Take a "wave" as we know it, an electromagnetic wave emerging from a transmitting antenna out into the free space around it. If we take a planar slice of that wave along the axis of outward propagation, and measure its "electric field component", we find two obvious and interrelated characteristics:

1) the wave varies its electric potential over space, and
2) the wave varies its electric potential over time.

The spatial variation means that, if we could "freeze" the wave's motion momentarily, and "walk along" its length with a "voltmeter", we would be able to measure a gradient in the potential-- a potential difference, a voltage-- between different points along the axis of travel. If we could quickly move past this "frozen", stationary wave pattern, sticking our separated voltmeter probes into it, we would get an "AC" reading on our meter as we moved past the static, "DC-like" "hills and valleys" of the wave's electric potential. If we traveled fast enough to display one or more "cycles" of voltage gradient per second, an oscilloscope would trace out the familiar sine-wave curve on its screen. (This is sort of like playing a phonograph record by holding it stationary and dragging the needle over it. "Unfreezing" the wave and detecting its passing with a normal radio receiver is like playing a record in the usual way-- where the record moves past a stationary needle. To those readers who don't know what a 'phonograph' is, I guess I'm betraying my age. Feel free to substitute "laser disk player" if it makes you feel better.)

If someone were to ask you what your "frozen" wave's frequency is, you would have to say "zero Hertz" (or cycles per second), because your wave is not moving, and frequency is how many hills and valleys pass a stationary measuring point in one second.

But there IS information embedded in the "shape" of the wave, waiting to be detected by relative movement between wave and detection device (radio). You can look down the wave and see humps and troughs, electrically speaking, so there is definitely a WAVELENGTH to each cycle, which would potentially affect the perceived frequency if the wave were moving. It stands to reason that, if we all agreed to allow our waves to travel at one, standard, fixed speed (the speed of light), the wavelength would directly influence the frequency (via an inverse proportion: frequency = speed of light divided by wavelength).

So you can, if you want, refer to this "static" wavelength variation in our frozen wave as a SPATIAL FREQUENCY-- which engineers routinely do in the field of image processing, where a highly-detailed picture graphic on a computer screen is said to have high spatial frequency components; while a soft, blurry picture is said to have a low spatial frequency content.

If we now "unfreeze" our electromagnetic wave and let it travel out freely from the antenna, and measure its frequency in the usual way, we're making a statement about how many of those cyclical hills and valleys wobble past in one second. Let's say we measure it with an oscilloscope.

Imagine that, at point "A" with respect to some arbitrary "ground" reference point, we measure a time-varying sine-wave wobble in the potential. Now we move our probe some distance away, to point "B". We detect a similar wobble, but we're not sure if the two "wobbles" occur at precisely the same instant in time.

So now we get the bright idea to use a "dual-channel" oscilloscope, which allows us to hook up two identical probes, spaced some distance apart. We find that a NORMAL EM wave shows a slight difference in voltage between points A and B, since the wave "hits" point A first and then point B only after a slight time delay. So point B's sine waveform is lagging slightly behind point A's in time, since the peaks and valleys of electrical potential are travelling between A and B in a small but finite time period. If we now SUBTRACT the reading at point B from that of point A, we will read a small sinusoidally-varying voltage which represents the difference in potential at a given moment in time -- the gradient -- between the two probes.

A normal EM wave is referred to as a "vector" wave because it has gradients of potential that have 1) magnitude and 2) a definite direction at any moment in time. In general we can say that if the electric potential is rising (going positive), we may depict it symbolically as an upward-pointing vertical arrow whose length depends on the magnitude of the potential with respect to "ambient" or no-wave conditions. If the potential happens to be falling, and has fallen to a lower value than ambient (going negative), we use a downward-pointing vertical arrow whose length corresponds to the magnitude or "voltage".

A GRADIENT-FREE WAVE OF "PURE POTENTIAL"

But now let's imagine a NEW kind of "wave"-- one without any spatial gradient at all. Contrary to what you may think, I am NOT talking about simply phase- cancelling two opposite-polarity electric waves, leaving a "zero", flat-line resultant (which is precisely how many of the Scalar EM researchers view the thing!).

