New Schrődinger Wave Mathematics Changes Experiments from Saying There is, to Denying There is Quantum Weirdness: it Changes How the Quantum World Appears to Work

With a clever new interpretation of the Schrődinger equation, those quantum experiments that allegedly prove that the quantum world is weird, no longer do so. When we approach the math from an unexpected angle, experiments that appeared to prove that time can go backwards in the quantum world, no longer say that. Experiments that appeared to demonstrate that a particle can be in two places at the same time, no longer say that. This requires a counter-intuitive approach to the math, rather than a counter-intuitive approach to the quantum world. QM makes sensible assumptions and misperceives the quantum to be weird. Our math from the Theory of Elementary Waves (TEW) makes weird assumptions and discovers that the quantum world is actually sensible. We pay the weirdness tax up front. QM does not pay the weirdness tax and is penalized with a permanent misperception of the quantum world. This article is paired with a lively YouTube video (18 minutes is Ted Talk length) that explains the same thing: “New Schrődinger wave mathematics changes experiments from saying there is, to denying there is quantum weirdness.”


Introduction
Although many experiments appear to portray the quantum world as weird, that changes when we adopt a new approach to the mathematics of a Schrődinger wave packet. Experiments that previously appeared to say that entangled particles separated by vast distances can communicate with each other faster than the speed of light, no longer say that. Experiments that previously portrayed wave particle duality, now say that waves and particles are different. To our astonishment, the quantum world is transformed, simply by taking an innovative approach to quantum mathematics.
Some of the greatest geniuses of all time, including Einstein and dozens of Nobel laureates, tried to figure this out, and failed. Surprisingly, this article will give you the code needed to understand what went wrong, and straighten it out.
We will first present the new approach to the Schrődinger wave packet, then apply that math to five quantum experiments to demonstrate that it works, and at the end of this article we will reveal how this solution was arrived at. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][37][38][39]   In what direction is it moving? Usually it is assumed to be stationary, representing the X axis. In our model the line is moving to the left, like a river flowing rapidly to the left, while a wave packet moves across the surface of the river, toward the right. The substrate or bottom layer is flowing to the left throughout Fig. 1. We call the river an Elementary Wave, for which we use the symbol AE from the ancient English and Viking alphabets. A Schrődinger wave packet (Ψ) is an aspect of an Elementary Wave, and is moving in the opposite direction. It is well known in QM that one wave can simultaneously flow in two opposite directions. For example, if a one dimensional plane wave coming from the right hits an infinite potential barrier it will bounce off and double back on top of itself. It becomes one wave moving simultaneously in opposite directions. What is different with TEW is that the second wave is usually absent, until something triggers it to emerge. Thus an elementary wave might travel to the left as a plane wave, but under specialized circumstances, when it encounters a particle, a Schrődinger wave packet will spring into existence, moving to the right and carrying the particle with it. The defining feature of an elementary wave is that it carries an intrinsic trigger mechanism for a Schrődinger wave packet to https://rajpub.com/index.php/jam This is like how a particle travels to a specific detector. QM teaches that the particle is a wave particle that can just fly out the door on its own. They have no convincing explanation for how the item happens to arrive at the detector with a probability that is higher than predicted by random numbers.
TEW says the whole process started earlier. The first step is for the detector to be in contact with you. When you receive their mailing (top row of Fig. 3), it contains a wave packet. When you place the particle in that wave packet (bottom row of Fig. 3), it is shipped to precisely the detector to which it is supposed to go. It is all pre-arranged.

