Maxwell's equations describe the electromagnetic field at the classical level. The full description is quantum electrodynamics. The problem you are referring to is the famous wave-particle duality. The electrodynamic field is a quantum system, for some states, a particle is a better approximation, for some others, waves.

A few photons behave mostly like particles, whereas many photons (coherent states) like waves. The solutions of Maxwell's equations in the one photon case can be used to calculate probabilities of the photon hitting a certain part of the screen after the two slits.

As for propagation in all directions: that is Huygens' principle applied to the wave. But the wave is used to calculate probabilities in this case. For one photon, you cannot tell if it travelled in all directions or just one direction, only that it did hit the screen at a given point. To the amplitudes used to calculate the probability of hitting that point, all possible paths contribute.

Maxwell's equations describe the electromagnetic field at the classical level. The full description is quantum electrodynamics. The problem you are referring to is the famous wave-particle duality. The electrodynamic field is a quantum system, for some states, a particle is a better approximation, for some others, waves.

A few photons behave mostly like particles, whereas many photons (coherent states) like waves. The solutions of Maxwell's equations in the one photon case can be used to calculate probabilities of the photon hitting a certain part of the screen after the two slits.

As for propagation in all directions: that is Huygens' principle applied to the wave. But the wave is used to calculate probabilities in this case. For one photon, you cannot tell if it travelled in all directions or just one direction, only that it did hit the screen at a given point. To the amplitudes used to calculate the probability of hitting that point, all possible paths contribute.

Thank you.

Dear Andrew,

Laszlo's answer is correct. Maxwell's equations apply to a field of uncountably many photons, whose influence we seek at global, macroscopic scale.

An isolated photon also carries electromagnetic properties, but the proper treatment is provided by the quantum optics or quantum electrodynamics. These take into account how many photons are there, and what is their organization. For instance there may be a fix number of photons (Fock state), or an undetermined number according to the coherent state or according to other types of states. Also the state may be monochromatic, or of many frequencies. Well, the quantum state of photons spans whole theories.

About the double-slit experiment, you mix things: the waves exit the slits according to Huygens' principle, which has nothing to do with the electromagnetic character of the photon, but with its wave-like character. A wave of photons, a wave of electrons, a wave of sound, all obey Huygens' principle. If this principle is not clear to you, maybe you'd read of it in Wikipedia, and if still not clear, then ask us for more explanation.

Now, the famous Dirac's dictum that a particle interferes only with itself, has to be understood properly: the quantum theory doesn't accept the concept of particle. The correct concept in the quantum theory is the wave-function. And the wave-function of a photon does not interfere with the wave-function of an electron.

However, the wave-function of photon(s) exiting a source, YES interferes with an identical wave-function exiting a second source identical with the first one (the famous experiment of Pfleegor and Mandel). If the experiment is not known to you ASK ME and I'll seek the article.

Best regards,

Sofia

I had never heard of the Pfleegor -Mandel experiment. Please give us the reference.

Very good question, Andrew. Maxwell's equations are theory. Photons may be connected with them (quantization included or not) as solutions of some sort.. I speak in such vague terms ("of some sort") in order to make that statement compatible with the statement that a field is constituted by photons, to which I do not object but there might be a deeper answer in the same direction.

Assume you have an algebra in which the electromagnetic field fits, and where positrons and electrons also are represented. That algebra already exists. Kaehler "created" it in (1960-62). Because of particle-antiparticle annihilation, the sum in that algebra will tell you what the sum of the two gammas is.

Details upon request.

The electric field depends on the nearby existence of electric charges. The amplitude of the field diminishes as 1/r with distance r from the charge. Photons are known to be able to travel billions of light years and after that trip they still can be detected by suitable photon detectors. The field in which such photons travel must exist always and everywhere. It is quite unlikely that this field is the electric field.

A more convincing carrier is the field that represents our living space. It deforms dynamically under the influence of massive objects and it is always and everywhere present. It also means that photons are not vibrations of the electric field. Spherical waves and spherical wave fronts tend to lose their amplitude quickly with increasing distance from the emitting source. A better choice is to interpret photons as strings of one dimensional wave fronts. These solutions of the wave equation keep their amplitude and as a consequence they can travel huge distances without losing their energy. Of course these wave fronts occur in the field that represent our living space. Each wave front carries a bit of energy. The photon contains a string of these energy bits.

