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The Equivalence Principle,the Covariance Principle and the Question of Self-Consistency in General Relativity

By Gladys Collins,2014-01-05 18:07
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The Equivalence Principle,the Covariance Principle and the Question of Self-Consistency in General Relativity

     The Equivalence Principle,the Covariance Principle and the Question of Self-Consistency in General Relativity

     理学论文 >> 物理学 >> 论文正文?The Equivalence

    Principle,the Covariance Principle and the Question of Self-Consistency in General Relativity

     The Equivalence Principle,the Covariance Principle and the Question of Self-Consistency in General Relativity

     作者;C. Y. Lo 发布时间;2003-8-28

     -

     The Equivalence Principle,the Covariance Principle and the Question of Self-Consistency in General Relativity

     The Equivalence Principle, the Covariance Principle

     and

     the Question of Self-Consistency in General Relativity

     C. Y. Lo

     Applied and Pure Research Institute

     17 Newcastle Drive, Nashua, NH 03060, USA

     September 2001

     Abstract

     The equivalence principle, which states the local equivalence between acceleration and gravity, requires that a free falling observer must result in a co-moving local Minkowski space. On the other hand,

    covariance principle assumes any Gaussian system to be valid as a space-time coordinate system. Given the mathematical existence of the co-moving local Minkowski space along a time-like geodesic in a Lorentz manifold, a crucial question for a satisfaction of the equivalence principle is whether the geodesic represents a physical free fall. For instance, a geodesic of a non-constant metric is unphysical if the acceleration on a resting observer does not exist. This analysis is modeled after Einstein

    illustration of the equivalence principle with the calculation of light bending. To justify his calculation rigorously, it is necessary to derive the Maxwell-Newton Approximation with physical principles that lead to general relativity. It is shown, as expected, that the Galilean transformation is incompatible with the equivalence principle. Thus, general mathematical covariance must be restricted by physical requirements. Moreover, it is shown through an example that a Lorentz manifold may not necessarily be diffeomorphic to a physical space-time. Also observation supports that a spacetime coordinate system has meaning in physics. On the other hand, Pauli version leads to the

    incorrect speculation that in general relativity space-time coordinates have no physical meaning

     1. Introduction.

     Currently, a major problem in general relativity is that any Riemannian geometry with the proper metric signature would be accepted

as a valid solution of Einstein equation of 1915, and many unphysical

    solutions were accepted [1]. This is, in part, due to the fact that the nature of the source term has been obscure since the beginning [2,3]. Moreover, the mathematical existence of a solution is often not accompanied with understanding in terms of physics [1,4,5]. Consequently, the adequacy of a source term, for a given physical situation, is often not clear [6-9]. Pauli [10] considered that he theory of relativity to be an example showing

    how a fundamental scientific discovery, sometimes even against the resistance of its creator, gives birth to further fruitful developments, following its own autonomous course." Thus, in spite of observational confirmations of Einstein predictions, one should examine whether

    theoretical self-consistency is satisfied. To this end, one may first examine the consistency among physical rinciples" which lead to

    general relativity.

     The foundation of general relativity consists of a) the covariance principle, b) the equivalence principle, and c) the field equation whose source term is subjected to modification [3,7,8]. Einstein equivalence

    principle is the most crucial for general relativity [10-13]. In this paper, the consistency between the equivalence principle and the covariance principle will be examined theoretically, in particular through examples. Moreover, the co

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