Zero energy waves
Many people believe, erroneously, that waves must carry energy. This is naive. A Schrődinger wave is a zero energy wave. It carries probability amplitudes, not energy. The Born rule is that if you take the absolute square of the amplitude you find the probability of a particle with that energy being there. Thus Schrődinger waves don't push particles around, or even influence them. Schrődinger waves describe Nature by providing us with the square root of the probabilities.
To reiterate: a Schrődinger wave packet may carry the amplitude for a Hamiltonian. But it does NOT contain, nor does it convey ENERGY.
In QM Hilbert space is often said to be highly abstract, in the stratosphere, in the "space of states." In TEW Hilbert space is interwoven in the Euclidean space of everyday experience. This idea of Hilbert space is explained in a reference in the Bibliography. [8] that are subject to wave dynamics. Each wave has an amplitude A, sometimes interacts with physical objects, and can undergo wave interference. We use the letter AE to refer to such an Elementary Wave. It has unusual characteristics.
For example, as we said, it carries an intrinsic trigger mechanism for the emergence of a Schrődinger wave packet. In most AE this wave packet is a latent potential, not expressed.
As we said before, the defining feature of an elementary wave is that it carries an intrinsic trigger mechanism for a Schrődinger wave packet to emerge, moving in the opposite direction. Such a trigger is activated when the AE encounters a particle with precisely the right characteristics.
Such a trigger might be activated if the AE of frequency f approaches a particle whose De Broglie frequency is f = E/2π , and if the particle is about to be launched from a gun, and if the particle makes a random choice of that specific AE rather than the other incident AE's. Under those circumstances the wave packet mechanism might be triggered and the wave packet would carry the particle off toward the detector from which that specific AE is propagating.
In TEW there is no wave particle duality. This is one of the axioms that define TEW. Another defining axiom is that wave function collapse occurs before we measure something. All the energy and momentum are carried in the particles, none of it in the waves. [8] According to TEW, at every point in space there are an infinite number of AE traveling in all directions and at all frequencies, at the speed of light. Because they carry no energy, most of them are invisible to our detectors. Our detectors can only see a wave particle AE-Π (where the symbol "Π" signifies a particle). There is no such thing as a particle without an elementary wave. The intrinsic nature of particles is that they must always be attached to one AE or another. They can jump from one elementary wave to another. But naked particles, disconnected from all elementary waves do not exist.
TEW endorses all of quantum mathematics. QM was invented for the purpose of allowing us to understand and control atoms, molecules, and subatomic particles. Fig. 5 shows a solution to the Schrődinger equation, allowing us to make pictures of electron orbitals of the hydrogen atom. This is one of a vast collection of triumphs of QM. When compared to the purposes for which it was created, QM is the most successful science of all time. This is a domain where TEW has nothing to say other than applause.
The reason that TEW exists is because there is something wrong with QM, as evident in quantum weirdness. Our hypothesis is that TEW will dispel all weirdness.

Equations of an elementary wave (AE)
Ementary waves can travel in two opposite directions simultaneously. Let's derive the equations. [32] We will divide our elementary wave in Fig. 1 into the part traveling left, which we will call Ψ L , and the part traveling right, which we will call Ψ R . The point x 0 (Fig. 1) is where we divide left from right. We will use a subscript of "L" or "R" to label other variables also.
Our thinking is guided by an asymmetry. While a wave function might flow in both directions (symmetrical), energy and momentum only flow to the right, not the left. Thus we anticipate a tiger (Schrődinger Wave) moving to the right, but an elongated tail moving left with high speed but no energy. In many ways we are more interested in the tail, https://rajpub.com/index.php/jam because if you control the tail, you control the tiger.
We define x L to be a location to the left of x 0 (see Fig. 1) and x R to be a position to the right. Our model is one dimensional. The vertical axis in Fig. 1 is amplitude. At x 0 the height and slope of the wave functions must be equal on both sides: Ψ L (x L ) = Ψ R (x R ). We define both slopes to be zero at x 0 : Furthermore the time, frequency and angular frequency must be equal on the two sides: The speed of the line is tricky. We claim the line moves to the left at light speed, while the wave packet (if it exists) moves to the right at v R (often less than light speed). We will attribute light speed c to the Ψ L and v R to Ψ R , remembering in the back of our mind that they are comprised of the same substrate, and the substrate is moving to the left at c.
Therefore the two wavelengths can be different. We will define Note that λ L >> λ R for wave packets moving slower than light.
Journal of Advances in Mathematics Vol (18) (2020) ISSN: 2347-1921 https://rajpub.com/index.php/jam The substrate Ψ L carries zero energy. The wave packet Ψ R also carries zero energy, as we said earlier, but it carries amplitudes for momentum. Variables such as E R , p R and k R exist only on the right side of Fig. 1.
In other words k L = k R . We define Note that p L and E L are undefined. As we said before, velocity v L = c, the speed of light. On the other hand, v R = c unless the wave packet moves at light speed.
We now define our two wave functions: where A is an amplitude variable.
Note that the ingredients with which to build a Schrődinger wave equation only exist to the right of x 0 .

The Schrődinger wave travels to the Right
We define E R = kinetic energy + potential energy (11) Taking the second derivative ∂ 2 /∂x 2 R of the wave function Ψ R = Ae i(k R x R −ωt) (Eq. 8 Right), we get: Multiplying both sides of E = p 2 R /2m + u by Ψ R , we get: which gives us the time independent Schrődinger equation. https://rajpub.com/index.php/jam The time dependent (TDSE) equation can be easily derived by differentiating our wave equation Ψ R = e i(k R x R −ωt) by ∂/∂t: We define E R = ω. Multiplying that by Ψ R we get: We can substitute that into the TISE:

Wave Packet
Until now we have been focusing on waves of a single frequency f and momentum p R . We now change that to a model that includes a cluster of frequencies ∆f and momenta ∆p R . The reason we do so is because Fig. 1 shows a wave packet moving to the right. In order to construct a wave packet we need a cluster of frequencies that we add into a superposition that exhibits constructive interference in a narrow range of distance (∆x R ).
In order to have a cluster of frequencies on the right side of Fig. 1, we need to have the same frequencies on the left. In the remainder of this article we will portray Elementary-Schrődinger Waves as having a nascent wave packet but not an explicit Schrődinger wave packet in most cases. The triggering of a Schrődinger Wave Packet to suddenly appear when the elementary wave approaches a particle, is an unusual event that occurs rarely and under special conditions.
In any volume of space there are a finite number of wave packets but an infinite number of elementary waves.

