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On the Theory of Relativity and the Laws of Transformation By RE CASTEL In Einstein's summary of the theory of relativity presented below, his "laws of nature" is anchored on "the postulate of the constancy of the velocity of light." Here the question "how much must the laws of nature be constituted" signifies the call for an invariance factor in the equations that will ensure the invariance of the laws of nature. As for the application of the laws of nature on specific aspects of nature, Einstein's proposition is the 'arbitrary' transformations of space and time, not the transformations of motion. Einstein ignores the idea that light, a form of motion, is transformed and not space or time. On close examination, it is clear that the theorem (E=mc2) is successful because it is according to the idea of the transformations of motion. But Einstein never forwarded a clear idea of the transformations of motion—as may be noticed in the following summary of his theory done late in his life. Every physical theory makes use of a co-ordinate system (description of place) and of the concept of time. In classical mechanics, which was founded mainly by Galileo Galilei and Isaac Newton, the determination of place are relative to an inertial system, that is, a system which is in such motion that Galilei's law of inertia is valid relative to it. According to this theory, there exist infinitely many inertial systems which move uniformly with respect to each other; relative to every such system the laws (of classical mechanics) must be valid. Time is treated as an independent quantity which is the same for all inertial systems. The modern equivalence of these inertial systems is called the "special theory of relativity." Special Theory Of Relativity. This theory has its origin in the conviction that the velocity of light has the same value for all inertial systems, a conviction which is substantiated by many physical facts. Starting from this principle one arrives at the conclusion that the determination of place (co-ordinates) and time are subject to different laws of transformation (for the passage from one inertial system to another) than was previously tacitly assumed (Lorentz-transformation). The content of the theory is the answer to the question: how must the known laws of nature be modified in order to account for the postulate of the constancy of the velocity of light? Hereby it was shown in particular that time is not "absolute," that is, independent of the choice of the inertial system. There further developed a law of motion which deviates from Newton's for the case of high velocities (that is, not small in comparison to the velocity of light). Another result is the theorem (E=mc2) of the equivalence of the inertial mass m and the energy E of a system (velocity of light, c), which has achieved special importance for the theory of chemical elements and of radioactive processes. General Theory Of Relativity. This theory is a generalization of the special theory of relativity, which removes the distinction of inertial systems as compared with co-ordinate systems or a different state of motion. This theory has its origin in a fact known for centuries that the inertia and the weight of a body are characterized by the same number (mass). It is in connection with this relation to weight that the theory yielded a new law of gravitation, which is valid to a greater degree of accuracy than Newton's theory of gravitation. The following question is characteristic for the entire theory of relativity: how much must the laws of nature be constituted so that they are valid in the same form relative to arbitrary systems of co-ordinates (postulate of the invariance of the laws of nature relative to an arbitrary transformation of space and time)? (Grolier Encyclopedia, 1963) Basically, in the purely kinematic interpretation, the classical idea is that there are motion transformations. Space is fixed and is unaffected by motion and time. Time flows equably towards the future independent of motion and space. And such that time is the same in all frames of reference. Motion is affected only by other motions and is independent of space and time. And thus the suggestion of only the motion transformations is clear.
The classical idea states that motion is transformed as affected by other motions. Thus, a motion with a velocity u in the unprimed frame of reference becomes u' in the primed frame upon the application of a velocity v. The relevant classical equations x'=x-vt and t'=t suggest that, with u'=x'/t' and u=x/t, we have u'=(x-vt)/t or u'=(x/t)-(vt/t), and so we have u'=u-v. Thus, for the phenomenon (light) observed in the differing frames, the velocity of light u=c in the unprimed frame becomes u'=c-v in the primed frame. However, the postulate of the constancy of the velocity of light requires that the velocity of light must remain the same in all frames of reference—i.e., u=c and u'=c. Because of this, the equation u'=c-v calls for an invariance factor γ. Since u'=c-v=c(1-v/c), the invariance factor should be γ=1/(1-v/c)=(1-v/c)-1. Thus, u'=(c-v)γ , which yields u'=c. The suggestion from the formulations clearly regards motion transformations upon the application of the velocity v on the velocity c of the phenomenon observed in the differing frames. But on account of the postulate, v cannot be applied to c in a rectilinear application—i.e., not as u'=c-v. Thus, v is applied to c in a rotational application—i.e., as u'=(c-v)γ. And therefore, upon the approximation and substitution for the computation of the transformations in the observed phenomenon, the equation suggests a change in the wavelength and frequency of c—which agrees with the electromagnetic wave theory and the equation c=λƒ. An invariance of the laws of nature is indeed established by the invariance factor γ. But the laws of nature expressed in the equations are evidently about the transformations of motion. It is clearly the velocity of light (a form of motion) that is measured with the transformation by a factor γ. Evidently, there is no arbitrary transformation of space and time; we have only the transformations of motion. site advocacies: renewable energy, clean technology, efficient engines, higher education, super foods & medicines... |
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