147.1 Phase Velocity 
Date: 05/10/04

My comments and excerpts in Bold.

Supra Phase Theory
of the Anu Building Block

In his stand against the ether, Einstein had argued, "we should not speak of things that can't be measured." Probably the number one reason for saying that was to insure the job of measurements. Today, the Aether not only has been experimentally shown to "exist", but the reversed, subluminal group wave Aether and the superluminal phase wave Aether could also be measured once it was defined as the existent medium. On the one hand we can define "something" and call it Aether. On the other hand this something is actually not in existence. We can assign any arbitrary, straight line measuring unit to it but only the circle is an absolute measure of it. To measure the void of non-existence, with an absolute circle, is not measuring, it is copying. The circle represents the finest forms within the non-existence. The absolute measure, the circle, is also the shape of the measured form. That form is 0 and 0 need not be measured. There is no need for any measurement of whole systems when it is known in its finest form. When we cheat and use the 1 as the unit of measure, we are using the straight line again, since the 1 is obviously a straight line. 1 always represented one 0, not one more 0. The non-existent void is all 0's and is absolute just as a curved circle is the absolute measure. So we can never add absolute 0's and call it two 0's. If there seem to be two 0's spinning together in the void, it is still one 0. Therefore the "Aether" is unity.

We are almost ready to make a phase change into a world, perhaps not beyond c velocity, but, rather, "going the other way" if you will, into unity. The date is December 21, 2012, 10:13 PM (Some say 11:11 AM.....don't blame me). Would you like to know what to expect?

"It is interesting that the modular hierarchy of the I-Ching also is a "wave of probability", and that if the electron is conceived as a concrescence, then, naturally, at the point of maximum symmetry, one might expect its appearance". O.E. Oeric.

Paraphrase: We might expect the appearance of the electron.

Try to imagine what this little statement means, at maximum concreascence (Dec 21, 2012). Matter....all matter is made of at least 1/2 electrons. Imagine every single electron making its appearance all at once. We would call it a dimension of pure light, wouldn't we.

Even if we don't have the ability to measure these things, we will still be able to use the phase change at the appropriate time. What does that mean, you may ask? Reversed phase waves and superluminal waves are the stuff of thought and prayer. I predict that between now and the event of the phase change, there exists a "winding up" that can be interpreted as a cycle which repeats in ever shorter increments, until it repeats almost instantly, in its last cycle on Dec 21, 2012. We are in the middle of these cyclings now. As the cycling gets tighter and tighter 2, more thoughts and prayers will be answered as external events become darker and darker. In other words, we will always have a mechanism that will bring us what we expect. It may not be measured easily but that is no reason to think it won't work.

You may just read the main excerpts of "Welcome to Superluminal Phase-wave Civilization", below, or go to the source document and get an idea of a coming supra phase change, or you may peruse the scientific experimenters and their comments about velocities over c and about the reversed wave.

Collected Evidence

1. Einstein Test 
2. Nonlocality With Time Reversibility 
3. Eric W. Weisstein's Site 
4. Quantum Nonlocality and the Possibility of Superluminal Effects 

Welcome to Superluminal Phase-Wave
Civilization by Douglass A. White (PDF)
e-mail: dpedtech@dpedtech.com

Some preliminary formulae:

matter wave = group wave
DeBroglie Lo=h/p=h/Mo Vo wavelength (Lo), Planck's constant to momentum (p), restmass (Mo), wiggle velocity (Vo)
Einstein E=h u E=energy, Planck's constant (h), frequency (u)
wave-lengths (L) and different wave numbers (k). relation for a particle's momentum is p = h / L. But k = 2 pi / L, so p = (h-bar) k, where h-bar = 2 pi h.
P = (phi)(phi)*. (P is the probability density, phi is the wave function, and phi-star is the star wave, the complex conjugate of the wave function. )


Einstein claimed that the speed of light is a constant: (c) = 3x10^8 m/s. Then he showed that matter was essentially the same as energy by the relation E = Mo c^2, where Mo is the rest mass of a particle.

Special Relativity tells us that if you start going very fast, when you get to relativistic speeds, drawing close to (c), things happen that prevent you from ever reaching (c), much less exceeding that speed limit.

* M1 = Mo / (1-(v/c)^2)^1/2. (Mo is rest mass, M1 is moving mass.)

According to this relation of velocity to mass that Einstein derived, the faster a particle goes, the more mass it has. It takes more and more energy to boost the speed of your little physical particle made of matter-wave packets any faster as it approaches light speed, and to reach (c) would take an infinite amount of mass-energy. When v = c, the ratio becomes unity, and the whole expression in the denominator goes to zero, which renders the equation meaningless unless M1 can become infinite, which is not likely, or the rest mass Mo can become 0, which is the case with light. So Einstein's equation suggests that whatever moves at c essentially becomes light and has no rest mass, while anything with mass must move slower than c....

But is this really the whole story?

What if v>c? For example, suppose v = 2c. ,Then v/c = 2, and the denominator becomes (-3)^1/2, or (3^1/2 i). The mass M1 of the superluminal object shifts into the imaginary dimension (and so does Mo). This ,dimension is orthogonal to the ordinary "mass dimension". M1 at zero velocity is, equal to Mo. Then it grows toward infinity as its speed increases. At light speed it reaches infinity, but suddenly jumps back to zero rest mass at c. Going beyond c the velocity goes to larger and larger multiples of c, and the mass of M1 goes to smaller ,and smaller multiples of Mo in the imaginary dimension. Its rest mass must be imaginary, and its moving mass is also imaginary. Sometimes these odd creatures are called tachyons. Tachyons always move faster than c, but no one has seen one -- supposedly. Another interesting aspect of this relativity equation is that it permits, the possibility of negative mass in both the real and the imaginary dimensions. Even, at subluminal speeds there is no reason that M1 and/or Mo can't have negative values. Suppose v = .2c.

* Mo^2 / (M1)^2 = 1 - (.2c/c)^2 = .6.

* (+-)Mo / (+-)M1 = (+-) .6^1/2.

What negative mass and imaginary mass are (not to speak of negative imaginary mass!) presents an interesting question. Mr. Einstein never really gave an answer to these funny possibilities. Most physicists simply assume that part of the mathematical model doesn't fit reality. But what kind of a model is it where you arbitrarily pick out the part you want and throw the rest away?

Personally I suspect that the negative masses represent mental phenomena. Negative mass is not the same as antimatter. Antimatter is matter running backwards in time. But it is still ordinary matter. A positron is an electron running oppositely in the time dimension. On the other hand a negative electron or a negative positron mass (not negative charge!) may be a mathematical representation of the notion you have in your mind when you see an electron or think about one. It is a mirror image of physical space in mental space. The imaginary superluminal tachyon mass of the matter or antimatter variety represents the shift of attention by the will in "imaginary" space. The tachyon mass at c is 0 in real mass and infinitely imaginary. As the attention moves faster and faster above c, the mass shrinks, becoming less and less imaginary. At infinite speed, it is no longer imaginary, and becomes real. This is a ninety-degree shift in phase space. The more relaxed you are, the faster you can shift attention (the lighter the imaginary mass is). If you are completely relaxed, you are completely real. The tenser you are (the more energy you expend on attention), the slower attention moves, and the more you move into imagination. Your world becomes less real. It takes a certain effort of attention to hold awareness focused on anything. Play with the equation and imagine how imagination works. Why shouldn't the mental world follow mathematical laws just like the physical world? The equations of special relativity use only high school math and the laboratory confirmations of relativistic effects are so ubiquitous, that no one ever questions Einstein's declaration about the speed of light. He achieves the status of authority, which is fine until it leads us to accept his assertions without question.

Phase Transition.

Although Einstein declared that (c) is the ultimate, unreachable speed limit for matter-wave packets, he neglected to inform us about the full significance of the simple equations on which the whole edifice of his theory stands. Physicists notice this funny discrepancy, but just briefly mention it and then continue on with their discussions.

See Feynman Lecture I.48 "Beats", sections 4 and 5 also Feynman's II, 24-4, Hecht, p.299, Harsany, p. 26, Herbert p. 68 et al., and so on.

An oscillation has an amplitude, wavelength (L), a frequency (u) or period (T = 1/u), and a phase. Fourier showed a general way in which we can represent any function as the superposition of a set of periodic oscillations (i.e. pure sine waves). If the oscillation has a time evolution, then it produces a train of waves that move along at a certain velocity. The train's velocity is the wavelength (L) times the frequency (u). Since this represents a displacement of the wave's phase through space over time, it is called the phase velocity (Vp).

* Phase Velocity = Vp = (L)(u) = L / T = w / k, where (w) = 2 pi / L and k = 2 pi / T.

An electron can be interpreted as a wave packet -- a superposition of pure periodic oscillations with the appearance of a lump or packet that behaves like a localized particle moving about. When de Broglie formulated his notion of matter waves, he based his reasoning on the Einstein-Planck relations that show how the energy (E) of a photon depends on Planck's universal constant of wave resolution (h) times the photon's oscillation frequency (u). He also used Einstein's famous equation showing the mass-energy relation.

* E = h u.

* E = Mo c^2 (Einstein's formula, where Mo is the rest mass of a particle).

* Mo c = h u / c. (We combine the two equations.)

* u / c = 1 / L. (Where L u = c gives us the speed of light in a vacuum.)

* Mo c = h / L (We substitute in the phase velocity of light: Vp = c = L u.)

* L = h / Mo c. (We rearrange to solve for L.)

This is the de Broglie wavelength for a photon. Now, taking (Me) as the mass of the electron and letting (c) become instead the velocity of the electron (Ve), de Broglie found a wavelength (Le) for the electron.

* Le = h / (Me Ve).

We can turn this around to express the characteristic matter-wave, or group-wave, velocity (Ve) of the wave packet that forms the electron.

* Ve = h / Me Le.

What does this equation mean? Think of an electron in orbit around a nucleus. It has angular momentum (Ln) that is restricted by the orbit to certain whole number (n) values:

* Ln = n h / 2 pi.

* Ln = pn rn (Momentum for the nth Bohr orbit, r is radial distance.)

We use the de Broglie relation as follows:

* pn = h / Ln.

* 2 pi r = n Ln.

