1 v 2i 1 vf

contain, as it were, the Galilean Transformation, since when the speed of light travels towards infinity, a transition from the Lorentz Transformation into the Galilean Transformation occurs (the denominator of the first equation approximates 1), i.e., if the speed of light is infinite, there would be an instant signal transmission, and thus absolute time. The discrepancy between the values of the classical transformation and those of the Lorentz Transformation is greatest for speeds approximating the speed of light.

A few months after the publication of the article "Zur Elektrodynamik bewegter Körper" (On the Electrodynamics of Moving Bodies) in the An-nalen der Physik, Einstein concluded that there is a general equivalence of mass and energy, which was expressed in the well-known formula E = mc2.151

In contrast to classical mechanics, the measurement of space and time in relativistic physics using the regularities of light clearly shows: "The means x =

c by which nature is recognized are nothing other than parts of precisely this nature."153 Physics can therefore no longer be understood as natural philosophy in the sense of a theory of nature "as it is." Rather, one is dealing with a theory of nature "as it appears when it is tested using real standards and clocks."154 Time can no longer be understood as a "container" for nature. Nature is not in time, but rather, time is in nature.

Space-Time Curvature—The General Theory of Relativity The restricted application of the special theory of relativity to uniformly moving systems called attention to the fact "that the previous theory of relativity needed to be generalized so that the seemingly unjust preference for uniform translation, as contrasted to relative movements of a different type, vanishes from the theory."155 The general theory of relativity156 solved this problem of formulating physical laws for all systems. It contains the special theory of relativity as a limiting case. The great achievement of the general theory of relativity was the inclusion of gravity, which occurred by expanding the principle of relativity to coordinate systems accelerated relative to one another and by considering the gravitational fields that were caused thereby. The recognition of the invariance157 of the speed of light made the idea of instant gravitational effects impossible and required the mathematical treatment of gravity according to a field theory. This is achieved by the general theory of relativity. The difference from the concepts of space and time in classical mechanics is obvious. In Newton, space and time were defined in advance as the solid stage on which the development of physical systems takes place, but space-time in the general theory of relativity is an essential part of this very development.158

The general theory of relativity makes use of the Gaussian method for the mathematical treatment of any continuum. In a four-dimensional continuum, it attributes four coordinates (xp x2, x3, and x4) to each event, whereby no distinction is made between space and time coordinates. This method replaces descriptions that use a reference body and is therefore not limited to describing a continuum with a Euclidean character.159

The connection of local space and time coordinates, as is known by the special theory of relativity, is replaced by a more general relationship that contains a so-called metric tensor gk (x, y, z, t). The space-time continuum of the general theory of relativity corresponds to the shape of a four-dimensional curved space. The expression "curved space" implies that the spatial arrangement of material bodies does not agree with the laws of three-dimensional Euclidian geometry.160 Instead, the theory uses Riemannian geometry,161 the simplest illustration of which can draw upon the geometry of a spherical surface. The two-dimensional surface of a sphere is finite and yet unlimited. A three-dimensional space with similar properties must be thought of as curved back into itself. Since, in Riemannian geometry, Euclidian geometry is locally valid in infinitesimally small areas of the curved spaces, the latter is to a certain degree included in the former.

Einstein's gravity equations were initially confirmed empirically in three respects, namely, by the rotation of the ellipses of the planetary orbits around the sun (complete explanation of the deviations in the perihelion of Mercury), the light deflection in a gravitational field (using the solar eclipse photographs of the 1919 British expedition), and the gravitational redshift of light. In addition, the predicted consequences of Einstein's theory in the form of time dilation have since been empirically confirmed numerous times.162

If, according to the special theory of relativity, it was movement that slowed down the operation of clocks, then according to the general theory of relativity, the same applies to gravity. These facts are frequently illustrated using the well-known "twin paradox."163 A twin who takes a journey into space at high speeds will be younger upon her return than the sister who remained at home. Similarly, one twin who was exposed to much stronger gravity on a heavenly body of higher density than the other was exposed to on earth finds on her return that the sister who stayed at home is older than she is.

Neither the special nor the general theory of relativity can define the direction of a time arrow; as in Newtonian mechanics, time here is also basically reversible. The theory of relativity did not falsify Newtonian mechanics, but rather specified the scope of its validity.

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