depends of the sign of the invariant. If you have an amount of electric charges producing an electric field at rest with respect to you, other observer can see magnetism too, but never only magnetism. He must have at least both.

  Respect to boson/fermion fields this was perhaps not very well explained in my starting question. The idea was:

   There are four interactions in Nature. Electromagnetic field is made by photons (bosons) and produced by leptons (fermions), weak and strong have their fields made by gluons (bosons) and their sources by quarks (fermions). This is the simplest scope and I know that if we think in unified electroweak the things are a little bit more complex, but that was not at all my intention to enter in this problem.

    Dear Viktor,

   Sorry, I have forgotten to mention your point respect to the bosons that mediate the weak interaction: W+,W- and Z0. And it is true, thank you, that you said W+, W- contain electric charge which arises when they decay outside of the nucleus.

   When I was putting the question I just was thinking in the general ideas of the fields (electromagnetic, weak and strong, i.e in Maxwells abelian equations and in Yang Mills non abelian equations) without entering in the possibility that you mention respect that these bosons can be also sources of the electromagnetic fields when the proton (antiproton, electron, positron) in the decay. Say I think that I am understanding your remark although I believe it outside of my question.

Dear Daniel: You write, "If the first invariant is positive then a given observer cannot avoid to have electricity while it is negative it happens the same with the magnetism." I think we are in agreement.

You also write, "If you have an amount of electric charges producing an electric field at rest with respect to you, other observer can see magnetism too, but never only magnetism". Again, I agree. However, and this was my point, the mere fact that one observer sees magnetism where another doesn't makes it clear, I think, that the split of the electromagnetic field into electric and magnetic components is not Lorentz-invariant, i.e., it is observer dependent. This was my point. Your point, I think, is that the split into electric and magnetic components cannot be completely arbitrary, and that this allows us to classify the electromagnetic field based on the sign of the E2 − B2 invariant. I appreciate and accept this point.

Regarding fermionic sources vs. bosonic interactions: I tend to believe that this is a somewhat artificial distinction. For instance, the electron field is not any less a field in QFT than the photon field. To the extent that they are asymmetrical, it's because a spin-1/2 particle can emit or absorb a spin-1 particle (if other quantum numbers are conserved) and have its spin change sign, but a spin-1 particle cannot emit or absorb a spin-1/2 particle. Nonetheless, even spin-1 particles can interact through the exchange of pairs of fermions: e.g., photon-photon scattering through the exchange of electron-positron pairs. However rare this phenomenon might be, it is an example of a "force" mediated by fermions. (Another example that goes beyond the four interactions that are usually considered "fundamental" is when two fermions exchange energy and momentum through the exchange of a Higgs boson.) So in my own mind, I have come to discard the "four fundamental interactions" narrative in favor of looking at the entirety of the Standard Model Lagrangian and treating all fields, be they fermionic or bosonic, on an equal footing.

Dear Daniel,

Questions such as this cross many boundaries in our understanding of physics. Although, an answer to this question can be elegantly provided in mathematical terms, it is difficult to understand what is physically happening. First, I think it is necessary to define what a photon is, what energy is, and what matter is; this will provide insight relative to your question. The outline below is brief and is referenced to “New Physics Framework”; if you want to see a more detailed discussion for each line item, please see “New Physics Framework”.

 1. Per Figure 1, a heat fiber oscillates back and forth along its own axis; it translates perpendicular to this movement at the speed of light. See Footnote 7A also for more information regarding the heat fiber and why it is called a heat fiber.

 2. A heat fiber is identified as a photon in Chapter 6. See Figure 10 in Chapter 6 for how an electromagnetic wave is formed when the fiber translates.

 3. The energy of this photon fiber results from its oscillation, not from its translation. For example, a fiber with a shorter oscillation stroke (higher frequency) will have more energy than a fiber with a longer oscillation stroke (lower frequency). A fiber with a shorter stroke will do more work in interactions with other fibers or other particles.