So simply said the electron moves with n (whole number) wavelengths per orbit and forms a stable standing wave around the nucleus. Substituting the rest mass of any particle in terms of its energy, we get the matter-wave packet's Matter Velocity ( Vm) in terms of light speed and a Phase Velocity (Vp), which simplifies the whole expression into the elegant Einstein-de Broglie Velocity Equation.

* Vm = (h / L)(c^2 / h u) = c^2 / (L u) = c^2 / Vp.

* (Vm)(Vp) = c^2. (The Einstein-de Broglie Velocity Equation)

Recall that (Vp) is the phase velocity (L u) derived above. This is the Einstein-de Broglie Velocity Equation stated clearly and unambiguously so you can see what is going on behind the smoke and mirrors of E = Mo c^2. Despite what people pretend, nobody really knows what mass and energy are. Velocity, on the other hand, is an observable that anyone can verify by simply opening his eyes and observing. The Einstein-de Broglie Velocity Equation can also be called the Sommerfeld-Brillouin Velocity Equation, because they also derived the relation between group and phase velocities while studying the superluminal behavior of EM waves in plasmas around 1914. They noted that the phase velocity is the inverse of the group velocity. But de Broglie's matter waves make the relation much more general.

We can make a nice graphic representation of the Velocity Equation by going back to our circle. Draw a circle with a compass on paper or with a graphics application on your computer screen, and then draw a diameter. Next choose a point anywhere on the circle and draw a triangle connecting that point to the two ends of the diameter. This will be a right triangle. Now drop a perpendicular from the point you chose on the circumference down to the diameter. This perpendicular line divides the big triangle into two smaller right triangles. All three triangles are similar. Label the perpendicular line "c". Label the short portion of the diameter "Vm". Label the long portion of the diameter "Vp". When (Vm) = (Vp), notice that they are also equal to (c), and the semicircular disc divides into equal quadrants. When (Vm) = 0, (Vp) becomes the whole diameter, and (c) degenerates to 0. When (Vp) = 0, (Vm) becomes the whole diameter, and (c) again degenerates to 0. Einstein arbitrarily declared that (Vm) had to be smaller than (Vp). Contemplate the little mandala you have drawn. It embraces the whole universe. In the case of light propagating in an unrestricted vacuum, both (Vm) and (Vp) have the value of (c). However, in the case of light passing through a dispersing medium, or a wave-guide, or in the case of the electron or any other particle of so-called matter -- the maximum "matter" velocity of the matter-wave packet is always less than the speed of light. This makes Einstein happy. We just arbitrarily label the part of the system that appears to go slower than light speed "Vm". Nevertheless, it is simply an optical illusion produced by the interference of the various superposed phase waves (Dw / Dk). When you look carefully at the equation and accept Einstein's other assertion that the speed of light is a constant (c), then you realize that if (Vm) must be less than (c), then (Vp) must be greater than (c) in order for the equation to hold. Most physicists tend to discount the phase waves as irrelevant, but they are not. They say phase waves are monotonous and lack all information content.

Oh yeah? Look again at the equation. Look again at the mandala. Messages are sent with subluminal matter wave packets, right? Yet for every value of a (Vm) packet there is a corresponding value of a (Vp) packet. (We mean a non-local "packet" not an individual phase wave.) Einstein says the c's are constant, although they seem to change the same as Vm and Vp on our little mandala.

But if we arbitrarily hold (c) constant (by zooming in close or far away from the circle as observer), then any "message" that is encoded with subluminal matter wave packets has a mirror image superluminal message with the same content that is encoded with phase-wave packets. To say that an object or a message is limited only to matter-wave transmissions deliberately ignores the phase-wave reflection of the object or message that is demanded by the equation. Here's something else interesting. Suppose we say that the "c" dimension is an imaginary dimension. In our graph let the perpendicular direction be in multiples of (i). The way the Velocity Equation is constructed we always get a real value because (c i)^2 = -(c^2). The direction of (c) can be forward or backward in time. Here is another interesting result. If we consider "negative" mass, we get by Einstein's mass-energy relation:

* E = (-Mo) (ci)^2 = (-Mo)(-1)(c^2) = Mo c^2.

We get a real and positive result for negative mass and "imaginary c", and the energy is the same as the relation computed with positive mass. The same thing can happen with Einstein's relativistic velocity equation. Because both sides of the equation are squared, the imaginary values may disappear and we can get a real ratio between M1 and Mo with the right combinations. You can work out the various possible combinations of positive, negative, real, and imaginary masses together with superluminal, luminal, and subluminal velocities. Here's an example with FTL velocity and the moving mass in imaginary-land.

* (M1 i)^2 = (Mo)^2 / (1 - (v/c)^2). (v>c)

* (3)(M1)^2 = (Mo)^2. (If v = 2c.)

* 3 = Mo^2 / M1^2.

* (+-) 3^1/2 = (+-) Mo / M1.

By the way, Feynman demonstrates that the appearance of imaginary wave numbers for a wave frequency has a physical interpretation and "means that the form of the wave changes -- the sine wave changes into an exponential." (II, 24-6) So the apparent "cutoff" frequency of a device may mean that it switches into a different modality. If you don't pay attention, you may miss what is going on and just toss out a valid mathematical description of something. The matter-wave packet represents an object of the observer's perception -- usually. So where is the phase-wave "packet"? What if the phase-wave packet can occur in his consciousness as a thought? Huh? The phase-wave packet is the context within which the matter-wave packet resides. Multiplication of the two wave "packets" could represent the interaction of the two. We can call them thought and experience. In this case the interaction means the process of manifesting the truth. When the product of the diffuse non-local thought and the focused local experience are equal to light speed squared, everything matches.

Perception through any of the senses is always an electromagnetic interaction, which means it is mediated by light, by photons. The (c)^2 in the equations represents the signal handshake that occurs between the observer and the object of observation across a separation of space. This is beautifully represented in our mandala. The light forms a spatial interface, and its wave front is orthogonal to the interaction of object and observer.

Quantum mechanically this would be written as P = (phi)(phi)*, where P is the probability density and phi is a wave function and phi* is the complex conjugate "star wave" of the wave function. (See Wolf's Star Wave for an insightful interpretation of the quantum wave function in terms of consciousness.) We also can turn the entire mandala into a quantum bubble of 4-wave mixing phase conjugation. But we do not have to go that far into quantum physics to get the gist of how our mandala works in ordinary experience.

The Velocity Equation already shows us that we have two photons handshaking with orthogonal wave fronts in the imaginary dimension of our space/time -- a retarded one that goes from object to observer, and an advanced one that goes from observer to object -- all at light speed. The advanced one goes backwards in time, so the two photons (the phase conjugate photon-antiphoton pair) seem stuck together into one "particle" as they travel through space. (m / s) = (-m / -s). The terms retarded and advanced are arbitrary relative terms and not intended to reflect on the intelligence of the observer or what or whomever he is observing. Our graph of the Velocity Equation does not show ordinary space/time, it shows the relative magnitudes of the velocities of the components of an interaction. When we detect a slow-moving material particle (the so-called "observable" matter-wave packet), we tend to miss the superluminal phase-wave "packet" that is associated with it (not to speak of the handshaking photon pair) because it is often all spread out on a much bigger scale. When we perceive photons, they are nicely superposed on top of each other in pairs.

But under the dispersion influence of a wave-guide the two split apart and move at different speeds. We call the slower one the matter-wave packet. The slower the matter-wave packet, the faster the phase-wave packet moves. Most of the time our attention is very focused on slow-moving local matter-wave packets. That means our mind is filled with thoughts (the complementary phase-wave portions.) If our attention holds very still on a matter-wave packet, its corresponding phase-wave "packet" fills the entire universe. The mind expands. If we also are sensitive to the wave front, our imagination expands orthogonally into the "light" dimension. Is this enlightenment? Maybe we should take up meditation. Study the equation. Contemplate the mandala.

Physicists tell us that phase waves are dumb and utterly monotonous and carry no energy or information: "Ultimately it is the monotony of phase waves that prevents them from carrying signals." (Herbert, p. 75) Meditation is boring, too, right? Common examples physicists give of real-world phase-wave packets include moving signs on theater marquees or waves flickering across an oscilloscope screen. There are also interesting phenomena of EM phase waves moving superluminally through plasmas and other dispersion media. This should clue you in to what really is going on. Those devices are neither dumb nor monotonous. Viewed properly they can carry a great deal of interesting information.

Our whole information explosion is based on the electronic media. However, to appreciate this, we, as observers, must shift our viewpoint from focusing attention on the localized temporally modulating matter-wave packets to "defocusing" onto the non-local, spatially modulating, superluminal phase-wave "packets". The phase-wave packets are non-local by nature. So it is of no use to set up experiments based on serial, digital viewpoints, when the message is spread out spatially in a global, parallel transmission. This is the fundamental problem with the EPR experiments and all the other arguments that try to show the impossibility of superluminal communication. From the matter-wave viewpoint we process information serially in the temporal dimension. From the phase-wave viewpoint we process information simultaneously in parallel across the spatial dimension. This requires the observer to take a viewpoint orthogonal to and transcendental to the spatial plane that acts as the wave-guide. I would like to know why the scientific establishment has spent so much time and energy trying to prove that superluminal communication is impossible when it is a common ordinary phenomenon that everyone experiences.

They even established a totally arbitrary border guard postulate called COP to keep people away from this unhealthy area. The observer's awareness is a transducer that can perceive information with equal facility in matter-wave, phase-wave or light-wave format depending on the modality of attention selected by the observer. If we try to send a message from point A to point B across space with a series of modulations, the message can only travel via the "group" wave packet modulations. Each phase wave that travels between A and B, regardless of its velocity, is completely regular and devoid of information, just as physicists point out. All the information of the phase wave "packets" is to be found distributed spatially across the interval between A and B along the medium of transmission, the wave guide, as a diffuse non-local pattern of wave interference in space rather than a little local bundle. In other words, you must rotate your attention ninety degrees from the transmission medium (or carrier wave) and perceive the entire length of the wave-guide at once rather than trying to pick up impulses as they come out at one end of a transmission link. This may also necessitate a significant shift of viewpoint perspective on the part of the observer. The group-wave packet and the phase-wave packet form a complementary pair. If one is local, then the other must be non-local. Together they fill space. BOTH are made from superpositions of infinite, monotonous sine waves. The message is not on any particular sine wave just like a sentence is not based on a single letter. It is in the combination of a set of such waves arranged in a certain way in space/time. Whether the signal is experienced as temporal or spatial depends on the observer's viewpoint. The timelike signal will always be subluminal by its very nature. And a lightlike signal will be luminal. Attempts to read a truly spacelike signal in a timelike manner will also fail unless the observer rotates ninety degrees and reads the message subluminally. You can walk down the street and enjoy the view a step at a time, or you can stand back orthogonal to the street at a distance and see the whole street in one glance. It's just a matter of perspective and personal preference.

