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Phase Conjugate Waves and their Relation to Scalar Electromagnetics

Jan. 22, 1996  

Anyone who has read enough about Scalar Electromagnetics, as described in Tom Bearden's books and papers, has noticed that since the late 1980's he has been emphasizing the importance of that mysterious phenomenon known as Phase Conjugation, or Time-Reversal of waves, in his writings on Scalar EM.

Just what are "time-reversed" waves? What exactly is their relationship to Scalar Electromagnetics? How does phase conjugation fit in with earlier works by Bearden which seemed to favor a simpler "180 degree phase cancellation" zero-vector approach to the engineering of spacetime stresses for the purposes of gravity/time bending?

This paper is both an overview of phase conjugation in the context of Bearden's work, and a critical analysis of it, with the goal of stimulating some reader response to the apparent "paradigm shift" that has taken place in Scalar EM.

I have been both a "fan" and a "critic" of Bearden's works for several years now; a "fan" because I honestly think he has opened up a whole new area of study in electrodynamics and I'm frankly fascinated by his approach; a "critic", self-appointed, because I do take him seriously enough to have combed very carefully through his books and papers in an effort to understand his position as thoroughly as possible.

Yet there are many problem areas, in my opinion, that need to be clarified or developed further; if they turn out to be problems in my understanding, some good dialogue should help clear it up. I've put out some "pingers" on the KeelyNet in the last couple of years, in a sincere effort to get a dialogue started among Bearden's readers (hoping that Bearden himself might join in occasionally); some of my "pings" read somewhat sarcastically but that's a reflection of my frustration (and seriousness) with the seeming lack of ongoing interest in pursuing this thing productively.

It is my hope that careful readers of Bearden, in fact, even Bearden himself, will take the time to follow the issues raised here and contribute any comments in response to this author, who feels that Scalar Electromagnetics will be the EM of the 21st century... to the extent that we can understand, clarify and develop it.

Introduction -- To Converge a Diverging Ray

[Note: Much of the descriptive material on phase conjugation was presented previously in the KeelyNet file PHASCONJ.ASC]

The following description is borrowed in part from Radio Shack's book Understanding Lasers, and in part gleaned from various science encyclopedias, with my own comments relating to Bearden's works on the subject.

We start out with a narrow, point-like light source-- a laser-- which produces a tight beam which stays tight (minimum diverging of the rays) for great distances. But we know that, as narrow as our coherent laser beam is (in contrast to, say, a flashlight beam), it still diverges perceptibly over distance (or over time, if we want to look at it that way).

Now suppose we want to reflect our beam off a mirror directly facing the laser itself-- so that the beam is reflected exactly back at the laser. Will we "recapture" all of our tight beam? No, because the beam is still diverging in (positive) time, even after we've changed its direction of travel by reflecting it. There is an instrument designed to reflect such a laser beam back on itself, and that instrument is called a Retroreflector.

A retroreflector is a double-mirror arrangement that sends light rays back in the direction that they came from-- that is, back to their point of origin.

But, being ordinary mirrors, although they reflect and change the direction of the traveling wavefront, the beam itself continues to diverge nonetheless, spreading out as it travels.

Question: Would it be possible to reflect the beam in such a way that all that diverging energy could be made to converge again, somewhat like a "reversal of entropy?" Or like a "reversed-time" version of the original beam?

Well, your first answer mi ght be "Of course! A lens can do that-- and that's how parabolic reflectors work, too, by reflecting diverging waves to a focal point, or into a parallel beam." But I'm talking about a much more exotic technique, in which the wave itself is apparently both space- and time reflected... the Phase Conjugate wave.

Phase Conjugation

Phase conjugation is an operation that can be performed on waves, so that they reflect back, like a retroreflector, but with some unusual properties. This technique uses a special kind of "mirror" to generate what is called a conjugate reflection of an incoming wave.

The simplest wave (monochromatic or single-frequency) is known as a sine wave. A sine wave can be thought of as a repetitive, circular motion "turned on edge" and drawn out across an area of space.

As a wave moves along in space and in time, we can chart that movement, on a graph, in terms of its angular phase displacement in degrees around a 360 degree circle, from an agreed-upon starting reference point. Thus we can talk about "phase angles" when we mean "wave travel" and/or "time elapsed" with respect to our starting "zero-phase" reference.

Viewed on an X-Y graph, the conjugate of a positive angle, 45 degrees for example, is found by reversing the sign of the angle: i.e., minus 45 degrees. Thus the positive angle in the first quadrant of the X-Y graph moves down into the 4th quadrant. (Remember the plastic protractor you used in high school math? It spanned the first 2 quadrants, from 0 to 180 degrees, a half-circle.)

Notice that if we increase an angle from 0 to 45 degrees on our graph, we are opening up the angle in a counterclockwise direction on the graph. Starting at 0 and opening an angle to -45 (the conjugate of +45), moves the angle arrow in the opposite direction, clockwise. Algebraically, an angle added to its conjugate sums to zero.

The 2-dimensional phase conjugate plane wave, then, is essentially a reversed version of the original wave-- the wave is at the same phase and shape, traveling in the same path as the incoming wave, but in exactly the opposite direction.