With this question of mine I appreciate RG even more.  The collective knowledge of competent people even if they would disagree in certain aspects,is a great initial condition to get the full insight into the matter of the question. 

Andrew:

I think we can all agree that your question is at the crux of particle-wave and mass-energy duality, both of which I believe are the same thing.  Both dualities can be shown to have the same origin, if we accept the wave-only nature of reality.

What we seem to be unable to rationally accept is the answer to the following question: How can a conglomerate of waves have a solid —mass-like—, permanent structure? The question can be rephrased as, how can a wave behave like a particle?  But we know it does.  If you are interested, I have ideas on how to answer this question, which I can share on request.

Nevertheless, let me parallel the above question with another question, why are we all ready to rationally accept the apparently mass-like (ink) structure of this thread, when it is really a conglomerate of transient luminous dots on a screen?  The answer is, because we know the process that constructs it.

QM is a functional model that explains the behavior of a scope of reality, it does not tell us how that scope is created, constructed, manifested, expressed, presented, collapsed, etc.  This does not, by the way, as we all know, diminish the usability of QM.  What this points to, is the need of a better model or a complementary one that would explain the process of expression, as I like to call it.

I believe the answer to your question in particular, lies in modifying the concept of the photon as an information package, not a wave.  We use the word already in the context of “force carrier”, why not accept the photon as a message of information (data), where messages do not interact with themselves, they are the information currency between wavicle transitions (interactions), managed by some infrareal accountant.  This is why I believe we should look into a discrete-event model in order to better predict photon behavior.

One last point about photons, why do we assume in photon experiments, that the source photon that interacts with a screen, a slit, a mirror, etc., is the same photon that interacts with the detector?  Can this be proven?  By the way, have some of these experiments been performed in a vacuum? Would this make a difference?

If many individual photons are involved in intermediate interactions (that is, a photon beam modeled as an event path), not just a lot of QM, but the whole of physics would have to be re-thought.  Ouch!

Regards,

Bernardo.

In our previous work, we predicted that weak coherent

radiation in the 1–100 THz frequency regime can be emitted

under some circumstances when a shock wave propagates

through a polarizable crystal, like NaCl 1. The coherence

of the emitted radiation comes from the spatial coherence of

the crystalline lattice and the constant propagation speed of

the shock wave. We believe the mechanism responsible for

this type of emission is fundamentally distinct from existing

sources of coherent optical radiation.

www.cmth.ph.ic.ac.uk/photonics/Newphotonics/.../Wijnands_OpQE29.p..

ocw.mit.edu/ans7870/6/6.007/s11/MIT6_007S11_lec36.ppt

www.mit.edu/~soljacic/shocked_crystals_PRE.pdf

There may be some misunderstanding here. A photon behaves as a particle or a wave according to how it is detected. If by an interference experiment, it acts as a wave. If by, say, the photoelectric effect, it acts as a particle. These are just the ways photons appear to us as a result of our measurements. In the theory of the quantization of the electromagnetic field, the factors of the harmonic components of the Fourier expansion of the electromagnetic potential are replaced by (creation and annihilation) operators. This introduces the idea of quasiparticles of the EM field (photons). (See "Advanced Quantum Mechanics" by Sakurai.) This is the theoretical relationship between Maxwell's theory and quantum theory. Whether or not this is a fruitful approach can only be answered by experiment.

Who ever looked through an image intensifier device at very low dose rates, knows that elementary particles and photons are never detected as waves. At the utmost the detection patterns that can be seen that at higher dose rates look like interference patterns. The density distribution of the locations where particles can be detected is a continuous function and has a Fourier transform. Thus that density distribution has a representation in the form of a wave package. However, at detection the particle is no longer represented by a location distribution. At detection it is represented by a single location.

The solutions of Maxwell's equations are classical, electromagnetic waves. They can be described as coherent superpositions of a macroscopic number of photons. A single photon can't be described by Maxwell's equations. It is posible to describe interference of classical electromagnetic waves through slits and compute the solution of Maxwell's equations with those boundary conditions. It is also possible to describe the transition amplitude of a single quantum particle with those boundary conditions. The two problems are distinct and it can be shown that as the number of particles increases one obtains the classical solution.