The so-called Kramers-Kronig relation that trades off absorption and dispersion is certainly true, but acts as a red herring when used to "prove" that superluminal communication is impossible via temporal, serial communication links. That is a non-issue if we are viewing from a non-local, spatial viewpoint. An example of how the K-K relation works is as follows. Suppose you flash a light at a certain time. Before and after that flash time the sine waves that make up its wave packet all cancel out. Couldn't someone awaiting that signal have a special filter that would screen out waves in such a way that he could pick up the light impulse ahead of time? "Yes, you could," say K-K, but their relation says that when his screen absorbs the waves in this way, it will also disperse them in such a way that it changes the phase velocity. His filter is a wave-guide and acts as a dispersion medium. It will adjust the phase velocity so that he ends up seeing the flash precisely at the proper time and not before hand. You can see from this example that the K-K relation is not relevant to our argument. It depends on looking at a signal from the localized, serial, temporal viewpoint. Go back and reread the passage quoted from Ursula Le Guin about the ansible at the beginning of this article. We are now experiencing a global phase transition from habitual focus on matter-wave modality to habitual focus on phase-wave modality. And some people are becoming proficient in both modalities and light-wave modality too. What is the evidence for this? Just look around. The evidence is very evident. You are reading this article. Probably you are looking at a computer screen. Movie screens, TV screens, and computer screens are all wave-guides that operate in phase-wave modality when they interface with the observer. Many of you currently spend a major portion of your waking lives experiencing in phase-wave mode, and you don't even realize it. How do phase-wave experiences differ from matter-wave experiences? Their properties are fundamentally different.

* Matter-wave packets are subject to mass and forces. Phase-wave packets are massless and therefore not subject to forces or any of Newton's laws, including gravity.

* Matter-wave packets are subject to the laws of special and general relativity. Phase-wave packets are not, so a phase wave can easily accelerate from 0 to (c) and on up to infinity without blinking an eye. Phase waves, being massless, can also pass right through black holes without getting either trapped or squeezed. Pretty cool, eh?

* Matter waves require increasing amounts of energy for greater accelerations according to the Einstein relations. A phase wave requires no or almost no energy for acceleration, and has no range limits other than the size of its universe and its guide. Its universe can be its guide.

* A phase wave will faithfully follow the direction of its guide, while a matter wave may jump the track.

* Wave functions are deterministic, but particles (matter-wave packets) are randomly distributed, abiding only by the probabilities of the wave function.

* Matter waves always stay under the c speed limit. Phase waves have no speed limit and you can make them jump about as you please on the wave-guide.

* According to the Velocity Equation, the slower the matter waves go, the faster their corresponding phase waves go. In some situations the phase waves can appear to go slower than the matter waves. For example, when a fan turns at certain speeds you will see a ghostlike fan rotating at slower speed, sometimes even backwards. Turn off a fan and watch phase waves alternately rotate forward and backward as the matter-wave fan blades slow down. These are lower harmonics of the superluminal waves that are too fast to see with your eyes. Another example is a caterpillar that moves forward slowly while ripples move backward along his body. Again, our eyes can only perceive a lower harmonic of the interference patterns as a phase velocity.

* Matter waves can hurt your physical body. Phase waves don't hurt but might cause your body to start looking like a potato if you don't keep your matter waves in shape.

* Compound matter waves are limited by the phase transition rates defined by their interaction rules (regular physics). Compound phase waves can morph freely with no restrictions as to size or shape other than that they require a wave-guide (phase-wave physics). Matter waves also require wave-guides, but they are much more restricted.

* A very "slow" phase wave packet or infinitely fast "standing" phase-wave packet (viewed orthogonally) becomes a mental image in the observer's consciousness. When an observer identifies with a slow phase wave (or any phase wave) it becomes either his matter-wave "body" or his object of attention (or both).

Learn to read the future with a crystal ball wave-guide. Place a ball made of clear glass or crystal over a capital letter "W" in a text. Observer the letter from about 15 cm above the ball. (The distance varies with the size of your ball.) Through the ball you will see the letter, somewhat magnified. The letter is in the object plane phase. Now slowly lift the ball straight toward your eye, focusing on the letter in the center of the ball. The letter will expand, bulge, distort, and then explode and disappear into a completely diffused fuzzy gray field or some fuzzy loops. This is the Fourier transform plane phase. If you keep drawing the ball upward toward your eye, you will see the gray field draw back together and reform into a letter "M". This is the image plane phase. Such a simple lens is an optical computer capable of phase-wave spatial modulations. The glass ball moves as a matter-wave packet. The light waves move at c. The object-image transforms and modulates in space as a phase-wave packet. The entire light field moves with all its component waves shifting in concert. Thus the individual bits of information that form the phase-wave image are not subject to speed limitations.

Your eye receives all the information in the space at one instant as a holistic image rather than getting a transmission bit by bit at a pokey speed limit. Each of the three worlds embodied in the Velocity Equation has its value. The imaginary vacuum world of pure light exists eternally beyond time and space and simply is, quietly embracing, interpenetrating, and enlivening all phenomena. At the single photon level it is coherent and always has perfect phase conjugation in space/time.

Because the imaginary photon is a gauge boson, any number of photons can become mutually coherent and form macroscopic quantum bubbles of any size. A photon's supposedly constant "velocity" has no standard and is nonexistent from its viewpoint. Only matter beings perceive light speed as a constant, and they experience it as a pair of overlapping conjugate velocities. They only detect photon velocities relative to absorption and emission terminals such as electrons. Lacking those, a photon's velocity is indeterminate. Denizens of the matter world live and evolve in localized habitats, and bound time frames, undergoing small-scale transformations as a series of vaguely point-like sensory flashes.

Due to a special property of nucleons (which is another discussion) matter has the ability to appear as stable physical structures that exist and develop in time. The phase world is a dreamlike shape-shifting fantasy (sometimes called the astral world of thoughts and dreams) with no limitations. Phase beings can morph at will and feel no pain. They can travel and communicate freely anywhere in creation with no boundaries. But if they are to become experiential to a matter being, they must be perceived through the medium of a wave-guide.

New-Age people humorously call this mode of perception "channeling". Movie screens, TV screens, and computer screens are nice practical wave-guides that are tuned to phase-wave modality.

Get into your favorite computer action game. The figures in better games nowadays move very realistically. But if you look closely, you will note that Lara Croft does not properly follow the laws of gravity or the other laws of Newton. Also, action figures in cartoons, computer games, and computer-generated films have unlimited morphing ability, unlike your current physical body. Watch a car or a plane on TV. It seems to move at high speeds, but you feel no accelerations or decelerations. When Starship Enterprise activates its warp drive, you observe acceleration to well over light speed, but feel no unpleasant side effects.

In your computer game you can even die many times with virtual blood all over the screen, and then your avatar gets up again like a cartoon character and resumes the "fight". Matter beings killed in battle don't just get up and continue fighting. They have to go build another body first, or whatever you believe they have to do. The killed body lies there and decomposes according to the matter-wave laws of chemistry. Go to an appliance store and observe the shelves of TV screens all showing the same program at once. This is superluminal phase-wave reality. The experience is spatial more than temporal. Watch as the scene changes. Flash! And you are in another place, or time, or viewpoint. All the screens on the shelf change at once, instantly and simultaneously, and in all their details. The cathode ray tube inside each specific TV operates in matter-wave modality. But the observer sees and processes the screen images in phase-wave modality.

Imagine millions of people watching the same show all at the same time, but in different spatial locations all over the country, all over the planet. To say phase waves transmit no energy is a joke. How much energy is transmitted when a million people laugh at a funny scene all at once, or when they cheer a Super Bowl touchdown, or when a late-night infomercial garners 10,000 orders for Golden Hits of the 60's. Somebody's taking you for a ride when they claim that phase-wave "packets" carry no energy potential.


Einstein Test
Back to Collected Evidence

Take the "Think Like Einstein" Test then come back here
.....hint.....click the 186,000 answer all three times.....
Do You Think Like Einstein?

On to more research:

Preliminary Stuff and Definitions.
We'll highlight anything that applies to nonlocality, superluminal, backward time, etc.

Nonlocality With Time Reversibility
Back to Collected Evidence

Excerpts from The Unconscious Quantum: Metaphysics in Modern Physics and Cosmology. Victor J. Stenger 1995. Buffalo NY: Prometheus Books, pp. 145-155.

End notes have been included in the text, with brackets.

Zigzagging through the Vacuum Aether

Salient points:

  • J. P. Vigier has pointed out that an aether consistent with causal precedence and relativity can theoretically exist [Kypriandis, A. and J. P. Vigier. "Action-at-a Distance": The Mystery of Einstein-Podolsky-Rosen Correlations" in Selleri 1988, p. 273]. This has been known for some time and not regarded as troublesome. Vigier refers back to a 1951 paper in which Dirac argued that a quantum aether would not have a definite velocity at certain spacetime points, because of the uncertainty principle [Dirac 1951]. Consequently, an aether in which all velocities are equally probable becomes possible. The resulting state is a vacuum, but at least it does not violate relativity. As mentioned above, Vigier and others have suggested that the vacuum aether may correspond to Bohm's quantum potential.

  • The vacuum is capable of producing interactions between particles at effectively spacelike separations. This occurs when quantum fluctuations in the vacuum cause a particle to zigzag backward and forward through spacetime. Let me explain.

  • No doubt the idea of motion backward in time makes a grievous assault on common sense. The world just does not seem to operate that way, as our ever-aging bodies testify. However, to a particle physicist raised on a diet of Feynman diagrams, motion backward in time is not all that disturbing.

  • All fundamental particle interactions work backward as well as forward and, with rare exceptions, do not distinguish between directions of time

  • [The rare exceptions occur in so-called CP violating interactions involving short-lived particles called K0 and B mesons, which are thought to have different probabilities in time-reversed directions.

  • These can be ignored in the current discussion since they play only a very indirect role in the structure of normal matter].

