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group velocity - 01-08-2007, 02:58 PM

Without directions the group velocity of electromagnetic waves is the speed of the envelope of wave packets, while each packet would be the superposition of infinitely many individual uniform waves having the same amplitude, wavelength, and frequency. However, two of these waves could want to share the same space-time coordinate even though at every instant many do share the same time but at different places. This allows reality to separate into past, present and future for those waves who wanted to share the same space.

On the other hand, for those waves, being able to share the same time would be forced to possess the same energy. Nevertheless, these singular wave energies could be added if and only if these waves also share the same space.

Two waves are said to be in phase if the difference of their phase angles is zero. Then they travel at superluminal phase velocity. If all waves travel at the same phase velocity then they form continuous space-time (true vacuum). Otherwise, if the phase angle difference is exactly 180° or p radians then they are completely out of phase. If all waves are completely out of phase then they form stationary quantized space and both their group and phase velocities are all zero. If the phase angle difference is exactly 90° or p/2 radians then they form electromagnetic waves of photons whose group and phase velocities are equal to the speed of light measured relative to the true vacuum. For all other phase angles between 0° and 90°, between 90° and 270°, between 270° and 360°, the superposed waves are standing matter waves whose group velocities never exceed the speed of light.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
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