@Stam

A more compact and consistent differential calculus including a wave equation is offered by quaternionic differential calculus. See: "Quaternionic Versus Maxwell Based Differential Calculus"; http://vixra.org/abs/1506.0111

This clarifies that the underlying differential calculus is a purely mathematical theory. Maxwell based differential calculus is strongly influenced by physical interpretations

One of these interpretations is the usage of coordinate time in stead of proper time.

The quaternionic differential calculus can also be applied to other fields than the electric field. It has a far wider applicability than Maxwell equations have.

Dear Jaskaran:

   You can also see, if you wish, my attached paper: "what is the meaning of the zeroes...?"

The problem that I have seen in this and all other experiments is that the understanding of the Photon, or Quantum of light that you are referring to is not complete.  We do not in our current understanding realize what a photon is.  This is the problem that Albert Einstein had tried to solve over the last 3 decades of his life.  What is the Quanta?

If however we look at the problem from the outside and not foist the current definitions on the problem we can clearly see that there is a problem with the definition and how it is looked at in the real world.  A Photon is a particle that may or may not have an overall charge, it may or may not have what we call mass, it may or may not be two things put together or more, it may or may not be.... and on and on.  

We have to stop looking at the particle that is a "Quantum" of anything as something it is not.  Quanta are parts of nature that are very small, they sometimes have an overall charge they sometimes are neutral, (although this does not mean they have or carry no charge), they can appear to move in random ways, they are hard to measure by themselves, they are everywhere, they get caught up in fields, they sometime appear to be in two places at one time, (although our ability to measure this is suspect), and they are Real.

We sometimes forget the last thing in favor of magic!  They are not magic they (The Quanta) are real particles and being the smallest parts of things that we can detect does not mean that it is the smallest part of things that exist.  

There is no magic there is no two places at one time there is only our inability to measure and our inability to let go of the past and move to better understanding of science today.  Why do we want to hold on to the old understanding so hard that we can not make advances today that are meaningful.  Mush of the technology of today could have happened anytime after 1915.  Many of the results that we see from experiments that are going on today and over the last 30 years or so have lead us to no better understanding of this than when Albert Einstein almost 100 years ago said that the Quanta had to "really exist in nature".  

Most of the work that I do in my lab points to the Quanta being just another particle with mass and properties just like that of all other particles.  It is however very small compared to all other things and so many things affect it and overwhelm its size and ability.  It is vary easy to move it out of the way or change its path.  It is almost impossible to make it do just the thing you want it to do unless you have lots of them in one place at one time.  This is in the light amplification by the stimulated emission or radiation (LASER) is what we have done and the results are great.  So we see that one photon may wonder or look to be in more than one place but when we place lot of them together in the same frequency range things look different. 

Start looking at the Quanta differently and realistically and we will have solutions. 

Remember that when we talk about Maxwell's equations we automatically add back in the misunderstanding of the quanta.  Maxwell's equations "assume" the "Quanta" is a "Wave" not a particle with wave like properties but only a "WAVE".  

This implies that we treat it as if there is not reality to the particle.  Also do not think that I am somehow saying that Maxwell's equations are wrong they are not.  I am saying that they do a great job of calculating what the "Quanta" is doing.

Any particle traveling through space and time that has a charge (including a dipole with an overall charge differential of Zero) and rotation will look like a wave when we try to measure it.  This does not make it a wave.         

The concept of "photon" arises from the quantization of electromagnetic waves (EM). In particular, the modes of an EM wave behave as harmonic oscillators which, when quantized, enable the EM energy to be described as consisting of an ensemble of particles of discrete energy, called photons. Photons, thus, are related to the intensity (energy density) of an EM wave. An EMITTED photon, then, represents one of the particles of energy making up the energy density of an emitted EM wave. On the other hand, the dependence of the intensity of an EM wave on position, "r",  represents the probability of finding the photon at r.  

I remember wishing that there was a many coordinate space (R^3N) version of Maxwell's equations that existed as a classical field theory and gave an isomorphism with quantum optics.  I found it could be done with some difficulty.  As usual for such approaches, the problem is to see when one obtains a "classical limit."  In the quantum optics case, it is clear that N->infinity is not sufficient (this is also true in regular quantum mechanics as well).  My EM teacher, David Aspnes, used to say "the photon only interferes with itself" meaning that two different photons don't interfere.  This is a good way to view it in the separable case (before symmetrization).  I found this a nice little maxim as I kept improving my understanding of the quantum case versus the classical Maxwell equations.  