  • Dirac had developed his fully-relativistic quantum theory of the electron in 1928, and discovered that it contained negative energy solutions.

  • These solutions were identified as anti-electrons or positrons.

  • Positrons were observed as predicted in 1932. Following StŁckelberg [StŁckelberg 1942] and Wheeler, Feynman re-interpreted positrons as electrons moving backward in time [Feynman 1948, 1949a, 1949b, 1965b].

  • Feynman's idea grew out of his earlier work at Princeton as a graduate student of John Wheeler.

  • Together they had developed a theory of electromagnetic waves involving solutions of Maxwell's equations that travel both ways in time, the so called retarded and advanced waves.

  • The advanced waves traveled backward in time, that is, they arrived at the detector before they left their source.

  • Despite their presence as valid solutions to Maxwell's equations, advanced waves had been previously ignored by less bold thinkers [For an amusing anecdote concerning Feynman's first talk on the subject, given before Einstein, Pauli, and other physics greats, see Feynman 1986, pp. 77-80].

  • Feynman later extended the idea to quantum field theory, in which waves are particles and vice versa, associating antiparticles with the advanced waves [Feynman 1948. See also StŁckelberg 1942].

  • Feynman noted that whether you say you have a particle moving forward in time with negative energy, or its antiparticle moving backward in time with positive energy, is really quite arbitrary at the fundamental level.

  • Energy conservation and the other laws of physics remain intact.

  • By reversing the charges and momenta of the backward particles, charge and momentum conservation are unaffected.

  • The violation of causal precedence by tachyons, if they are ever found, will result not from their motion backward in time but from their superluminal motion.

  • In the case of the known elementary particles, whether they move backward or forward in time they still remain within the light cone and retain causal precedence.

  • That is, they do not exchange cause and effect from one reference frame to another.

  • And, as I will now show, the apparent nonlocality proposed by Vigier is simply an artifact that can be understood without superluminal motion.

  • In Fig. 5.3, the Feynman diagram for the zigzag process is illustrated [Purists will object that the Feynman diagram is generally drawn in terms of four-momenta rather space and time.

  • However, the space-time diagrams I show are an equivalent way of describing the same ideas.

  • Even the purists must admit that one can go from a momentum space to a spacetime description by a canonical transformation].

  • As usual, the time axis is up and a single spatial axis is indicated to the right.

  • An electron starts at point A and follows a path through spacetime at constant velocity, changing its position as time progresses.

  • At point B, a fluctuation in the vacuum results in a momentum transfer to the electron, which turns it around so it goes backward in time.

  • At point C, another vacuum fluctuation causes the electron to turn around again and resume its forward course in time, passing point D at the same time as the interaction B, but at a point separated by the distance BD.

  • Thus it appears that the particle has made an instantaneous jump from B to D.

  • Actually, it is possible to view this nonlocal artifact without introducing motion backward in time, as illustrated in Fig. 5.4. Note that all the particles are moving in one time direction.

  • At time C an electron positron pair is created by a vacuum fluctuation.

  • The positron goes to the left and collides with the original electron at B where they annihilate each other, the annihilation energy disappearing into the fluctuating vacuum.

  • In the meantime, the electron from the pair created at C continues on and is interpreted as the original electron from A transported instantaneously from B to D.

  • The net result, in either view, is an effectively instantaneous jump of the electron over the spacelike separation BD.

  • At time B the electron disappears and reappears at D some distance away.

  • A quantum jump, a "spooky action at a distance," has taken place. However, when the event is not just viewed at one instant, but over the progression of time, nothing unusual has taken place.

  • Note that conservation of momentum is maintained overall and no other laws of physics are violated.

  • The impulse delta(p) at B is exactly balanced by the opposite impulse at C.

  • The impulses at B and C individually violate momentum conservation, but this is allowed by the uncertainty principle, provided the spatial distance delta(x) between B and C is less than h/delta(p).

  • Zigzagging in spacetime has been around since Feynman first introduced his diagrams.

  • Feynman diagrams with effective spacelike interactions have appeared in hundreds of physics papers, books, and on thousands of chalkboards for over forty years.

  • They are as much a part of the language of particle physics today as the word particle itself.

  • So Vigier tells us nothing new when he says that quantum field theory allows for effectively spacelike interactions.

  • A particle can undergo a spacelike quantum jump over a distance that is of the order of its de Broglie wavelength.

  • This is simply another way of viewing a particle's wavelike properties that you may find very useful. It provides a picture of a particle traveling through spacetime with a well-defined position and momentum.

  • But because of impulses received from random vacuum fluctuations, the particle randomly jumps around in space within a region whose size is of the order of the particle's wavelength, and so appears to the detection apparatus as a spread-out wave packet.

  • I see no reason why nonlocality, within an indeterministic quantum mechanics that still contains particles of definite momenta and positions, cannot be formulated in this fashion.

  • An ensemble of similarly prepared electrons will have measured positions whose distribution is given by |psi|^2.

  • Could vacuum fluctuations be the hidden variables?

  • If so, they do not provide for nonlocal connections across the universe, or even across the room, for the material bodies of normal experience whose de Broglie wavelengths are infinitesimal.

  • Macroscopic objects do not produce measurable wavelike effects.

  • If a one kilogram object is moving at 10^-10 meters per second, surely very close to being at rest (nothing is ever exactly at rest), it will have a de Broglie wavelength of 7x10^-24 meter, far smaller than the size of a nucleus.

  • Its zigging and zagging would never be noticed.

  • This illustrates why quantum effects are not observable in everyday life, at least for the familiar objects that we think of as material "bodies."

  • And it demonstrates why Vigier's idea, while qualitatively correct, does not provide quantitatively for holistic connections over macroscopic distances - certainly not the whole universe.

  • Light and other electromagnetic waves, however, do exhibit quantum effects on the macroscopic scale.

  • The wavelength of visible light is in the range 4-6x10^-7 meter.

  • Though this is small by macroscopic standards, light diffraction effects are observable to the naked eye.

  • Radio waves can be of macroscopic and even planetary dimensions.

  • Long wavelength radio photons appear instantaneously at widely separated receivers.

  • In the vacuum fluctuation picture being considered here, individual radio photons hit all receivers at once by zigzagging through spacetime - not by some superluminal transfer of energy.

  • The vacuum is thought to be alive with particles and antiparticles that are constantly being created and destroyed, or zigging and zagging through spacetime if you prefer.

  • Measurable effects have been calculated by quantum field theorists and checked to great accuracy against experiment for decades, with no violations of fundamental laws of physics evident or implied.

  • Zigzagging in spacetime can produce what appears to be superluminal motion, but only when the wavelengths of the particles are of comparable dimensions.

  • And even this is the result of random quantum fluctuations, and so cannot be perceived as transmitting superluminal "signals."

  • The measurable effects referred to above are precisely those quantum effects that physicists infer from observations in the laboratory, almost exclusively involving atomic and subatomic phenomena.

  • The objects emitting and absorbing these zigzagging particles have sizes that are comparable to the wavelengths involved.

  • For particles to similarly zigzag across the universe, the wavelengths would have to be of extragalactic extent.

  • Such waves could not be emitted or detected by anything of human dimensions, like a brain or scientific instrument, by any conceivable application of existing knowledge.

  • One cannot simply speculate about possibilities, but must check the numbers.

  • Much of pseudoscience is qualitative hand-waving.

  • Until a concept can be made quantitative, or at least put on a firm logical foundation, it is not science [Some people have proposed that nonlocal effects are occurring in the alleged cold fusion process, so that energy is transferred holistically to a lattice without the telltale gamma rays or neutrons expected from nuclear processes.

  • But this is also impossible for the same quantitative reason described here.

  • The interatomic spacings in a material lattice are far greater than the distances at which spacelike interactions involving nuclear energies can take place.

  • The wavelengths of nuclear particles are comparable to nuclear dimensions].

  • Certainly spacelike correlations across the universe, making the universe one "interconnected whole" are not possible unless you imagine particles of infinite wavelength.

    Spacelike correlations such as close-packed Anu tori are all one and all interconnected. I wonder why this author thinks it impossible.

  • In short, the vacuum aether does not provide a quantitatively feasible metaphor for the holistic universe.

  • And what about the paradoxes of superluminal motion discussed earlier?

  • Do they not exist for the effective superluminal motion produced by zigzagging in spacetime?

  • No, since, as we have seen, no distinction between cause and effect is made at the elementary level.

  • Only with complex systems, such as macroscopic bodies, do causal paradoxes present interpretational problems.

    Local EPR in Reverse Time

  • As long as superluminal effects are not observed in experiments, any interpretation of quantum mechanics that requires nonlocal effects is not parsimonious.

  • If, as many seem to think, conventional quantum mechanics is nonlocal, then proper scientific method demands that we seek alternative, local interpretations.

  • Now I would like to show how the EPR "paradox" can in fact be almost trivially resolved by interpreting the experiment in reverse time.

  • As far back as 1953, French physicist Olivier Costa de Beauregard had argued that the EPR paradox could be resolved by including the action of advanced waves [Costa de Beauregard 1953].

  • He pointed out that the exclusion of advanced waves is a classical prejudice that has no a priori justification.

  • If they are present as solutions of Maxwell's equations, we make an added hypothesis in ruling them out, namely the hypothesis that I have called causal precedence.

  • (Note that this is the same hypothesis used by Einstein to rule out superluminal motion.)

  • The following explanation of the EPR experiment goes along similar lines, but uses Feynman's association of antiparticles with the advanced waves.

  • Let us again consider the Bohm/EPR experiment in which a singlet (total spin zero) system decays into two electrons that go off down opposite beam lines A and B.

  • At the ends of the beam lines are the usual spin meters that can be oriented in any direction perpendicular to the beams.

  • Nonlocality is implied when the decision on what orientation to use at A is made just before the detection, so no time is left for a signal to reach B without traveling faster than light.

  • Now view the EPR experiment from the frame of reference that is time-reversed from the normal, familiar one, as illustrated in Fig. 5.5.

  • The detectors at A and B then become polarized positron emitters.

  • Suppose emitter A is set so that it gives a positron with its spin aligned along an axis x perpendicular to the beam line.

  • Emitter B generally can emit a positron of any arbitrary spin axis orientation.

  • Let us first examine the special case in which the axis of emitter B happens to be the same as A and emits a positron whose spin is opposite to that of A.

