Abstract In this article the authors will build the model of photon in time-domain. Since photon is a very short time wave, the authors need to build it in the time domain. In this photon model, there is an emitter and an absorber. The emitter sends the retarded wave. The absorber sends advanced wave. Between the emitter and the absorber the mutual energy current is built through the combination of the retarded wave and the advanced wave. The mutual energy current can transfer the photon energy from the emitter to the absorber and hence the photon is nothing else but the mutual energy current. This energy transfer is built in 3D space, this allow the wave to go through any 3D structure for example the double slits. The authors have proved that in the empty space, the wave can be seen approximately as 1D wave and can transfer energy from one pointer to to another point without any wave function collapses. That is why the light can be seen as light line. That is why a photon can go through double slits to have the interference. The duality of photon can be explained using this photon model. The total energy transfer can be divided as self-energy transfer and the mutual energy transfer. It is possible the self-energy current transfer half the total energy and it also possible that the part of self-energy part has no contribution to the energy transferring of the photon. In the latter, the self-energy items is canceled by the advanced wave of the emitter current and the retarded wave of the absorber current or canceled by the returned waves. This return wave is still satisfy Maxwell equations or at least some time-reversed Maxwell equations. Furthermore, the authors found the photon should satisfy the Maxwell equations in microcosm. Energy can be transferred only by the mutual energy current. In this solution, the two items in the mutual energy current can just interpret the line or circle polarization or spin of the photon. The traditional concept of wave function collapse in quantum mechanics is not needed in the authors’ photon model. The authors believe the concept of the traditional wave collapse is coursed by the misunderstanding about the energy current. Traditionally, there is only the energy current based on Poynting vector which is always diverges from the source. For a diverged wave, hence, there is the requirement for the energy to collapse to its absorber. After knowing that the electromagnetic energy is actually transferred by the mutual energy current, which is a wave diverging in the beginning and converging in the end, then the wave function collapse is not needed. The concept energy is transferred by the mutual energy current can be extended from photon to any other particles for example electron. Electrons should have the similar mutual energy current to carry their energy from one place to another and do not need the wave function to collapse.
Abstract In this article the authors will build the model of photon in time-domain. Since photon is a very short time wave, the authors need to build it in the time domain. In this photon model, there is an emitter and an absorber. The emitter sends the retarded wave. The absorber sends advanced wave. Between the emitter and the absorber the mutual energy current is built through the combination of the retarded wave and the advanced wave. The mutual energy current can transfer the photon energy from the emitter to the absorber and hence the photon is nothing else but the mutual energy current. This energy transfer is built in 3D space, this allow the wave to go through any 3D structure for example the double slits. The authors have proved that in the empty space, the wave can be seen approximately as 1D wave and can transfer energy from one pointer to to another point without any wave function collapses. That is why the light can be seen as light line. That is why a photon can go through double slits to have the interference. The duality of photon can be explained using this photon model. The total energy transfer can be divided as self-energy transfer and the mutual energy transfer. It is possible the self-energy current transfer half the total energy and it also possible that the part of self-energy part has no contribution to the energy transferring of the photon. In the latter, the self-energy items is canceled by the advanced wave of the emitter current and the retarded wave of the absorber current or canceled by the returned waves. This return wave is still satisfy Maxwell equations or at least some time-reversed Maxwell equations. Furthermore, the authors found the photon should satisfy the Maxwell equations in microcosm. Energy can be transferred only by the mutual energy current. In this solution, the two items in the mutual energy current can just interpret the line or circle polarization or spin of the photon. The traditional concept of wave function collapse in quantum mechanics is not needed in the authors’ photon model. The authors believe the concept of the traditional wave collapse is coursed by the misunderstanding about the energy current. Traditionally, there is only the energy current based on Poynting vector which is always diverges from the source. For a diverged wave, hence, there is the requirement for the energy to collapse to its absorber. After knowing that the electromagnetic energy is actually transferred by the mutual energy current, which is a wave diverging in the beginning and converging in the end, then the wave function collapse is not needed. The concept energy is transferred by the mutual energy current can be extended from photon to any other particles for example electron. Electrons should have the similar mutual energy current to carry their energy from one place to another and do not need the wave function to collapse.