I find these - very classic - answers most confusing. In Physics we use concepts to represent phenomena that we can observe, and to which we can report measures. We have the concept of particles : they exist at a single location  (of space time), and we added the concept of field (which exists everywhere and propagate) to avoid the idea of the action at a distance. Now many think that a particle can behave as a wave, but one cannot know where it chooses to do it, and conversely that a field can behave as a particle, without announcing what it is. This is just irrational. Science is based on laws that can predict a result, without the need to leave the decision to the object that is observed. One can represent particles as waves : this is just what is done in models where  a beam of particles is assumed to follow some general equations : they can be represented as a field, variables defined everywhere, with the solutions computed or measured afterwards. For fields we need more. One aspect of the topic that has not been discussed so far is the continuity of fields : can we assume that they propagate without any trouble ? In the macroscopic world we know of shock waves, which are discontinuities in the field. And whenever a photon is invoked, there is some discontinuous process at work. So, one can look for an answer in discontinuities in the underlying fields. And in the celebrated Planck's law, the frequency should come from a field, isn't ? And for people who use freely photons, just remind that in the - also celebrated - Standard model, the photon is not an elementary particle, but a composite.

One can represent discontinuities in any field as particles, which have a definite path, and even a charge. They behave like particles, but their true meaning is different.

Jean Claude,

There are many things wrong with how we approach the science of our day.  One of the things that I have noticed is this exactly. As a research scientist it is my job to question the validity of old science.

The problem is that if I assign a property to something then that something has  a physical existence unless we want to go back in time to the turn of the century, "before the last one 1900".  This would have been when we thought of the light quanta or photon as only being a disturbance in the "Aether" or light carrying Aether.  This was shown more than one hundred years ago to be as Albert Einstein put it "Superfluous" or unnecessary.  It took almost 200 years from the time of Newton to make it perfectly clear that the light that is emitted from a star does not travel on Aether.   It may act like a wave but in reality it is a particle that has wave like properties.   Why is this so hard to except?

If I take a bar magnet and then I through the bar the think that I realize is that the bar has a wave function that is associated with its propagation.  So if a Photon is a neutral particle the same as a Bar Magnet with an over all charge of zero but it has two ends that have charge then as it propagates through space it will also have a wave function associated with its motion.

It is time to really remove the Aether from the problem.  

"Light Quanta", are particles with wave like properties.   Any other interpretation brings back the aether or introduces magic.  

Einstein had the hardest time with the spooky action at a distance but most of this was because he thought of everything as a wave and he loved the wave functions of James Clerk Maxwell. 

Just because the function can calculate the fields as they move through space does not make them something other than the properties of a particle which is traveling through space at the speed of light.  Mass or no mass as we define it.

I have not wanted to be disrespectful of others thoughts on the issue but why is that no one will say anything about the Elephant in the room, There is no aether, and if there is not aether then light quanta are particles.

Please correct me if I am wrong but the logical side of this argument is that the understanding of the past has not helped us understand what is really going on with light. 

The next thing that will come from this new understanding is that the particle of light or photon that is left over after it is absorbed or deflected is more than likely responsible for quantum uncertainty and the random nature of matter on the smallest of scales.

The photon must consist of solutions of the homogeneous wave equation of some field. That field is the medium in which it propagates. The homogeneous wave equations that I know have special solutions in odd numbers of participating dimensions. These special solutions are wave fronts. These wave fronts can be described by one-parameter functions that keep their form during the travel of the wave form. For three dimensional (spherical symmetric) wave fronts the amplitude diminishes as 1/r with distance r from the emitting source. For one-dimensional wave fronts the amplitude stays constant. Since photons can travel huge distances and after that they have sufficient energy left to be detected by suitable photon detectors it is sensible to suggest that photons exist out of strings of wave fronts that occur in the medium through which they travel. The electric field does not have huge extensions. Thus another field must act as transport medium. It must be always and everywhere present. In contrast to the electric field is our deformed living space a good candidate.

