Characteristics of Relativistic After-effects

 13 July 02:30   

    In classical physics, ω and k for ablaze are accompanying by

    :$omega\; =\; c\; k\; ,$

    In relativistic physics, weve apparent that for after-effects with no appropriate advertence frame, such as light, ω and k are accompanying by

    :$omega^2\; =\; c^2\; k^2\; +\; mu^2\; ,$

    If μ=0 then the relativistic blueprint reduces to the classical, so we can accept that, for light, μ does according zero.

    This agency that ablaze does not accept a mimimum frequency.

    If μ is not aught then the beachcomber getting declared are dispersive. The appearance acceleration is

    

    :$u\_p\; =\; frac\; =\; sqrt\}$

    This appearance acceleration consistently exceeds c, which at first may assume like an abstract conclusion. However, the accumulation acceleration of the beachcomber is

    

    :$u\_g\; =\; frac\; =\; frac\}$

    = frac = frac

    which is consistently beneath than c. Back beachcomber packets and appropriately signals bear at the accumulation velocity, after-effects of this blazon are physically reasonable even admitting the appearance acceleration exceeds the acceleration of light.

    Another absorbing acreage of such after-effects is that the beachcomber four-vector is alongside to the apple band of a beachcomber packet in spacetime. This is calmly apparent by the afterward argument.

    The spacelike basic of a beachcomber four-vector is k, while the timelike basic is ω/c . The abruptness of the four-vector on a spacetime diagram is accordingly ω/kc. However, the abruptness of the apple band of a beachcomber packet affective with accumulation acceleration is c/u_g, which is aswell ω/kc .

    Note that if we accept k is aught we accept ω=μ. In this case the accumulation acceleration of the beachcomber is zero. For this cause we sometimes alarm μ the blow abundance of the wave.