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OK suppose you have a detector placed at a distance L from the X-wave antenna whose arrival time of the longitudinal signal is shorter than the time it takes for the peak to reach the front, could we then use a matrix array network of such tiny senders and receivers, maybe at the micron scale if not at the nano-scale, to make an ultra-fast computer chip?

What about for X-wave radar? Can the time it takes the peak to reach the front correspond to a great enough distance for useful radar ranging? Need some way to delay the peak relative to the front. Can the peak be switched to a delay line after the front has left the transmitting antenna?

These longitudinal X-waves sound like the urban legends of Tesla scalar waves.

On Aug 23, 2010, at 5:40 PM, Waldyr A. Rodrigues Jr. wrote:

If you look carefully to the extraordinary solutions of Maxwell equations
you will find that they have longitudinal electric and/or magnetic fields
(which I found, can be modulated)...They FAA (finite aperture
approximations) can be generated with antennas (some I invented) and can be
transmitted for long distances. The peaks of the FAA travel at superluminal
speed for a while (until the peak arrives at the front), then the pulse
explodes in two, it is amazing ...

-----Mensagem original-----
De: JACK SARFATTI [mailto:sarfatti@pacbell.net] Enviada em: segunda-feira, 23 de agosto de 2010 21:27
Para: Waldyr A. Rodrigues Jr.
Assunto: key question re: X-Waves

Is there any possibility of real signaling faster than light with X-Waves
e.g. with practical application to fast computing and/or propulsion?
From what I can tell orthodox causality is never violated - no genuine
faster than vacuum light propagation of energy and decodable information.
Why was... interested in X-wave antennas? Is there X-wave radar? What
advantage does it have over ordinary radar?

So far no actual faster-than-light messaging seems possible with these finite aperture EM X-Waves, but apparently they do have advantages over ordinary EM waves - possible application to radar, sonar, oil-exploration, computing, propulsion? I don't know yet.

Waldyr wrote in

J. Emlio Maiorino and Waldyr A. Rodrigues, Jr.
January, 25 2001

"During the last decade of the last century two kinds (a) and (b) of super-
luminal wave motion have been theoretically predicted and experimentally
verified. They are:

(A1) Superluminal group velocities of electromagnetic field congurations
propagating in dispersive media with absorption or gain [18].

(A2) Superluminal group velocities of tunneling microwaves [38, 39, 40,58].

(A3) Superluminal group velocities of tunneling electrons [73].

(A4) Superluminal propagation of microwaves in air [48, 65, 109].1

(B) Superluminal velocities of peaks of QUPWs [117, 133].2

The main purpose of this work is to clarify the meaning of the superluminality
involved in these phenomena, and to investigate its implications (if
any) for the foundations of Relativity and Quantum Theory. ...

we found it a good idea to begin
this introduction by recalling the main results of the theory of Sommerfeld
and Brillouin (SB) [14], who long ago investigated the propagation of light in
dispersive media with absorption. They studied the propagation in a dispersive
medium (in the z-direction) of a particular transverse electromagnetic
field configuration which Brillouin called a signal ...

Such a signal with compact support in the time domain is generated by
an abrupt turn-on and then a turn-off of a special source (see e.g., [156])
and has a front [21, 145], i.e., the discontinuity defined by eq.(1.2). The
first important observation to be made is that Fourier theory implies that
electromagnetic signals with compact support in time domain in general have
infinite frequency spectra ...

We also observe that signals with a Fourier transform defined over a
finite frequency spectrum, are in general non-causal. This means the following:
a band limited frequency spectrum pulse shows signal components at negative
times. ...

Sommerfeld & Brillouin introduced five different types of velocities:5

(i) The phase velocity, at which zero crossings of the carrier wave moves.

(ii) The group velocity, at which the peak of a wave packet moves.

(ii) The front velocity, at which the first appearance of a discontinuity moves.

(iv) The energy velocity, at which the energy would be transported by the wave.

(v) The signal velocity, at which the half-maximum of the wave amplitude moves.

3The opposite statement is not true, i.e., a signal with have infinite frequency spectrum
is not necessarily finite in the time domain. A well known example is that of a Gaussian
wave packet.

4This is a general result. Indeed, from Fourier theory (see, e.g., [137]) it follows that
any pulse with a band limited frequency spectrum is unbounded in the time domain, i.e.,
is acausal.

5The precise definitions of the ve kinds of velocities are given in Chapter 6.

Sommerfeld & Brillouin (SB) found that in a region of anomalous dispersion 6 near an absorption
line, all velocities (i-v) are different. In particular, they found that the phase
and group velocities may be superluminal, without upper bound, and even
negative! They concluded that group velocities, when superluminal or negative,
have no meaning, and this conclusion is repeated in almost all textbooks,
as e.g. [141, 67]. Nevertheless superluminal (and even negative) group
velocities have a precise meaning, being associated with the extraordinary reshaping
phenomenon, ...

SB found that the front velocity is always the velocity of light in vacuum.
Moreover, in all situations studied by them it was found that the energy and
signal velocities were subluminal.

The natural question that experimentalists ask themselves after the experimental
observation of superluminal group velocities predicted by the
studies of SB is: are there situations in which the energy and signal velocities
may become superluminal?

This question is indeed very important because if genuine superluminal
energy and signal velocities were possible, the Principle of Relativity (PR)
would be in serious danger.7

Now, the fact is that some authors claim that their experiments show superluminal
signal velocities and superluminal velocities of energy transport.

Among these experiments are tunneling of microwaves experiments [97], an
experiment showing the superluminal tunneling of a single photon wave function
[140] and experiments in dispersive media with gain [18]. Even experiments
showing negative group velocities have been performed [11]8. Are
these claims supported by theoretical analysis?

to be continued - leave them hanging twisting in the wind. ;-)