BACK-UP OF MY FIRST SCIENTIFIC DOCUMENT ______________________________________________ THESIS (INTRO): In Special Relativity, there exists a vagueness. It can be fixed with clever application of Einsteins 2nd Postulate of Special Relativity (invariance of c), but only at the cost of rejecting and replacing General Relativity as we know it. POINT 1 - The train of logic is pretty undeniable. Before Einstein, Newtons Laws of Mechanics were very strong. Similarly, Maxwells Electromagnetism represented a synthesis of earlier physical theories into a beautiful whole. POINT 2 - The problem was that Maxwells Electromagnetism was at odds with Newtons laws of mechanics, through electromagnetic radiation that was predicted to move at a speed that didnt seem relative to anything; the speed of light. POINT 3 - Einstein felt that the key to unification was to keep the spirit of relativity alive under the constraints that the speed of light is a constant. Reflected in the postulates of Special Relativity. POINT 4 - Using the postulates, Einstein uncovered a solution to the problem of making the theories connect, through the Lorentz transformation. Here is the Lorentz transformation, from (such and such source). POINT 5 - However, theres a vagueness in his solution. Einstein built the theories with the Galilean Laboratory in mind. The Galilean Laboratory has extents. POINT 6 - Heres what happens when we apply the same logic to a zero-dimensional point. Vagueness appears in whether or how fast a single particle (the Blain Laboratory) rotates in a Special Relativistic situation. POINT 7 - Vagueness solved by Einsteins 2nd Postulate in the World Frame. Orient the particle towards the photon at all times, always. At first it might seem pointless to bother resolving this ambiguity, and easy to just ignore it altogether. Given that we’ve tested Special Relativity beyond any serious doubt, that might be your immediate temptation. However, a failure to resolve the ambiguity leaves a gaping hole in Special Relativity. If the Blain Laboratory is not rotating, then the Lorentz transformation reduces to the Galilean transformation and everything is fine. However, it’s just as valid to claim that the Blain Laboratory is spinning in any arbitrary pattern, in which case it becomes impossible to properly apply the Lorentz transformation to correct the reference frames. The speed of light can never be corrected in this situation, and once we lose the speed of light, we lose all of physics! Luckily, before we panic, we can find a solution as quickly as we detected the problem, if we keep in mind that the entire purpose of Special Relativity is to stitch together the physical theories of mechanics and electromagnetism. The only way that will work is if everyone can agree upon the speed of light in all relevant (i.e. inertial) reference frames. In cases of ambiguity, the correct answer is furnished by Einstein’s second postulate; namely, the constancy of the speed of light. In the case of the Blain Laboratory, if it is spinning wildly, it finds that the rest of the universe suffers from the effects of time dilation and length contraction (as described earlier), and the photon approaching it may arrive along a different path and at an earlier time than we expect. To maintain the speed of light, we are forced to state that the Blain Laboratory doesn’t rotate wildly. The Lorentz transformation reduces to the Galilean transformation and the speed of light is maintained. Furthermore, although it makes no mathematical sense to talk about the orientation of a zero-dimensional particle, note that the concept of orientation is tied very tightly with the concept of rotation, and therefore it is important to consider the real, physical consequence of orientation of the Blain Laboratory. ………………………………………. In the diagram above, a train is passing by a Blain Laboratory which is affixed to the Earth on a platform that can rotate. As the train passes Checkpoints A and B, a flashlight is pointed at the Blain Laboratory to signal the passing of the train. If we arbitrarily decide that the Blain Laboratory is orientated towards Checkpoint A, we might run into trouble if we then (also arbitrarily) decide to orientate the Laboratory towards Checkpoint B. It will cause a rotation, and there’s really no purpose. As a single point, an interaction from any direction constitutes an interaction for the entire point, regardless of what direction the interaction swooped in from. We can conclude that the Blain Laboratory can be said that its orientation can always arbitrary as long as it doesn’t change. Yet we run into a new problem here. The orientation of the Blain Laboratory is arbitrary, but with respect to what? With all the Lorentz transformations going on all over the place, what can we trust to maintain its angle of orientation with respect to the Blain Laboratory to prevent it from rotating with respect to light? There is no answer to be found among particles with mass. The only answer is to ensure that the Blain Laboratory maintains constant orientation with respect to incoming photons. We could choose any arbitrary angle, but a good rule of thumb is to simply assume the Blain Laboratory is always oriented towards any incoming photon, all the time, always. Your first choice will skew the angles of future choices, but it doesn’t affect final results of calculations. Even if the Blain Laboratory is at an angle of 0° to the first photon, it will then be at an angle of 0° +/- ϴ, for some arbitrary angle theta (ϴ), satisfying the constraints that the Blain Laboratory be stationary (non-rotating) and therefore orientated at some fixed angle with respect to an incoming photon. Rule of Thumb The Blain Laboratory is oriented towards any and every incoming photon, even multiple photons simultaneously, always. To summarize, we can fix Special Relativity by basing it upon the Blain Laboratory instead of the Galilean Laboratory. They’re similar, but the Blain Laboratory allows a new, specialized inertial state just for particles: arbitrary rotations. This addition might seem like it will only affect very particular domains, such as particle physics, but is has a major effect even on the large scale! POINT 8: This is not the same old Special Relativity. Look what happens when a train passes a train station platform: (i) collinearly, and (ii) not collinearly. Woah! ……………………………………………………… The figure above demonstrates the behaviour of the Blain Laboratory when a light source is moving collinearly with it versus when a light source is not moving collinearly. The first case works out exactly as Einstein would have expected. The second case most certainly does not. By the rule of thumb, the Blain Laboratory reorients (but does not rotate) towards every new photon, and the Lab basically tracks the train as it passes the station. This implies that the Lorentz transformation is no longer applied just once, for the single velocity of the train. The third diagram shows the velocity of the train as perceived by the Blain Laboratory. This result leads to a drastically different foundation for a new theory of gravity. It might just be worth the effort to continue down this path and build that theory of gravity. It may offer us a chance to connect Special Relativity and gravity (whatever its form) with quantum mechanics, finally unifying physics.
Posted on: Sat, 29 Nov 2014 08:29:12 +0000
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