  • Then the total spin of the system of two positrons will be zero. When the two positrons moving backward in normal time along the beam lines come together they will form a two positron state that, from angular momentum conservation, will have total spin zero.

  • That is, a singlet state will be locally produced.

  • If instead the spin of B were in the same direction as A, then a triplet state would be formed.

  • However, the experiment, when viewed in the normal time sequence, was designed to include only singlet states as the electron source.

  • Viewing this in reverse time, the triplet states that are formed are discarded (locally) from the sample.

  • [Actually, a triplet state can also be formed from oppositely-spinning electrons, but this will also be discarded from the sample].

  • It is precisely this selection that produces the correlation that is observed in the experiment.

  • Putting it another way, no correlations will be observed in a Bohm/EPR experiment if triplet states are included in the (normal time sequence) source.

  • By using only singlets, we force a correlation.

  • If emitter B emits a positron with a spin along some other arbitrary axis, say the y axis, then it is a matter of chance (with calculable probabilities) whether a singlet or triplet is formed when the positrons collide.

  • But once again a correlation is enforced by locally tossing out the triplet states. The equations for all this are the same as in standard quantum mechanics, and do not fundamentally distinguish between the two directions of time.

  • Thus the quantitative correlation will be the same as that calculated assuming the macroscopic time direction.

  • This way of viewing the EPR experiment may also shed some light on why a deterministic theory is necessarily nonlocal. (Logicians note that I am not saying determinism is the only means for nonlocality).

  • If you insist on producing a specific state, then you must know the orientation of one positron emitter relative to the other at the moment of emission.

  • But this is unnecessary when you are willing to take your chances on what state is produced when the two positrons collide.

  • In short, the Bell's theorem correlation occurs because of a local selection of singlet positron pairs at the point where the positrons come together.

  • Since the elementary processes involved can be viewed in either time direction, and since the process is local in the time-reversed reference frame, we may conclude that the EPR experiment is fundamentally local.

  • An apparent paradox occurs only when we insist on viewing the experiment in our prejudiced time direction.

  • As Costa de Beauregard has put it, "retarded causality looks trivial and advanced causality looks paradoxical" [Costa de Beauregard 1987, p. 263].

  • Actually, I would have said it the opposite.

    The result of the experiment is, of course, tied directly to the conscious decisions to expect a certain result. The fundamentally local conclusion leans heavily in the direction that any superluminal claims is a local time reversal or a reversed wave. However, we should still be open to multiple energy levels or velocities of this reversed wave relative to the forward wave.

  • Costa de Beauregard does not conclude, however, that the consequences of time symmetry are trivial.

  • On the contrary, he takes the directionlessness of time and causality at the elementary level to be so profound as to imply "the existence of subtle phenomena termed 'psychic' in a broad sense, inside the human, the animal, and possibly the vegetal kingdoms" [Costa de Beauregard 1987, p. 284].

  • I could not disagree more.

  • The behavior of the microworld appears paradoxical only when we insist on applying to it concepts from the macroworld that have no meaning at the elementary level.

  • [It might be argued that the EPR experiment, being conducted in a normal-sized laboratory, is part of the "macroworld."

  • However, as I have noted in several places, the distinction between quantum and non-quantum effects is not one of scale.

  • Quantum effects, including anything to do with photons, can appear on any scale.

  • The EPR experiment, whether performed with electrons or photons, involves elementary interactions and so must be viewed in those terms].

  • The fact that our commonsense prejudices do no apply cannot be taken to mean that the microworld possesses mysterious properties.

  • On the contrary, we have found that the microworld is far simpler than the macroworld and can be understood with a minimum set of physical ideas that do not have to be supplemented by emergent qualities such as a direction of time and causal precedence.

    Time Symmetry in Quantum Mechanics

  • The fact that the basic laws of physics do not contain inherent time asymmetry continues to bother modern thinkers.

  • Several have taken the view that since time asymmetry is such an obvious, common experience, our formulation of the laws of physics will not be correct until they demonstrate time asymmetry at their deepest levels [Penrose 1989, pp. 302-347].

  • Others have proposed that the absence of directionality of time in elementary particle physics demonstrates that we should look to macroscopic physics, not elementary particles, for the fundamental laws of nature [Prigogine 1984].

  • My view agrees with what I sense is the developing interdisciplinary consensus:

  • Two sets of natural laws exist, one at the elementary level of fundamental particles that possesses a high degree of symmetry, and another that emerges at the levels of many particles where the elementary symmetries are accidentally broken and new laws appear to describe the structures that thereby evolve.

  • In the usual application of classical physics, the equations that govern the evolution of a physical system must be solved subject to certain boundary conditions.

  • Because of our normal conception of time flow, these boundary conditions are usually taken to be initial conditions - that state of the..........

  • Then the equations predict the future motion of the system, which is usually what we want to know.

  • Prediction is the most common application of science, and its greatest power.

  • However, the equations computed with final conditions can also be used to postdict the past.

  • We can use celestial mechanics to precisely date the past appearances of solar eclipses and comets, verifying certain historical events.

  • For example, an eclipse occurred on March 28, 585 BCE that may have been the one reported to have been predicted by Thales of Miletus that perhaps triggered the development of Greek science and philosophy.

  • Nothing forces us to chose either initial or final boundary conditions.

  • And in fact, the most general methods of classical mechanics make no distinction between initial and final conditions.

  • In quantum mechanics, the situation appears at first glance to be fundamentally different.

  • Conventional quantum mechanical formulations incorporate a distinction between past and future.

  • This is despite the fact that the Schrödinger equation and all relativistic formulations of quantum mechanics are time symmetric.

  • [While the non-relativistic Schrödinger equation does not appear, at first glance, to be time-symmetric, it becomes so if you change ˇ to its complex conjugate *. See the later discussion on the transactional interpretation].

  • In the Copenhagen description of the measurement process, the act of measurement selects the state of a system from among all its possible states.

  • This is a non reversible process, performed in the reference system in which the arrow of time is selected by the prejudice of everyday experience.

  • However, an important subtlety should be noted.

  • The arrow of time, we have seen, is determined by the direction in which entropy increases.

  • If we imagine a local system being organized by outside energy, it will have a decreasing entropy with reference to the arrow of time of the outside system.

  • Should we not define its local time arrow in the opposite direction, and describe measurements in this system with reference to this time direction?

  • Issues of this sort have led quantum cosmologists to investigate ways in which time asymmetry can be built into cosmology, notably Penrose [Penrose 1979], Page [Page 1985], and Hawking [Hawking 1985].

  • However, Gell-Mann and Hartle have shown that a time-symmetric quantum cosmology can be developed using a time-neutral, generalized quantum mechanics of closed systems in which initial and final boundary conditions are related by time reflection symmetry [Gell-Mann 1991].

  • Thus even the quantum universe appears to be time-symmetric (except for a few rare processes), despite our psychological perception of a unique direction of time.

  • In an electronically disseminated paper [Sommers 1994], Paul Sommers has shown how time-symmetric quantum mechanics provides the natural way to view the contextuality of quantum mechanics.

  • In classical physics, as I have noted, the normal procedure is to predict the future paths of particles using a set of initial conditions and solving the appropriate equations of motion.

  • However, in quantum mechanics initial conditions alone do not suffice to determine the future. Each possible outcome is not pre-determined, but occurs with some probability.

  • Furthermore, the set of possible outcomes differs for different arrangements of the detectors.

  • Sommers suggests instead that quantum probabilities must be calculated using final conditions as well as initial conditions.

  • The universe is presumed to be subject to a final boundary condition which limits the set of possible final states, just as the possible final states for a laboratory experiment are limited by a particular arrangement of detectors.

  • He further explores how particular types of final boundary conditions might account for the classical nature of the universe.

  • A quantum system can thus be viewed as being influenced by its future as well as its past.

  • The final condition defines all the possible outcomes, with a quantum mechanical probability calculated for each.

  • One of these outcomes happens in accordance with these probabilities.

  • As long as the dice are being tossed to determine the outcome, that is, we do not have deterministic hidden variables, then the macroworld can develop with a future that is not already written in the stars.


    Costa de Beauregard, O. 1953. Comptes Rendus 236, pp. 1632-1634.
    Costa de Beauregard, Olivier 1987. Time. The Physical Magnitude. Vol. 99 of the Boston Series in the Philosophy of Science, ed. by Robert S. Cohen and Mark W. Wartofsky. Boston: Reidel.
    Dirac, P. A. M. 1951. Nature 168, p. 906.
    Feynman, R. P. 1948. "Spacetime Approach to Non-relativistic Quantum Mechanics." Rev. Mod. Phys. 20, pp. 367-387.
    Feynman, R. P. 1949a. "The Theory of Positrons."Phys. Rev. 76, pp. 749-759.
    Feynman, R. P. 1949b. "Spacetime Approach to Quantum Electrodynamics." Phys. Rev. 76, pp. 769-789.
    Feynman, Richard P. 1965b. "The development of the space-time view of quantum electrodynamics." Nobel Lectures Physics 1963-1970. New York: Elsevier, 1992.
    Feynman, Richard P.1986. Surely You're Joking, Mr. Feynman. London: Unwin. First published by W. W. Norton, 1985.
    Gell-Mann, Murray and James P. Hartle 1991. "Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology" in the Proceedings of the 1st International A. D. Sakarov Conference on Physics, Moscow, May27-31, 1991 and in the Proceedings of the Nato Workshop on the Physical Origin of Time Asymmetry, Mazagon, Spain, September 30-October 4, 1991, ed. by J. Haliwell, J. Perez-Mercader, and W. Zurek, Cambridge University Press, 1992.
    Hawking, S.W. 1985. Physical Review D32, 2989. Page, D. 1985 Physical Review D32, 2496.
    Penrose, Roger 1979 in General Relativity: An Einstein Century Survey, ed. by S. Hawking and W. Israel, Cambridge: Cambridge University Press.
    Penrose, Roger 1989. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford: Oxford University Press.
    Prigogine, Ilya and Isabella Stengers 1984. Order out of Chaos. New York: Bantam.
    Selleri, Franco, ed. 1988. Quantum Mechanics Versus Local Realism: The Einstein Podolsky-Rosen Paradox. New York: Plenum Press.
    Sommers, Paul 1994. "The Role of the Future on Quantum Theory." High Energy Astrophysics Institute, University of Utah, gr-qc.xxx.lanl.gov electronic bulletin board paper number 9404022 (unpublished).
    StŁckelberg, E. C. G. 1942. "La mťchanique du point matťriel en thťorie de la relativitť." Helv. Phys. Acta 15, pp. 23-37.