The phase difference between any two points of the reversed wave has a sign opposite to that of the phase difference between the same points on the original wave. (I specify 2-D plane waves here because that's how we usually think of EM waves; the implications of this with regard to 3-D waves-specifically circularly polarized waves--are worthy of another paper, as they may take some of the ambiguity out of the exact meaning of phase conjugate waves vs. phase inverted waves, since direction of phasor rotation may play a part, and this distinction becomes ambiguous in 2 dimensions).

Because of the phase conjugate wave's property of direction- and path reversal, we will find that, if the source of the incoming (slightly diverging) light is a narrow laser beam, the phase conjugate reflection wave will return to the source by precisely retracing its path back down that beam.

That may sound exactly like retroreflection. However, it is actually more like a "time-reversed", as opposed to merely a "path-reversed" version of the original wave, reconstructing the light's phase and amplitude. Because of the way the phase-conjugate reflection wave precisely retraces the path of the original wave, it automatically compensates for things that happened to the laser beam on its trip from the laser out into the distance, which the retroreflected wave cannot do.

For example, light diverging out from a source may experience distortions; the phase conjugate wave experiences the same distortions, but in the opposite direction and sequence, as if it were going backward in time. Thus the spreadout, distorted light in the phase conjugate beam re-converges in focus on the light source.

Physicists involved in nonlinear optics, the field in which the phenomenon was evidently first discovered, call this the Distortion Correction Theorem. What is still somewhat controversial is whether the effect is actually a "time reversal" of the wave in the truest sense, or just a special sort of "length-" and "path-reversal."

History of the Phenomenon

American scientists first learned about phase conjugation in the early 1970's. Researchers at the P. N. Lebedev Physical Institute, Moscow, U.S.S.R., led by Boris Ya Zel'dovich, had discovered an intriguing phenomenon in 1972: The scientists distorted an intense beam of red light from a pulsed ruby laser by directing it through a frosted glass pane. The distorted light was then sent down a long tube filled with methane gas under high pressure.

Interactions occurred between the beam and the molecules of the gas (called stimulated Brillouin scattering) and, acting as a mirror, the gas reflected the beam backward. When the reflected light passed back through the same piece of frosted glass, a nearly perfect, undistorted optical beam emerged.

The backward-traveling wave is, in essence, a time-reversed replica of the original incident wave. To explain this by way of analogy, we might compare the retracing of light waves back through the distorting media as "running a movie backward". As described by Shkunov and Zel'dovich:

"The relation between the wave fronts of two mutually reversed waves is analogous to the relation between the positions of two opposing armies on a military map. The front line of each army coincides with that of the other, and the directions of desirable movement are opposite. One can say that the front lines are mutually reversed: a convex part of one's army front corresponds to a concave part of the other."

Tom Bearden maintains that this time-reversed wave really IS "time-reversed", and carries with it all the magical properties one would expect of energy that is actually flowing backward in time...

How Do We Make A Phase Conjugate Mirror?

We need a nonlinear medium in which to mix waves; that is, one in which waves do not simply linearly superpose (co-exist as if the other were not there), but modulate one another, which implies multiplication of amplitudes as well as the possible generation of harmonic frequencies.

In optics this has been done by beaming high-powered laser light through certain gases (Bearden mentions ionized gas), possibly under pressure, as explained above. Other examples of nonlinear materials are semiconductors, crystals, liquids, plasmas (which are ionized gases), liquid crystals, aerosols (as in the atmosphere), and atomic vapors. (See the article Applications of Optical Phase Conjugation by D.M. Pepper, Scientific American, 4/86(? my photocopy undated!), in which the author used a phase conjugate mirror [a crystal], excited by lasers, to undo the distortions caused by inserting a kitchen spatula into the path of the laser beam!)

The term "nonlinear medium" here means a medium that is altered or affected by light; i.e, whose index of refraction suddenly changes when the energy inputted to the medium exceeds a certain "threshold."

Linear materials, by contrast, are not affected in this way, under usual conditions. Linear conditions allow two or more waves to pass through the medium and through one another as if neither "knows" of the other's existence; the only "interference" that this superposition produces is the vector sum of the waves' instantaneous amplitudes and phases at a given position or time.

Thus we detect standing waves in a linear medium whenever two oppositely propagating waves pass through each other. In a standing wave, the resultant of the two waves "flaps up and down," so to speak, without moving left or right; in other words, its nodes are stationary in position, while its antinodes alternately increase and decrease in amplitude and polarity.

The two techniques most used in the generation of phase-conjugate waves are Stimulated Brillouin Scattering and Degenerative 4-Wave Mixing (the latter also mentioned by Bearden). Both rely on the laser's ability to interact with the nonlinear optical properties of a specific medium. When a material-- gas, liquid, or solid-- is penetrated by light of intensity great enough to compete with the atomic forces that bind the material together, the material is modified (crossing the threshold into nonlinearity), as is also the light penetrating it. This nonlinear interaction generates the SBS or DFWM time reversed waves.

In stimulated Brillouin scattering, the modified material generates sound waves (at optical frequencies) that serve as an appropriate reflective surface to produce the time-reversed waves. (Traditionally, the frequency of scattered light has been regarded as identical to that of the incident light.