Einstein guessed that the macroscopic electromagnetic wave is built by thousands of photons, however, no one has offered a theory about how the macroscopic electromagnetic wave is built from photons. A concrete theory about photons is needed to answer this question. Current theory for photons is Maxwell’s equation which has the solution of waves, but it is difficult to describe the photon as a particle. There is the paradox problem of wave-particle duality. This article offers one solution to solve this problem by introducing the normalized mutual energy flow. The interaction of the retarded wave and advanced wave produce the mutual energy flow. The mutual energy flow satisfies the mutual energy flow theorem. The mutual energy flow theorem tells us that the energy that goes through each surface between the emitter and the absorber is all same. That means the mutual energy flow is different in comparison to the waves. The wave, for example, the retarded wave, its amplitude is decreased with the distance from the source to the point of the field. The mutual energy flow does not decrease. The author noticed this and claimed that the photon is the mutual energy flow. In this article the author updated this claim that the photon is the normalized mutual energy flow. Here the normalization of mutual energy flow will normalize the mutual energy flow to the energy of a photon, which is E = hf. E is the energy of the photon; h is Planck constant; f is the frequency of the light. This normalization is similar to the normalization in quantum mechanics. After this normalization the relation between an electromagnetic wave and photon as a particle becomes clear. This article will prove that the macroscopic wave of an electromagnetic field can be built by thousands of normalized mutual energy flows, which describes the photons. The mutual energy flow is an interaction of the retarded wave and the advanced wave. The retarded wave and the advanced wave satisfy the Maxwell equations. There are two additional waves which are the time-reversal waves which satisfy time-reversal Maxwell equations. The advanced wave and the two time-reversal waves are all real and physical electromagnetic fields. The time-reversal waves cancel all self-energy flows of the retarded wave and advanced wave. Hence, the waves do not carry any energy, the energy is only transferred by the normalized mutual energy flows which are the photons. Hence, all energy is transferred by the photon instead of waves. This offers a solution to paradox of the duality of wave-particle.
The particle and wave duality is solved through the self-energy and the mutual energy principles. Welch has introduced the time-domain reciprocity theorem in 1960. This author have introduced the mutual energy theorem in 1987. It has been proved that the above two theorems are same theorem in time-domain or in Fourier domain. This author believe there is an energy flow from transmitting antenna to the receiving antenna. Hence this theorem is a energy theorem instead of a mathematical theorem i.e. the reciprocity theorem. This author found that the mutual energy is the additional energy when the two waves are superposed comparing to the situation when the two waves alone stayed in the space. It is often asked that if the two waves are identical what is the energy after the two waves are superposed, 4 or 2 times? this author's answer are 2 or 4 depending whether the sources of the waves are involved or not. However this author noticed that a more important situation, which is the superposition of two waves: one is retarded wave sent from the emitter, another is the advanced wave sent from the absorber. This situation actually described the photon. This author have found that, instead there are two photons the retarded photon and the advanced photon like some author believed, there is only one photon. The reason is that the two waves the retarded wave and the advanced wave they both bring one photon energy, which are sent to the space, but these energy are returned with the time-reversed waves. The additional energy because of the superpose process of the two waves is just with 1 photon's energy instead of 2 photon's energy. This energy is sent from the emitter to the absorber. These build this author's photon model. This photon model is proved by this author through the notice of the conflict between the energy conservation and both the superposition principle and the Maxwell equations for single charge. This conflict force this author introduced the mutual energy principle and the self-energy principle. Self-energy principle tell us the self-energy (the wave's energy before superposed) time-reversal return to its source and hence do not transfer any energy from emitter to the absorber. The mutual energy principle tell us that transferring the energy from the emitter to the absorber is only done by the mutual energy flow. This author also proved that the mutual energy flow theorem, which says that the energy transferred by mutual energy flow is equal in any surface between the emitter to the absorber. The wave function collapse process is explained by the two processes together the first is the self-energy time-reversal return to their sources (instead of the targets), the second is that the mutual energy flow brings a photon's energy package from emitter to the absorber. The wave's probability property is also explained that because only when a retarded wave synchronized with an advanced wave the energy can be transferred. The photon energy is transferred only when the retarded wave (one of solution of Maxwell equations) and the advanced wave (another solution of the Maxwell equations) are synchronized, otherwise the two waves are returned by two time-reversal waves. Time-reversal wave are not satisfy Maxwell equations but satisfy the time-reversal Maxwell equations. Hence, 4 time-reversal Maxwell equations which describe the two additional time-reversal waves are added to Maxwell equations. Hence, the photon's package wave is consist of 4 waves which are corresponding to 4 self-energy flows. There are two additional energy flows, which are the mutual energy flows that is responsible for transferring the energy from emitter to the absorber. The time-reversal mutual energy flow which is responsible to bring the energy back from the absorber to the emitter if the absorber only obtained a half photon or a part of photon.
