No electric wave can exist without a magnetic wave - where there is a changing electric field (displacement current) between electric field minima and maxima there will be an associated magnetic field that forms a wave that travels with the electric field wave.  Maxwells equations demand (show) this.  Likewise, if there is a magnetic field wave then between the changing magnetic fields there will be electric fields (Faraday's Law) that are an electric field wave.  These always exist together.  There is never a magnetic wave without an electric field and never a magnetic wave without an electric field.  Faraday's law and the displacement current are part of Maxwell's equations.

The assertion in the text following the headline of the question on this page is incorrect, as also indicated by Malcolm White here above. In particular, in vacuum the electric-field vector E and the magnetic-field vector B satisfy identical equations. The two vector fields differ in a fundamental manner in that empirically we have units of electric charge, but do not have units of magnetic charge (we have magnetic dipoles, but empirically no magnetic monopoles [1] - Dirac [2] postulated the existence of a magnetic monopole, the Dirac monopole, deducing from it the quantization of the electric charge). But these issues aside, there are a variety of reciprocity relations [3] that connect the two vector fields.

[1] E Goto, HH Kolm, and KW Ford, Search for Ferromagnetically Trapped Magnetic Monopoles of Cosmic-Ray Origin, Phys. Rev. 132, 387 (1963). [I owe this reference to DC Mattis, through his discussions in Sec. 3.2 of his book The Theory of Magnetism I: Statics and Dynamics, corrected 2nd printing (Springer, Berlin, 1988).] 

[2] PAM Dirac, Quantised Singularities in the Electromagnetic Field, Proc. Roy. Soc. (London) A 133, 69 (1931).

[3] https://en.wikipedia.org/wiki/Reciprocity_(electromagnetism)

An analytical equation that represents a moving electric field wave may be a solution of a wave differential equation.  But not all solutions of a wave differential equation can represent a wave.  So, conditions have to be found for existence of a wave.  One cannot produce electromagnetic waves just by varying electric field and magnetic field, because they may vary simultaneously and periodically, but they may not move.  So, conditions have to be found for propagation of waves.  That is, having  oscillation is not sufficient, the oscillation has to move to transfer energy, and conditions have to be found for moving oscillations; through mathematics.

The solution to these two wave equations is simply a matter of solving differential equations. What people  pay less attention to is the actual derivation of the wave equations themselves. The electric field equation is only correct where the E field derives from Faraday's law. It does not apply where the E field derives from Gauss's law. This is a fact which is generally overlooked. For it all to tie up consistently, the displacement current needs to be the vector A, which is known as the magnetic vector potential. See the article in the link.

http://gsjournal.net/Science-Journals/Research%20Papers-Mechanics%20/%20Electrodynamics/Download/228

I agree with Prof. Frederick David Tombe.  We need to pay attention to the actual derivations of the wave equations.  An analysis for the derivations may give ideas to derive equations giving solutions representing propagating waves.  Solutions may give variations in fields and may give an opinion that waves are propagated, but solutions should confirm that waves are propagated, not just oscillated.  It seems from our experiments that only one field is propagated  in wave form where as the other field has mere oscillation.  This can be confirmed  by having an analysis for the actual derivations of wave equations. 

The relationship between A and the displacement current is more complicated than Mr Tombe states, depending on the gauge that is chosen.  Even then, if the correct gauge is chosen, E=-jwA, which is not the same as the displacement current being the vector A (jwD=A=jweE).  I have used w as omega and e as epsilon.

Reply to Malcolm White.

Your objection does not hold. The relationship between E and A within the context of Faraday's law is explained between equations (1) and (3) in the link below. Before this matter can even be discussed rationally, we need to ascertain a physical context within which the EM waves are occurring. Mainstream textbooks lack that physical context.

http://gsjournal.net/Science-Journals/Research%20Papers-Mechanics%20/%20Electrodynamics/Download/228

Professor Malcom White mentioned in his first comment that "no electric wave can exist without a magnetic wave". Both electric field and magnetic field may vary simultaneously and oscillate, but one oscillating field is propagated when the other oscillating field is not propagated. If the electric field oscillation is propagated and the magnetic field oscillation is not propagated, then the corresponding electromagnetic wave becomes an electric field wave. So, there are electric field waves, which are light waves, and they exist without magnetic field properties.Similarly, there are magnetic field waves without electric field properties, they are the radio waves.In this connection, I like to quote the phrase of Professor F.D. Tombe: "we need to ascertain a physical context within which the EM waves are occurring", although it was stated in another context.

