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Speed of Light and Theory of Relativity

The only reason behind the existence of the Special Theory of Relativity is the experimental fact that the speed of light in a vacuum is independent of any motion of the source or receiver. This is because the usual concept of speed is inconsistent with the invariance of c unless one redefines length and time units accordingly.

In his paper 'On the Electrodynamics of Moving Bodies' (published in 1905), Einstein derives his theory by considering the propagation of a light signal in two different reference frames, each of which being defined by its own set of detectors (stop-watches) that should serve to define the locations (and thus the speed of light) in each frame. Two different sets of detectors would indeed by necessary if the speed of light is invariant in each reference frame, but Einstein then suddenly makes the assumption that he doesn't need the second set of detectors, but can obtain the location in the primed frame by using the location in the unprimed frame and projecting this into the primed frame by means of the Galilei transformation x'=x-vt (note that here x' is not the variable x' in Einstein's 1905 paper but the transformed coordinate (which he denotes as ξ)). This however corresponds to the usual concept of 'speed' which can not be applied to light (this is for instance immediately apparent from the example in the box below). Half aware that this obviously would lead to an inconsistency with the principle of the invariance of c, he then decides to multiply the right hand side of the equation by an ad-hoc factor γ, i.e. x'=γ.(x-vt), such that the equation is formally valid again. The rest of his derivation is then devoted to determining this ad-hoc factor γ for this so called 'Lorentz transformation'. It should be obvious however that this procedure is no less mathematically flawed than having for instance the inconsistent 'equation' 1=2, multiplying the right hand side by a factor k , i.e. 1=k.2, and then...

The only reason behind the existence of the Special Theory of Relativity is the experimental fact that the speed of light in a vacuum is independent of any motion of the source or receiver. This is because the usual concept of speed is inconsistent with the invariance of c unless one redefines length and time units accordingly.

In his paper 'On the Electrodynamics of Moving Bodies' (published in 1905), Einstein derives his theory by considering the propagation of a light signal in two different reference frames, each of which being defined by its own set of detectors (stop-watches) that should serve to define the locations (and thus the speed of light) in each frame. Two different sets of detectors would indeed by necessary if the speed of light is invariant in each reference frame, but Einstein then suddenly makes the assumption that he doesn't need the second set of detectors, but can obtain the location in the primed frame by using the location in the unprimed frame and projecting this into the primed frame by means of the Galilei transformation x'=x-vt (note that here x' is not the variable x' in Einstein's 1905 paper but the transformed coordinate (which he denotes as ξ)). This however corresponds to the usual concept of 'speed' which can not be applied to light (this is for instance immediately apparent from the example in the box below). Half aware that this obviously would lead to an inconsistency with the principle of the invariance of c, he then decides to multiply the right hand side of the equation by an ad-hoc factor γ, i.e. x'=γ.(x-vt), such that the equation is formally valid again. The rest of his derivation is then devoted to determining this ad-hoc factor γ for this so called 'Lorentz transformation'. It should be obvious however that this procedure is no less mathematically flawed than having for instance the inconsistent 'equation' 1=2, multiplying the right hand side by a factor k , i.e. 1=k.2, and then...

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