Richard Jernigan -> RE: Richard and other thinkers (Mar. 8 2014 23:10:58)
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In general, the word "relativity" in physics arose to point out that there was no preferred coordinate system for the laws of physics. Why did people ever think there would be? Maxwell's highly successful formulation of electrodynamics implied that there was a preferred coordinate system. Electromagnetic waves were seen as propagating through a stationary medium, the "luminiferous ether". So if an observer were moving with respect to this medium, the velocity of light would be affected by the observer's motion, just as we strike the waves more often as we speed up our boat, or sound gets to us quicker if it's traveling downwind. The existence of a preferred coordinate system was an absolutely unavoidable mathematical consequence of combining Maxwell's equations and Newtonian dynamics, regardless of whether it was materially manifested. Various experiments were devised to detect the "luminiferous ether", or in the more modern view, the preferred coordinate system, where the velocity of light was that predicted by Maxwell's equations. All failed in an unexpected way. No variation in the observed speed of light was detected. Michelson and Morley's experiments in 1887 were particularly well designed, precise and well documented. The observed velocity of light was the same throughout the year, as the earth moved in its orbit at high velocity through the assumed preferred system. Michelson and Morley put the fox among the chickens. Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" explored the implications of the absence of a stationary luminiferous ether, or preferred coordinate system. The results are called the theory of Special Relativity. He derived the Lorentz transformation from the following postulates: 1) The laws of physics are the same in all inertial coordinate systems, 2) the speed of light is the same for all observers. Postulate 1) has considerable tacit content. An inertial coordinate system is one in which space is Euclidean, and which undergoes no acceleration. Such coordinate systems are mathematical abstractions which do not exist in nature. Space is warped by the presence of mass and energy, and the forces of nature, in particuar gravity exist throughout the universe, subjecting every observer and his coordinate system to acceleration. Exploring the abstraction a little further, in effect, if A and B are two inertial coordinate systems, then A sees B as moving in a straight Euclidean line at constant speed, while B sees A moving in a straight Euclidean line at constant speed in the opposite direction. Given this abstraction and postulating the same observed speed of light for observers stationary in each of A and B results in the Lorentz transformation. The mathematics is elementary analytic geometry. What is revolutionary are the effects, including time dilation. A sees B's clocks as running slower than his own, and B sees A's clocks as running slower than his own. If A and B ever got back together and compared their clocks, the twin paradox would result. The twin paradox is not that the returning rocketeer is younger than his earthbound twin. This really happens. The twin paradox is that in special relativity, the twin in coordinate system A sees his brother in B aging more slowly, and the twin in B sees his brother in A aging more slowly. But since coordinate systems A and B move steadily away from one another in Special Relativity, observers that are stationary in each never get back together again. Special Relativity's relevance to physics was to establish the strongly non-intuitive consequences of its two simple postulates. General Relativity deals with the closer approximation to large scale physical reality by developing the laws of electrodynamics and motion in the more generalized arena of non-inertial coordinate systems: ones experiencing acceleration. The mathematics is a little more complicated, tensors instead of vectors, curved space instead of flat Euclidean space, etc. Today's senior math undergraduate might say, "Well, it's just tensor calculus and differential geometry," and she would be right. What is revolutionary is not the math, but the effects of matter and motion upon the measurement of space and time. Special Relativity is a special case of General Relativity--zero acceleration.The results of General Relativity continuously approach those of Special Relativity as you move toward less acceleration and flatter space. The two are mutually exclusive, in the sense that the postulates of Special Relativity are more restrictive, but they do not contradict one another. To travel away, then return home and meet his older twin, the rocketeer must first accelerate to high speed, then turn around and come back to earth. Both speeding up and turning are accelerations. Special Relativity simply does not apply. Its first postulate, inertial coordinate systems, is violated. But the twin paradox doesn't occur. If the calculations of General Relativity are carried out, the traveler really is younger than his twin when he returns, as we see with traveling atomic clocks and cosmic rays. It's been a long time since I read Gamow's "1, 2 3,…Infinity" as a high school freshman, but he was a highly qualified working physicist, and I doubt that he got anything wrong. RNJ P.S. I agree with Ricardo's take on dark matter. P.P.S. This is not to say that the mathematical abstraction of inertial coordinate systems isn't useful. For example, the trajectories of intercontinental missiles are predicted using inertial coordinate systems, and the guidance systems used by these missiles use inertial coordinate systems. The error so induced is small compared to the uncertainties caused by the randomness of the atmosphere on reentry, and the uncontrolled error of the reentry aerodynamics of a vehicle that is in fact partly burning up. You need detailed knowledge of geographical variations in the earth's gravitational field to achieve the accuracy that U.S. missiles do. But Newtonian dynamics in an inertial coordinate system are used in the calculations.
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