To Hans,

"The photon must consist of solutions of the homogeneous wave equation of some field. " . Why ? The wave equation exists in SR, in the vacuum, for the EM field. It does not tell us that the photon is a solution of this equation. However one can study fundamental solutions of this equation, or more exactly of the same equation on distributions, and it gives Dirac's like solutions, that is discontinuous solutions.

"The electric field does not have huge extensions." So you do not accept the idea of photons emitted by far away stars...

"Thus another field must act as transport medium." Why look for complicated answers ?

One intriguing question : how do you detect photons, if not as a perturbation in an existing EM field ? Even in the black body the photons are assumed to be emitted in a discontinuous process, generated by heating the body, but the photons come from the EM field of the atoms or molecules. They do not come from some mysterious medium. And to measure the radiation which is emitted one use basic EM fields.

A single photon propagates according to the electromagnetic wave equation that follows from Maxwell's equations. That is how a single photon is diffracted in going through two slits.

If photons go through double slits one at a time, they form the same diffraction pattern as electrons going through double slits one at a time.

To George,

Sorry, I missed your answer. Where did you find that I evoked aether in my post ? As far as I know, the EM field is a generally accepted representation of a physical phenomenon, even for by the quantum physicists. Why this field should be continuous ?

"Light Quanta", are particles with wave like properties. Any other interpretation brings back the aether or introduces magic." 

Of course, that the photon chooses to behave like a particle or a wave, as its will, is no magic... A discontinuity in the field can be represented in the usual formalism, and behave like a particle, it has trajectory and a support, exactly as one represents shock waves. There no need to invoke anything more than the usual representation of fields. But, of course, there is no mystery, so it is not so fancy.

Dear Andrew

Figure 1, in the attachment, provides a view of the photon fiber, which is also called a heat fiber in this article. The energy of a photon (heat fiber), given by Planck’s law E = hν, arises from its light-speed oscillatory motion along its length and about its origin (which is at its mid-length), rather than its translational motion. Its oscillatory motion is perpendicular to its translation; thus, a waveform is traced as it translates. Hence, light and radiation, in general, are not waves, themselves, but are photon fibers that trace a waveform as they translate.

Please remember that Maxwell’s wave equations for radiation only state that a waveform develops in the propagation of light. Based on Einstein’s work, light comes in the form of individual particles – photons. By combining the work of Maxwell and Einstein, a logical conclusion is that Einstein’s photon traces Maxwell’s waveform. The diffraction of photons in the double slit experiment results from the oscillatory motion of the photon along its length and about its origin, which is at the photon’s mid-length.

Per Maxwell’s wave equations, photons have electric and magnetic properties. In Figure 1, perpendicular elements develop along the fiber length, due to Lorentz length contraction, as it oscillates back and forth at light-like speed along its length. These perpendicular elements give its B-field as it also twirls about its origin. The E-force potential of the photon arises due to the movement of its B-field elements per Maxwell’s equations. It should be noted that the E-component of the electromagnetic wave is not a field; it is an electric force potential that moves in synchronization with the B-field elements and at right angles to it. The energy given by the fiber oscillation is related to its oscillation range or stroke; shorter strokes yield shorter wavelengths and higher frequencies, and thus greater energies.

Since photons are components of the electron, it is detailed in Figure 1 of the attached article that introduces the electron in Figure 2. The article is excerpted from a larger body of work. Please select the “title” hyperlink to view the photon and electron.

Regards,

Dan S. Correnti

Article UNVEILING of the ELECTRON (Post #1) [A Proposed Electron Structure]

As George Van Hoesen suggests, the relationship between Maxwell's electromagnetic field and emitted/absorbed photons was probably established by Einstein. To me it seems that all the interesting answers to Andrew Wutke's question don't clearly point out that there are also differences between Maxwell's field conception and Einstein's contribution, which in my opinion could be of some interest.

Maxwell's solutions describe a classical field of forces over the whole “physical space” – by which is meant the luminiferous aether carrying the forces. Stam Nicolis points out that there are classical propagating waves among the solutions of Maxwell's equations.

Einstein focuses rather on the matter-field interaction, which in modern parlance corresponds to production and detection (observation) of electromagnetic signals. As pointed out in this thread, Einstein didn't associate any message conveying information with signals, but gave them a solid mass-like structure.

