![]() In other words, for an observer in system S’ the effect which occurs at B would precede in time its cause which originates at A.” It is evident that we could then take a velocity u great enough uV/C^2 will be greater than one. The same thing, more generally, holds for models.Īs Tolman put it in 1917: “Let us suppose now that there are no limits to the possible magnitude of the velocities u and V, and in particular that the causal impulse can travel from A to B with a velocity u greater than that of light. Just an abstraction of it. The cult of equations is naive, interpretation is everything. Then I use the usual Relativity formula (due to Lorentz) of time as it elapses in S’:Įquations help, but they are neither the beginning, nor the end of a story. The time elapsing between the cause and its effect as measured in the units of system S will evidently be as follows in the calligraphy below. ![]() The problem of faster than light communications can be attacked in the following manner.Ĭonsider two points A and B on the X axis of the system S, and suppose that some impulse originates at A, travels to B with the velocity u and at B produces some observable phenomenon, the starting of the impulse at A and the resulting phenomenon at B thus being connected by the relation of cause and effect. Why? Time is local, faster than light data travel is nonlocal. One could synchronize all clocks on all planets in the galaxies, and having faster than light communications would not change anything. Wikipedia weirdly claims that faster than light communications would allow to travel back in time. But the interpretation is apparently less so. The mathematics are trivial (they are reproduced in my picture below). There is actually a “proof” of that alleged impossibility, dating all the way back to Einstein (1907) and Tolman (1917). For example, are there communication speeds faster than light? (Throwing some material across will not work: its mass will increase, while its speed stays less than c.) The question naturally arises whether velocities which are greater than that of light could ever possibly be obtained in other ways. One could furiously imagine a spaceship somehow surfing on a wave of warped space, expanding for the same obscure reason same obscure reason as the Big Bang itself, that is…) 100c/10 = 10c, according to standard cosmology. Thus it expanded at the minimum average clip of ten billion light years, every billion years. The grossest, yet simplest, proof of that is simple: the observable universe is roughly 100 billion light years across, and it is ten billion years old. ![]() The subject is not all sci-fi: modern cosmology brazenly assumes that space itself, after the alleged Big Bang, expanded at a speed at least 10^23 c (something like one hundred thousand billion billions time the speed of light c). It is also clear that adding impulse to a mass will make it more massive, while its speed will asymptotically approach that of light (and, as I explained, the reason is intuitive, from Time Dilation). From the basic equations of relativity it is clear that if one adds speeds less than the speed of light, one will get a speed less than the speed of light. There are theories everywhere, and the more ingrained they are, the more suspiciously they should be looked at. ![]()
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