Imagine that, at point "A", we measure a time-varying sine-wave wobble in the potential, with respect to a no-wave "ambient" reference potential. Now we move our probe some distance away, to point "B". We detect an identical wobble, which we display on our oscilloscope screen-- there's our sine shape again, but this time with NO time delay from that of point "A". Even if we move one of the probes to point "C", we measure exactly the same waveform-- and there's NO time lag between them. It's as if a long row of people decided to clap their hands exactly in synchronization, rather than one after another.

This type of wave could be called SCALAR because there is a MAGNITUDE in every part of the wave, but no DIFFERENCE in magnitude between any of its parts. If we used dual-probe measurements here, we would see ZERO GRADIENT along the wave.

This compares to your Physics text's use of the temperature of a room as an example of a scalar quantity-- the whole room is 72 degrees inside, with nice, even heating. There is therefore no directionality-- no gradient-- in the temperature. It's the same in all directions (space) at the same time.

Now, that doesn't mean you could not turn the heat off and take a temperature reading an hour later on a January day and not notice a difference! The room will be noticeably colder. But if it's EVENLY colder throughout the room, then the temperature is still a SCALAR quantity -- magnitude without direction -- when direction is defined in SPATIAL terms. If you look at it as the change over TIME, then you could call it "vectorial" rather than "scalar", but only if you choose to model the passing of TIME with your direction arrow, as opposed to modelling the difference in temperature from one SPATIAL point to another in the room.

Back to our "new" EM wave: Instead of room temperature, let's imagine that there is no measureable difference in potential between any two or more points along the wave, spatially. But let's say that, a second later, all points have suddenly risen, TOGETHER, the equivalent of several "volts" with respect to ambient. And then, another second after that, all points have suddenly dropped "negative" with respect to ambient, together and with no time delay between points. A measurement between any two SPATIAL points would continue to read "zero" even as the overall potential oscillated up and down. This would be an example of a SCALAR oscillation-- a SCALAR WAVE -- and no normal radio receiver would detect any signal since there is no measureable DIFFERENCE in potential from one point to the next. The radio itself is "bobbing up and down", electrically speaking, with the wave energy, so it cannot detect any spatial potential difference (voltage drop) between its own "ground" and "hot" side of its circuit.

Notice, also, that if all points vary exactly in step, with no time lag between them, this implies INSTANTANEOUS "communication" between all points.

The normal EM wave experiences a short time delay between points due to the fast but finite speed of light propagation time.

The scalar wave bobs up and down, but simultaneously at all points along its length, like a bouncing "DC offset" on the scope screen. So its "wavelength" has straightened out to INFINITE length -- straight and horizontal -- while its "frequency" or movement has all been transferred into the "time domain". We see it as the up-and-down bouncing of the value of potential all across the 'wave'. Its "information content" is all time-varying potential with no spatial gradient. Effective propagation speed, therefore, is INFINITE, since it took zero time for every point in the wave to experience the same variation in potential.

Our "frozen" wave, described earlier, had its "frequency" transferred totally into a "space domain" distribution of static hills and valleys. It had no time-variation at all. Its "information content" was all motionless spatial "shape" variations with no time variation. Its "time-domain" frequency went to zero Hz, since it was "frozen" motionless.

Our "normal", familiar EM waves are half-way in-between: they're both space- and time-varying entities.

BUT BOTH THESE WAVES ARE FANTASIES BECAUSE... RIGHT?

At this point you may be wondering why I would indulge in such fantasies as creating "stopped-motion" waves and "instantaneous, gradient-free" waves. Well, because I've found a way to model them mathematically/graphically which suggests how they may be engineered on the lab bench with the proper technology. And one of these wave configurations, or something along the same line, seems to fit the current description of the "Scalar" waves in Tom Bearden's Scalar Electromagnetics.

The seed for these ideas was in the many hours of frustration I experienced in trying to sort out Tom Bearden's clear-as-mud hints, spread across his many books and papers, and mutated and developed across several years of research and publication on his part.

As I've already elaborated on in my critique file, ANDERSEN.ASC/.ZIP/.HTM, I've come up with several mutually-contradictory ways of interpreting Bearden's various descriptions of what a scalar wave is and how to go about making one. Originally it appeared that all you needed to do is phase-cancel a carrier wave, either by outphasing twin transmitters/antennas pointing at a common target, or by winding non-inductive coils such as the bifilar, caduceus, or Mobius types. Every indication was that such an approach simply nulled the superposed output wave to "zero" and yet we were supposed to believe that there was an invisible "stress on the aether" hidden inside that null. (I have noted elsewhere that if the Poynting vector is regarded as a "real" component of the wave, it would account for a longitudinal component remaining even after the transverse electric and magnetic vectors had been cancelled out. I also recognize that Bearden denies any transverse components in a vacuum EM wave.) Besides, "psychics" and other "sensitives" assert that they can sense these "tachyon energy" fields around such coils.