The difference I wish to point out is the following. Whereas Maxwell tried hard to substitute Newton's metaphysical space with a physical entity – the aether – Einstein posited that rational mechanics is a faithful description of Nature, and that it is equipped with an inherent concept of space. In fact, then it was commonly accepted that the laws of physics match “dynamical space”. Maxwell himself, besides modeling electromagnetic fields geometrically, also gave a Lagrangian interpretation of electromagnetism. Today, experimental verification of a geometry is no longer required. The “configuration space” of the quantal description is actually a sample space. Summing up, Maxwell thought that a geometrical representation is unavoidable to grasp his theory, whereas the photon picture takes over intuitive representations from electromagnetism or mechanics, if at all.

Maxwell's equations applies to photons,  with one important change; namely, that the electric and magnetic fields are non-commuting operators, called field operators.  These fields are made operators to incorporate the quantum uncertainty principle, which takes the form that one can not measure the number of photons and the field's phase simultaneously. Another way of saying that is that the order in which one makes a measurement matters.  Using a vector field operator to generate both the electric and magnetic field operators,  produces the photon creation and annihilation description.

If one forms a suitable ensemble average, or forms a  wave packet of incoherent photons,one recovers the classical Maxwell field equations,  The classical limit for bosons is a classical field theory;  whereas, the classical limit for fermions is classical particle dynamics.  The Ehrenfest theorem is the original method for obtaining the classical limit and applies to quantized fields, as well as to particle dynamics.

Maxwell's equations applies to photons,  with one important change; namely, that the electric and magnetic fields are non-commuting operators, called field operators.  These fields are made operators to incorporate the quantum uncertainty principle, which takes the form that one can not measure the number of photons and the field's phase simultaneously. Another way of saying that is that the order in which one makes a measurement matters.  Using a vector field operator to generate both the electric and magnetic field operators,  produces the photon creation and annihilation description.

If one forms a suitable ensemble average, or forms a  wave packet of incoherent photons,one recovers the classical Maxwell field equations,  The classical limit for bosons is a classical field theory;  whereas, the classical limit for fermions is classical particle dynamics.  The Ehrenfest theorem is the original method for obtaining the classical limit and applies to quantized fields, as well as to particle dynamics.

For those who wanted info on Pfleeger-Mandel (of which I was also ignorant until now) see

http://scienceblogs.com/principles/2010/11/19/interference-of-independent-ph/

for a readily understood presentation and

Phys. Rev 159 (5) 1084 (1967)

for the original paper

This is wave and particle duality problem, it is still a open question. Up to now, no one has a solution. But thing is changed. Recently I have introduced a new electromagnetic field theory: Mutual energy principle and self-energy principle which solved the wave particle duality problem.

According to this new these two principle, a photon is the mutual energy flow which is build by retarded wave and advanced wave. The retarded wave and the advantaged wave satisfy the Maxwell equations. The retarded wave is sent by emitter randomly. The advanced wave sent by absorber randomly. When this two wave are synchronized, the mutual energy flow is produced. The mutual energy flow is responsible to transfer the energy of the photon from the emitter to the absorber. The two wave of Maxwell equations, the retarded wave and the advanced wave do nothing for transferring the photon energy, they are returned through time-reversal processes. I have proved the mutual energy flow theorem which can guarantee the energy go through in any surface between the emitter and the absorber are exactly same, this energy is the photon's energy. In this theory photon need 4 waves: retarded wave, advanced wave and two corresponding time-reversal waves which is used to balance out the retarded wave and the advanced wave.

This solved the wave and particle duality problem. Because the mutual energy flow are thin in the place of emitter and absorber, it becomes thick in the middle between the emitter and the absorber. Hence, the mutual energy flow looks particle at the place of emitter and absrober, and looks like wave at the middle between the emitter and absorber.

For details pleas see http://www.openscienceonline.com/journal/archive2?journalId=726&paperId=4042

See:

"Article Quaternionic versus Maxwell based differential calculus

and https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project#The_behavior_of_continuums

and "Article Rediscovered dark quanta

Maxwell equations use only subset of the five terms of the quaternionic first order partial differential and decorates the equations with measuring units.

Dear Shuang-ren Zhao.

It sounds very interesting with only one exception. There cannot be time reversal process because time is clock indication which is a measurement of clock's state. Clock can only speed up or slow down relative to other clocks and even if it started to tick backward other clock would still monotonically increment the count. There must be another explanation.

