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.
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.
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. 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.
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.
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.
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.