As is often the case, this is not true in actuality. As first predicted by Brillouin in 1914, a slight line broadening occurs due to motion of the scatterers [Doppler effect] and also due to variations in the directions or magnitudes of their polarizability tensors [due to chemical reactions]. The Brillouin effect, simply stated, is as follows:

Upon the scattering of monochromatic radiation (light of one color or electromagnetic waves of one frequency), a doublet is produced, in which the frequency of each of the two (spectral) lines differs from the frequency of the original line by the same amount, one having a higher frequency, and the other having a lower frequency. (Radio engineers will recognize a description of a carrier wave surrounded by an upper and lower sideband here... Is this a clue as to how we might generate a phase conjugate wave using conventional radio transmission techniques?)

In degenerative 4-wave mixing, the interaction uses a holographic process in a nonlinear material to generate the conjugate waves. Lasers are used to produce two pump waves (of the same frequency; hence the term "degenerate"), beamed at one another through the nonlinear medium. The pump waves "lock" or modulate one another, producing a kind of a "phase-grating" in the medium which alters the index of refraction within the medium (Bearden calls this cross-modulated resultant a "scalar stress wave.")

Next, a third, weaker "tickler" beam is input into the system, and this setup generates the phase conjugate reflection wave which backtracks down the path taken by the third wave, but at a greater intensity or amplitude than the weak tickler wave. This process is mathematically expressed as a multiplying of the waves' instantaneous amplitudes and phases, as opposed to a vector summation, which occurs in a linear medium.

Bearden cites the literature in saying that up to all the energy inputted to the system via the two "pump" waves can be transferred into the phase conjugate output wave-- and so a powerful, time-reversed wave can be produced from a relatively weak "tickler" input.

Of course, power still has to be put in at the pump waves--but, says Bearden, what if we use the powerful and limitless scalar stresses of the fiery core of the Earth itself-- stimulated via Tesla-type resonance--as our pump waves? Then it would appear that we can input a tiny input wave and extract enormous phase conjugate energy out! But back to our description.

While our scientists have been exploring the phenomena and techniques for producing phase conjugated waves at the optical frequencies since the 1970's, Tom Bearden asserts that the Soviets (and perhaps the Germans before them, during WW2) had developed the technology at microwave and radar frequencies long before the '70s. Here the effect is probably generated by means of certain solid (not gaseous) materials and/or crystalline substances (Bearden refers to them as RAM-- Radar Absorbent Materials.)

Think on this a while and you'll see the tremendous potential for Star-Warstype directed energy beam weapons (See Bearden's Fer-De-Lance: A Briefing On Soviet Scalar Electromagnetic Weapons, 1986, Tesla Book Co.) Bearden also points out that the equations imply that phase conjugation is a general phenomenon, occurring in all types of waves, not just electromagnetic.

Even sound waves, which are longitudinal or compression/rarefaction waves in the density of air molecules, can be and evidently have been phase conjugated to produce acoustic missiles which converge on their targets (rather than diverge and dissipate over distance) and blast them with the full, coherent energy that they had when they were first generated, much like a laser beam. But Are They Really "Time-Reversed" Waves?

Earlier I mentioned that there is some controversy over the exact meaning of the phrase "time-reversed waves." While most physicists today will only allow for the interpretation "path- or length-reversed", Tom Bearden and some others believe that what we have here is really a time-reversed wave in its truest sense-- i.e., this wave is traveling backward in time and looks spatially reversed to us forward-time observers.

Bearden cites certain experiments which have been performed by researchers in phase conjugation, which show that a true phase conjugate mirror material does not recoil when it emits a phase conjugate photon, whereas a normal photon or a "pseudo-conjugate" photon emission will cause the mirror to recoil measurably (Newton's 3rd Law-- Action/Reaction).

On that basis Bearden forays into the stranger end of the spectrum of possibilities... What if these waves really are a means to alter and/or reverse the flow of time in a localized material or area? What would the effects be in or on biological systems (like people)?

Bearden forsees a time when electromagnetic healing will be used on a large scale, in which future physicians will irradiate their patients with timereversed EM "disease signatures" or patterns; their time-reversal transforms them into healing patterns in the same way that our laser beam was distortion corrected by sending its phase conjugate reflection back down the distortion path.

Perhaps even aging may be reversed in this way, since a particle of mass "passes through time" via the exchange of virtual photons, according to some interpretations of Quantum Mechanics. Who knows? Maybe H.G. Wells' "Time Machine" could become a reality-- or already has...

It goes without saying that he who holds the key to Time holds the key to the engineering of reality itself.

Going Deeper: Are Phase Conjugate Waves and Advanced Waves the Same Thing?

In researching Phase Conjugation (in order to better understand Tom Bearden's claims regarding it), it occurred to me that I had already heard of "Time Reversed" waves somewhere before. Ah yes, I'd read that Maxwell's wave equations, like so many others in mathematics, actually allow for two solutions -- a "positive" one and a "negative" one.

What makes it really interesting is that these terms "positive" and "negative" here mean, not electric charge polarity, but direction of time flow. But what is "negative time"? Does it exist? Can we experience it? Or construct a machine that will generate some at the flick of a switch?