To the contributors to the discussions on this page

To my astonishment, I notice that the discussions on this page have taken a very unscientific turn. Everything to be known about the Maxwell equations have already been investigated in great detail, leaving no room for speculations, and certainly not of the kind being presented here. Quasi-science is no science at all. The interested may wish to consult the extensive book Handbook of Radiation and Scattering of Waves (Academic Press, London, 1995), by AT de Hoop [1].

The Maxwell equations are local differential equations, so that they apply in any open region centred around any point in space. Now consider the case where the electric field vector E(r,t) were identically vanishing in an open neighbourhood of r = r0. From the relevant Maxwell equation, it follows that ∂B(r,t)/∂t is identically vanishing in the same open neighbourhood of r = r0. That is, in this open region B(r,t) ≡ b(r), where b(r) is independent of t. This implies that B(r,t) is independent of t everywhere in the defining region, since otherwise at some point in this region ∂mB(r,t)/∂tm must be singular for some finite value of m. This is ruled out by the fact that one can differentiate both sides of the relevant Maxwell equation any arbitrary number of times without producing singularity on either side. One can go through a similar argument by assuming that B(r,t) were identically vanishing in an open neighbourhood of r = r0.  □

[1] http://www.atdehoop.com/Books/DeHoopAT_book_2008/DeHoopAT1995Handbook.index.html

http://www.atdehoop.com/Books/DeHoopAT_book_2008/DeHoopAT1995Handbook.index.html

To Professor Behnam Farid,

Both fields B and E may satisfy identical equations derived from  non-controversial Max well equations.  The question is not about the equations, but about the interpretations for solutions of the identical wave equations.  

Dear Udhaya, what interpretation are you referring to that we possibly do not know of? There is no ambiguity in vacuum, and in the presence of matter in general there is no problem of principle. In the case of non-linear material, all types of things can happen, but these are not mysterious things. In general, in dealing with the wave equations, one arrives at certain dispersion relations (the theory of resolvents can be brought to bear in this case, leading one to identify the types of electromagnetic modes a given system supports), and there may or may not be propagating modes as solutions. What is important, is that B and E are not independent vector fields (contrary to the explicit claim made on this page), but satisfy local coupled differential equations. One could liken these vector fields with respectively the real and imaginary parts of an analytic function, which satisfy coupled Cauchy-Riemann differential equations, implying that these parts do not vary independently as functions of the complex variable z.

To summarise, I repeat what I indicated earlier, that the discussions on this page clearly suffer from unscientific tendencies, of the kind encountered on various popular social media.

  This question is basically wrong. In electrodynamics there are no electric waves or mangnetic waves. For instance, if you had an electric wave thus E would change in the space, in time or both but by Maxwell equations (Faraday or Ampere) you would obtain a magnetic wave associated too. And the same if you did that with the magnetic wave.

  Notice that the Poynting vector which gives the linear momentum that the wave can carry is function of both: electric field and magnetic field. Therefore if an electric wave could be isolated it could carry electromagnetic momentum and force.

I feel that I have to give some additional explanations regarding my question as well as article.  Magnetic field may vary in a coil, but may not get propagated, and the variation in the magnetic field may be used for self-induction, and magnetic field wave may not be produced.  Similarly when both inter-related magnetic field and electric field oscillate simultaneously, at least one field is not propagated.  This observation is made from existing properties of electromagnetic waves.  The present mathematics theory known to me is not sufficient  to assume that simultaneously oscillating magnetic fields and electric fields are simultaneously propagated.  This fact support the announcement made in the article, and this fact forces me to search for a  mathematical evidence mentioned in the question. 