Eric W. Weisstein's Site
Back to Collected Evidence

Portions of this entry contributed by Waldyr A. Rodrigues, Jr.

  • A superluminal phenomenon is a frame of reference traveling with a speed greater than the speed of light c.

  • There is a putative class of particles dubbed tachyons which are able to travel faster than light.

  • Faster-than-light phenomena violate the usual understanding of the "flow" of time, a state of affairs which is known as the causality problem (and also called the "Shalimar Treaty").

  • It should be noted that while Einstein's theory of special relativity prevents (real) mass, energy, or information from traveling faster than the speed of light c (Lorentz et al. 1952, Brillouin and Sommerfeld 1960,

  • Born and Wolf 1999, Landau and Lifschitz 1997), there is nothing preventing "apparent" motion faster than c (or, in fact, with negative speeds, implying arrival at a destination before leaving the origin).

  • For example, the phase velocity and group velocity of a wave may exceed the speed of light, but in such cases, no energy or information actually travels faster than c.

  • Experiments showing group velocities greater than c include that of Wang et al. (2000), who produced a laser pulse in atomic cesium gas with a group velocity of about 1.7% of the original pulse width.

  • In each case, the observed superluminal propagation is not at odds with causality, and is instead a consequence of classical interference between its constituent frequency components in a region of anomalous dispersion (Wang et al. 2000).

  • It turns out that all relativistic wave equations possesses infinity families of formal solutions with arbitrary speeds raging from zero to infinity, called undistorted progressive waves (UPWs) by Rodrigues and Lu (1997).

  • However, like the arbitrary-speed plane wave solutions, UPWs have infinite energy and therefore cannot be produced in the physical world.

  • However, approximations to these waves with finite energy, called finite aperture approximations (FAA), can be produced and observed experimentally (Maiorino and Rodrigues 1999).

  • Among the infinite family of exact superluminal solutions of the homogeneous wave equation and Maxwell equations are waves known as X-waves. X-waves do not violate special relativity because all superluminal X-waves have wavefronts that travel with the speed parameter c (the speed of light) that appears in the corresponding wave equation.

  • The superluminal motion of the peak is therefore a transitory phenomenon similar to the reshaping phenomenon that occurs (under very special conditions) for waves in dispersive media with absorption or gain and which is in this case responsible for superluminal (or even negative) group velocities (Maiorino and Rodrigues 1999).

  • Several authors have published theories claiming that the speed-of-light barrier imposed by relativity is illusionary. While these "theories" continue to be rejected by the physics community as ill-informed speculation, their proponents continue to promulgate them in rather obscure journals.

  • An example of this kind is the Smarandache hypothesis, which states that there is no such thing as a speed limit in the universe (Smarandache 1998).

  • Similarly Shan (1999ab) has concluded that the superluminal communication must exist in the universe and that they do not result in the casual loop paradox.


Barashenkov, V. and Rodrigues, W. A. Jr. "Launching of Non-Dispersive Sub and Superluminal Beam." N. Cimento B 113, 329-338, 1998.
Born, M. and Wolf, E. Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 7th ed. Cambridge, England: Cambridge University Press, 1999.
Brillouin, L. and Sommerfeld, A. Wave Propagation and Group Velocity. New York: Academic Press, 1960.
Chiao, R. Y.; Garrinson, J. C.; and Mitchel, M. W. "Superluminal Signals and Loop Paradoxes Revisited." Phys. Lett. A 245, 19-25, 1998.
Enders, A. and Nimtz, G. "On Superluminal Barrier Traversal." J. Phys. I (France) 2,169-1698, 1992.
Enders, A. and Nimtz, G. "Evanescent-mode Propagation and Quantum Tunneling." Phys. Rev. E Stat. Phys., Plasmas, Fluids Rel. Interdisc. Topics 48, 632-634, 1993a.
Enders, A. and Nimtz, G. "Zero-Time Tunneling of Evanescent Mode Packets." J. Phys. I (France) 3, 1089-1092, 1993b.
Jakiel, J.; Olkhovsky, V. S.; and Recami, E. "On Superluminal Motions in Photon and Particle Tunnellings." Phys. Lett. A. 248, 156-160, 1998.
Landau, L. D. and Lifschitz, E. M. Electrodynamics of Continuous Media, 2nd ed. Oxford, England: Pergamon Press, 1984.
Lorentz, H. A.; Einstein, A.; Minkowski, H.; and Weyl, H. The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. New York: Dover, 1952.
Maiorino, J. E. and Rodrigues, W. A. Jr. "What Is Superluminal Wave Motion?" Sci. & Tech. Mag. 2, Aug. 1999. http://www.cptec.br/stm.
Matolcsi, T. and Rodrigues, W. A. "Geometry of Spacetime with Superluminal Phenomena." Algebr. Group Geom. 14, 1-16, 1997.
Mignani, R. and Recami, E. Special Relativity Extended to Superluminal Frames and Objects (Classical Theory of Tachyons). Report. November 1973.
Nimtz, G. "Superluminal Signal Velocity." Ann. Phys. 7, 61-68, 1998.
Nimtz, G.; Enders, A.; and Spieker, H. "Photonic Tunneling Times." J. Phys. I (France) 4, 565-570, 1994.
Oliveira, E. C. and Rodrigues, W. A. Jr. "Superluminal Electromagnetic Waves in Free Space." Ann. Physik 7, 654-659, 1998.
Recami, E. "Superluminal Motions in Special Relativity." In Proceedings of the Conference on Mysteries, Puzzles, and Paradoxes in Quantum Mechanics. Lake Garda, Italy, 31 Aug.-5 Sep. 998 (Ed. R. Bonifacio). New York: AIP, 1999.
Rodrigues, W. A. and Lu, J. Y. "On the Existence of Undistorted Progressive Waves (UPWs) of Arbitrary Speeds in Nature." Found. Phys. 27, 435-508, 1997.
Rodrigues, W. A. and Maiorino, J. E. "A Unified Theory for Construction of Arbitrary Speeds (). Solutions of the Relativistic Wave Equations." Random Oper. Stoch. Eq. 4, 355-400, 1996.
Rodrigues, W. A. Jr. and Vaz, J. Jr. "Subluminal and Superluminal Solutions in Vacuum of the Maxwell Equations and the Massless Dirac Equation." In Adv. Appl. Clifford Alg. 7 (Supl.), 453-462, 1997. http://xxx.lanl.gov/abs/hep-th/9511182/.
Rodrigues, W. A. Jr. and Vaz, J. Jr. "Subliminal and Superluminal Electromagnetic Waves and the Lepton Spectrum." In Proc. 4th Int. Conf. Clifford Algebras and Their Applications in Mathematical Physics, Aachen, Germany 1996 (Ed. H. Habetha). Dordrecht, Netherlands: pp. 319-346, 1998. http://xxx.lanl.gov/abs/hep-th/9607231/.
Shan, G. "Quantum Superluminal Communication Does Not Result in Casual Loop." CERN Preprint. 1999a.
Shan, G. "Quantum Superluminal Communication Must Exist." CERN preprint. 1999b.
Smarandache, F. "There Is No Speed Barrier in the Universe." Bull. Pure Appl. Sci., 17D, 61, 1998. http://www.gallup.unm.edu/~smarandache/NoSpLim.htm.
Wang, L. J.; Kuzmich, A.; and Dogariu, A. "Gain-Assisted Superluminal Light Propagation."
Nature 406, 277-279, 2000.

© Eric W. Weisstein


Quantum Nonlocality and the Possibility of Superluminal Effects
Back to Collected Evidence

John G. Cramer

Department of Physics, Box 354290 University of Washington, Seattle, WA 98195-4290, USA Voice: (206) 543-9194 or 616-4635; Fax: (206) 685-4634 E--mail address: cramer@phys.washington.edu Web site: http://faculty.washington.edu/jcramer

Published in the Proceedings of the NASA Breakthrough Propulsion Physics Workshop, Cleveland, OH, August 12-14, 1997


EPR experiments demonstrate that standard quantum mechanics exhibits the property of nonlocality, the enforcement of correlations between separated parts of an entangled quantum systems across spacelike separations. Nonlocality will be clarified using the transactional interpretation of quantum mechanics, and the possibility of superluminal effects (e.g., faster-than-light communication) from nonlocality and non-linear quantum mechanics will be examined.


Albert Einstein disliked quantum mechanics, as developed by Heisenberg, Schrödinger, Dirac, and others, because it had many strange features that ran head-on into Einstein's finely honed intuition and understanding of how a proper universe ought to operate. Over the years he developed a list of objections to the various peculiarities of quantum mechanics. At the top of Einstein's list of complaints was what he called "spooky actions at a distance". Einstein's "spookiness" is now called nonlocality, the mysterious ability of Nature to enforce correlations between separated but entangled parts of a quantum system that are out of speed-of-light contact, to reach faster-than-light across vast spatial distances or even across time itself to ensure that the parts of a quantum system are made to match. To be more specific, locality means that isolated parts of any quantum mechanical system out of speed-of-light contact with other parts of that system are allowed to retain definite relationships or correlations only through memory of previous contact. Nonlocality means that in quantum systems correlations not possible through simple memory are somehow being enforced faster-than-light across space and time. Nonlocality, peculiar though it is, is a fact of quantum systems which has been repeatedly demonstrated in laboratory experiments.

In 1935 Einstein, with his collaborators Boris Podolsky and Nathan Rosen, published a list of objections to quantum mechanics which has come to be known as "the EPR paper" [1], in which they lodged three complaints against quantum mechanics, one of which was nonlocality. The EPR paper argued that "no real change" could take place in one system as a result of a measurement performed on a distant second system, as quantum mechanics requires.

