Einstein s Lorentz Transformation is a Mathematical Game

Transcription

1 No. Einstein s Lorentz Transformation is a Mathematical Game Zeng Qingping Air Force Radar Academ ( th Department) Room 8-A-, No.88, Huangpu Street, Wuhan, Hubei, China [Abstract]: This paper indicates that the calculation of time dilation in relativit theor is as the indirect calculation of t from positive transformation. While, the calculation of the length contraction is different. X is gotten from the inverse transformation, and then is resolved. From the mathematical point, if we reverse the calculation methods, it will be time contraction and length dilation In addition, this paper adopts Einstein s methods and gets W relativit theor. When W is given infinite value, there will be infinite relativit theories. From these, we can conclude that Einstein s Lorentz transformation is a mathematical magic, and it is not onl without an mathematical logic, but also without an phsical significance. [Kewords]: Einstein s Lorentz transformation, positive transformation, inverse transformation, the geniture of infinite relativit theories. Introduction Through the speculation on the mathematical logic of special theor of relativit, we can easil find that the calculation of length contraction in relativit theor is as the calculation of X from inverse transformation. While, the calculation of time dilation directl uses t in positive transformation. From the mathematic point, it is without logical reasoning; it is also without fied phsical meaning from the phsical point. If we reverse Einstein s calculation methods, it will be time contraction and length dilation; if both are used reverse transformation, it will be time and length contraction. On the other hand, if both are used positive transformation, it will be time and length dilation. This question belongs to the basic question of the relativit theor. In other words, the basis of the relativit theor is not onl without logical reasoning in mathematics but also without fied phsical meaning in phsics. Now that the different calculation will lead to different time and space dilation and contraction, which just illustrates that Einstein s relativit theor is magical. At the same time, it illustrates Lorentz transformation is a pure mathematical game without fied phsical meaning. In addition, the paper assumes light velocit is an optional value w, and adopting Einstein s calculation methods, we also get w relativit theor. w Relativit theor has onl high-order infinite small amount of differences with respect to Einstein s relativit theor. The infinite value of w will bring infinite relativit theories, which is just like what Lorentz stressed local time is just a mathematical hpothesis without real phsical meaning

2 Einstein s Lorentz Transformation The reason wh we call it Einsteins Lorentz transformation is that Lorentz himself did not rewrite the transformation into time and space contraction. Dilating the mathematical transformation to time and space transformation is what Einstein has done. Let us look at the following transformation process of Einstein. He assumes a point P in the space, the position is P(,, z) in S ais frame and the time is indicated b t, just like Fig. showing. Three coordinates in another ais frame S are parallel to ais frame S. P moves along the direction at the speed of v. The time coordinate of t in S is P (,, z ). So, the relativit theor wants to solve the relationship of two coordinates in ais frames S and S of point P. (, z, ) P (,, z ) o o z z Fig. Two Ais Frames with Relative Speed V Einstein s transformation is based on the same light velocit in different ais frames. The relativit theor assumes the following eperiments: there will be a flash at the moment when two ais frames coincide; then, observing wave movements in two frames before the flash. In two ais frames, optical pulse is a spherical wave from the origin to the surrounding. The pre-wave movement of flash should not have an different impacts on two ais frames. So, the pre-wave movement equation in S sstem is: z ( ct ) () To maintain the same speed of light, the pre-wave movement equation in S sstem is: z ( c t) () So, in Lorentz transformation of relativit theor, on the one hand, Einstein maked and z z ; that is, he believed the coordinate position was not affected because it was perpendicular to relative movement direction. On the other hand, he treated and t as the linear function of and t. That is:, z z, a bt, t e ft (3) Now, we substitute (3) formula to () formula, and there will be:

3 ( a ce ) z ( c f b ) t (cef ab) t (4) Comparing (4) formula with () formula, we can find: a c e, c f b c, cef ab (5) Because we have known that the origin ( ) in S is the vt in S, so, we substitute it to (3) formula, and the following result can be obtained b av (6) Then we substitute (6) formula to (5) formula, the following equations set can be found a c e cef av c f a v c (7) We can conclude the following results through equation combination a f, e c, b v (8) Then we can get new transformation equation through substituting (8) formula to (3) formula z z vt (9) t ( c ) t There are the positive and negative smbols here. How do we definite the smbol? When v c,. And the above formulas should be reduced to the Galilean transformation, so the issue of positive and negative smbols can be resolved. The last results are as follows: z z ( ) () vt t t c This is Einstein s Lorentz +transformation in formula v, c. 3

