Absolute SpeedDate: 08/12/97 at 17:57:08 From: Chris MacPhee Subject: Absolute speed The absolute speed, within the Einsteinian universe, is c (the speed of light). If a ship going 1/100 of c shines a flashlight, what could happen to the light emitted? If it goes 101/100 of c, the speed of light is not a constant. If it goes at c, what happens to the law of Conservation of Momentum as well as the law of Conservation of Energy? Thanks, Chris MacPhee Date: 08/14/97 at 12:01:24 From: Doctor Marko Subject: Re: Absolute speed Hi Chris, Incidentally, strictly speaking, you are asking a physics question and not a math question. You have to be careful when asking questions like this because it is important to regard speed as a relative concept and not an absolute one. What I mean is that someone can answer your question by saying: "Well, with respect to the ship, the light travels at c." and think to be done. But since I believe that your question had to do with the light's speed relative to the observer at rest (the one that sees the ship moving at .01c) I will continue. The answer to your question lies within your first sentence, which is also one of the postulates of Einstein's theory of relativity - which is to say that the speed of light is c, and always c, and c from all the inertial reference frames (that is the unaccelerating frames). Sounds weird and we ordinary people have no intuition for that, because after all we do not see light as having speed since it is so blazing fast, so we think of it as instantaneous. Yet this notion seems to be verified by experiments (such as the Michelson-Morley experiment). So, then your next question is the right one - what happens to the conservation of momentum and energy laws? Well, Einstein felt that the laws of conservation of momentum and energy were so compelling that he wondered if it was possible to keep them in some form. In order to keep the conservation laws, he discovered that he needed to change the definition of momentum and energy, to what is called relativistic momentum and energy. Now the formulas go something like this: Newtonian momentum: p = mv relativistic momentum: p = gamma mv, where m is the mass, v is the speed, and gamma is the relativistic factor: gamma^-1 = Sqrt(1-(v/c)^2). To sort of conclude (and if you want to, please keep asking more questions), what is remarkable about Einstein's theory is that to the best of our knowledge, the relativistic momentum and energy are conserved, as tested by countless experiments. Also note that when speeds are small compared to the speed of light (we write that as "v<<c", i.e. "v much, much less than c") then gamma is approximately 1, and the relativistic theory and the Newtonian theory differ almost indistinguishably from each other. Cool? -Doctor Marko, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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