Elementary particles can zigzag in time. Observers see the reflection instants as pair creation/annihilation events.

https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project/Zigzag

Dear Andrew Wutke,

In the equation of physics the time is always in symmetry. So if there has retarded wave, the advanced wave should be allowed. If there has the retarded wave, and advanced wave, the time-reversal waves corresponding to the retarded wave and the advanced wave should be also allowed. Hence there are 4 waves, this 4 waves are balance out. 4 waves together transfer the energy is 0. But there the mutual energy and mutual energy flow which are the interference effect of the retarded wave and the advance wave, which can transfer the photon energy. Hence photon is nothing else, it is just the mutual energy flow.

I introduced the concept of mutual energy in 1987, in that time I have published 3 papers about the mutual energy theorem in Chinese. In that time I begin think about the energy is perhaps only transferred in the space by mutual energy. The similar theorem actually is published by Welch in 1960, but Welch call it as time domain reciprocity theorem, which obstruct the other people to understand actually this theorem is a energy theorem instead of mathematical formula. My papers are in Chinese, only a few people perhaps read it.

The original mutual energy theorem is try to solve the energy transfer in the space, sphere wave expansion, the energy transfer between transmitting antenna to the receiving antenna. However if the energy transfer between two antenna is done by mutual energy, why not the photon also do the same thing? Recently I build the photon model with mutual energy flow. The only thing confuse me is that the retarded wave and advanced wave are sent to empty space, the energy is lost, and go to outside of our universe. That is not possible. Finlay in last April, I solved this problem by the two conflicts between Maxwell equations, superposition principle and energy conservation. There are conflicts, the only solution to solve all these conflicts are introduce two additional new waves, which are time-reversal waves corresponding to the retarded wave and the advanced wave.

By the wave, advanced wave has been introduced by action-at-a-distance theory, Wheeler Feynman's absorber theory, interpretation of Quantum mechanics of John Crammer. But it still not accept by all physicist. I believe it. The additional two another time-reversal waves are applied to make the whole theory self-consistent. This is perhaps the only solution.

Dear Shuang-ren Zhao.

You English seems to be good enough to translate your work as a draft and improve later.

I am not questioning your reasoning without seeing it all.

The absurdities of time travel in my area of interest can be described as artifacts of Einstein Clock Synchronisation Method (ESM) for Special Relativity. As you can see on the attached diagram, of the static view of two systems: K stationary and K' moving, time t' is distributed along the x/x'axes so at distance L' for example, the past of K' is in direct contact with present time t at corresponding L/gamma in K

This could be demonstrated using a couple of clocks manufactured in one factory, then distributed then synchronised. Therefore, all of them are contemporary. The reason for that is that the ESM is based on the requirement that forces the instantaneous light velocity to be homogeneous in any inertial system as it was in the absolute rest frame.

Therefore, clocks can appear out of synch with current reality but they are just shifted in phase that's all. And it does not make STR invalid in any way, you just need to understand what the Einstein's time definition implies.

There is another case where backward in time motion appears when a hypothetical faster than light signal is transformed to a moving system and is also sufficiently fast, including the infinite speed.

Perhaps in your model you have just discovered the faster than C case an you need a proper interpretation to expose this.

Dear Andrew Wutke,

My view of point is that if people can accept the concept of wave function collapse, they should also accept the concept of time-reversal return of a wave. Actually time-reversal return is also a collapse process, instead collapse to the target of the wave, but here it collapse to its source.

Since mutual energy flow has done the energy transfer for a photon, the waves do not need to collapse to its target. The waves should collapse to their sources. The mutual energy flow transfer the energy and the wave themselves collapse back to their sources together will just equal the wave function collapse. Wave function cannot even offer a formula, the time-reversal process satisfy time-reversal Maxwell equations (which are not Maxwell equations).

By the way, a common mistakes are thinking a time reversal wave of the retarded wave is the advanced wave, that is wrong. Both retarded wave and advanced wave all have their time reversal wave. Hence their are 4 waves. The waves has 4 energy flow, but there are also two additional energy flows which are mutual energy flows.

Mutual energy flow do not decrease with 1/r. The mutual energy flow are same in any surface between emitter to the absorber. The mutual energy flow can also bring the momentum from emitter to the absorber. The mutual energy flow can transfer also the action and reaction. That is a magic.