 4. The oscillation of photon fibers is the only energy source in the universe. Because the oscillation of a fiber is perpetual, the law of energy conservation is given for all processes.

 5. Per Figure 1, perpendicular elements develop along the fiber axis, due to Lorentz contraction, as it oscillates back and forth at light-like speed along its axis. These perpendicular elements give its B-field as it twirls about its origin, which is at the mid-length of its oscillation range.

 6. Per Figure 2, fibers combine to form a cylindrical B-field, which is an electron; thus, electrons are fields, not hard particles. The reason why fibers combine to form a cylindrical B-field is given by Maxwell’s equations; see Chapter 2 for the electron’s derivation and Footnote 15. This tiny field has both particle and wave characteristics.

 7. The construction of other particles, such as protons and neutrons, consist of cylindrical B-fields also, similar to the electron. See Chapter 4 for example. Thus, all matter is a compilation of cylindrical B-fields, which consist of oscillating and twirling heat fibers (photons).

 8. The charge of an electron is negative because it’s circumferential B-field is left-handed, while that of the proton is right-handed. A neutron has no charge because it consists of a mixture of left-handed and right-handed twirling fibers.

 9. Many ad-hoc particles result from the collision of high energy parent particles in particle accelerators; this is due to re-formations of photon fibers into unstable cylindrical B-fields. Due to this instability, the fibers immediately re-form into a stable grouping or radiate separately.

 10. Although the neutron is stable when it is bound in a nucleus, it is unstable outside the nucleus because it has fibers twirling in opposite directions; this opposition causes the neutron to break up, which gives rise to other particle formation and radiation. This phenomenon is one example of why the majority of the ad-hoc particles created in particle accelerators immediately break-up upon their creation.

 11. Gravity fields develop from the oscillation movement of each half B-field of each particle along its corresponding z-axis. See Figure 2 for a view of the circumferential half B-fields of a particle and Chapter 8 for explanation and derivation of gravity fields. As explained in the book, spacetime is a measuring tool, not a structure, process or mechanism. General relativity is Newton’s gravitational law adjusted for relativistic effects. It is also shown that dark energy and matter are not required to provide explanation of some universal phenomena.

 12. Finally, in order to answer your question on electric/magnetic fields, the above topics in physics have to emerge and be understood physically, not just mathematically.

(a) Not only does an electron have a circumferential B-field when it translates, it also has a B-field when it is at rest because it is a B-field. The B-field is not measurable when it is at rest because the effects of each half B-field cancel each other due to the opposite rotational direction of their photon fibers as the half fields oscillate inward and outward along their common z-axis. Please refer to Figure 2. When the whole B-field translates, while the half fields are also oscillating, there is a net movement in the forward direction; this gives a measurable net B-field.

(b) Since the electron only consists of and is a B-field, there is no electric field. The electric force is mobilized when a half B-field of an electron overlaps a half B-field of another electron, for example. At the overlap zone, a change in the intensity and direction of each B-field is felt by the other; thus, per Maxwell’s equations, an electric force is mobilized along the z-axis of each electron due to the change in “B”. The force is repulsive because the rotational directions of the half fields are opposite.

 I know this has been much more than you asked for, but the whole picture needs to be understood physically in order to understand part of it.

Best Regards,

Dan S. Correnti

Dear Correnti,

Thank you very much for your contribution, although I couldn't follow it :

1. It seems that you follow your book that unfortunately I haven't read it.

2. In your last comments you mention the magnetism of the electron as due to a B-field. I don't know exactly what do you mean by this, but the magnetism of a free electron is well established as a Bohr magneton.

I would appreciate so much if you could help to answer the question of what is the difference between the photons of the electric field and the magnetic field and how can we reach the usual field equations from this image made with particles. That is to say, if we can make to vary in space an "electric" photon for obtaining a "magnetic" photon or so on. 

@Dan S. Correnti:

The Harmonic Photon.

The complex problem as defined by Mr. Baldomir -“...what is the difference between the photons of the electric field and the magnetic field and how can we reach the usual field equations.” - has a simple solution:

The differences between the various states of the Photon is governed by the alternating numerical architecture of the harmonic prime root quantum frequencies - which determines the composition of the gravity, electronic and magnetic fields.