Let's apply the going probability theory that these scientists love to apply to particles. Lets say that there exists the probability that Einstein, Podolsky and Rosen objected to nonlocality because there is the probability that any nonlocality could never be measured and quantified. This would mean a death knell for any science that was based upon measurement, hence, their careers. After all, Al, himself cautioned, with inappropriate self-interest to the others, "In his stand against the ether, Einstein had argued we should not speak of things that can't be measured." This mantra was taken up by all others who realized that if it could not be measured, there was really no need for any measurers. So the velocity of space at 186,000 mps was transferred to being lights velocity, where it could look like it was being measured. In matters of self-interest, space twisting and rotation was changed to matter causing it and light bending was perverted to being bent by gravity rather than what space actually does....the unmeasurable optical medium, space, is able to bend the optical phenomena, itself, while appropriate light sources were said to radiate "travelling" light. They also never mentioned, or realized, that light manifests only near mass, which is the ONLY thing capable of radiating light. Space has NEVER radiated light. They also neglected to mention that there is no such thing as light in deep space, all because the medium of space could not, then, be measured, hence, putting all of them out of the business of measuring.

A decades-long uproar in the physics literature followed the publication of the EPR paper. The founders of quantum mechanics tried to come to grips with the EPR criticisms, and a long inconclusive battle ensued. EPR supporter David Bohm introduced the notion of a "local hidden variable" theory, a partially reformulated alternative to orthodox quantum mechanics that would replace quantum mechanics with a theoretical structure omitting the paradoxical features to which the EPR paper had objected. In Bohm's hidden-variable alternative, all correlation were established locally at sub-light speed.

Neither did the "measurers" want to hear about any "hidden-variable" theory because they couldn't make a living from measuring something that was unmeasurable. So what did the hidden-variable theory become?

Working physicists, however, paid little attention to hidden variable theories. Bohm's approach was far less useful than orthodox quantum mechanics for calculating the behavior of physical systems. Since it was apparently impossible to resolve the EPR/hidden-variable debate by performing an experiment, physicists tended to ignore the whole controversy. The EPR objections were considered problems for philosophers and mystics, not Real Physicists.

"Working physicists, however, paid little attention to hidden variable theories." Of course they did...that is the motive then and that is the motive today.

In 1964 this perception changed. John S. Bell, a theoretical physicist working at the CERN laboratory in Geneva, proved an amazing theorem which demonstrated that certain experimental tests could distinguish the predictions of quantum mechanics from those of any local hidden-variable theory [2,3]. Bell, following the lead of Bohm, had based his calculations not on measurements of position and momentum, the focus of Einstein's arguments, but on measurements of the states of polarization of photons of light.

Even in this "scientific" instance we see Al and his backers of measurements, trying to dominate with "particle" position and momentum, while Bell and Bohm are measuring "states of photons". The necessary science for measuring space, needs to be established and in place before any correct measurments of real science can take place. The question is, Is there enough information about the qualities of space? Even today, there is no guarantee that anyone with a Degree even understands there are no such things as particles. Such things are learned elsewhere.

Excited atoms often produce two photons in a process called a "cascade" involving two successive quantum jumps. Because of angular momentum conservation, if the atom begins and ends with no net angular momentum, the two photons must have correlated polarizations. When such photons travel in opposite directions, angular momentum conservation requires that if one of the photons is measured to have some definite polarization state, the other photon is required by quantum mechanics to have exactly the same polarization state, no matter what measurement is made. Such correlated photon pairs are said to be in an "entangled" quantum states. Experimental tests of Bell's theorem, often called "EPR experiments", usually use entangled photons from such an atomic cascade.

"Excite atoms often produce two photons", it says. How very naive. The twisting still goes on today. Entangled waveforms are said to be preposterous. Action that requires an explanation or measure, if you will, that shows a faster than light measure, is what? Preposterous!! But, science has a measure of these things, today....soooo

EPR experiments measure the coincident arrival of two such photons at opposite ends of the apparatus, as detected by quantum-sensitive photomultiplier tubes after each photon has passed through a polarizing filter or splitter. The photomultipliers at opposite ends of the apparatus produce electrical pulses which, when they occur at the same time, are recorded as a "coincidence" or two photon event. The rate R(q=theta) of such coincident events is measured when the two polarization axes are oriented so as to make a relative angle of q. Then q=theta is changed and the rate measurement is repeated until a complete map of R(q=theta) vs. q=theta is developed.

Now, measure, is giving the field some respectability.

Bell's theorem deals with the way in which the coincidence rate R(q) of an EPR experiment changes as q starts from zero and becomes progressively larger. Bell proved mathematically that for all local hidden-variable theories R(q=theta) must decrease linearly (or less) as q=theta increases, i.e., the fastest possible decrease in R(q=theta) is proportional to q=theta. On the other hand quantum mechanics predicts that the coincidence rate is R(q=theta) = R(0) Cos2(q=theta), so that for small q=theta it will decrease roughly as q=theta^2. Therefore, quantum mechanics and Bell's Theorem make qualitatively different predictions about EPR measurements.

Even under measure, at that time, any EPR experiment was given marginal attention.

When two theories make such distinctly different predictions about the outcome of the same experiment, a measurement can be performed to test them. For quantum mechanics and Bell's theorem this crucial EPR experiment was performed first in 1972 by Freedman and Clauser[4], who demonstrated a 6s=sigma (six standard deviation) violation of Bell's inequality. A decade later the Aspect group in France performed a series of elegant "loophole closing" experiments that demonstrated 46s=sigma violations of Bell's inequality [5,6]. In these experiments the predictions of quantum mechanics were always confirmed, and very significant violations of the Bell Inequalities are demonstrated.

When the first experimental results from EPR experiments became available, they were widely interpreted as a demonstration that hidden variable theories must be wrong. This interpretation changed when it was realized that Bell's theorem assumed a local hidden variable theory, and that nonlocal hidden variable theories can also be constructed that violate Bell's theorem and agree with the experimental measurements. The assumption made by Bell that had been put to the test, therefore, was the assumption of locality, not the assumption of hidden variables. Locality, as promoted by Einstein, was found to be in conflict with experiment.

Even when the Bell's inequality was finally sorted out with the Aspect groups premises and conclusions, the Bell results leaned heavily away from Einstein's locality claims.

Or to put it another way, the intrinsic nonlocality of quantum mechanics has been demonstrated by the experimental tests of Bell's theorem. It has been experimentally demonstrated that nature arranges the correlations between the polarization of the two photons by some faster-than-light mechanism that violates Einstein's intuitions about the intrinsic locality of all natural processes. What Einstein called "spooky actions at a distance" are an important part of the way nature works at the quantum level. Einstein's faster-than-light spooks cannot be ignored.

The conclusion is: There really is, either a "effect then cause" wave traveling backward......or......there is a faster than light velocity in effect, or both. We can even change the common assumption of light velocity to the Transference Velocity of Space, which doesn't have any measurement system....or does it? If one can square light (c^2) one can also square the velocity of space (Vs^2). Or is this already called Phasewave velocity (Vp)?

A clarification about the nature of nonlocality is perhaps appropriate here. Locality in the form of memory could explain the correlation of photon polarizations for any one choice of measurements, e.g., vertical vs. horizontal polarization. It is the freedom of the observer to measure using many different polarization axes (or even circular rather than linear polarization) that leads to the need for nonlocality. To put it another way, if you were constructing a classical science-museum simulation of an EPR experiment (not using actual photons), you would need signal wires running from each measurement to the other to make the simulation operate as quantum mechanics does. Nature seems to have such wires, but we are not allowed to use them.

Above, the hypothesis is forwarded to explain why a nonlocal communication must be some kind of "memory". This memory shouldn't replace the correct communicative mechanism. This is the space structure of the Anu that has already been layed down throughout the whole of space, from the beginning. It is this Anu that is One and communicates superluminally, even with no mass in it. It doesn't really have a complicated memory as it is within the human brain, but space has a grid which acts exactly like the early, unconscious, computer memory....the toroidal circles of magnetic material, hand threaded with tiny wires, in 45 degree diagonals, in two directions. This was used to detect a on(1) and off(0) condition in the computer memory. Anu are also threaded with these magnetic lines and act as unconscious memory. The only duty of the Anu is to create Phi waves (The Golden Ratio). This is the secret of nonlocality. Al understood that geometry was the basis of the perfect medium but he said nothing of the perfect Phi wave of that medium.


Quantum mechanics (QM) was invented in the late 1920's when an embarrassing body of new experimental facts from the microscopic world couldn't be explained by the accepted physics of the period. Heisenberg, Schrödinger, Dirac, and others used a remarkable combination of intuition and brilliance to devise clever ways of "getting the right answer" from a set of arcane mathematical procedures. They somehow accomplished this without understanding in any basic way what their mathematics really meant. The mathematical formalism of quantum mechanics is now trusted by all physicists, its use clear and unambiguous. But even now, six decades later, its meaning remains controversial.

The part of the theory that gives meaning to the mathematical formalism is called the interpretation. For quantum mechanics there are several competing interpretations, with no general consensus as to which should be used. The orthodox interpretation of quantum mechanics used (sparingly) in most physics textbooks was developed primarily by Bohr and Heisenberg and is called the Copenhagen interpretation (CI). It takes a "don't ask -- don't tell" approach to the formalism which focuses exclusively on the outcomes of physical measurements and which forbids the practitioner from asking questions about possible underlying mechanisms that produce the observed effects.

The nonlocality of the quantum mechanics formalism is a source of some difficulty for the Copenhagen interpretation. It is accommodated in the CI through Heisenberg's "knowledge interpretation" which views the quantum mechanical state vector (y=psi) as a mathematically-encoded description of the state of observer knowledge rather than as a description of the objective state of the system observed. For example, in 1960 Heisenberg wrote, "The act of recording, on the other hand, which leads to the reduction of the state, is not a physical, but rather, so to say, a mathematical process. With the sudden change of our knowledge also the mathematical presentation of our knowledge undergoes of course a sudden change." The knowledge interpretation's account of state vector collapse and nonlocality as changes in knowledge is internally consistent, but it is rather subjective, intellectually unappealing, and the source of much of the recent misuse of the Copenhagen interpretation (e.g., "observer-created reality").

And the Copenhagen Interpretation (CI) is now juxtaposed against the transactional interpretation (TI). If you hear the message, please step to the "right" side of the line......

An more objective alternative interpretation of the quantum mechanics formalism is the transactional interpretation (TI) proposed a decade go by the author. A reprint of the original paper[7,8] can be found on the web at

By applying probability theory to our two choices, we can say that there must be more than a mere two probabilities we can choose from.


