"Does Destructive Interference Destroy Energy?"

Kirk T. McDonald, Professor, Princeton University: "While the answer is well-known to be NO, and energy is conserved in the superposition of waves, discussion of this is sparse in textbooks." 


"The key here is that the energy associated with a wave has two forms, generically called “kinetic” and “potential”, that are equal for a wave propagating in a single direction, while in the case of destructive (or constructive) interference of counterpropagating waves one form of energy decreases and the other increases such that the total energy remains constant".


Mention of "the trivial case of a null wave (with zero energy)"



> Counterpropagating Waves from Two Sources in One Dimension


>> Transverse Waves on a Stretched String

Destructive interference destroys the potential energy, but doubles the kinetic energy.

Constructive interference doubles the potential energy, but destroys the kinetic energy.


>> Transmission Line

Destructive interference destroys the inductive energy, but doubles the capacitive energy.  
Constructive interference doubles the inductive energy, but destroys the capacitive energy.


>> Plane Electromagnetic Waves
Destructive interference destroys the magnetic energy, but doubles the electric energy. 
Constructive interference doubles the magnetic energy, but destroys the electric energy.



> The Double Slit Experiment with a Single Source


>> Consider scalar waves (i.e., scalar diffraction theory)
>> Consider flow of energy via the Poynting vector S = E × H



1. Plane wave:
2. Plane Waves, Spherical Waves, and Gaussian Beams
Excerpt: "If a pebble is dropped into still water, it generates a wave which spreads out in all directions from the point where the pebble hit the surface of the water. In this appendix, we shall discuss what happens when the number of dimensions of the wave increases from two (an x–y plane) to three (an x–y–z space)."
Relevant Quora Question
3. Foundations of "Scalar Diffraction Theory"

4. Professor Kirk T. McDonald

(Picture with the director of Fermi Lab)


"What happens if two laser beams hit each other precisely 180 degrees out of phase? Do they cancel each other out? Is there actually a net loss of energy then?"


The Aharonov-Bohm effect


Consider the experimental setting shown at the picture below with an electron emitter, a double-slit screen, a solenoid generating a magnetic field B strictly confined inside the solenoid (no magnetic field on the outside) and a phosphorescent screen where the electrons fall.


If you change the intensity of the magnetic field of the solenoid, do you expect an influence on the electrons?

As mentioned, there is no magnetic field on the outside to exert a force on the electrons.

The experiment shows that there is an influence. This is explained by the Aharonov-Bohm effect.


Video of demonstration: https://youtu.be/OgDPK5MLVnE (Link posted by Dr. Robert Duncan)
Demonstration: http://demonstrations.wolfram.com/AharonovBohmEffect/



The Aharonov–Bohm effect: "an electrically charged particle is affected by an electromagnetic potential (V, A), despite being confined to a region in which both the magnetic field B and electric field E are zero."

(cf. charged particle in Faraday cage)

Original Aharonov-Bohm paper: http://bit.ly/2AgNHsG


An electromagnetic potential is a "four-vector". The first component is the electric potential (or electrostatic potential) which is a scalar potential and the other three make the magnetic vector potential.


Reference paper: http://mafija.fmf.uni-lj.si/seminar/files/2010_2011/seminar_aharonov.pdf




"The Aharonov-Bohm effect or when the value of the (electromagnetic) (vector) potential A matters"

An effect that can be used for remote detection of magnetic fields

https://www.youtube.com/watch?v=1P68eba7zEs - link posted by Dr. Robert Duncan
Transcript part I - The Math
"Well, I hope you like quantum mechanics. This is a course on classical electromagnetism but I figure I can sneak in a little enrichment here and there. So we're going to mix in some quantum.
As we've said many times before, the actual value of potential whether it be A or V isn't supposed to matter. Only the fields are physical and classically that's always true. But hey, by now no one's going to be all that surprised if quantum mechanics strolls in and casually flips over the table.
The basic plan in quantum mechanics is to obtain the eigen functions describing allowed particle states by solving Hψ equals Εψ (note: attached 1st figure) with the Hamiltonian H being something with that we sometimes call the kinetic term minus H bar squared over 2m * del squared and a potential term U.
In E and M we modify this a bit. The scalar potential V fits right in at the end. We just replace U with q times V the potential energy of a charge q in a potential V. The kinetic term has to be fiddled with in a not obvious way to accommodate a vector potential. We'll just take this as a given. It's not our goal today to drive all this from first principles; just to get the flavor.
At the end of the day though we expect certain rules to be obeyed. We expect that if A and V do anything weird, it will have at the very least be something that turns out not to be observable. Sort of like how psy squared is often complex. But the only observable thing is the square magnitude of psy which is always real because things are real. But there's a little snag: something called Berry's phase.
Suppose you have an eigenstate psy prime of a particular Hamiltonian, one that doesn't have a vector potential present. Think of it as your base state. Then we change things up by moving into a region that doesn't have a magnetic field but does have a vector potential (A). So A is nonzero but del cross A is zero. In this situation the eigenstates psy of this new Hamiltonian with nonzero A can be built from the old psy primes. In fact they differ only by a phase factor where the phase can be obtained from a line integral of A where the line is the path traveled by some object. This is pretty abstract so let me emphasize what's happening here." (Please refer to next part).



