{"title":"三维亚美尼亚变换方程","authors":"R. Nazaryan, H. Nazaryan","doi":"10.15761/AMS.1000106","DOIUrl":null,"url":null,"abstract":"In this article, we derive new transformation equations of relativity in 3D using the following guidelines: 1. We use only vector notations to obtain the new transformation equations in a general form. 2. In the process of deriving new transformation equations in vector form, we also keep the term v r → → × 3. Newly obtained transformation equations need to satisfy the linear transformation fundamental laws. 4. Addition of velocities we calculate in two different ways: by linear superposition and by differentiation, and they need to coincide each other. If not, then we force them to match for obtaining the final relation between coefficients. After using the above mentioned general guidelines, we obtain direct and inverse transformation equations named the Armenian transformation equations, which are the replacement for the Lorentz transformation equations. Correspondence to: Robert Nazaryan, Physics Department, Yerevan State University, Alek Manukyan Street, Yerevan 0025, Armenia, E-mail: robert@armeniantheory.com Received: March 12, 2016; Accepted: April 26, 2016; Published: April 29, 2016 Introduction to the Armenian transformation equations in 3D The Lorentz transformation equations, as we know them, in two dimensional time-space (t,x) or in four-dimensional time-space (t,r), when the inertial systems move at a constant relative velocity v along one of the chosen axis, are linear orthogonal transformations. In these cases Lorentz transformations are a group and satisfy the fundamental linear transformation rules: L(v)L(u’)= L(u). Where the resultant transformation is a Lorentz transformation as well with the 2 ' u=(v+u)/(1+ ) vu c . In general, when the relative resultant velocity velocity of the inertial systems S and S have an arbitrary direction, then the Lorentz transformation is not a group and are therefore less discussed as a case. Only a few brave authors mention and discuss this general case (axes of the inertial systems they take parallel to each other as usual). The main linear transformation law fails for the general Lorentz transformation. Since, however, a resultant transformation must be a Lorentz transformation as well, physicist need therefore to add an extra artificial transformation called the Thomas precession, to compensate for the error. This is the Achilles heel in the Lorentz transformation equations in 3D and more precisely in all special and general theory of relativity. Therefore it is an imperative, that the Lorentz transformation equations be replaced by new ones, which must be consistent with linear transformation fundamental laws and have a common sense in respect to reality. Here we shall derive these New transformation equations, using pure mathematical logic without any limitations and the following three postulates: 1. All physical laws have the same mathematical(tensor) form in all inertial systems. 2. There exists a boundary velocity, denoted as c, between micro and macro worlds, which is the same in all inertial systems. 3. The simplest transformation equations of the moving particle between two inertial systems have only when relative velocity, measured in two inertial systems, satisfy the reciprocal relation These first two postulates are almost the same as the Special Relativity Theory postulates, but the third postulate is quite new and necessary for receiving the simplest transformation equations without ambiguity problems in orientation of the inertial systems axes. All authors that I know, derive the Lorentz transformation equations using two Cartesian coordinates (t, x) or as a general way using four Cartesian coordinates (t, x, y, z). Nobody (that I know of) uses vector notations to derive general transformation equations for relativity. Many authors artificially construct 3D Lorentz transformation equations in vector form using one dimensional Lorentz transformation equations and therefore those generalized results cannot be correct. The laws of logic tell us, that we need to go from the general case to the special case. That’s why we derive our new transformation equations using the most general considerations and adapting vector notation. The great merit of the vectors in the theoretical and applied problems is that equations describing physical phenomena can be formulated without reference to any particular coordinate system, without worry that coordinate systems axes are parallel to each other or not. However, in actually carrying out the calculations we need to find a suitable coordinate system (our third postulate) where