In electromagnetic theory and quantum theory, there are superposition principle. The author found that there are 5 dierent kinds of superpo-sitions. The superposition principles have some dierences. The research about these dierences is a key to open the the door of many physical diculties. For example the particle and wave duality problem, and to judge which interpretation of the quantum mechanics is a correct one. The rst two superposition principles are the superpositions with and without the test charges. The slight dierent superposition principles are the superposition with a retarded wave only and the superposition with the advanced wave only. According to theory of this author, the emitter sends the retarded wave, the absorber sends the advance wave. Hence, normal electromagnetic eld actually is consist of retarded wave and advanced wave. This two wave together become the normal electromagnetic eld. This kind of electromagnetic eld can be seen approximately as retarded wave, this kind wave also has its own superposition. This kind of superposition is also dierent with the superposition when we consider the retarded wave and also the advanced wave. In this article this author will discuss the dierences of these dierent situations of superpositions. This author will also discuss the dierent physical result with a few dierent su-perposition principles. In this article this author will prove only when the self-energy principle is accept, all kinds of superposition can be accept. Otherwise only the superposition with test charge or the superposition with only one kind wave either retarded waves or advanced waves can be accepted. Hence, the discussion about the superposition also support the concept of the self-energy principle which means there must exist the time reversal waves. That also means the waves do not collapse but collapse back. Wave collapse means collapse to target of the wave, for example, the retarded wave will collapse to a absorber and the advanced wave will collapse to a emitter. Wave collapse back means the retarded wave sent from emitter will collapse back to emitter; The advanced wave sent from the absorber will collapse back to an absorber. Hence, one purpose of this article is to clarify the superposition principles, and another purpose is to 1 support this author's electromagnetic eld theory which is started from two new axioms the self-energy principle and the mutual energy principle.
In electromagnetic theory and quantum theory, there are superposition principle. The author found that there are 5 dierent kinds of superpo-sitions. The superposition principles have some dierences. The research about these dierences is a key to open the the door of many physical diculties. For example the particle and wave duality problem, and to judge which interpretation of the quantum mechanics is a correct one. The rst two superposition principles are the superpositions with and without the test charges. The slight dierent superposition principles are the superposition with a retarded wave only and the superposition with the advanced wave only. According to theory of this author, the emitter sends the retarded wave, the absorber sends the advance wave. Hence, normal electromagnetic eld actually is consist of retarded wave and advanced wave. This two wave together become the normal electromagnetic eld. This kind of electromagnetic eld can be seen approximately as retarded wave, this kind wave also has its own superposition. This kind of superposition is also dierent with the superposition when we consider the retarded wave and also the advanced wave. In this article this author will discuss the dierences of these dierent situations of superpositions. This author will also discuss the dierent physical result with a few dierent su-perposition principles. In this article this author will prove only when the self-energy principle is accept, all kinds of superposition can be accept. Otherwise only the superposition with test charge or the superposition with only one kind wave either retarded waves or advanced waves can be accepted. Hence, the discussion about the superposition also support the concept of the self-energy principle which means there must exist the time reversal waves. That also means the waves do not collapse but collapse back. Wave collapse means collapse to target of the wave, for example, the retarded wave will collapse to a absorber and the advanced wave will collapse to a emitter. Wave collapse back means the retarded wave sent from emitter will collapse back to emitter; The advanced wave sent from the absorber will collapse back to an absorber. Hence, one purpose of this article is to clarify the superposition principles, and another purpose is to 1 support this author's electromagnetic eld theory which is started from two new axioms the self-energy principle and the mutual energy principle.
In electromagnetic theory and quantum theory, there are superposition principle. The author found that there are 5 different kinds of superpositions. The superposition principles have some differences. The research about these differences is a key to open the the door of many physical difficulties. For example the particle and wave duality problem, and to judge which interpretation of the quantum mechanics is a correct one. The first two superposition principles are the superpositions with and without the test charges. The slight different superposition principles are the superposition with a retarded wave alone and the superposition with the advanced wave alone. According to theory of this author, the emitter sends the retarded wave, the absorber sends the advance wave. Hence, normal electromagnetic field actually is consist of retarded wave and advanced wave. This two wave together become the normal electromagnetic field. This kind of electromagnetic field can be seen approximately as retarded wave, this kind wave also has its own superposition. This kind of superposition is also different with the superposition when we consider the retarded wave and also the advanced wave. In this article this author will discuss the differences of these different situations of superpositions. This author will also discuss the different physical result with a few different superposition principles. In this article this author will prove only when the self-energy principle is accept, all kinds of superposition can be accept. Otherwise only the superposition with test charge or the superposition with only one kind wave either retarded waves or advanced waves can be accepted. Hence, the discussion about the superposition also support the concept of the self-energy principle which means there must exist the time reversal waves. That also means the waves do not collapse but collapse back. Wave collapse means collapse to target of the wave, for example, the retarded wave will collapse to a absorber and the advanced wave will collapse to a emitter. Wave collapse back means the retarded wave sent from emitter will collapse back to emitter; The advanced wave sent from the absorber will collapse back to an absorber. Hence, one purpose of this article is to clarify the superposition principles, and another purpose is to support this author's electromagnetic field theory which is started from two new axioms the self-energy principle and the mutual energy principle.