As it turns out, these concepts have been discussed at some length in the popular scientific press recently. To shed some light on this, I quote the following extracts from the book Faster Than Light-- Superluminal Loopholes In Physics, (1988) by Nick Herbert, PhD., pp. 77-97:

Like Dirac's equation, Maxwell's wave equation for light also has two solutions, the so-called "retarded solution" that describes a wave traveling forward in time and the "advanced solution" that describes a light wave traveling backward in time. Both of these waves travel at the same speed-the speed of light in vacuum-- but in opposite temporal [time] directions. The retarded wave travels in the normal direction-- from past to future-while the advanced wave goes the other way-- from the future into the past...

Ordinary light waves are called "retarded" because you always receive them after they are sent; advanced waves, on the other hand, are always received before they are sent... Although advanced waves are permitted by Maxwell's equations, no advanced waves have ever shown up in any experiment. All light waves that we know about seem to be of the retarded variety.

For more than a hundred years physicists have wondered about how to interpret the mysterious advanced-wave solution to Maxwell's equations. Because of the lack of experimental evidence, most are content to ignore the advanced solution, dismissing it as an option that nature simply chose not to exercise...

In 1945, John Wheeler and his graduate student Richard Feynman, then at Princeton University, proposed a novel way of looking at light that gives the backward-in-time solutions of Maxwell's equations equal status with the forward-in-time solutions...

The Wheeler-Feynman model, called the "absorber theory of radiation", makes electromagnetism a two-way street as far as the time dimension is concerned. They base their time-symmetric theory on the assumption that every light wave emitted by an atom must be somewhere absorbed by another atom and that these two events, light emission plus light absorption, should be considered as a single inseparable process.

In conventional radiation theory, an atom emits a wave of light without regard to the light's eventual absorption. As the light wave leaves its present atom, traveling in a particular direction, the atom recoils in the opposite direction. The recoil of an atom as it emits light is no mere theoretical construct but has actually been observed in certain atomic beam experiments.

Conventional radiation theory explains this atomic recoil as the reaction of the emitted wave back on the atom. As you jump from a boat onto the dock, the boat will recoil for a similar reason, responding to your backward push.

[Newton's Third Law -- Action/Reaction] Wheeler and Feynman proposed that the emitted wave has no effect whatsoever on the atom. In their model, the atom's recoil is caused by a light wave that travels backward in time from the atom that eventually absorbs the light...

In conventional radiation theory, light from atom A travels at a speed of 186,000 mps to atom B which passively absorbs the light. Atom A recoils because the emitted light pushes back on it (self-interaction) as the light escapes from its parent atom.

Atom B recoils because it absorbs the incoming light wave's momentum, like a baseball player being pushed back as he catches a fast ball. According to the Wheeler-Feynman theory, the situation is more complicated-- radiation occurs in two steps.

First atom A emits, without recoiling (no self-interaction), a half-sized (retarded) wave that travels forward in time at a speed of 186,000 mps to the absorber atom B.

Atom B recoils as it takes up this light's momentum. Then, stimulated by its recoil motion, atom B emits a half-sized (advanced) wave that travels backward in time at a speed of 186,000 mps to atom A. Atom A recoils as it takes up this advances wave's momentum.

The timing of the emission and absorption events guarantees that at any moment the half-sized advanced wave sent back in time from the absorber always finds itself at the same position in space as the half-sized retarded wave sent forward in time from the emitter. Thus the two waves fuse together to form a single full-sized wave which appears to have been sent from the emitter and received by the absorber.

Because of this exact superposition of advanced and retarded waves, the Wheeler-Feynman model produces the same apparent wave motion as conventional radiation theory. The two theories give the same result but propose radically different models of what is actually happening. Conventional radiation theory is a simple matter of cause and effect.

Wheeler-Feynman theory involves a handshaking procedure much like data exchanged between two computers in which a data transfer initiated by one computer is not completed until the exchange has been acknowledged by a message sent back from the second computer."

So now we understand that Maxwell's wave equations predict, mathematically at least, a retarded (positive, forward time) and an advanced (negative, time reversed) pair of solutions.

Positive (Normal) Time Flow vs. Sequence of Events

It seems necessary at this point to clarify our understanding of the direction of time flow. In what direction does time flow? The quick answer is obvious: Time flows forward! Always has and always will! At least that is our empirical observation of it.

Okay, then: Does time flow from Past to Future or from Future to Past? Now things get a bit tricky; better think on this a little and word our answer carefully!

Let's go back to our particle A - particle B illustration.

We have a particle (an atom, etc.) emitting waves-- we'll call it particle "A". Like a tiny radio transmitter, it sends out ordinary "retarded" waves in our positive time, at the speed of light; the wavefront reaches particle B a fraction of a second later (hence the term "retarded").

Since (+) time can be described as continually moving from the Past into the Future, we can say we are "sending the retarded waves into the future", because our wavefront hits particle B a few picoseconds later (in the future, with respect to our starting time at particle A; but once the wave has hit particle B, the "future" has become "Now".)