Transcript part II 
"The wave functions for particles in a vector potential, even where there is no B field and maybe not even an E field, pick up phases when they travel through that region. Different phases depending on the pass involved. But no problem, right? The square magnitude of the new psy makes the phase factor go away, right? Unless God forbid we have more than one particle. Then we get interference, real physically observable interference between the two particles that depends on the value of the vector potential. Ridiculous as it sounds, this is pretty easy to rig up and test empirically. Remember if it can't be tested, it might as well be a unicorn.
A solenoid has a B field inside and no B field outside and so classically someone outside the solenoid shouldn't be able to tell whether there's anything going on inside the solenoid. Maybe there's a field in there, maybe someone turned it off, who can say. A stream of particles behaving quantum mechanically can say, as it turns out. Take that stream and split it, so that some go around the solenoid one way and some go the other way and they then recombined.
If there's no field in the solenoid, A is zero outside the solenoid and nothing weird happens. If there's a B in the solenoid it turns out that there's a non zero A outside the solenoid which we'd normally write off as unphysical. But it will lead to a Berry phase and those particles and interference on the other side. And that actually happens. We call this the Aharonov-Bohm effect and it has been intensely studied in the domain of quantum conductance.
As computing tech gets smaller and smaller. The fact that electrons do all sorts of intrinsically quantum things matters more and more. So here's a fairly common arrangement and studies of quantum conductance. We have a conducting channel, a little strip of silicon or whatever that electrons can move through. In the middle of that channel are a couple of antidots: circular non conductive regions from which electrons are excluded. And we can run a little magnetic field through the region, normal to the screen. In this particular example the B field is non zero in some of the channel. I'm using this set up because the core physics is still there and mostly because I happen to like one of the authors from one of the relevant studies.
Anyway, we shoot a current through the channel and something magical happens as we dial up the electron energy. So here comes some electrons shooting through the channel. Here's a plot of electron energy versus conductance. Electrons run through this thing taking every possible path going around the antidots. So some will go this way, some will kind of go over here and skip along and go that way. Maybe some guys can try to go that way. The magnetic field in the region is trying to steer those electrons around in circles, with a circle radius depending on the velocity of the electrons which in turn depends on the electron energy. As we ramp up the energy we eventually hit a radius that exactly matches the radius of the antidot pair. Classically what would happen at that point is electrons would get stuck in orbits around the antidots. Just kind of going around and around and what we do see experimentally is a big dip in the measured conductance at and about that energy. But that's not all we see.
We also see these finer oscillations in the conductance, layered on top of the coarser pattern. And if we do all the detailed calculations we find they have exactly the right period to be attributed to the Aharonov-Bohm effect. The vector potential in the neighborhood, not the field is leading to interference between electrons taking different routes through this thing. And that interference oscillates between constructive and destructive. There is no conceivable way that this could happen classically, it is simply impossible. But in quantum systems it does happen. So let's sum up. Classically a particle can't sense potentials, only fields. But a particle behaving quantum mechanically can sort of smell nearby B fields through their resulting vector potentials. And that's cool I guess."