William Hooper claimed he could measure a "motional BxV field" akin to gravitational field around such coil arrangements. (NASA has allegedly tried to reproduce Hooper's experiments but concluded that the effect, if any, is negligible, at least with non-superconducting coils.)

Gelinas took out a patent, for Honeywell Corp., on an "A-field, magnetic vector potential communications device" consisting of a current-modulated toroidal coil (transmitter) and a Josephson Junction (SQUID-like receiver), which was predicted to work through Faraday shielding. (Followup unknown.)

All of these schemes, like some macroscopic version of the AHARONOV-BOHM EFFECT (cancel the B-field and you still have an A-field, which can still affect electrons' phases), supported the notion that "Science" was all wrong about vector-zeroing two or more waves of energy: and Tom Bearden identified this as the very core concept of his newly-announced (early 1980s) Scalar Electromagnetics.

After a while I began to notice (late 1980s) that he was relying much more heavily on an explanation for an "undulatory" theory of gravitation proposed by the famous mathematician E.T. Whittaker (1903,4), which set forth a "potential" consisting of pairs of bi-directional waves, essentially an infinity of such pairs, in a harmonic sequence. Bearden applied this concept to his 'electrogravity' or Scalar EM. By varying the internal structure of this mixture, one could tailor an artificial "potential" which would have intensity characteristics that matched those of gravity, with its "inverse- square law". (This view, interestingly, implies that a plain vanilla "DC" potential can be broken down into harmonic spectral components via a Fourier transform!)

As time went on, Bearden began to add some of his own wrinkles to Whittaker: Not only was each frequency pair a standing wave composed of a "wave" radiating out from the center of a body and an "antiwave" coming back into the body from all points outside-- bi-directional EM waves-- but now Bearden began to specify that the incoming "antiwave" must be a true PHASE CONJUGATE of the outgoing wave-- in other words, its TIME-REVERSED TWIN (similar to the "advanced" vs. "retarded" waves in the Wheeler-Feynman ABSORBER theory), not just another positive-time wave propagating in the opposite direction.

So the earlier view of uni-directional, phase-nulled, zero-vector "scalar" waves had now metamorphosed into a harmonic "lattice" of bi-directional wave pairs where one wave in each pair was time-reversed.

In the meantime, the researchers, New Agers and psychics were still winding non-inductive coils and claiming that their "do-nothing" devices were actually putting out beams of invisible (more invisible than EM waves!) scalar energy. It seems that Bearden had moved on, leaving his earlier followers behind.

When I wrote ANDERSEN.ASC, critiquing what I saw as a confusing paradigm shift in his concepts of scalar EM, Bearden wrote back (see BDNLTR.HTM) to clarify some of his views. Though very cordial and helpful, it was filled to the brink with his up-to-the-minute researches into electrodynamics and he did not directly address all of the points made in my ANDERSEN.ASC file, although toward the end he did attempt to answer some of those points.

One of the remarks he made was that 'you can make all kinds of "scalar"-type waves'. (Of course, I would like to know which ones HE "believes" in, and which are 'useless' as far as Scalar EM is concerned!)

Another remark, which led to Ed Mason's SCALAR7.HTM and followup Q&A with me, was that the earlier, phase-nulled coil configurations DID INDEED ZERO to NOTHING.... most of the time.... but SOMETIMES you could get an apparent anomalous gravitational (or other) effect if you did your "vector-zeroing" with a NONLINEAR CORE at the center of your coil(s).

This remark, along with his more recent mention of Richard W. Ziolkowski's "adding the PRODUCT set" of waves, to Bearden and Whittaker's SUMS of waves, brought the subject of MODULATION into the picture.

MODULATION IS ESSENTIALLY MULTIPLICATION

Along these lines, in an article called "Tesla's Electromagnetics And its Soviet Weaponization", found on page 113 of the book "Analysis of Scalar/Electromagnetic Technology", Tesla Book Co., 1990, Bearden states:

"Equipment to produce such scalar waves can easily be designed.... One simply opposes or adds E fields and/or B fields to produce resultant vector zeroes. In addition, a modulating process should be utilized, as opposed to a simple mixing of the waves, so that the EM components lock together into a single wave."