Now if you're quick, you probably noticed that I've already jumped to the conclusion that time flows from Past to Future in the above paragraph. How did I arrive at that decision? Because future things happen after past (and present) things, by definition. Obvious, but not necessarily simple!

Although it may be conceptually difficult, we must be careful not to confuse this description of time flow with the other way of looking at it, that is, as regards events that take place:

We often speak of events as "future", then as happening "now", then as being "past". Thus it might be tempting to say that we (and time itself) flow from future to past. Or, that time flows past us. But we must look at it the other way around: If events that lie ahead eventually pass by and then lie behind us, as in the A to B example given above, then we as conscious observers, and time itself, flow from past to future. It is the events that move from future to past, just as the telephone poles and trees seem to move "backward" past our car windows when we drive forward. And so a wave emitted from a transmitting antenna radiates outward into the future, as well as outward into the space dimensions around us. (This fits in with Einstein and Minkowski's view that space and time are not really totally separate things; rather, the two can be viewed as a single complex entity called spacetime.)

And so I would argue with those who casually remark that time flows from future to past, on the observation that things future become things past: No-Time (and consciousness) flows from past to future, it is the events (things) that flow from future to past.

All of the above may seem a bit tedious, but I found that I had a hard time understanding "time-reversed waves" until I was able to sort out these ideas on time vs. the events happening in time. And I just assumed that you would be as conceptually cloudy on the subject as I was, and probably still am! (Hope I haven't offended anyone.)

Comparing Advanced Waves and Phase Conjugate Waves

Now let's compare Wheeler-Feynman's "advanced waves" with Bearden's Scalar EM application of "phase conjugate waves" and see if they're the same thing.


1) Re-capping the Wheeler-Feynman scenario, a half-amplitude RETARDED wave travels from particle A to particle B in POSITIVE time.

2) Once the retarded wave gets to particle B, B emits a half-amplitude ADVANCED wave which travels from particle B to A in NEGATIVE time (backward in (+) time, we would say).

3) Both particle A and particle B exhibit recoil.

Now when we positive time observers look at this sequence of events, what do we see? Well, as viewed from our POSITIVE time standpoint, the Advanced wave would be seen as traveling BACKWARD in DIRECTION as referenced to its original negative time description above; i.e., in our positive time, we see the Advanced wave's direction of travel to be REVERSED-- it is now going in the SAME direction as the Retarded wave-- from A to B (opposite of its travel, in NEGATIVE time, from B to A). Read that again if it seems confusing.

Their SPATIAL phases would line up perfectly, at each point along a wavelength or at each moment in (+) time; and thus the two individual half-amplitude waves would ADD UP (sum) to ONE composite FULL-AMPLITUDE wave, traveling in (+) time from particle A to particle B.

Thus, an ordinary electromagnetic wave, in the Wheeler-Feynman view, may be made up of two half-amplitude waves, perfectly superposed-- SPATIALLY IN PHASE, yet TEMPORALLY (time-wise) OUT OF PHASE-- if by "phase" we mean + or time! (Maybe we ought to use the term "polarity" instead?)

(Notice that the above example described an emitter and an absorber of waves, whereas the examples below describe an emitter and reflector arrangement. I hope I'm not making my whole presentation irrelevant by comparing apples and oranges here! But let's explore the concepts.)


Now we come to an even stranger scenario:

1) A RETARDED wave travels from source A to "mirror" B in POSITIVE time, as in the case previously mentioned.

2) A PHASE CONJUGATE antiwave travels from B to A, also in POSITIVE TIME, or so the "length-reversal-only" interpretation would lead us to believe (like an ordinary mirror reflection but...)

3) There is NO RECOIL on particle B, and...

4) The reflected beam RE-CONVERGES upon the source A, precisely backtracking the path taken by the A to B wave. And if there were any distortions to the wave on its way to B, they are "undone" on the way back to A.

The literature tends to emphasize the unusual spatial reversals exhibited by the PC wave; they do call it a "time-reversed" wave, but don't really explain what that means. What I find strange is that Tom Bearden says that this wave pair is also said to be "in phase spatially, and out of phase temporally" (just like what Nick Herbert said about the retarded/advanced pair in the first example above)! How can this be?

How could the Wheeler-Feynman "Advanced" wave and the Bearden "Phase Conjugate" wave both be "in phase spatially and out of phase temporally", if one member of the first pair travels with its companion, but the Phase Conjugate member of the 2nd pair travels in the opposite direction from that of its companion? And both models claim that one of the two waves is traveling backward in time?

In the Retarded/Phase Conjugate pair, the two wave paths track each other precisely. One fans out while the other fans in. One represents photon scattering, a time-forward entropy, while the other apparently represents a regathering of scattered photons, a time-reversed entropy called negentropy by Bearden. Yes, their diverging/converging beam width paths are identical. But they're traveling in opposite directions, in our (+) time-- or are they? If they are, that's a description of a standing wave. Why?

Whenever any two waves travel in opposite directions, they slide alternately in and out of spatial phase with one another; their summation gives rise to a standing wave. When the two waves exactly superpose, they sum to a resultant wave which is twice the amplitude of either wave by itself. A moment later, as the waves are crossing and are slipping out of phase, the resultant begins to decrease in amplitude.

