Particle-wave symmetry in Quantum Mechanics And Special Relativity Theory

Transcription

1 Partile-wave symmetry in Quantum Mehanis And Speial Relativity Theory Author one: XiaoLin Corresponding author: XiaoLin Li, Abstrat: In 5-dimensional spae-time, Quantum Mehanis have a speial partile-wave symmetry. To partile wave, its phase veloity, and its group veloity, is equal, and the two speed value is invariant. This is very similar with the light speed C in Speial Relativity Theory. We mark this speed with. But, different partile has different, not all partiles have same. To one value, there exist one kind of partile. Partile in Speial Relativity Theory is just one kind. In Speial Relativity Theory, = C. Light speed C is just a speial instane of. Quasi-partile in Condensed Matter Physis, is another sample of. The new partile-wave symmetry ontain the Lorentz symmetry. The new partile-wave symmetry is a extension to Lorentz symmetry. The Lorentz symmetry is just a speial instane of partile-wave symmetry. But the new partile-wave symmetry no longer is limited by speed light C. The partile-wave symmetry has variable speed. So, Speial Relativity Theory will be just a derived result of Quantum Mehanis. In 5-dimensional spae-time, in new theory, spae and time is not relative, spae and time is obsolute. We need rethink about these physial onepts, mass-energy equation, rest mass, inertial mass, gravitational mass. From the new symmetry, we an get new kind of partiles whih perhaps have relationship with osmi dark matter and radio burst. Keywords: 5-dimensional spae-time; partile-wave; phase veloity; group veloity; partile-wave symmetry; new speed ; Lorentz symmetry; Speial Relativity Theory; quasi-partile; obsolute spae-time; mass-energy equation; inertial mass; gravitational mass; dark matter; radio burst. Introdution In author first paper[1], author introdue a new physis model. If we assume that the partile wave is present in 5-dimensional spae-time in Quantum Mehanis, then we an derive out all results in Speial Relativity Theory. But, in the first paper, this desription is the first step toward a new theory. What is the

2 essene of this new model? How to extend the model? So author be ontinue to desribe the model in this paper. We extend the model, then we will get a new theory model. The new theory is a new symmetry in Quantum Mehanis. This is the partile-wave symmetry. Then we will explain the new theory in detail. 1. Partile-wave symmetry in Quantum Mehanis In author first paper[1], author introdue a new physis model. In this new model, there exist three onepts. First. In Quantum Mehanis, partile wave is present in 5-dimensional spae-time. One dimension is time. Four dimensions is spae. The new 4th dimension spae, and 3-dimensional spae, forming orthogonal relationships. Total of 4-dimensional spae, like 3-dimensional spae, is Hilbert spae. This like figure 1. Figure 1 Two. In 5-dimensional spae-time, to partile wave, De.Broglie equation still holds. Three. In 5-dimensional spae-time, to partile wave, its phase veloity, and its group veloity, must be equal. And to the two veloity, its speed value is invariant. The invariant speed value is light speed C. There exist a formula (1.1). g p (1.1) From above three onepts, we an derive out all results in Speial Relativity Theory. For example, mass-energy equation, Lorentz symmetry, Lorentz transformation. In 5-dimensional spae-time, one dimension is time, four dimension is spae. In 5-dimensional spae-time, to partile wave, its phase veloity and its group veloity, all are 4-dimensional vetor, not 3-dimensional vetor. The veloity value is invariant always. And the value is light speed C. This like figure.

3 Figure Please read author first paper[1], to know detailed derivation of the new model. Don t desript repeatedly. In the first paper, author just desript this model and its derivation. But don t point out these questions answer. What is the essene of this new model? How to extend the model? So author be ontinue to desribe these answers in this paper. In fat, the new model means that exist a new physis symmetry. As long as that the new physis symmetry existene is true, we an get this new model, then get results in Speial Relativity Theory. The new physis symmetry is partile-wave symmetry. We know, in urrent 4-dimensional spae-time, to partile wave, its phase veloity is p, and its group veloity is g =. Phase veloity is not equal with group veloity. Only to the photon wave in vauum, phase veloity is equal with group veloity, p C. g In fat, to partile wave, its phase veloity is not equal with its group veloity. This phenomenon will take a physial paradox. In Quantum Mehanis, partile and wave is aompanying. Partile veloity is partile movement speed. Phase veloity is wave movement speed. To partile wave duality, this property will fore that the two speeds must be equal at anywhere. They must have the same pae. This is partile-wave speial property. Other wave not has this speial requirement, beause other wave not has the speial partile wave duality. To partile wave, if its phase veloity is not equal with its group veloity, not have same pae. This will lead to a bad result. Partile move to a point, but wave not move to that point. On the other hand, wave move to a point, but partile not move to that point. We ompute a wave funtion, get the hane finding the partile at a point, but an t find any partile at that point. Beause partile movement speed is not equal with wave speed, partile an t move to that point. So this phenomenon will take a physial paradox. So, In order to avoid this paradox, phase veloity must be equal with group veloity. But in urrent 4-dimensional spae-time, phase veloity is not equal with group veloity, this is a fat result. To this paradox, how to explain it? We how to solve this