The troubling part, for me, is his insistence on one half of the mix being TIME-REVERSED waves:

"The only way to effectively do this is to couple a normal EM monochromatic wave with its phase conjugate wave. The two are in phase spatially, and 180 degrees out of phase in the time dimension." [footnote, p. 113]

The reasons I am troubled are brought out in my ANDERSEN.ASC file; not the least of which is the fact that he says that you need a time-reversed wave component in your mix to make a scalar wave--- and then says that when optics people pump a laser with counterpropagating (normal, positive time laser) beams, they're creating a scalar wave in the mirror material itself! So do you need a time-reversed wave or don't you? And is it the "scalar wave" or is it the "time-reversed wave" that allows antigravity production? Or are they the same? Or interchangeable??? This point, in my opinion, has never been made clear in all of Bearden's writings to this day.

Suffice it to say that I find his use of wave terminology imprecise and I do not know how to resolve the difficulties-- ESPECIALLY his diagram of a multi- harmonic "scalar potential" consisting of bi-directional sine wave components that seem to "snake past" each other like passing trains on adjacent, parallel, curving tracks-- when that is NOT the way we depict wave travel. Waves don't "snake along"; they simply MOVE along, intact (well, actually they expand in a spherical manner like the layers of a growing onion, but you know what I mean!). So I still can't visualize what Bearden means by the phrase "spatially in phase, 180 degrees out of phase in the time dimension". Yet I do understand what Wheeler and Feynman meant. But I can't figure out if that's what Bearden means, whether he has adopted their model or not!

HOWEVER---

There seems to be a way to get around these difficulties if we forget about explicitly time-reversing the waves, and do the equivalent through the use of multiplication/modulation.

Modulation is essentially multiplication of one wave with another, point by point in the time domain. So I decided to see what the "movie" would look like if I ran two waves into each other (counterpropagating, bi-directional) but MULTIPLYING their instantaneous values rather than ADDING them. Adding or summing leads to a STANDING WAVE, which implies a LINEAR background (uncurved spacetime). Multiplying or CROSS MODULATING them-- which is equivalent to "adding" against a NONLINEAR background (curved spacetime), like adding exponents is equivalent to multiplying the base numbers, leads to a curious new wave which looks like a "frozen" sine wave of TWICE the spatial frequency, riding up and down on a moving "DC offset". This was new! [You can view this by downloading my software animations, SCW.EXE and 4WAVE.EXE, from this website.]

I also did some thinking about the type of "modulation" I was modelling by simply multiplying two waves together point by point. It was like AM, but more precisely like "carrier-suppressed double-sideband", for the radio engineers out there. I thought about the similarities between an object and its "mirror reflection", about the apparent spectral "splitting" that occurs in Stimulated Brillouin Scattering (a method of producing phase conjugate waves) and then realized that, if we were to heterodyne an AM radio carrier with another wave at the same frequency, so that the difference frequency was "zero beat", the other beat frequencies that would be produced would be an upper sideband, now shifted down into the audio range, and a lower sideband WHOSE FREQUENCY WAS SHIFTED TO BELOW ZERO HZ-- therefore "reflected" back up into the "positive" frequencies-- with reflected (reversed) phase-cycling direction. Therefore the lower sideband is actually a time-reversed or phase-conjugate copy of the upper sideband, and now the lower is "folded" back onto the upper so that the two are perfectly superposed in the frequency domain, cycling their phases together, in the same way that Optics people see their phase-conjugate image as a length-reversed version of the original wave! [Which relates to the Distortion Correction Theorem in optics; see the full development of this in AM.ASC]

Then I thought about another mathematical curiosity that we're all trained to know and despise: the fact that numbers have dual roots. For example, the square root of 16 is 4: 4x4=16. But -4 is also a valid root: -4x-4=16. Although the exact connection is still a little hazy in my mind, it occurred to me that all these concepts were interrelated on a basic level, along with Bearden's observation (along with many others) that the Wave Equations "run both ways" -- forward and backward. In time. Or length, if you're an Optics guy. Still more seductive is to see a connection to the "real" and "virtual" images encountered in optics and holography. And, wonder of wonders, the references to optical phase conjugation are starting to mention, more and more often, its kinship to holographic principles.

------------------ continued in file PRODWAV2.HTM ---------------------