The 'Photon' functions in discrete units of vibration that arises from the systematic decimal expansion of an orderly numerical system of harmonic prime root frequencies as defined by ‘The Prime Root Matrix’.

The key to the dilemma is that harmonic quantum frequencies consist of base-paired prime roots which alternate at specific intervals based on the numerical composition of the Photon - in fact, the system of prime roots include exact quantum frequencies for the orbital configuration and triangulation of electrons which identifies the periodicity of each atom in the harmonic ‘Atomic and Molecular Matrix’ - which defines the periodic table of elements.

The various but precise numerical quantum states of ‘The Harmonic Photon’ give rise to the alternating quantum frequencies of gravity, electricity and magnetism - from which the '..usual field equations' are derived.   

@ Daniel B. & Nilotpal B.

Here is the requested link for the book.

The tiny cylindrical B-field is the electron, which consists of one set of photons; there are no other photons. Please see Figure 2.

This set of photons gives the electron's charge/electric force capability per item 12(b) above; and is the electron's circumferential B-field per item 12(a) above; and also gives the electron's magnetic dipole field per Figure 9 in Chapter 5 of the book; Bohr magneton is a result of this dipole field.

The book offers a new framework, which is different than QFT. If you have other questions, please let me know on this page or with a separate message.

Regards,

Dan S. Correnti 

The link didn't get attached, so here it is again.

Book New Physics Framework (Post #5.3)

    Dear Correnti,

    Thank you for your contribution.

‘The Quantum Gravity Matrix’

‘The Prime Root Matrix’ - which is the functioning Number System that governs quantum frequencies - is directly integral to the ‘Quantum Gravity Matrix’ - which reveals the harmonic and numerical scale of gravity in aspect ratio to Universal micro and macro functions - based on real numerical intervals and actual units of measure in terms of time, distance and harmonic order.

Merging of quantum mechanics with the Number System that governs Cosmic gravity reveals the function of a fundamental pattern between quantum intervals of the ‘The Harmonic Photon’ and ‘The Atomic and Molecular Matrix’ and the ‘Prime Root Matrix’.  A numerical and harmonic unification of the gravity, electronic and magnetic fields.

This discovery reconciles the mathematical core of physics to a definite harmonic ‘Universal Number System’ that governs energy and matter - from which the calculus of angular momentum and wave functions emerge as field equations. All endowed with musical attributes.

It should be intuitive that gravity functions in the Photon in accordance to the number systems of other gravitational forces that are build upon the same numerical and harmonic architecture.

In fact, the configuration and distribution of quantum prime roots to the grid of electronic frequencies and particles are directly in calibration with the ‘Quantum Gravity Matrix’ of the Earth.

It is a ‘Numerical and Harmonic Universe’.

    Dear Alwyn,

    Thank you for your interest.

Dear Daniel,

I just want to give a very very small contribution to your discussion.

Some years ago, after the exam Electromagnetic fields for communications,  I believed, that  the B and E were "two sides of the same coin",  potential and kinetic energy of a EM wave, so far so good... 

I believed also that everything could be described as a EM wave with a certain frequency. The static fields were the particluar case of  waves with zero frequency In reality never possible to form exactly because of an amplitude not even containable in this universe.

Well this idea I realized later was very wrong... driven by the fact that the exam was exclusively based on the application of Maxwell equations to find EM waves, antennas, metallic wave guides, optics fibers, masers and lasers. The relation were all ejwt based on waves and periodic oscillating fields .

  There is no wave at all at 0 frequency, but the fields at 0 frequency exist as quite distinct entities...the anomaly are the transients which produce waves during their reconfigurations..or rather we are not necessarily inside big waves...

It is natural to pass from one to the other , but correct me if I'm wrong, the fact that it is not possible to cancel the effects of one completely at any point by adopting an appropriate observer (slower than the speed of light) making appear the other only , I think it is sufficient to state that there is an intrinsic difference in their nature.

