Wave Propagation Physics
In order to understand this seemingly contradictory behavior it is important to point out that electromagnetic propagation is characterized by five unique waveform velocities [Brillouin L, Wave Propagation and Group Velocity (Pure and Applied Physics), New York: Academic Press, 1960]. These include:
- Phase velocity – the speed at which the phase of any one spectral frequency component of the wave travels.
- Group velocity – the speed at which the variations in the shape of the wave’s amplitude (known as the modulation or envelope of the wave) propagates (see diagram below).
- Front velocity – the speed of an abrupt signal discontinuity (signal abruptly turned on or off). It is considered as the very beginning of the signal in time, and it never exceeds “c”, the speed of light (see diagram below).
- Energy velocity – the speed of energy transfer.
- Signal velocity – the speed of information transfer, which, under various conditions, may be equivalent to one or more of the above four velocities.
The “front velocity will correspond to the speed at which the first, extremely small (perhaps invisible) vibrations will occur, while the signal velocity yields the arrival of the main signal, with intensities on the order of the magnitude of the input signal.” [Brillouin]
In most cases, the signal velocity is equivalent to both the group and energy velocities. While the front velocity cannot exceed the speed of light, in special cases (e.g. media or circuitry that amplifies the initial or anterior-most portion of a waveform and attenuates the posterior portion), “… the group velocity … can be greater than the velocity of light, can be infinite and even negative!” [Brillouin]. That is, the detection of a pulsatile input or extended-in-time waveform at the output of the medium can precede its complete detection of the waveform at the input.
During the time interval between the arrival of the wavefront (front velocity) and the actual detection of the group waveform, electromagnetic energy begins to propagate through the medium, the magnitude of which is not detectable until the oscillations achieve sufficient amplitude. These very early, very low amplitude (typically undetected) perturbations (referred to as “forerunners” by Brillouin) actually contain sufficient information to reproduce a temporally advanced signal. Signal Advance Technology acts to temporally advance the wave envelope of an analog signal resulting in earlier detection.