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This number is typically bigger than one: the denser the material, the more the light is slowed down. However, at certain frequencies (e.g. near absorption resonances, and for x-rays), n will actually be smaller than one. This does not contradict the theory of relativity, which holds that no information carrying signal can ever propagate faster than c, because the [phase velocity]? is not the same as the group velocity. |
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This number is typically bigger than one: the denser the material, the more the light is slowed down. However, at certain frequencies (e.g. near absorption resonances, and for x-rays), n will actually be smaller than one. This does not contradict the theory of relativity, which holds that no information carrying signal can ever propagate faster than c, because the [phase velocity]? is not the same as the group velocity or the [signal velocity]?. |
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where vg is the group velocity. This value should not be confused with n, which is always defined with respect to the phase velocity. It is possible in some rare cases for the group index to be less than one (implying vg > c), but these cases always occur at frequencies corresponding to absorption resonances in the medium, which strongly attenuate and distort the waveform, making the group velocity of the wave essentially meaningless. In these cases, the [signal velocity]? of the wave vs is the rate that which energy is transmitted, and this is always less than c. Various attempts have been made to perform superluminal communication by exploiting these circumstances. |
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where vg is the group velocity. This value should not be confused with n, which is always defined with respect to the phase velocity. For frequencies corresponding to regions of anomalous dispersion in a material, it is possible for the group velocity vg to exceed the speed of light in a vacuum, c . While this would seem to indicate that superluminal communication is possible, in reality this is not so; in this case the information (or energy) of the light beam propagates at a rate known as the signal velocity: :vs = c2 / vg, which is always less than c if vg > c. |
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