  I think that now I understand what you want to say. Perhaps you are speaking about the transverse modes of propagation within a waveguide or so on. If that is the case, the problem is not the wave equation but its boundary conditions for keeping certain modes of oscillation as solutions of Maxwell equations. 

Dear Udhaya,

I am dismayed that you are repeating the things that according to my earlier explanation on this very page lead to contradictions. Alternatively, assuming the simplest case of the electromagnetic phenomena in vacuum, the resolvents of the wave equations corresponding to E and B are identical, so that E cannot be propagating if B is not, and vice versa. Aside from the further fact that I have emphasised twice earlier on this page − regarding the local connection between E and B brought about by the Maxwell equations, one should not forget that in the process of eliminating B for deducing the wave equation for E, and in the process of eliminating E for deducing the wave equation for B, one goes from a first-order differential equation (as regards the spatial variation of the fields) to a second-order one, thereby increasing the number of required boundary conditions to be satisfied by respectively E and B by one. These additional boundary conditions link E and B over the entire relevant space.

Lastly, I have just checked the paper that you have linked to your above question. I would certainly not have recommended its publication if I had been its referee. Further, and I say this with a heavy heart, IJSR is not a reputable journal. My strongest advise to you, as a young aspiring scientist, is that you should think many times over before deciding to publish your thoughts in any form. The academic world is a tough and unforgiving environment, and you should not be so carelessly damaging your name and your future prospects by getting your thoughts that at first glance may appear beguilingly true published in 'predatory and fake scientific journals' [1]. These journals do not have your prospects as an aspiring scientist at heart, as they are there for reasons of their own, which have no baring on advancement of science. Reputable scientists are remembered by their best publications, but aspiring scientists by their worst. If I were you, I would certainly retract the paper before it is too late.

[1] L Tin, et al. http://www.dgt.uns.ac.rs/pannonica/papers/volume18_3_3.pdf

You will find that IJSR is listed here as 'predatory and fake'.

 I shall follow the advice of Professor Behnam Farid.  I know very well that the announcement made in the article will not give any impact in physics, because there is no significant contribution which is made by using the statement  "every electromagnetic wave consists of an electric field wave and a magnetic field wave".  So, nothing in physics is going to be affected because of this announcement.  But, the same reason justifies the announcement indirectly, because there is no important contribution to deny the announcement.   Following the advice of Professor Daniel Baldomir I shall try to fix boundary conditions for keeping certain modes of oscillation as solutions of Maxwell equations.  I thank both of them.

Dear Udhaya, I am very glad that you took my advice in good spirits.

Regarding what you have written in bold, it is not the task of science or the scientist to be wedded to things that are irrelevant at best, since life is far too short to be wasted in this way. Once you have several major scientific contributions on your name, perhaps then you may afford the luxury of uttering irrelevant things.

  Dear Udhaya,

  The usual boundary conditions are a "perfect conductor" as physical boundary, which means that its electrical conductivity is very high (notice that this is not related with the superconductors with the Meissner effect) and therefore E (D) is strictly perpendicular to a metallic surface (cilinder or rectangular) while the magnetic field H (B) is always parallel. Every lab has this instrumentation for working with students and surely you have been in contact with it. Perhaps you have an extra idea of introducing the polarity and my advice is that you look for in the literature.

  The solution of the electromagnetic waves in different quantized modes is very well known and mainly worked by the engeneers of telecommunications. There are a huge amount of bibliography on the subject that surely you can find. In any case I wish you a successful work!

Yes, partial differential wave equation., second order in space and time, from

Maxwell in free space.

If you listen to the radio the answer is afirmative, and is evidence.

In Maxwell's theory, you do not have two separate waves moving along side by side, one electric and one magnetic, but a single electromagnetic wavefront propagating at c in which both fields transversally oscillate as they induce each other.

The problem of polarity was addressed by Louis de Broglie in the 1930's, and he concluded that the only way this could be resolved was if EM energy propagated as separate quanta and that the only way that polarization could be explained was if a photon involve 2 half-spin half-photons that could be polarized on a plane perpendicular to the direction of motion.