4 problem? In fat, exist this paradox, this means that 4-dimensional spae-time view have defetive. The 4-dimensional spae-time view does not reflet the real physis spae-time. If we wath the partile wave in 5-dimensional spae-time, we an find that this paradox does not exist. In 5-dimensional spae-time, to partile wave, phase veloity is equal with group veloity. To this result, author first paper[1] have detailed desription. In 5-dimensional spae-time, to partile-wave, there exist formula (1.1). Use this formula, we an derive out all results in Speial Relativity Theory. So, it prove that this view (in 4-dimensional spae-time, to partile wave, phase veloity is not equal with group veloity) is an illusion. This illusion is from dimensional observation limited. Human only an sense three spae dimensions, human an not sense four spae dimensions. But fat physis proess is happen in 4 spae dimensions. So we get this illusion. In 5-dimensional spae-time, take formula (1.1) and De.Broglie equation, we an derive out results in Speial Relativity Theory. Then we will ask a question. To phase veloity and group veloity, in real physis world, does there only have one speed value, light speed C? There does not exist other speed value? Instead, if only exist one speed value, this is the very surprising thing. The light speed C must not be a speial position in real physis world. In formula (1.1), if phase veloity and group veloity is other speed value, so we an ross Speial Relativity Theory. The light speed C, is just one speed value between total possible value. The light speed C, no longer is in a speial position. So, we an extend theory. Human thinking, no longer be limited by light speed C. In fat, in formula (1.1), the speed value, an be extended to other value. phase veloity and group veloity, an be any onst speed value. These other status, is onsistent with Quantum Mehanis priniple also. These other speed partile wave, is possible partile wave in real physis world. So, we get formula (1.). onst (1.) p g In (1.), for ease of identifiation and extension, similar light speed C, we identify the onst speed with. So get formula (1.3). The flag in lower right orner, be used to identify this speed is a speial role, like the light speed C. But different with light speed, this speed

5 value is variable. There exist many speed value. To eah speed value, there exist one kind of partiles. Different kind of partiles, have different speed value. Partiles in Speial Relativity Theory, is just one kind, just There is still a broad range for humans to disover. = C. The human deteted world, is just a small area. g p (1.3) The formula (1.3) will take a new model into physis. In 5-dimensional spae-time, to partile-wave, its phase veloity is equal with its group veloity, and its speed value is invariant. This is a new symmetry between partile and wave. Simply all it by partile-wave symmetry. This like figure 3. Figure 3 To eah kind partile wave, to its partile-wave symmetry, the invariant, is a absolute speed. At any time, in any point, is this speed value. This speed, its value does not hange when inertia oordinates transform. In any inertia oordinates, we only an take the same speed value. This is similar with light speed C in Speial Relativity Theory. But, there exist a important differene between Speial Relativity Theory. In Speial Relativity Theory, all partiles have the same invariant light speed C. But, in partile-wave symmetry theory, eah kind of partiles have its own invariant, there exist different. Please attention another important differene. In partile-wave symmetry, there exist two speed, phase veloity and group veloity, not one speed. The speial dual property, will take many differene between Speial Relativity Theory. In Speial Relativity Theory, all partiles have the same invariant light speed C. But, in partile-wave symmetry theory, eah kind of partiles have its own invariant, there exist