4 We can get Lorentz reverse transformation from the solving of and t in () formula z z ( ) () vt t t c The above equation set is Einstein s Lorentz reverse transformation. If we put the light source on the z point in S ais frame, and it flashes each one time at t and t ; then the flash time interval observed in S ais frame is t t t We can get t t and t t according to t t in () formula. c c c So, the time interval which static sstem person see is: t t t t t t ( t t) c c This is the derivation of time dilation formula of relativit theor. If there is a stick placed along the ais, and position of both sides are () and, we can get the length of the stick: l. Now, there is an observer in S ais frame measuring the length of the stick. When the stick passes the observer along the ais at the speed of v, and the observer marks down the arrival time of the both sides t and t, we can definite the length of the stick is l vt vt. We can get vt from () formula and then get vt and vt. So the length which the static sstem person sees is: l ( vt) ( vt) l (3) This is the derivation of length contraction of relativit theor. The access of this formula is different from () formula. So, the trick of Einstein is: using Lorentz transformation () formula to get time dilation result and then using Lorentz reverse transformation () formula to get length contraction result. 3. Einstein s Lorentz Transformation is a Magic We find four defects in Lorentz transformation of relativit theor. First, be lack of mathematical logic. The calculation of the length contraction in relativit theor is as the calculation of from reverse transformation ; while, the calculation of the time dilation is directl calculated from 4

5 positive transformation. From the mathematical point, it is without logical reasoning; from the phsical point, it is without concept meaning. If we reverse the methods, there will be time contraction and length dilation. If both are calculated and t from reverse transformation, there will be time and length contraction. Otherwise, there will be time and length dilation. This belongs to the bases of the relativit theor. In other words, the bases of the relativit theor are not onl without mathematical logic reasoning, but also without phsical conception meaning. Since different solving methods have different time and space views, this just indicates that Einstein s relativit theor is random and optional. In addition, it also indicates Lorentz transformation without fied phsical meaning, and it is just pure mathematical transformation. Second, vague conception. Light wave is sent out in dnamic sstem or static sstem is still a question which Einstein did not eplain clearl. If it is sent out in dnamic sstem, the light source is athletic, otherwise, it is still. If there is fire flash because of the collision between the origins, there will be two light sources at the same time, one in static sstem and the other in dnamic sstem. The wave equations in two ais frames are different because of three cases. As shown in Figure -4, the full lines represent true spherical waves, and the broken lines represent spherical waves which another observer has seen. Now the question is Einstein wants to join two spherical waves. For instance, in figure 4, two origins have sparkles because of the coincidence or friction. In fact, two origins are both light source, and the are with the same frequenc and status. How did Einstein join two spherical waves? That is so-called flash pre-wave movement should not have an different impacts on two ais frames. The fact of the combination is the combination of the pre-wave space position echoing to the length contraction, and it has nothing to do with the light velocit. Though he added in S sstem, the equation of the pre-wave is z ( c t ) ; to maintain the light velocit, the equation of the pre-wave is z ( c t) in S sstem. Fig. Light Source in Dnamic Sstem Fig.3 Light Source in Static Sstem But this has nothing to do with the hpothetic precondition. In other words, we can narrate like this the space position of pre-wave movement of light wave should not have different impacts on two ais frames and in S sstem, the equation of the pre-wave is z ( c t ) ; to maintain the variabilit of the light velocit, the equation of the pre-wave is z ( wt) in S sstem. In this case, we can also deduce the results of Lorentz transformation. In other words, 5