@Stefano, we used to say that electrostatics is not the zero frequency limit of electrodynamics.  Is this what you are referring to?  

I don't really know if it is proper to affirm  that electrostatics and magnetostatic is the zero frequency limit of electrodynamics...

Dear Stefano,

Thank you very much for answer which I fully agree with it. Maxwell only changed the Ampere's law introducing what are known as displacement currents and getting the electromagnetic waves as solutions, but this not the only solution at all. Notice that we need to distinguish every day between ac and dc currents.

On the other hand, mainly since the discovery of Special Relativity, people is always accustomed to say that electricity and magnetism are two faces of the same coin, what is absolutely wrong. Magnetism is the 300.000.000 (in mks units) smaller than the electricity and it is true that are components of the same electromagnetic field tensor. therefore they transform as components of a Lorentz tensor which different to say that electricity transforms in magnetism and so on. What is true is that if you have, say one ion with three electric charges, and you see only an electric field, you cannot say that in another system of coordinates in motion with respect to you they are going to see also ONLY electric field. They are going to see an additional magnetic field besides a different a different electric field as yours. What is important is that there are two invariants associated to these fields and which are the same value for every observer that you have. In fact we can characterize the fields are electric,  magnetic or  waves. Notice that the electromagnetic waves have nules both invariants, electric is positive and magnetic negative por the scalar invariant. Therefore the waves cannot transform in another thing than in waves being electric field always orthogonal to the magnetic one also with very smaller amplitude (most of the books of electromagnetism  don't enter in these details).

Dear Clifford,

What is very clear, as I have been speaking in a previous post for Stefano, is that electromagnetic waves and electricity or magnetism are separated phenomena. In fact this is in agreement with topological non triviality of the Lorentz group (perhaps it would be better to speak about the Poincare group instead for introducing energy-momentum tensor too). Therefore electrostatics cannot be reached from electromagnetic waves behaviour or magnetostatics. And by the way, magnetostatics cannot be reached from electrostatics too.

Dear Clifford,

In one of the posts you have said that you liked to use same times magnetic sources for making the calculations of magnetism easier (I think to remember this point). This seems in contradiction with my above statements about electricity and magnetism, but it isn't. The reason is that the motion equations of electrodynamics (no the action) have as symmetry what is known as duality rotations which keeps invariant the tensor energy momentum of electrodynamics ( we have proven it in my book and also its classification for the electromagnetic magnitudes associated). In such a form that you can work with magnetic poles instead of magnetic field or so on. In certain aspects, making the proper substitutions, it is possible to work with electric sources instead of magnetic ones or vice verse. The same for the fields, but this is only a pure mathematical symmetry and n

Dear Viktor,

Do you know that in QED you can make with the photons the same subtleties that I have just made with the fields? Or in another words, could we attach a certain behaviour as distinguishing if they belong to one "electric" field or a "magnetic" one?. In all that I know there are the multipolar distinction as Alexei have told in a very clever form that LL used, and the virtual photons that allow to introduce certain disturbances on the perturbative approach in the electric and magnetic interactions. But this is not very clear for me.

Dear Viktor,

There was a point in our discussion that I didn't answer you when you said that you don't want to distinguish the fundamental interactions, where exchange particles are bosons, from the others where the exchange can be fermions. I have to disagree with you because the fermions cannot be in the same state having the same quantum numbers (Pauli's exclusion principle) and this is not followed in most of the cases if you consider the exchange of fermions for the basic interaction.

Dear Daniel,

there is another thing...I don't think it is related well to this thread..

At my II course of Phisics (electromagnetism) Prof. Roberto Caciuffo (you can find him in RG as a known scientist) whom I very much estimated for his brilliant insights, told us once that the differential form of Maxwell equations is not necessarily granted from the  integral form of the E-M laws derived by experiments. Or rather the integral form which is the primary for the E-M fields, does not necessarily assure us that the Maxwell equations  given in differential form hold...because Physics is not Math...