6 different.so, in fat, partile-wave symmetry is a extension to Lorentz symmetry. But, the theory physis essene is hanged. The partile-wave symmetry is derived from partile wave duality. Partile wave duality produe this partile-wave symmetry. This symmetry, does not have assoiation with light speed C. This symmetry, its physial soure is partile wave duality property. Its soure is not spae-time symmetry. This is the biggest differene between partile-wave symmetry theory an Speial Relativity Theory. In fat, the Lorentz symmetry in Speial Relativity Theory, is only a speial instane of partile-wave symmetry. When from partile-wave symmetry. = C, we an derive out results of Speial Relativity Theory The partile-wave symmetry, is a more wide range symmetry than Lorentz symmetry. Partile-wave symmetry is not inonsistent with Lorentz symmetry. Lorentz symmetry is still valid. But Lorentz symmetry is only a speial instane of partile-wave symmetry now. When human mind jump out of the Lorentz symmetry range, human mind will jump into a more wide range. Human no longer be limited by light speed C. Disover new physis phenomena, break the light speed C, will be possible. Now human will find the partile whih its value is more than the light speed C. One human have found this partile, human will break the limitation by the light speed C. In the new partile-wave symmetry model, the mass-energy equation in Speial Relativity Theory, need extended also. Replae the light speed C with,we get a new mass-energy equation, it is formula (1.4). Please attention this fat. This new mass-energy equation have meaning only when we observe physial proesses in 4-dimensional spae-time. In 5-dimensional spae-time, there does not exist rest mass. E m P m 4 P m 0 4 (1.4) When we observe partile in 5-dimensional spae-time, the partile is ompletely similar to the photon. Just replae C with have rest mass also.. So we get formula (1.5). Similar to photon, partile not

7 E m P m P (1.5) Please distinguish arefully. In formula (1.4), physial quantity is in 4-dimansional spae-time. In formula (1.5), physial quantity is in 5-dimansional spae-time. In different spae-time, the physial quantity has great differene. If you feel onfused, please read author first paper[1] arefully. This paper explains the differene arefully. In 5-dimensional spae-time, to partile wave, De.Broglie equation still holds. It is formula (1.6). But, in this formula, physial quantity is in 5-dimansional spae-time, not in 4-dimensional spae-time. Only energy and frequeny is same between 5-dimansional spae-time and 4-dimensional spae-time, beause they are salar. To momentum, it is not same in different spae-time system, beause it is a vetor. To wavelength, it is also not same in different spae-time system. E h h P (1.6) Partile-wave symmetry is independent with dimension. In Quantum Mehanis, in 3-dimensional spae-time, and in 4-dimensional spae-time, and in 5-dimensional spae-time, all have partile wave. So, all have partile-wave symmetry. Partile-wave symmetry is derived from Quantum Mehanis. This is a another important differene between partile-wave symmetry and Speial Relativity Theory. Speial Relativity Theory only is valid in 4-dimensional spae-time. Speial Relativity Theory is dependent with dimension. But partile-wave symmetry is independent with dimension. Partile-wave an even appear in phase spae. In Quantum Mehanis phase spae, there exist partile-wave symmetry also. This question, will be disussed arefully in next hapter. Sine the value is variable, but why human an t found other kind of partile. For now, human only an found Speial Relativity Theory partiles, = C. This an be guessed from a fat. For now, all experiment must use eletromagneti tehnique. But all eletromagneti tehnique is limited by the light speed C. So human an t found these different partiles. Human must reate new experiment tehnique.

8 But, in Condensed Matter Physis, there exist one speial kind of virtual partile. It is Quasi-partile. This Quasi-partile, only is result of Quantization. Quasi-partile not be found in real spae-time. It is not a real partile. But in Quantum Mehanis, Quasi-partile is a valid partile. Quasi-partile has partile wave also. Quasi-partile is satisfied to De.Broglie equation. But, Quasi-partile have muh smaller speed than the light speed C. Quasi-partile only have speed in 3-dimensional spae, and not have rest mass. It is very similar to the photon. But Quasi-partile is not Speial Relativity Theory partile. In fat, Quasi-partile an be as a example of other of further study. value. Quasi-partile have partile-wave symmetry also. To this topi, It is worthy At above desription, to one partile, its value is invariant. So partile-wave is a linear symmetry. This is a sample status. But we an guess. To same kind partile, the value may be variable. Perhaps, value is variable with energy hange, like f (E). And perhaps, value is variable with position hange, like i f ( t, x ). These status an t be exluded. These status is nonlinear symmetry. But these status is partile-wave symmetry also. Phase veloity is equal with group veloity also. To this kind of nonlinear symmetry status, Speial Relativity Theory an not be used ompletely. But we an use the partile-wave symmetry theory also. As long as these physis proess keep that phase veloity is equal with group veloity, these physis proess an perhaps happen, these proess is not onflit with Quantum Mehanis priniple. Quantum Mehanis does not forbid that these status happen. To this topi, It is worthy of further study. So, the partile-wave symmetry is a new onept. It have more wide range than Lorentz symmetry. Replae Lorentz symmetry with partile-wave symmetry, physial range will be extended greatly.. Absolute spae-time in partile-wave symmetry In the new partile-wave symmetry model, spae and time, will be bak to absolute spae-time in Newtonian mehanis. Spae is absolute, and time is absolute. Spae-time system

