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If the world is to be understood, if we are to avoid such logical paradoxes when traveling at high speeds, there are some rules, commandments of Nature, that must be obeyed. Einstein codified these rules in the special theory of relativity. Light (reflected or emitted) from an object travels at the same velocity whether the object is moving or stationary: Thou shalt not add thy speed to the speed of light. Also, no material object may move faster than light: Thou shalt not travel at or beyond the speed of light. Nothing in physics prevents you from traveling as close to the speed of light as you like; 99.9 percent of the speed of light would be just fine. But no matter how hard you try, you can never gain that last decimal point. For the world to be logically consistent, there must be a cosmic speed limit. Otherwise, you could get to any speed you wanted by adding velocities on a moving platform.
Let us suppose that an explosion occurs on Mars, which is observed by an astronomer on earth, who records the instant when he sees the flash. If light travelled instantaneously with an infinite velocity, this instant would coincide with the time... recorded by the... observer on Mars. In this way a meaning could be attached automatically to absolute time and the simultaneity of events at different places; indeed, the classical theory is now regarded as the limiting form of Einstein's theory when the velocity of light becomes infinite. But as there is a mass of experimental evidence supporting the view that light takes a finite time to travel... the terrestrial observer must correct the time recorded on his watch. This correction... will depend on assumptions concerning the velocity of light and the measurement of distance. Thus the concept of a world-wide simultaneity ceases to be a primitive idea.
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I have lately spent some Thoughts relative to the Nature of Light, whether it be subject to the common Laws of Motion. In this particular Newton seems to contradict himself. For in his Principia Sect. 14th he applies the common Laws of Motion to account for Reflection and Refraction, as he does also in one Part of his Optics where he proves the Sine of Incid. to Sine Refr, in a given in a given Ratio. But in another Part he says, “nothing more is requisite for producing all the Variety of Colours and Degrees of Refrangibility than that the Rays of Light be Bodies of different Sizes, the least of which may make Violet, and the Greatest the Red"; this manifestly is not consistent with the Theory of Motion applied to Bodies, where the Magnitude of the Bodies is of no Consequence. Now it is evident that if the common Theory of Motion can be applied to Light, the Red Light must have had the greatest Velocity before Incidence, as it suffers the least Deviation, for if the Vels of all the Difft colour'd Light were equal before Incidence, they must by Newton's Principia Sect. Sect. 8. Prop. 1. have continued equal after, and therefore must have suffered the same Deviation. The Determination of this Point seems to be of considerable Importance, as we so often apply the Theory of Motion to Light.
...the principle of the limiting character of the velocity of light. This statement... is not an arbitrary assumption but a physical law based on experience. In making this statement, physics does not commit the fallacy of regarding absence of knowledge as evidence for knowledge to the contrary. It is not absence of knowledge of faster signals, but positive experience which has taught us that the velocity of light cannot be exceeded. For all physical processes the velocity of light has the property of an infinite velocity. In order to accelerate a body to the velocity of light, an infinite amount of energy would be required, and it is therefore physically impossible for any object to obtain this speed. This result was confirmed by measurements performed on electrons. The kinetic energy of a mass point grows more rapidly than the square of its velocity, and would become infinite for the speed of light.
Velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments of 'MM'. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.
...the famous assertion by Einstein that the length of a rod depends on its velocity and on the chosen definition of simultaneity. ...is based on the fact that we do not measure the length of the rod, but its projection on a system at rest. How the length of the projection depends on the choice of simultaneity can be illustrated by reference to a photograph taken through a focal-plane shutter. Such a shutter... consists of a wide band with a horizontal slit, which slides down vertically. Different bands are photographed successively on the film. Moving objects are therefore strangely distorted; the wheels of a rapidly moving car for instance, appear to be slanted. The shape of the objects in the picture will evidently depend on the speed of the shutter. Similarly, the length of the moving segment depends on the definition of simultaneity. One definition of simultaneity differs from another because events that are simultaneous for one definition occur successively for another. What may be a simultaneity projection of a moving segment for one definition is a "focal-plane shutter photograph" for another.
Some of the effects predicted by the theory [of loop quantum gravity] appear to be in conflict with one of the principles of Einstein's special theory of relativity... that the speed of light is a universal constant. ...Photons of higher energy travel slightly slower than low-energy photons. ...the principle of [general] relativity is preserved but Einstein's special theory of relativity requires modification. ...A photon can have an energy-dependent speed without violating the principle of [general] relativity!
A feature of the relativity theory which seems to have aroused special interest among philosophers is the absoluteness of the velocity of light. In general velocity is relative. If I speak of a velocity of 40 km/s, I must add “relative to the earth”, “relative to Arcturus”, or whatever reference body I have in mind. No one will understand anything from my statement unless this is added or implied. But it is a curious fact that if I speak of a velocity of 299.796 km/s, it is unnecessary to add the explanatory phrase. Relative to what? Relative to any and every star or particle of matter in the universe.
The only thing known to go faster than ordinary light is monarchy, according to the philosopher Ly Tin Wheedle. He reasoned like this: you can't have more than one king, and tradition demands that there is no gap between kings, so when a king dies the succession must therefore pass to the heir instantaneously. Presumably, he said, there must be some elementary particles — kingons, or possibly queons — that do this job, but of course succession sometimes fails if, in mid-flight, they strike an anti-particle, or republicon. His ambitious plans to use his discovery to send messages, involving the careful torturing of a small king in order to modulate the signal, were never fully expanded because, at that point, the bar closed.
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