In electromagnetic theory and quantum theory, there are superposition principle. Traditionally there are only one kind superposition principle. However, in this author's theory the retarded wave and advanced wave are all involved, the superposition become multiple. For example this author need to deal the problem how to superpose the retarded wave and the advanced wave. This author found that there are 5 different kinds of superpositions. The superposition principles have some differences. The research about these differences is a key to open the door of many physical difficulties. For example the particle and wave duality problem, and to judge which interpretation of the quantum mechanics is a correct one. The first two superposition principles are the superpositions with and without the test charges. The slight different superposition principles are the superposition with a retarded wave alone and the superposition with the advanced wave alone. According to theory of this author, the emitter sends the retarded wave, the absorber sends the advance wave. Hence, normal electromagnetic field actually is consist of retarded wave and advanced wave. This two waves together become the traditional electromagnetic fields. This kind of electromagnetic fields can be seen approximately as retarded wave only, this kind wave also has its own superposition. This kind of superposition is also different with the superposition when we consider the retarded waves alone and also the advanced waves alone. In this article this author will discuss the differences of these different superpositions. This author will also discuss the different physical result with a few different superposition principles. In this article this author will prove the superposition with test charge and the superposition with retarded waves alone or advance wave alone can be see one kind of superposition. This superposition is correct and can be derived from the mutual energy principle. This will be referred as first kind of superposition. The superposition without test charge and the superposition with the retarded waves and advanced waves can be seen as one kind of superposition. For this kind of superpositions are not correct naturally. This kind of super position are applied to N-charge's Poynting theorem. In order to make this superposition work, the self-energy principle have to be applied. Without self-energy principle this kind of superpositions will violate the energy conservation law. Considering the self-energy conservation this kind of superposition become the superposition of first kind. This is referred as second kind of superposition. The third kind of superposition is for the traditional electromagnetic field. Here the traditional electromagnetic field means the electromagnetic field where the advanced waves are omit. When the advanced waves are omit doesn't mean the advanced waves do not exist, that is only means the retarded wave and the advanced wave are with nearly same intensity and can be treated together in some situation, for example, in wave guide, or in the free space where the absorber are uniformly distributed at infinite big sphere. Abstract Only when the self-energy principle is accept, all kinds of superposition can be accept. However different superposition has different physical meanings. Otherwise only the superposition with test charge or the superposition with only one kind wave either retarded waves or advanced waves can be accepted. Hence, the discussion about the superposition also support the concept of the self-energy principle which means there must exist the time reversal waves. That also means the waves do not collapse but collapse back. Wave collapse means collapse to its target, for example, the retarded wave will collapse to an absorber and the advanced wave will collapse to an emitter. Wave collapse back means the retarded wave sent from emitter will collapse back to an emitter; The advanced wave sent from the absorber will collapse back to an absorber. Hence, one purpose of this article is to clarify the superposition principles, and another purpose is to support this author's electromagnetic field theory which is started from two new axioms the self-energy principle and the mutual energy principle.
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.
This author has replaced the Maxwell equations with the corresponding mutual energy principle, self-energy principle as the axioms in electromagnetic eld theory. The advantage of doing this is that it can overcome the diculty of the Maxwell equations, which conicts to the energy conservation law. The same conict also exists in the Schrödinger equation in the quantum mechanics. This author would like to intruded the mutual energy principle to quantum mechanics, but has met the diculty that there is no advanced solution for the Schrödinger equation. This diculty is overcome by introducing a negative radius. After this, all the theory about the mutual energy can be extend from the eld satisfying Maxwell equations to the eld satisfying Schrödinger equation. The Schrödinger equation can also be derived from the corresponding mutual energy principle. However, this doesn't mean both sides are equivalent. The mutual energy principle cannot derive a single solution of Schrödinger equation. The mutual energy principle can only derive a pair solutions of the Schrödinger equations. One is for retarded waves and another is for advanced waves. The retarded wave and the advanced wave must be synchronized. The solutions of the mutual energy principle is in accordance with the theory of the action-at-a-distance and the absorber theory. A action is done always between two objects, for example a source (emitter) and a sink (absorber). The mutual energy principle tell us that a particle is an action and a reaction between the source and the sink. In other hand the wave satisfying Schrödinger equation only need one source or one sink. From the mutual energy principle, it is easy to derive the mutual energy theorem, the mutual energy ow theorem, corresponding HuygensFresnel principle. All these will solve the wave-particle duality paradox.
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.
For photon we have obtained the results that the waves of photon obey the mutual energy principle and self-energy principle. In this article we will extended the results from photon to other quanta. The mutual energy principle and self energy principle corresponding to the Schrödinger equation are introduced. The results are that a electron, for example, travel in the empty space from point A to point B, there are 4 different waves: the retarded wave started from point A to infinite big sphere; the advanced wave started from point B to infinite big sphere; the return wave corresponding to the above retarded wave which is a time reversal wave of the retarded wave; the return wave corresponding to the above advanced wave which is a time reversal wave of the advanced wave. There are 5 different energy flow corresponding to these waves: the self-energy flow corresponding to the retarded wave; the self-energy flow corresponding to the advanced wave; the return flows corresponding to the above two time reversal wave; the mutual energy flow of the retarded wave and the advanced wave. It is found that the mutual energy flow is the energy flow, or the charge intensity flow, or electric current of the electron. Hence, the electron travel in the empty space is a complicated process and do not only obey one Schrödinger equation. This result can also extend to Dirac equations. This 4 waves and 5 flow together can offer a correct interpretation for the duality of the quantum.