9 does not hange when inertia oordinates transform. In first paper[1], author s thinking is limited by Speial Relativity Theory also. In first paper[1], author think that time is absolute and spae is relative. This onlusion is error. In this artile, author orreted it. In Quantum Mehanis, to spae-time system, it either an be real world spae time (5 dimensional spae time, four dimensions spae, one dimension time), or it an be virtual spae-time (phase spae and time). In virtual phase spae time, there exist partile wave also. To virtual phase spae time, we no longer an think that spae-time is expanding or is shrinking. But, Quantum Mehanis is valid in real spae-time or virtual spae-time. So, in Quantum Mehanis, the spae-time should be absolute, not be relative. In the new partile-wave symmetry model, spae-time either an be real world spae-time, or an be virtual phase spae-time. In the two spae-time system, partile-wave symmetry model is valid. So, in partile-wave symmetry theory, spae-time is absolute, not is relative. Spae-time expanding or shrinking, in Speial Relativity Theory, its essene is that, the frequeny and wave-length of partile-wave have hanged. If there not exist partile-wave, there not exist frequeny and wave-length hanging, human an t observe these effets of spae-time expanding or shrinking. In fat, these effets in Speial Relativity Theory, is effets of partile wave. Human only an observe the hanges of material, an t observe the hanges of spae-time. Material is formed by partiles. The frequeny and wave-length hanges of partile wave, is equivalent with hanges of spae-time. Human an t distinguish the differene between the two hanges. So, Speial Relativity Theory is orret also. But, the equivalene an only be limited in ertain range, ould not be unlimitedly expanded. If we expand the equivalene unlimitedly, this will get error results, and this will limit human thinking. For example, to photon, it only have momentum omponent in 3-dimensions spae, not have momentum omponent in 4th spae dimension. So, to this status, we an t use Lorentz transformation. If we use Lorentz transformation, then we will get a infinite delay time. In fat, the infinite delay time result is a flag that the theory is invalid in this status. To virtual phase spae time system, the equivalene no longer is valid also. The phase spae time system, is a virtual spae time system reated by human. In phase spae time system, these virtual Quasi-partiles is very similar to photon. Human does not have need to reate a expanding or shrinking virtual spae time system. Human does not have need to built a huge obstale for

10 themselves. So, human need a new theory model, to replae the expanding or shrinking spae time in Speial Relativity Theory. Partile-wave symmetry is this new theory model. Partile-wave symmetry an get all results in Speial Relativity Theory, it is not onflit with Speial Relativity Theory. And, if we use this new symmetry, we an extend theory to a more wide range. In any spae time system, as long as Quantum Mehanis is valid, partile-wave symmetry is valid also. Whether in real spae-time, or in virtual phase spae time, partile-wave symmetry is valid. This disussion will lead to a very interesting question. The human living world, the real world spae time, whether it is a kind of virtual quantum phase spae time also? If not, but why the two spae-time system have same partile-wave symmetry? This topi is worthy of further study. 3. The partile mass in partile-wave symmetry Beause this topi is very important, so we disuss about it in a separate hapter. From the first paper[1], in the new 5-dimensional partile-wave model, the partile mass onept is derived from formula (.1) below. P m (.1) In formula (.1), speed is partile speed in 4-dimensional (3 spae dimension, one time dimension). This onept, is derived from Newtonian mehanis. Then we extended it into Quantum Mehanis. This mass, is inertial mass aurately. Similar to Speial Relativity Theory, beause partile-wave symmetry, there exist a formula (.). So, the inertial mass is assoiated with energy. So, the inertial mass, has another name, energy mass. In fat, the inertial mass, and the energy mass, is a same quantity. E m (.) In the new 5-dimensional spae-time model, if partile only has the 4th dimension momentum omponent. That is, partile has zero momentum omponent in 3-dimensions. This status, is the stati status in 3-dimensions. In this status, observing in 3-dimensions, the mass is just the rest mass. Either in Newtonian gravity, or in the general theory of relativity, there exist a onept of gravitational mass. In the two gravity theory, the rest mass is equal with gravitational mass. Beause in Speial Relativity Theory, have same gravity. E m. So, this means that, same energy partile will But, in partile-wave symmetry, value is variable. Different kind partile, have different