The photon energy transfer is from point to point. But the wave according to the Maxwell equation spreads from the source point to the entire empty space. In order to explain this phenomenon the concept of wave function collapse is created. This concept is very rough, if there are many partition boards with small holes between the emitter charge and the absorber charge. The light is clear can go through all these small holes from emitter to the absorber. But according to the concept of the wave function collapse the wave must collapse N times if there are N holes on the partition boards. Collapse one is strange enough, if the wave collapse N times, that is unbelievable! In another article we have proved that the photon energy is actually transferred by the “mutual energy flow” which is point to point instead of spread to the entire space. Since energy can be transferred by the mutual energy flow, the concept of the wave function collapse is not necessary. In order to build the mutual energy flow it is required to build the self-energy flow also. The self-energy flow is spread to the entire empty space. What will do for the self-energy flow, it is possible the self-flow also collapse to the absorber. However if self-energy flow collapse we have also meet the same problem as the whole wave collapse that means if there are partition sheets with N holes, the self-energy flow has to collapse N times. In the article about mutual energy principle we have propose another possibility in which the self-energy flow instead collapse, we believe it is returned. It is returned with a time reversal process, hence the self-energy dose not contributed to the energy transfer of the photon. The return process can be seen as also a collapse process, however it is collapse to the source of the wave instead of the target of the wave. In this article we will discuss the self-energy flow and the time reversal process in details.
Quantum mechanics has the quantization. The quantization offer us a method from the mechanic equation to build the quantum wave equation. For example the Canonical quantization offers a method to build the Schrodinger equation from Hamilton in classical mechanics. This is also referred as first quantization. In general, Maxwell equation itself is wave equation, hence, it doesn't need the first quantization. There is second quantization, for electromagnetic field. The second quantization discuss how many photons can be created when the energy of electromagnetic field is known. This is not interesting to this author. This author is interested how to build a particle from the wave equations (Maxwell equations or Schrodinger equation). Here the particle should confined in space locally. It should has the properties of wave. Our traditional quantization is to find the wave equation. This author try to build a particle from this wave equation, this process can be called as particleization. This author has introduced the mutual energy principle, the mutual energy principle successfully solved the problem of conflict between the Maxwell equations and the law of the energy conservation. The mutual energy flow theorem is derived from the mutual energy principle. The mutual energy flow is consist of the retarded wave and the advanced wave. The mutual energy flow theorem tell us the total energy of the energy flow passes through any surfaces between the emitter to the absorber are all exactly same. This property is required by the photon and any particle in quantum mechanics. Hence, this author has linked the mutual energy flow to the photon and also other particle. The mutual energy flow has the property of waves and also confined in space locally. However there is still a problem, the field of an emitter or the field of an absorber decreases according to the distance from the field point to the source point. If the current (or charge) of a source or sink for a photon is constant. The energy of the photon which equals the inner product of the current and the field will depended on the distance between the the source and the sink of the photon. If the distance increases, the amount of photon energy will decrease to infinite small. This is not correct. The energy of a photon should be a constant E=hv. The energy of the photon cannot decrease with the distance between the emitter and the absorber. In order overcome this difficulty, this author suggests a normalization for the mutual energy flow. It is assume that the retarded wave sent from the emitter has collapse back in all direction. But the mutual energy flow build a energy channel between the source and sink. Since the energy can only go through this channel, the total energy of one photon must go through this channel. Hence, the total energy of the mutual energy flow has to be normalized to the energy of one photon. The mutual energy flow will increase to the energy of one photon. This leads that the amplitude of the wave does not decrease on the direction along the energy channel. The amplitude of the advanced wave also does not decrease on the direction of the energy channel. The electromagnetic wave in the space between an emitter (source) and an absorber (sink) looks like a wave inside a wave guide. The wave in a wave guide, the amplitude does not decrease alone the wave guide if the loss of energy can be omitted. This wave guide can be referred as the “nature wave guide”. In the nature wave guide the advanced wave leads the the retarded wave, hence, the retarded wave can only goes at the direction where has advanced wave. The retarded wave also leads the advanced wave. The advanced wave can only goes in the direction of the retarded wave. This normalization process successfully particularized the the mutual energy flow. This author believe this theory about the normalization/particleization of the mutual energy flow is also correct for other particle for example electron.