When the two finally slip to 180 degrees phase difference (when one wave's "crest" coincides with the other's "trough"), they momentarily cancel, leaving a zero-amplitude resultant. Then they gradually slip back into phase, and the cycle repeats. The net result is a "flapping-polarity", but non-traveling, fixed-node position standing wave, as mentioned earlier.

The point is, oppositely-traveling waves are never "always in phase spatially"-- they're in and out of phase cyclically. Wheeler-Feynman's Advanced wave, on the other hand, is always in phase spatially with its companion since it travels with it in the same direction in (+) time.

So what does Bearden mean when he says "in phase spatially, out of phase temporally"?


Well, either Bearden is confused (possible), or I'm confused (probable), or he is saying "spatially in phase" when what he really means is that the two waves occupy precisely the same path-- the original beam traveling and diverging from A to B, and the Phase Conjugate wave converging from B back to A, down exactly the same route.

If that's what Bearden means, then I submit he is using the phrase "spatially in phase" incorrectly, muddying the issue. But perhaps that's not what he means. The point is that it's impossible to tell, without ambiguity. We ought to be using precise terminology here: such as agreeing upon a zero-time reference, and referring the instantaneous phase of each of the two waves to that reference phase point. This would be our "temporal" phase (assuming + time). If the two waves are both traveling in the same direction, their "spatial" phase would be referenced to the starting reference also.

If we want to "turn back the clock" and talk in terms of negative or reversed time, we should make that clear also, since the phrase "temporally out of phase" is ambiguous, when your'e talking about time reversal-- does it mean, "out of phase in our normal (positive) time," or does it imply "positive vs. negative" time?

Then, we need to be precise in talking about the direction of propagation or travel for each wave. If Bearden really does mean that the two waves are at all times in phase spatially, then he must agree that they are traveling together in one and the same direction-- from A to B, in positive time. But it doesn't sound to me like he or the scientific literature on phase conjugation are saying that; both seem to be describing a reflected wave which travels, in our positive time, from the "mirror", B, back to A. (If Bearden were to correct me on this point I would appreciate it.)

What is different about the phase conjugate reflection is that it is always reflected precisely back to the source-- as opposed to an ordinary mirror, which reflects at an angle on the other side of the perpendicular-- remember how you learned in school that the "angle of incidence equals the angle of reflection"? So if a ray of light hits a mirror at 30 degrees to the left of a line drawn straight into the mirror, the reflected ray will leave the mirror at 30 degrees to the right of perpendicular.

The phase conjugate mirror would reflect the ray right back at the angle of incidence-- 30 degrees left of perpendicular, right back down the path to the light source. So, if you were to look at your face in a regular mirror, you would see all of it (light from many directions is reflected into your eyes); but in a phase conjugate mirror, you would see nothing but the pupils of your eyes! Any other light, such as from your chin, would be relected right back to your chin. It would never reach your eyes, and thus it would be invisible to you in such a mirror.

What's the Point of All This, Already!?

The whole reason I began this examination of the fine points of phase conjugate waves is that, as I read Bearden's several books and papers published over the years (approx. 1983 to 1993), it seems to me that he has shifted his emphasis from "Sum-Zero Vector EM Waves" (180 degree time-phase cancellation [summation, superposition] of two or more EM waves, specifically said to be traveling together in the same direction) to "Modulating EM Waves with their Phase Conjugate Replicas" (said to be a lattice of bidirectional plane waves per Whittaker's 1903,4 papers) as far as his recipe for making his famous "scalar" waves. The two seem to be mutually contradictory.

Again, I'll admit that I had a hard time sorting him out on this, and maybe I'm misunderstanding the whole thing-- Did he change his mind on what you need to do to make a scalar wave or potential, or is he augmenting his theory with an alternate way of making scalars? In some of his writings, he describes the phase conjugate method as a "better way" to make scalar waves. In others, he says it's the only way. I say that there's a world of difference between "a better way" and "the only way"!

In his earlier (mid-1980's) books, he was talking exclusively about summing "opposing" EM waves to zero: phase cancellation, as mentioned above. But notice that even the word "opposing" can be taken in two different senses: I can have two waves traveling from left to right in the same direction, but 180 degrees displaced in time phase (opposing E and B vectors, opposite in polarity); that's Bearden's earlier description and that's what most of the "free-energy crowd" are visualizing when you say "scalar wave".

It's also what you get in the "nulls" in-between the "lobes" of a phased-array or interferometer-type antenna system. (See Toward A New Electromagnetics, Part 4: Vectors and Mechanisms Clarified (1983), pp. 12-13; slides 22, 23; also Fer-De-Lance (1986), p. 25, slide 23.) I'm also quite aware, by the way, that Bearden denies transverse waves in vacuum, though his diagrams in the above-cited books "look" transverse because of limitations in illustrating the concept of longitudinal potentials.

The other sense of "opposing" two waves is to have them oppose in direction of propagation, i.e, one travels left to right, the other travels right to left, and they meet head-on, interpenetrate, and add vectorially into a standing wave. His "Whittaker Potential" as described in Gravitobiology and later papers seem to depict this view (with the added conditions that the "antiwave" be a true phase conjugate of the "wave" and that the waves are multiplied, not added together).