The transactional interpretation, a leading alternative to the Copenhagen interpretation, uses an explicitly nonlocal transaction model to account for quantum events. This model describes any quantum event as a space-time "handshake" executed through an exchange of retarded waves (y=psi) and advanced waves (y*=psi) as symbolized in the quantum formalism. It is generalized from the time symmetric Lorentz-Dirac electrodynamics introduced by Dirac and on "absorber theory" as originated by Wheeler and Feynman[9,10]. Absorber theory leads to exactly the same predictions as conventional electrodynamics, but it differs from the latter in that it employs a two-way exchange, a "handshake" between advanced and retarded waves across space-time leading to the expected transport of energy and momentum.

CI or TI or AI?

Fig. 1 Schematic of an advanced-retarded transaction

Pictures are worth 1,000 words, so here is 2,000 words worth.

This advanced-retarded handshake, illustrated schematically in Fig. 1, is the basis for the transactional interpretation of quantum mechanics. It is a two-way contract between the future and the past for the purpose of transferring energy, momentum, etc, while observing all of the conservation laws and quantization conditions imposed at the emitter/absorber terminating "boundaries" of the transaction. The transaction is explicitly nonlocal because the future is, in a limited way, affecting the past (at the level of enforcing correlations).

So true, but....

To accept the Copenhagen interpretation one must accept the intrinsic positivism of the approach and its interpretation of solutions of a simple second-order differential equation combining momentum, mass, and energy as a mathematical description of the knowledge of an observer. Similarly, to accept the transactional interpretation it is necessary to accept the use of advanced solutions of wave equations for retroactive confirmation of quantum event transactions, which smacks of backwards causality. No interpretation of quantum mechanics comes without conceptual baggage that some find unacceptable.

Above, is the either/or choice you are forced to make.

With the advanced waves employed in the transactional interpretation it is easy to account for nonlocal effects. Fig. 2 shows a transactional diagram of an EPR experiment, which in the TI involves twin handshakes between both measurements (D1 and D2) and the source (SO). The two-link transaction can only satisfy energy, momentum, and angular momentum conservation laws if the measurement outcomes at D1 and D2 match when the same measurement is made. Thus, the correlation between measurement outcomes is enforced, not across a spacelike interval, but across negative (y*=psi) and positive (y=psi) lightlike intervals (if the EPR experiment uses photons). Therefore, the nonlocality of quantum mechanics is readily accounted for by the transactional interpretation.

Above, the new interpretation is now trying to pass off spacelike intervals as lightlike intervals. Where have we seen non-measurable space attributed to measurable light, in the past? It was from Al and the gang who gathered around Al and his "genius".

Fig. 2 Transactional diagram of an EPR experiment.

From one perspective the advanced-retarded wave combinations used in the transactional description of quantum behavior are quite apparent in the Schrödinger-Dirac formalism itself, so much so as to be almost painfully obvious. Wigner's time reversal operator is, after all, just the operation of complex conjugation, and the complex conjugate of a retarded wave is an advanced wave. What else, one might legitimately ask, could the ubiquitous y*=psi notations of the quantum wave mechanics formalism possibly denote except that the time reversed (or advanced) counterparts of normal (or retarded) y wave functions are playing an important role in a quantum event? What could an overlap integral combining y with y*=psi represent other than the probability of a transaction through an exchange of advanced and retarded waves? At minimum it should be clear that the transactional interpretation is not a clumsy appendage gratuitously grafted onto the formalism of quantum mechanics but rather a description which, after one learns the key to the language, is found to be graphically represented within the quantum wave mechanics formalism itself.

The "key to the language" is the ability to measure the language. Now for more blah, blah, after the quantum "handshake/transaction has taken place between physicists. After detecting the crescendo of the transfer of the key, to future scientists, we come down off the Mount of Lies, to ask a stupid, diversionary question:

Can quantum nonlocality be used for faster-than-light or backward-in-time communication? Perhaps, for example, a message could be telegraphed from one measurement site of the EPR experiment to the other through a judicious choice of which measurement was performed. The simple answer to this question is "No!" Eberhard has used the standard formalism of quantum mechanics to prove a theorem demonstrating the impossibility of such nonlocal superluminal communication [11,12]. Briefly, the quantum operators characterizing the separated measurements always commute, no matter which measurement is chosen, so non-local information transfer is impossible. Nature's superluminal telegraph cannot be diverted to mundane human purposes.

Above, the question, "Can nonlocality be used for faster than light or backward in time communication". The immediate answer from the classic theory killers is a brutal, NO"!!! However.........simply ask the questions, "How immediate do all similar suns communicate, seeing they are all One"? "How immediate do all similar electrons communicate, seeing they are all One"? "How immediate do all similar Anu communicate, seeing they are all One"? "By what velocity, is a thought about the circumference of the universe, traveling"? "Why does any rearrangement of matter, here on earth, immediately rearrange the whole of universe"? "If all these Sun, electron and Anu structures rely upon a constant flow of information to maintain their structure, how is it possible for that information flow to be interrupted, at light velocity, so that they blink off and on"? "Have you ever seen our Sun blink off for 8 minutes due to a light velocity interruption in its information flow"? "Why did the RNG "egg" sensors, around the world, register an immediate response, even hours "before" a "future event", from large groups of people, psychically responding to the coming event - "911"?

Reread original article, "Welcome to Superluminal Phase-wave Civilization", 1, for any non-local energy or information transfer. It has to be there somewhere.


This prohibition against superluminal communication, as stated above, is a part of standard quantum mechanics. However, this prohibition is broken if quantum mechanics is allowed to be slightly "non-linear", a technical term meaning that when quantum waves are superimposed they may generate a small cross-term not present in the standard formalism. Steven Weinberg, Nobel laureate for his theoretical work in unifying the electromagnetic and weak interactions, investigated a theory which introduces small non-linear corrections to standard quantum mechanics [13]. The onset of non-linear behavior is seen in other areas of physics, e.g., laser light in certain media, and, he suggested, might also be present but unnoticed in quantum mechanics. Weinberg's non-linear QM subtly alters certain properties of the standard theory, producing new physical effects that can be detected through precise measurements.

"However, this prohibition is broken if quantum mechanics is allowed to be slightly "non-linear", a technical term meaning that when quantum waves are superimposed they may generate a small cross-term not present in the standard formalism." So here is the "breaker" of that Monolithic "thou shalt not". As long as a slight non-linearity exists in the system, there can be "superluminal communication". Communication is a two way handshake.

Tapping ZPE, requires doped-wire impurities and slightly detuned frequencies. 4/15/02 Robert Grace

Two years after Weinberg's non-linear QM theory was published, Joseph Polchinski published a paper demonstrating that Weinberg's non-linear corrections upset the balance in quantum mechanics that prevents superluminal communication using EPR experiments [14]. Through the new non-linear effects, separated measurements on the same quantum system begin to "talk" to each other and faster-than-light and/or backward-in-time signaling becomes possible. Polchinski describes such an arrangement as an "EPR telephone".

Above, the experiments.....

The Weinberg/Polchinski work had implications that are devastating for the Copenhagen representation of the wave function as "observer knowledge". Polchinski has shown that a tiny non-linear modification transforms the "hidden" nonlocality of the standard QM formalism into a manifest property that can be used for nonlocal observer-to-observer communication. This is completely inconsistent with the Copenhagen "knowledge" interpretation.

Luckily, this author is giving audience to these incredible claims. Elsewhere you might see the whole idea of superluminal communication, either ignored or hopelessly "debated" until you have completely forgotten what the debate was about.

Thus, the Copenhagen interpretation is not "robust" because it is inconsistent with a tiny modification of the standard formalism. The transactional interpretation, on the other hand, can easily accommodate this modification of the formalism and is robust enough to be tested and verified (or falsified) by the same effect. If quantum mechanics has any detectable nonlinearity, we get a faster-than-light and backwards-in-time telephone.

So, the Copenhagen Interpretation was changed. Is it not the CI anymore, yet it carries the same name. In a few years you will see my interpretations renamed by other professional scientists and they will surely call it by their own name, yet the CI was corrected and it still carries its old name. Strange science, this science.

But is quantum mechanics non-linear? Atomic physics experiments have been used by several experimental groups to test Weinberg's non-linear theory. So far, these tests have all been negative, indicating that any non-linearities in the quantum formalism are extremely small, if they exist at all. These negative results are not surprising, however, because the atomic transitions used involve only a few electron-volts of energy. If quantum mechanics does have non-linear properties, they would expected to depend on energy and to appear only at a very high energy scale and particularly at the highest energy densities. Weinberg-Polchinski tests should be made, if possible, with the highest energy particle accelerators. Perhaps then we can find out what connections might be made with Polchinski's EPR telephone.

Yes, indeed, test the hell out of the whole spectrum of non-linearity because therein lays the answers.

This work was supported in part by the Division of Nuclear Sciences of the U. S. Department of Energy under Grant DE-FG06-90ER40537.


[1] Albert Einstein, Boris Podolsky, and Nathan Rosen, (1935) Physical Review 47, 777-780.
[2] John S. Bell, (1964) Physics 1, 195-200.
[3] John S. Bell, (1966) Reviews of Modern Physics 38, 447-452.
[4] Stuart J. Freedman and John F. Clauser, (1972) Physical Review Letters 28, 938-941.
[5] A. Aspect, J. Dalibard, and G. Roger, (1982) Physical Review Letters 49, 91.
[6] A. Aspect, J. Dalibard, and G. Roger, (1982) Physical Review Letters 49, 1804.
[7] John G. Cramer, (1986) Reviews of Modern Physics 58, 647-687.
[8] John G. Cramer, (1988) International Journal of Theoretical Physics 27, 227-236.
[9] J. A. Wheeler and R. P. Feynman, (1945) Reviews of Modern Physics 17, 157.
[10] J. A. Wheeler and R. P. Feynman, (1949) Reviews of Modern Physics 21, 425.
[11] P. H. Eberhard, (1977) Nuovo Cimento 38B, 75.
[12] P. H. Eberhard, (1978) Nuovo Cimento 46B, 392.
[13] Steven Weinberg, (1989) Physical Review Letters 62, 485.
[14] Joseph Polchinski, (1991) Physical Review Letters 66, 397.



1.  Welcome to Superluminal Phasewave Civilization (PDF)

2.  18.3 The 26 Levels and Duration of the Temporal Heirarchy x 64

Impossible Correspondence Index

© Copyright. Robert Grace. 2004