equations can have the simplest form. Therefore to receive the correct transformation equations we need to use only vector notations and focus on it entirely. Using this new promising approach and one additional postulate we derive truly correct transformation equations in the general and simplest form. The other question can arise why are we calling our newly received transformation equations the Armenian Transformation Equations? The answer is very simple. This research was done for more than 40 years in Armenia by an Armenian and the manuscripts were written in Nazaryan R (2016) Armenian transformation equations in 3D Volume 1(1): 22-23 Adv Mater Sci, 2016 doi: 10.15761/AMS.1000106 Armenian. This research is purely from the mind of an Armenian and from the Holy land of Armenia, therefore we can rightfully call these newly derived transformation equations the Armenian Transformation Equations and the theory the Armenian Theory of Relativity or ATR. Summary of the Armenian transformation equations In 3D Direct and Inverse Armenian transformation equations Direct transformations Inverse transformations","PeriodicalId":408511,"journal":{"name":"Advances in Materials Sciences","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Armenian transformation equations in 3D\",\"authors\":\"R. Nazaryan, H. Nazaryan\",\"doi\":\"10.15761/AMS.1000106\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we derive new transformation equations of relativity in 3D using the following guidelines: 1. We use only vector notations to obtain the new transformation equations in a general form. 2. In the process of deriving new transformation equations in vector form, we also keep the term v r → → × 3. Newly obtained transformation equations need to satisfy the linear transformation fundamental laws. 4. Addition of velocities we calculate in two different ways: by linear superposition and by differentiation, and they need to coincide each other. If not, then we force them to match for obtaining the final relation between coefficients. After using the above mentioned general guidelines, we obtain direct and inverse transformation equations named the Armenian transformation equations, which are the replacement for the Lorentz transformation equations. Correspondence to: Robert Nazaryan, Physics Department, Yerevan State University, Alek Manukyan Street, Yerevan 0025, Armenia, E-mail: robert@armeniantheory.com Received: March 12, 2016; Accepted: April 26, 2016; Published: April 29, 2016 Introduction to the Armenian transformation equations in 3D The Lorentz transformation equations, as we know them, in two dimensional time-space (t,x) or in four-dimensional time-space (t,r), when the inertial systems move at a constant relative velocity v along one of the chosen axis, are linear orthogonal transformations. In these cases Lorentz transformations are a group and satisfy the fundamental linear transformation rules: L(v)L(u’)= L(u). Where the resultant transformation is a Lorentz transformation as well with the 2 ' u=(v+u)/(1+ ) vu c . In general, when the relative resultant velocity velocity of the inertial systems S and S have an arbitrary direction, then the Lorentz transformation is not a group and are therefore less discussed as a case. Only a few brave authors mention and discuss this general case (axes of the inertial systems they take parallel to each other as usual). The main linear transformation law fails for the general Lorentz transformation. Since, however, a resultant transformation must be a Lorentz transformation as well, physicist need therefore to add an extra artificial transformation called the Thomas precession, to compensate for the error. This is the Achilles heel in the Lorentz transformation equations in 3D and more precisely in all special and general theory of relativity. Therefore it is an imperative, that the Lorentz transformation equations be replaced by new ones, which must be consistent with linear transformation fundamental laws and have a common sense in respect to reality. Here we shall derive these New transformation equations, using pure mathematical logic without any limitations and the following three postulates: 1. All physical laws have the same mathematical(tensor) form in all inertial systems. 2. There exists a boundary velocity, denoted as c, between micro and macro worlds, which is the same in all inertial systems. 