To confuse the issue even more, in his AIDS: Biological Warfare book (1988) he seems to use confuse the meaning of the phrase "180 degrees out of phase" in his descriptions of what a scalar wave is! Some examples:

Quote: "In [phase conjugate optics], the scalar EM wave formed by two waves 180 degrees out of phase with each other, and locked (modulated) together by a nonlinear medium, is blithely called the pump wave... even in PCO our scientists do not yet realize that the 'pump' wave is a scalar wave, a wave of artificial potential, and a gravitational wave that pumps the nuclei of the atoms in the nonlinear medium. They also still do not understand that it is the nucleus of the atom that produces the phase conjugate replica wave in PCO." (AIDS, p. 58-59)

Comment: The two pump waves in a phase conjugate mirror are propagating in opposite directions; they're not 180 degrees out of phase! Phase (the term implies time phase) is irrelevant here, since counter-propagating waves are cyclically in and out of phase, and their relative starting phases merely shifts the resultant standing wave forward or backward by some phase angle. To refer to direction of propagation in terms of phase is technically incorrect, confusing and out of harmony with earlier works such as Fer-De-Lance.

Also, if the product of the pump waves is the "scalar wave" and is "gravitational" already, then why do we need the time-reversed phase conjugate wave (which is only produced when a "tickler" is inputted to the pumped mirror material) at all? Is the production of the "scalar" wave from the pump waves merely a step toward the real goal of generating a phase conjugate wave? Or is the PC wave merely a handy byproduct of making scalar waves from "opposing" pump waves? In other words, which is it, the "scalar wave", or the "phase conjugate wave", that is the true Golden Fleece of Scalar EM?

Quote: "Thus we have produced a scalar effect from zeroing vector operation between electromagnetic forces. I have called this scalar electromagnetics, and pointed out that it is truly electrogravitation." (p. 81)

Comment: If the waves are counter-propagating, as are the pump waves in a phase conjugate mirror, then they're not zeroing! Whether you add or multiply these waves, there's a non-zero, oscillating resultant, because the waves' relative phases are constantly shifting relative to one another.

(More recently, Bearden has introduced the term "non-translating" to describe the scalar wave, evidently in the sense of "stationary, not traveling". Well, this would seem to favor something like a standing wave, and not like the pre1988 "phase-nulled" wave, since in the earlier version both EM wave components were "traveling together in the same direction" and so the "pure compressive/tensile stresses on spacetime" would also be moving along as a resultant-- translating along with the component vector waves! And just when I thought it was safe to wind me a Mobius coil!)

Quote: "The simplest scalar EM wave may be considered as two EM waves locked together (modulating each other), where one component wave carries positive energy and time and the other component wave carries negative energy and time." (p. 104)

Comment: Here he is cross-modulating two waves, a "positive energy and time" one with a "negative energy and time" one. May I assume that the "negative" one is a phase conjugate wave? If that's what is needed to make 'the simplest scalar EM wave', then how did our previous two "pump" waves make such a scalar wave, when both of them were just plain positive energy and time EM waves, with the only difference between them being their direction of propagation? (Researchers in nonlinear optics are using lasers to "pump" the PCM; they know nothing of "negative energy and time" pump beams-- yet they're making phase conjugate waves with no problem.

Other Observations: The AIDS book appears to reflect a stage of revision or transition in Tom Bearden's thinking. In it the reader will find most of the older Fer-De-Lance text and some of the illustrations from it. The KaluzaKlein 5-D view of Scalar EM is still presented, which seems to be absent in newer works such as Gravitobiology (1989).

"Energetics", the term the Soviets allegedly used for these esoteric areas of science, was previously defined in terms of zero-vector, scalar EM waves; now the term is applied to phase conjugation, the use of which is speculated to have begun as early as the 1950s. If the Soviets were telling the truth, phase conjugation was stumbled upon in the laboratory in 1972 or thereabouts. Then again, that's probably what they'd like us to believe.

The "secret of antigravity" was formerly explained in terms of Kaluza-Klein theory and the cancelling of gravitational "bleedoff" as EM vector fields. Now, again, phase conjugation has taken its place as the "magic secret" of gravitation/antigravity.

The earlier distinction between the random, statistical natural potential and the internally ordered artificial potential has now given way to the view that energy itself is "any ordering... in the virtual particle flux", a paradigm shift that has raised the hackles on some of Bearden's older readers, who wonder where unstructured "noise" fits into that scenario. (Bearden apparently holds this view because it seems contradictory that observed order in our universe should grow out of the integration of total randomness.) This shift of viewpoint led directly to his redefinitions of energy, potential, and even voltage, among other terms, in his 1993 paper The Secret of Free Energy, in which he advances the concept of impressing a current-free potential gradient onto a chargeable "collector" mass of free electrons in order to synthesize power from the virtual photon flux without depleting the source of potential-ever.

