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lalbatros
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Question on "Two theorems for the group velocity in dispersive media"
In the paper (1), the authors show that the group velocity can be faster than light, slower than light, infinite, or even negative without contradicting the causality principle.
I have no doubt about the validity of this result, simply by considering some examples.
However, their derivation is based only on the causality principle.
The causality principle, as I understand it, does not forbit faster than light transmission of a signal.
The causality principle only assumes that effects follow their cause.
In the derivation, the causality principle is formulated from the Kramers-Kronig relation.
There is no further hypothesis about the refraction index.
It is not even assumed that it must conform to classical relativistic physics.
This where I have a problem.
Indeed, the index of refraction is the result of the responses of the material to an excitation.
These responses should satisfy the Maxwell's equations and the laws of motion from special relativity.
Therefore, in these responses, the speed of light should play a particuliar role: never "a signal" should go faster than light.
My impression is that the limitation by the speed of light is not taken into account by only using the Kramers-Kronig relation.
Therefore, I cannot be totaly sure that the derivation in (1) is fully valid.
I cannot exclude that, by taking the limitation by the speed of light into account, the result would not be modified.
One way, maybe, to solve this problem could be the use a retarded potentials formulation where the limitations by the speed of light would be automatically taken into account.
Could you help me on that question?
(1) http://physics.princeton.edu/~mcdonald/examples/optics/bolda_pra_48_3890_93.pdf
In the paper (1), the authors show that the group velocity can be faster than light, slower than light, infinite, or even negative without contradicting the causality principle.
I have no doubt about the validity of this result, simply by considering some examples.
However, their derivation is based only on the causality principle.
The causality principle, as I understand it, does not forbit faster than light transmission of a signal.
The causality principle only assumes that effects follow their cause.
In the derivation, the causality principle is formulated from the Kramers-Kronig relation.
There is no further hypothesis about the refraction index.
It is not even assumed that it must conform to classical relativistic physics.
This where I have a problem.
Indeed, the index of refraction is the result of the responses of the material to an excitation.
These responses should satisfy the Maxwell's equations and the laws of motion from special relativity.
Therefore, in these responses, the speed of light should play a particuliar role: never "a signal" should go faster than light.
My impression is that the limitation by the speed of light is not taken into account by only using the Kramers-Kronig relation.
Therefore, I cannot be totaly sure that the derivation in (1) is fully valid.
I cannot exclude that, by taking the limitation by the speed of light into account, the result would not be modified.
One way, maybe, to solve this problem could be the use a retarded potentials formulation where the limitations by the speed of light would be automatically taken into account.
Could you help me on that question?
(1) http://physics.princeton.edu/~mcdonald/examples/optics/bolda_pra_48_3890_93.pdf
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