You can find in this paper a possible solution in conformity with Maxwell's equations:

https://www.omicsonline.org/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.pdf

The wave by itself does not have polarity, polarity(separation of positive and negative charges) can be induced in matter sitting in a field (dc or ac electric field.)

a polarized electric field is a different thing, it means that it vibrates only in a certain plane, usually after it goes through a polarizer.

Dear Prof. Juan Weisz

Polarization generally just means “orientation.” It comes from the Greek word polos, for the axis of a spinning globe. Wave polarization occurs for vector fields. For light (electromagnetic waves) the vectors are the electric and magnetic fields, and the light’s polarization direction is by convention along the direction of the electric field. Generally you should expect fields to have three vector components, e.g. (x,y,z), but light waves only have two non-vanishing components:the two that are perpendicular to the direction of the wave. In this experiment, we will be concerned with the polarization of light. The most elegant tests of quantum mechanics have been performed by measuring correlations of the polarization of photons from atomic transitions. This is beyond the scope of these experiments, but it's good to keep in mind that some of nature's

thornier problems are lurking in the corners.

The previous paragraph is the one available in a book.  There are many such definitions and conventions given in many books. I can give my own definition and my own interpretation for polarity, which is not a matter concerned.  The proposal is the following: every electromagnetic wave is free from electric field wave or free from magnetic field wave.

Dear Prof. André Michaud

I thank you for providing your article, and I got the article.  Maxwell equations are assumed, the wave differential equations derived Maxwell equations are assumed.  The claim is that the wave differential equations do not give the conclusion that both magnetic field waves and electric field waves exist simultaneously.  I think that some new method should be devised mathematically to discuss wave differential equations. 

Sankar

Do not agree with your last sentence, the rest is ok if you want to use a different definition.

If you want to talk about electric field direction, from charges, it has direction according to the sign of the charge. Points away for positive charge, points in for negative charge.

This is for static fields.

According to Maxwell a time varying electric field gives rise to a magnitic field, so both

should exist simultaneously in a wave.

It is Maxwell theory you are up against, and believe me that would be too great a challenge for present day paradigms. ENM theory is too well established by now.

In books you can find the wave equation for both electric and magnetic field derived from Maxwell theory. but one cannot exist without the other.

the best, juan

Prof. Weisz

I thank you for your comments.  The article is not against the well established Maxwell equations.  The article is not against the wave differential equations derived from Maxwell equations.  But, it is against the following classical interpretation:  Both electric field waves and magnetic field waves exist simultaneously.  Apart from other reasons, the main reason is the following:  The mathematics does not support this interpretion.

Dear G. Udhaya,

There is not separate electric field waves and magnetic field waves existing simultaneously.

There is electromagnetic energy existing physically, described by Maxwell's theory as involving mutually inducing electric and magnetic components, that are described by Maxwell's equations as mutually inducing electric and magnetic mathematic fields representations.

The fields descriptions are not the energy. they are only our current mathematical descriptions of our perception of what the physically existing electromagnetic energy can be.

The map (the fields representations) must not be confused with the real country (the really existing electromagnetic energy).

do no understand well because maxwell is usually though as a classical theory.

some do interprete electric field at the level of a wave function, and try to make it

quantum, with h drppping out, but they are minority I think.

experimentally you are able to shake magnets and charges a la par using

enm waves.

To everyone interested:

I could not answer the question asked by me, directly. But, I like to present a strong evidence for the following theory: An electromagnetic wave contains only an electric field wave or only a magnetic field wave. This evidence is presented in the article attached. This evidence indirectly concludes that it is not possible to find a mathematical evidence to establish that wave differential equations lead to wave solutions.

Article Two Expressions for Electrostatic Forces and For Magnetic Fo...

To everyone who contributed:

I found that atomic physics and astrophysics help to find the important number 1.063 mm (approximately), in connection with the question. This number divides the electromagnetic waves into two classes. If the wavelength of an electromagnetic wave is less than 1.063 mm, then it is an electric field wave which is free from magnetic fields, and if the wavelength of electromagnetic wave is greater than 1.063 mm, then it is a magnetic field wave which free from electric fields. Details are given in the article attached.