11 value. From formula (.), this means that, same energy, different kind partile, will have different rest mass. So, the rest mass is equal with gravity mass, if this result is valid in partile-wave symmetry also. So, we an get a new result. If two partile have different kind, even if the two partile have same energy, but they have different gravity. So, this will take great hange to gravity. Gravity question will hange to be more omplex. If partile-wave symmetry is true, and if there exist real partiles whih its we will observe new gravity phenomenon. C. So If there exist a new kind of partiles, it have more less value than the light speed C. Although this kind of partiles have small energy, but it have great rest mass. So, it have great gravity. If human an found it, human an use it to hange a gravity system. This result does make us to think about the osmi dark matter easily. If there exist this kind partiles in galaxy spae, so only exist few of this kind partiles, an take great gravity effets. This new partiles perhaps is not involved in eletromagnetism. Perhaps it is involved in eletromagnetism, but its energy is small, so the eletromagnetism effet is very small. So, for now, human does not find this kind partiles. The osmi dark matter perhaps is this kind of partile. On the other hand, there perhaps exist this kind partiles, its value is more than the light speed C. So, although it has great energy, but it has small rest mass. So, its gravity effets is small also. If there exist this kind partiles in universe, only exist few of this kind partiles, they an release great energy. This phenomenon is very similar to osmi radio burst. This kind partiles perhaps an explain it. This kind partile gravity does not have obvious great differene between ordinary partiles whih we have known. So, we an t distinguish it from ordinary partiles. Only when it burst, we an distinguish it. So, if the new partile-wave symmetry is true, we need to rethink about these onepts, mass, rest mass, inertial mass, gravity mass, gravity. Conlusion From above desription, we get a new partile-wave symmetry in Quantum Mehanis. This new symmetry is a extension to Lorentz symmetry. The partile-wave symmetry inlude Lorentz symmetry, and have more wide range than Lorentz symmetry. From the new partile-wave symmetry, we an derive out all results in Speial Relativity Theory. Speial Relativity Theory is only a speial instane of partile-wave symmetry. Then human no longer be limited by light speed C. And the spae time no longer is relative, but the spae time is obsolute. Human will enter 5-dimensional spae time. Then we take a new onstant value is variable. into physis. is similar to the light speed C. But, its is the flag of different kind partiles. Different partiles have different. Then we get a result. Different kind partiles, although have same energy, but have different rest

12 mass, and have different gravity. This new kind partiles, perhaps is the answer, to osmi dark matter and radio burst. There exist many questions need to be study. How to disover the 4th spae dimension in real world? How to disover the kind of partile that its more than C? If the new partile-wave theory is true, it will take great hange to physis. Referenes: [1] XiaoLin Li A new equivalent theory with Speial Relativity Theory,partile wave in 5-dimensional Spae-time International Journal of Physis, August 016, ol. 4, No. 5 [] Broglie, Louis de, The wave nature of the eletron, Nobel Leture, Deember 1, 199 [3] "The Feynman Letures on Physis(olume I,II,III)",R. P. Feynman,R. B. Leighton,M. Sands, ISBN ,ISBN ,ISBN [4] Gianfrano Bertone, Dan Hooper, Joseph Silk Partile Dark Matter: Evidene, Candidates and Constraints Physis Reports, 004, ol. 405, No. 5 [5] D R Lorimer, M Bailes, M A Mlaughlin, D J Narkevi, F Crawford A bright milliseond radio burst of extragalati origin Siense, 007, ol. 318, No. 5851