Combined with the principle of mutual energy of electromagnetic field, mutual energy theorem, mutual energy flow theorem and Wheeler - Feynman absorption theory, we propose a mutual energy flow interpretation for quantum mechanics. The Wheeler-Feynman absorber theory suggests that the light wave is composed of both the advanced and the retarded waves. John Cramer gave a simple model of photon with plane waves. The author put forward the mutual energy theorem and the principle of mutual energy. The principle of mutual energy is a formula which removes the remainder of the self-energy terms from the Poynting theorem. The principle of mutual energy as the electromagnetic field axiom can ensure that the classic electromagnetic theory building does not fall to overcome the many difficulties if the Maxwell equations have been applied as axioms. From the principle of mutual energy, radio waves, light waves are all consists of the retarded wave of the emitters and the advanced wave of the absorber. The retarded wave and the advanced wave are not simply superimposed, but combined very close together into one. The retarded wave and the advanced wave constitute the mutual energy flow. The energy flows from the emitter to the absorber in the form of energy flow. The integral of the flux of the energy flow to time is constant on any surface between the emitter and the absorber, which is the energy of the photon. Photon is nothing else, it is just the mutual energy flow. In this paper, we should further clarify that the mutual energy flow theorem tells us that the waves in the space are much like the waves in the waveguide as a quasi-plane wave. Although this quasi-plane wave is composed of the retarded wave of the emitter and the advanced wave of the absorber, we can also think of it as a purely retarded wave. The vacuum space naturally constitutes the waveguide of the mutual energy flow. Since the field between the charge and the other charge can be regarded as a plane wave, it naturally avoids the problem of self-energy divergence. Recently, Afshar experiments supported the John Cramer transactional interpretation. We found that, this experiment can also be explained by using the principle of mutual energy flow. Hence, Afshar experiment also supports the author's mutual energy flow interpretation. To make our theory self-consistent, we also introduced the principle of the return of the self-energy flow.
Quantum physics has the probability interpretation. From the knowledge of light, we know that wave is always spread out, and hence the electron wave should also spread out. That means the electron wave beam should like the light wave beam become diverged from the source. When the electron is received by an atom we thought the wave collapse. The place to collapse is depends on the probability calculated from the square of absolute value of the wave function. The recent new discovery tell us that the light is not just wave, it is a combination of waves, retarded potential and advanced potential. These two potentials together produce the mutual energy current or referred as M-current. Another light energy current is P-current related to Poynting vector. We found P-current doesn't carry any energy for light. The contribution of P-current to energy transfer can be omitted. The light energy is transferred only by M-current. The beam of M-current doesn't like the beam of P-current which is diverged from the source, instead, the M-current beam first diverges from a source and then converged to a sink. Since the M-current at the place to be received is localized at one electron, the concept of wave function collapse is needless. The probability results of light is because that we have use P-current to roughly calculate the M-current. We thought if Schrödinger knew today's light theory, he would for sure also build his wave theory for quantum mechanics similar to the new light theory with M-current. Hence we claim that the M-current theory is not only suitable to the light but also can be applied to the quantum physics. This means all particles are M-current. The M-current is composed of not only the retarded wave, but also the advanced wave. M-current is an inner product of a retarded and an advanced waves.