Bohm-Aharonov Effect, Interferometry and Weaponisation - T.E. Bearden 1984

Document Approved For Release by the CIA:
"In theory one may deliberately make a beam containing zero electric and magnetic fields, simply by properly phase-locking together two or more beams (...) all at the same frequency."
"In the perfect hypothetical case, for example, two single-frequency beams phase-locked together 180 degrees apart" (Fig.1)
"In the real world, one would be phase-locking two beams containing narrow bandwidths, and how much zero-field is obtained at the center of the bandwidth would depend on the "Q" (sharpness) of each beam".
"Note particularly that one may deliberately create the zero-field, pure potential condition by opposing magnetic or electrical fields so that they sum to zero (Figure 1). That is, the "zero fields" can be resultant vector zeros, where the combining vector components still exist. In this case, one creates a deliberate, artificial scalar potential which contains all the energies of the separate infolded [Bohm's term] vector field used to make the resultant vector zero. All this infolded energy has been transformed to stress of spacetime, or pure potential. (Table 1). However, it does not have a randomized substructure as is usual in quantum electrodynamics, but has a determined, known substructure consisting of the constructed infolded E and B field vectors."
"If one rhythmically varies all the individual summation vectors in the substructure by the same factor, one produces pure potential stress waves -- scalar waves -- without ever creating external electric and magnetic fields. These are pure waves of spacetime, and they are oscillating curvatures of spacetime itself. They are pure waves of compression and rarefaction of the massless charge of spacetime, and are properly represented as longitudinal waves rather than transverse waves. Thus they are non Hertzian in nature."
"According to the Bohm-Aharonov effect, if two zero-field scalar wave beams are crossed in a distant region, real physical effects exist in that distance interference zone. In short, one may create "transmitting scalar interferometers" (Figure 2) to produce energetic effects at a distance, in a specified region."
"In the interference zone of two intersecting scalar beams, the out-of-phase regions no longer have sum-zeroed substructure components, so E and B fields appear there, created by the now out-of-phase substructure superpositions."
"By establishing a resonance between the distant site and the projector sites, randomized field zeroing that occurs in the natural temperature oscillations at the distant site can be utilized to extract energy from the site to the projectors".
The Perfect Missile Shield
"By utilizing three-dimensional truncated Fourier expansion techniques with multiple transmitted frequencies, the scalar interferometer beams can be made to interfere in specific geometric patterns, such as giant hemispheric shells of glowing energy, quite useful in a strategic ABM defense of a large area."


"One synchronously rotates the interferometer beams so as to gradually change the location of the distant interference zone, which is creating the spot."
"By using multiple transmitters and fairly broad beams, an interference grid can be created over an entire continent or substantial portions of it."
"In each grid block in the interference zone, energy can be produced or extracted".
"Direct evidence for such usage by the Soviets over North America has been presented.[q]"
"The Soviet scalar electromagnetics weapons development program appears to have been well underway at the time of the beginning of the "microwave radiation" of the U.S. Embassy in Moscow, about 1959 or 1960. (Table 8*). A good description of the history of this microwave radiation has been given by Brodeur from a normal electromagnetics viewpoint.[r]. Note that "twin beams" were utilized in the radiation, at least from time to time and a variety of systemological difficulties were induced in personnel in the Embassy."
*Table mentions that four U.S. Presidents requested for the microwave radiation to cease. It was decreased significantly and then increased.
"The West is almost totally defenseless against these frightful Soviet scalar electromagnetics weapons, and an immediate "Manhattan Project" to develop defenses" "is urgently needed if we are to survive at all".
(T.E. Bearden 1984)



Tom Bearden comments on Interferometer Weapons ("Longituinal EM wave weapons") and Quantum Weapons

"Also, just about every major weapons lab on Earth has finally discovered longitudinal EM waves, it appears." 

"To my knowledge, the most powerful weapons on earth are the quantum potential weapons I first wrote about in Gravitobiology".


"Three nations have them: Brazil, Russia (under ruthless KGB control, not in the regular armed forces), and the "friendly little nation". Presently China either is just getting them or is very close to getting them. China has certainly had longitudinal EM wave weapons (interferometer weapons) for some decades. Lunev put in a thing in his book which clearly shows that."

"The Chinese also seem to have recently deployed another weapon, an extraordinary type of electromagnetic pulse weapon, but one which uses negative energy pulses instead of positive energy pulses. (...) I also believe the KGB (Russians) have them".


At another text, T.E. Bearden says that the French government almost certainly developed Intererometer Weapons. "Some physicists in the French government must have realized that plasmas - such as were being used in the Priore tube - could also transduce input transverse EM waves into longitudinal EM waves. So they started with that, and would have logically progressed to the LW interferometry."


Reference on the Priore project (Word document) http://www.cheniere.org/priore/background.doc


Note: MEG stands for "Motionless Electromagnetic Generator"