6 with respect to the mathematical derivation of Lorentz transformation, it has nothing to do with the variabilit of the light velocit. In the final analsis, Lorentz transformation is the solving of the following equation set. When t function appears, we make the parameters as zero. ( ct ) ( ct) a bt t e ft b av The so-called transformation is substituting a linear function to a chi square function, then for calculation. You can make c c or c c for calculation. When appearing t function, we make parameters as zero. The derived results have different numbers but with the same forms. That is so-called the unchangeable forms under Lorentz transformation. Because the equation set has been given, the structure form of the results is unchangeable form and onl parameter c or c is changeable. You can add g ht, t e ft and z iz jt, t e ft on the basis of one dimension transformation. This tpe of 3D transformation is unchangeable in structure forms, which is inevitable in mathematical calculation. As a mathematician, Lorentz knew it was the inevitable results of the mathematical calculation. So, he did not give an phsical meaning, just a tpe of mathematical transformation which just as he said local time is just a mathematical hpothesis without true phsical meaning. The person who epanded, rose, carried it to the sk even borrowed to utilize Lorentz transformation was Einstein. Just like the introductions of the relativit theor books, Lorentz was not clear about the phsical meaning of t and its transformation. In fact, in m opinion, Lorentz is not unclear. As a mathematicians and phsicists, he deepl knew that transformation was just a mathematical game without an phsical meaning. So, he did not give an phsical meaning. And Lorentz stressed that local time t was just a mathematical assumption without an true phsical meaning. Third, a mathematical game If we adopt the above methods of Einstein, and reverse the calculation methods of and, we will get the conclusion of time contraction and length dilation. If both are used reverse transformation, there will be time and length contraction. Otherwise, if both are used positive transformation, there will be time and length dilation. The calculations are as follows: If we put a light source on the z point in and t, then the measured flash time interval is t t t. [Imitation] We can get t t c S ais frame, and it flashes each one time at from Lorentz transformation formula () b imitating the t length solving method of relativit theor. Then we can get t c Fig.4 Two ais frames flash simultaneousl t t and t, so the c 6

7 time which the static sstem person has seen is : t t t t t t t t c c This is the derivation of the derivation of the time compression formula If there is a stick placed along the ais, and position of both sides are () and, we can get the length of the stick: l. Now, there is an observer in S ais frame measuring the length of the stick.. When the stick passes the observer along the ais at the speed of v, and the observer marks down the arrival time of the both sides t and t, we can definite the length of the stick is l vt vt. [Imitation] We can directl get ( vt ) from positive transformation () formula b imitating time variabilit solving trick of relativit theor. So, we can also get and ( vt ). So, the length of what the static sstem person seeing is: ( vt ) ( vt ) vt ( ) This is a derivation of length dilation formula. We can find from the above analsis that relativit theor is magic, and it is just a mathematical game. It is without confirmed phsical meaning. Fourth, the creation of infinite relativit theories. [Imitation] Adopting the magic trick of Einstein, the w Lorentz transformation is deduced on the basis of different observed light velocit in different ais frames. We assume the light source is in the dnamic sstem S, the observer in (3) S measuring the radiation velocit of light wave which is with respect to light source is c, and the observer in S measuring the light velocit is an optional value w. Now let us assume the following eperiments: when the moment that two ais frames coincide, there will be light wave emission at the common origin, and then we can observe the pre-wave movement of the light wave in two ais frames. Obviousl, light waves should be spherical waves which are origin-centered in two ais frames. And the pre-wave movement should not make different impacts on different frames. So, in S frame, the equation of the pre-wave should be: z ( c t ) (g) To maintain the variabilit of the light velocit, the equation of the pre-wave in S frame should be: z ( wt) (g) Now, we adopt Einstein s calculation methods of formulas from () to () and the following equation set can be easil gotten: 7

8 z z vt () ct t w This is w Lorentz positive transformation stated in the paper, and Einstein s Lorentz transformation, ct c t w w c v. Compared with c has onl high-order infinite c c small amount of differences in time transformation, that is, and the structure is w c v unchangeable. The formula of length transformation is full equal to that of Einstein. Solving the equation set of (), we can get w Lorentz negative transformation : z z c vwt c wt t c This is so-called w Lorentz negative transformation If we put a light source on the z point in () S ais frame, and it flashes each one time at t and t, then the measured flash time interval is: t t t. Adopting the methods of the relativit theor, we can directl calculate the positive transformation formula () and get the following result: ct ct ct t t t w w w If there is a stick placed along the ais, and position of both sides are () and, we can get the length of the stick: l. Now, there is an observer in S ais frame measuring the length of the stick. When the stick passes the observer along the ais at the speed of v, and the observer marks down the arrival time of the both sides t and t, we can definite the length of the stick is l vt vt. Adopting the methods of Einstein, we can get wt from the reverse transformation formula (), then we can get the following result: 8

