Phase and group waves contain no information that is not dependent on their component luminal waves: they cannot transmit information faster than light. That's one of the points made by Chen. However, Van Flandern contends that the propagation of gravity does indeed transfer information faster than light: it "tells" the vector of interaction where and how to interact. This is what Van Flandern means when he defines the speed of gravity: "The 'speed of gravity' refers to whatever causally links the source of gravity to the 3-space acceleration of a target body." (emphasis added) This plain-language definition of an information-carrying wave was given a name by Sommerfield and Brillouin: the "front" wave, as detailed in "Superluminal but Causal Wave Propagation" by Mojahedi and Malloy. The authors explain the mathematical description of the front wave, and demonstrate that:

"...under no circumstances the so called 'front velocity' may exceed the speed of light in a vacuum, and in fact under all circumstances the 'front velocity' is exactly luminal. In other words, the requirement of Einstein causality that no 'signal' (information) can be transmitted superluminally is satisfied in all cases, since the 'front velocity' is always luminal. This means that the presence of the genuine information should not be associated with the pulse maximum, half maximum, or the envelope, but indeed is contained within the singularities (points of non-analyticity) of the pulse."

"The mathematical proof that no signal (information) may be detected sooner than t₀ = x/c can be seen via contour integration of an expression such as Eq. (8)..."

I won't try to type in the relevant equation in html, because that would make my eyes bleed--you'll have to look at the Mojahedi-Malloy paper. But the point is, Van Flandern is confused: he's claiming that experiments such as Walker-Dual and the later Walker paper, both of which deal explicitly with phase and group velocities, show something of import about front velocity as defined by Sommerfield-Brillouin and presented by Mojahedi-Malloy.

It's a bait-and-switch: the experiments Van Flandern cites are not relevant to the physical quantity Van Flandern is dealing with.

cable, I would think that for an unmodulated signal 1.) there would be no phase velocity, and possibly no group velocity, definable; and 2.) the information carried by the wave would be defined only by the non-analytic signular points where the field transmitter "turns on" and when it "turns off"--and so a receiver must wait until the entire signal has been transmitted before knowing the full "information" content of the field. (In this case I suppose that would be a simple sum of the constant field vector over the elapsed time, since there is no other information carried.)

But all EM waves are modulated, strictly speaking, even if one proposes a theoretically monochromatic transmission--ie simple sine waves. After all, the definition of an electromagnetic wave is a field that varies over time, eh? And since Walker-Dual explicitly used oscillating fields they were explictly using modulated waves.

That's what Chen was getting at, I think, when he said that "...there is no way one can transmit information by single sine modulation. Any true information content must possess some decently complicated Fourier spectrum. We should thus in fact define 'information' as a signal with some decently elaborate Fourier spectrum."

Such a signal may well produce superluminal phase or group velocities, but as Mojahedi and Malloy point out, that violates neither special relativity nor causality. Van Flandern's superluminal gravity, on the other hand, does violate special relativity, as he himself admits.



<font size=-1>[ This Message was edited by: DStahl on 2003-01-13 17:56 ]</font>