The magical powers attributed in the older books to "zero-vector" scalar waves has now become the domain of "time-reversed antiphotons" and "negative energy". Indeed, in AIDS and in Gravitobiology, Bearden finally reasons his way to the point of stating that the "full photon" (our good old EM) has always carried both positive and negative energy and time, and so it in itself is and has always been a scalar wave! (AIDS, pp. 109, 110) (Underlying his reasoning is his and Frank Golden's insistence that the EM wave in vacuum is longitudinal, not transverse, and that E and B fields, as such, do not exist, but only their potentials exist; QMers would agree with the latter part.)

Well if the regular EM wave is scalar after all, then it is gravitational, too. (Sounds like the Wheeler-Feynman model, doesn't it?) Well if that's the case, why go to all the trouble of making special "vector-zero scalar waves" at all? Does this view finally obsolete his earlier "phase-cancellation" views? Wouldn't some good old-fashioned EM standing waves, maybe aimed at a target on 3 opposing axes (x,y,z) do the electrogravitational trick?

So maybe Tesla's "stationary" waves, observed after a thunderstorm in 1899, were what we would call standing waves today, after all? And what does all this mean for the labors of Hooper, Smith, et al, spending hours at the winding machine, making non-inductive coils in exotic configurations in the belief that you had to null magnetic field "bleed-off" in order to get gravitational effects?

In Pursuit of Understanding

Am I simply "nit-picking" here? Isn't the author of a new theory allowed to revise his theory? Of course he is. It's not nit-picking but a sampling of the many fine details found in Bearden's writings that seem inconsistent at this point-- and I realize that it could be my own lack of understanding. But I'd like to get this out into the reading public's attention for discussion. If I were Bearden, I'd appreciate the interest that led to such an analysis as this one. It means that somebody out there is listening, and it's time to get a dialogue going among the isolated admirers of Bearden's Scalar Electromagnetics.

Why is all of this so important-- the fine distinctions, I mean, in the pages above?

Because those of you out there who are attempting to experiment and build scalar devices-- like Bearden urges us to do-- from what little information you can glean (since Bearden inevitably tells us that his inventor friends want all the salient details kept proprietary) have all been laboring under the assumption that you must somehow cancel or null out the E or B fields generated by your devices. And, that this phase cancellation, rather than simply making all the energy "go away" somewhere, is indeed the key to stressing the vacuum.

This is the underlying assumption in Joe Misiolek & the TVQ group's work, that of Warren York and Matt Campbell, the Smith Caduceus Coil, the Bifilar Coil, the various Mobius-wound coils, the shorted-loop Tesla coil, W. Hooper's patents, etc.

Yet Bearden mentions Hooper (admiringly) as the only researcher who took the "zero-sum vector" approach seriously at a time when mainstream science said "sum-zero means the energy has been nulled out, so there ain't no EM to deal with!" BUT... Hooper worked with non-inductive coil configurations which cancelled their magnetic "B fields," leaving only the magnetic vector potential "A field" and/or what he called the "motional electric BxV field". Note that Hooper did not use phase conjugate mirrors but he did claim that the BxV field produced by his phase-nulled coils was essentially gravitational nonetheless. (See U.S. Patent 3,610,971, All Electric Motional Field Generator, 10/5/71, by W. J. Hooper.)

And didn't Tom Bearden's earlier works describe just such a sum-zero wave as the key to everything from altering gravity to bending Time itself? If my noninductive bifilar coil can warp the spacetime in my room, why go through all the trouble and expense of setting up a phase conjugate mirror?

Ah, but Bearden told me over the phone that "it's not just a matter of phase-cancelling waves at 180 degrees. They have to be in phase spatially, but 180 out of phase in the time dimension." I didn't get the chance to ask him whether that remark automatically obsoleted his earlier books such as Fer-DeLance or whether this phase conjugation was a later enhancement, an add-on.

So, are the researchers who are tinkering with such phase-cancelled fields just wasting their time, then? Should they be performing experiments with phase conjugate mirrors instead? Or do both methods generate "scalars", stress spacetime, bend time, alter gravity?

To read Bearden's more recent works you'd conclude that the earlier methods don't work at all-- but he never comes right out and says it, to my knowledge. He says that even if you synthesize a (positive time) waveform whose characteristics precisely mimic a phase conjugate wave, reversed wavefront and all, this "pseudo-conjugate" wave will still cause normal recoil of a PC mirror (i.e., it won't be a "magic" wave) because-- and this is the issue at stake here--Bearden maintains that the photon and (time-reversed) antiphoton are NOT identical, based on the "recoil" problem.

As I've said before in my KeelyNet files, Tom Bearden seems to be a genius in many ways. Maybe he writes at a level quite a bit over most of our heads. Maybe that's why I've had such a hard time comprehending, not only what he is saying, but also trying to discern how much he has modified/developed his theory and to what extent.

But, as I also said in that file, if he is serious about wanting to see this Scalar Electromagnetics catch on, he is going to have to be as patient with us newcomers as we are impatient with him; we need to keep asking questions and to think deeply on the details of what he is saying, as I think I've done in this paper-- and hopefully he will be willing to clarify some of the finer points (in simpler language, sometimes) for guys like me.

As always, I invite any comments or criticisms of the conclusions I've drawn here. The more brains we have in the Think Tank, the better!

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