3. The simplest transformation equations of the moving particle between two inertial systems have only when relative velocity, measured in two inertial systems, satisfy the reciprocal relation These first two postulates are almost the same as the Special Relativity Theory postulates, but the third postulate is quite new and necessary for receiving the simplest transformation equations without ambiguity problems in orientation of the inertial systems axes. All authors that I know, derive the Lorentz transformation equations using two Cartesian coordinates (t, x) or as a general way using four Cartesian coordinates (t, x, y, z). Nobody (that I know of) uses vector notations to derive general transformation equations for relativity. Many authors artificially construct 3D Lorentz transformation equations in vector form using one dimensional Lorentz transformation equations and therefore those generalized results cannot be correct. The laws of logic tell us, that we need to go from the general case to the special case. That’s why we derive our new transformation equations using the most general considerations and adapting vector notation. The great merit of the vectors in the theoretical and applied problems is that equations describing physical phenomena can be formulated without reference to any particular coordinate system, without worry that coordinate systems axes are parallel to each other or not. However, in actually carrying out the calculations we need to find a suitable coordinate system (our third postulate) where equations can have the simplest form. Therefore to receive the correct transformation equations we need to use only vector notations and focus on it entirely. Using this new promising approach and one additional postulate we derive truly correct transformation equations in the general and simplest form. The other question can arise why are we calling our newly received transformation equations the Armenian Transformation Equations? The answer is very simple. This research was done for more than 40 years in Armenia by an Armenian and the manuscripts were written in Nazaryan R (2016) Armenian transformation equations in 3D Volume 1(1): 22-23 Adv Mater Sci, 2016 doi: 10.15761/AMS.1000106 Armenian. This research is purely from the mind of an Armenian and from the Holy land of Armenia, therefore we can rightfully call these newly derived transformation equations the Armenian Transformation Equations and the theory the Armenian Theory of Relativity or ATR. 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引用次数: 0
摘要
在本文中,我们利用以下准则推导出新的三维相对论变换方程:1。我们只用向量符号来得到一般形式的新变换方程。2. 在导出向量形式的新变换方程的过程中,我们也保留了v r→→x3项。新得到的变换方程需要满足线性变换基本定律。4. 我们用两种不同的方法计算速度的加法:线性叠加和微分,它们需要重合。如果不是,那么我们强制它们匹配以获得系数之间的最终关系。利用上述一般准则,我们得到了正变换方程和反变换方程,称为亚美尼亚变换方程,它是洛伦兹变换方程的替代。通讯作者:Robert Nazaryan,埃里温州立大学物理系,Alek Manukyan街,埃里温0025,亚美尼亚,E-mail: robert@armeniantheory.com录用日期:2016年4月26日;正如我们所知,在二维时空(t,x)或四维时空(t,r)中,当惯性系统沿着选定的一个轴以恒定的相对速度v运动时,洛伦兹变换方程是线性正交变换。在这些情况下,洛伦兹变换是一个群,并且满足基本的线性变换规则:L(v)L(u ')= L(u)。得到的变换也是洛伦兹变换2 ' u=(v+u)/(1+) vu c。一般来说,当惯性系统S和S的相对合成速度具有任意方向时,则洛伦兹变换不是一个群,因此较少作为一种情况进行讨论。只有少数勇敢的作者提到并讨论了这种一般情况(惯性系的轴像往常一样彼此平行)。对于一般的洛伦兹变换,主要的线性变换定律失效了。然而,由于结果变换也必须是洛伦兹变换,因此物理学家需要添加一个额外的人工变换,称为托马斯进动,以补偿误差。这是三维洛伦兹变换方程的致命弱点更准确地说,是所有狭义相对论和广义相对论的致命弱点。因此,必须用新的洛伦兹变换方程来代替旧的洛伦兹变换方程,新的洛伦兹变换方程必须符合线性变换的基本定律,并且在现实方面具有通用性。在这里,我们将使用没有任何限制的纯数学逻辑和以下三个假设推导这些新的变换方程:在所有惯性系中,所有物理定律都具有相同的数学(张量)形式。2. 在微观世界和宏观世界之间存在一个边界速度,记为c,这在所有惯性系中都是相同的。3.在两个惯性系之间运动质点的最简单变换方程只有在两个惯性系中测量的相对速度满足互反关系时才有。前两个公设几乎与狭义相对论的公设相同,但第三个公设是相当新的,并且是得到最简单变换方程所必需的,它不会引起惯性系轴方向的模糊问题。我认识的所有作者,都用两个笛卡尔坐标(t, x)来推导洛伦兹变换方程,或者用四个笛卡尔坐标(t, x, y, z)来推导洛伦兹变换方程,(据我所知)没有人用矢量符号来推导相对论的广义变换方程。许多作者用一维洛伦兹变换方程人为地构造了矢量形式的三维洛伦兹变换方程,因此这些广义的结果是不正确的。逻辑定律告诉我们,我们需要从一般情况转到特殊情况。这就是为什么我们用最一般的考虑和适应向量符号来推导新的变换方程。矢量在理论和应用问题中的巨大优点是,描述物理现象的方程可以不参考任何特定的坐标系来表述,而不必担心坐标系轴是否平行。然而,在实际执行计算时,我们需要找到一个合适的坐标系(我们的第三个假设),其中方程可以具有最简单的形式。因此,为了得到正确的变换方程,我们只需要使用向量符号,并完全关注它。利用这一新的有希望的方法和一个附加的假设,我们得到了真正正确的一般和最简单形式的变换方程。
In this article, we derive new transformation equations of relativity in 3D using the following guidelines: 1. We use only vector notations to obtain the new transformation equations in a general form. 2. In the process of deriving new transformation equations in vector form, we also keep the term v r → → × 3. Newly obtained transformation equations need to satisfy the linear transformation fundamental laws. 4. Addition of velocities we calculate in two different ways: by linear superposition and by differentiation, and they need to coincide each other. If not, then we force them to match for obtaining the final relation between coefficients. After using the above mentioned general guidelines, we obtain direct and inverse transformation equations named the Armenian transformation equations, which are the replacement for the Lorentz transformation equations. Correspondence to: Robert Nazaryan, Physics Department, Yerevan State University, Alek Manukyan Street, Yerevan 0025, Armenia, E-mail: robert@armeniantheory.com Received: March 12, 2016; Accepted: April 26, 2016; Published: April 29, 2016 Introduction to the Armenian transformation equations in 3D The Lorentz transformation equations, as we know them, in two dimensional time-space (t,x) or in four-dimensional time-space (t,r), when the inertial systems move at a constant relative velocity v along one of the chosen axis, are linear orthogonal transformations. In these cases Lorentz transformations are a group and satisfy the fundamental linear transformation rules: L(v)L(u’)= L(u). Where the resultant transformation is a Lorentz transformation as well with the 2 ' u=(v+u)/(1+ ) vu c . In general, when the relative resultant velocity velocity of the inertial systems S and S have an arbitrary direction, then the Lorentz transformation is not a group and are therefore less discussed as a case. Only a few brave authors mention and discuss this general case (axes of the inertial systems they take parallel to each other as usual). The main linear transformation law fails for the general Lorentz transformation. Since, however, a resultant transformation must be a Lorentz transformation as well, physicist need therefore to add an extra artificial transformation called the Thomas precession, to compensate for the error. This is the Achilles heel in the Lorentz transformation equations in 3D and more precisely in all special and general theory of relativity. Therefore it is an imperative, that the Lorentz transformation equations be replaced by new ones, which must be consistent with linear transformation fundamental laws and have a common sense in respect to reality. Here we shall derive these New transformation equations, using pure mathematical logic without any limitations and the following three postulates: 1. All physical laws have the same mathematical(tensor) form in all inertial systems. 2. There exists a boundary velocity, denoted as c, between micro and macro worlds, which is the same in all inertial systems. 3. The simplest transformation equations of the moving particle between two inertial systems have only when relative velocity, measured in two inertial systems, satisfy the reciprocal relation These first two postulates are almost the same as the Special Relativity Theory postulates, but the third postulate is quite new and necessary for receiving the simplest transformation equations without ambiguity problems in orientation of the inertial systems axes. All authors that I know, derive the Lorentz transformation equations using two Cartesian coordinates (t, x) or as a general way using four Cartesian coordinates (t, x, y, z). Nobody (that I know of) uses vector notations to derive general transformation equations for relativity. Many authors artificially construct 3D Lorentz transformation equations in vector form using one dimensional Lorentz transformation equations and therefore those generalized results cannot be correct. The laws of logic tell us, that we need to go from the general case to the special case. That’s why we derive our new transformation equations using the most general considerations and adapting vector notation. The great merit of the vectors in the theoretical and applied problems is that equations describing physical phenomena can be formulated without reference to any particular coordinate system, without worry that coordinate systems axes are parallel to each other or not. However, in actually carrying out the calculations we need to find a suitable coordinate system (our third postulate) where equations can have the simplest form. Therefore to receive the correct transformation equations we need to use only vector notations and focus on it entirely. Using this new promising approach and one additional postulate we derive truly correct transformation equations in the general and simplest form. The other question can arise why are we calling our newly received transformation equations the Armenian Transformation Equations? The answer is very simple. This research was done for more than 40 years in Armenia by an Armenian and the manuscripts were written in Nazaryan R (2016) Armenian transformation equations in 3D Volume 1(1): 22-23 Adv Mater Sci, 2016 doi: 10.15761/AMS.1000106 Armenian. This research is purely from the mind of an Armenian and from the Holy land of Armenia, therefore we can rightfully call these newly derived transformation equations the Armenian Transformation Equations and the theory the Armenian Theory of Relativity or ATR. Summary of the Armenian transformation equations In 3D Direct and Inverse Armenian transformation equations Direct transformations Inverse transformations