9 l ( wt) ( wt) l (3) This is the length contraction formula of w relativit theor which adopts relativit transformation methods. The result is full equal to that of Einstein. You can give evaluate c with w or an value, and ou will get t t. What does this mean? This means that the transformation is optional without special phsical meaning. Especiall, Einstein used the tricks obtaining the value of the length contraction l l from the Lorentz transformation which based on the unchangeable light velocit hpothesis. But this paper gets the value of the length contraction l l which bases on the changeable light velocit hpothesis. The results are full equal, and there are high-order infinite small amount of differences between time dilations. It is obvious that Lorentz transformation is without phsical meaning, just a pure mathematical transformation formula, or, we call it interesting mathematical games. As the mathematical researcher, we can discuss Lorentz s interesting mathematic games. The above adopts the methods of flight fire with fire. We get the new w relativit theor which bases on the optional value of light velocit hpothesis through using Lorentz transformation and adopting Einstein s magic tricks. Because of the option of the value w, when given infinite values, there will be infinite relativit theories. 3 Conclusion The reasons wh the paper indicates Einstein s Lorentz transformation is a interesting mathematical game are that: first, adopting Einstein s transformation method, assuming the value of w is optional, we can get the length contraction value which is full equal to that of Einstein and there are onl high-order infinite small amount of differences between time dilations. Second, if we reverse Einstein s calculation method, it will be time contraction and length dilation; if both are used reverse transformation, it will be time and length contraction. On the other hand, if both are used positive transformation, it will be time and length dilation. Third,the ke point is no matter how to change the transformation, the solving structure is the same. So, the chapter indicates Lorentz transformation is a interesting mathematical game, which is just like what Lorentz stressed that transformation is without real phsical meaning. {Above translat possible hove problems, so please ou consciention understand these article} References. Wu Daou, The principle of Relativit Theor, Science Press, 983. Li Guodong, Song Desheng, The Development Histor of Electro-magnetics, Guangi People Press, 986 9

10 3.Zeng Qingping. The Summar of Natural Science Principles-- Interpretation about the important difficult problems of phsics law. Science publisher of Hubei, in Wuhan,China,9.6 4.Zeng Qingping.Summarization of Question on EM Theor, Proceedings of ILLMC Zeng Qingping.Summarization of Negative to Mawell s EM Theor, Proceedings of ILLMC Zeng Qingping.Problems on Demonstration of the Electric Field Producing the Magnetic Field.Proceedings of ICMMT 98. (ISTP). 7.Zeng Qingping.Problems on Demonstration of the Magnetic Field Producing the Electric Field. Proceedings of ICMMT 98. (ISTP). 8.Zeng Qingping.Questions on Mawell s Electromagnetic Field Theor. Proceed-ings of ICEEA 94. (SCI). 9.Zeng Qingping.Negative Viewpoints to Mawell s Electromagnetic Field The-or.Chinese Journal of Radio Science, or Proceedings of ICRS 95, p7~3..zeng Qingping.On Theor of Relativit in Mass Spectrometer. Proceedings of CMSC 99, in China..Zeng Qingping.Questions on EM Theor and the Separative Viewpoints on Elec-tric field and Magnetic field, Journal of Air Force Radar Academ, VoL Zeng Qingping. Summarization of Question on EM Theor, Proceedings of ILLMC. 3.Zeng Qingping. Summarization of Negative to Mawell s EM Theor, Proceedings of ILLMC Epecting the references that ou published []Disputes Eisting in the Phsical Natural of Electromagnetic Induction []Verification of General Lorentz Magnetic Force [3]Eperimental Method to Negate Mawell Theor [4].Mathematical Model of Independent Radiation Magnetic Field [5]The Essence of Electric Wave Is not Energ [6] About the Phsical Essence of Michelson-Morle Eperiment [7] Light Velocit Obes Galileo s Relativit Principle [8] Compton s Scattering Eperiment of Roentgen Ras Obes Newton s Law [9] Clock Becoming Slower Is the Necessit of Newton s Law [] Einstein s Lorentz Transformation Is a Math Game.