Elementary Wave traveling to the left
In Equation 8 we already stated the wave function for the elementary wave traveling to the left: When that wave equation is combined with the Schrődinger equation of the wave traveling right, you get a compound equation that defines and elementary wave AE.
Compound equations are well known in quantum mathematics. For example in a wave equation for a potential well it is commonplace to have a plane wave defined if x < 0 or |A| < x, but another wave equation for the well itself (when 0 ≤ x ≤ |A|. Could QM and TEW be two versions of the same theory? Could TEW be an "interpretation" of TEW? No! The way to disprove that idea is if we can design an experiment that would produce different results if QM were true than if TEW were true. We have published three such experimental designs, one of which is found in Fig. 6. At that nanosecond when an electron is fired from the gun, the Laser also fires and closes the right slit at t ≥ 0.
According to TEW, if both slits are open prior to t = 0 then AE from the target screen will cause wave interference on the gun side of the double slit barrier. Therefore when a particle is fired at t = 0, it will be in the context of wave interference. Therefore the target screen will say, "wave interference." If the particle wants to go through the right hand slit, which is now closed, then the right hand side of that interference fringe pattern will be obliterated, as evident in the Figure, in C. The appearance of the target screen will be different if QM is correct, than if TEW is correct.
If the target screen looks like A (see Fig. 6 We previously showed in Fig. 2 that our wave packet is consistent with quantum math. We claim that TEW supports all of quantum math without change. In this section we will show how the TEW version of a Schrődinger wave packet fits perfectly with introductory QM with respect to a plane wave crossing a potential well or tunneling through a barrier. The emphasis in these three examples is that you should be familiar with what TEW is saying vis-á-vis these three experiments. TEW is designed to leave quantum math unchanged, but get rid of quantum weirdness. The weirdness banishing aspect will not be covered in this section. In the center of Fig. 7 is time T1, showing a wave packet traveling toward the right, consisting of a total amplitude (in black) and the real part (in purple) of the amplitude. The energy eigenstate is a sum of plane waves Φ E = Ae ikx which is a wave packet that moves to the right and flattens out over time.
Below that in Fig. 7 are two yellow arrows, reminding us that although the elementary wave travels to the left, the wave packet travels to the right. Below that in Fig. 7 is a later time, T2, when an interesting turbulence is taking place inside the wave packet as it crashes into the barrier. This illustrates what we said earlier about waves moving in two opposite directions in QM. Three things are happening simultaneously: Equation 26 is the wave moving to the right, Eq. 27 is the reflected wave moving to the left, and Eq. 28 represents the decaying potential in the "classically forbidden area" to the right of the barrier. Because the wave is moving into the barrier at the same time as it is reflected in the opposite direction, where ω = E therefore there are standing waves just to the left of the barrier.
You will notice that Fig. 7 and its discussion is identical to introductory QM. Why is that? The goal of TEW is to get rid of the weirdness of the quantum world, but preserve quantum equations unchanged. Our view is that Quantum Mathematics is the most magnificent and powerful science that humans have ever had, and must be preserved intact.
Meanwhile there is something absurdly wrong with weirdness such as Schrődinger's cat or backwards in time cause-and-effect.  Meanwhile the Schrődinger wave packet is following its elementary wave in the opposite direction. At time T2 (bottom of Fig. 8) the wave packet has passed through the barrier, almost as if the barrier were not present. This is "tunneling".
In QM the wave packet and the particle are the same thing. But in TEW we draw a distinction. TEW says there is no such thing as wave particle duality. So how does TEW understand "tunneling"? In our view the Schrődinger waves in our diagrams represent probability amplitudes. This means that if you take the absolute square of the Schrődinger equation |Φ E | 2 = |Φ * E × Φ E | you would find the probability of finding a particle of that energy at that location.
Supposing you had an experiment with a potential barrier in the center, as shown in Fig. 8. If you ran the experiment a thousand times, you might find that the particle from a gun on the left would hit a detector on the left 390 times, and would hit a detector on the right 610 times. That is what we mean in TEW when we say that the wave and particle are different. If you ask, "If the particle is not identical with a wave packet, then how did it tunnel through the wall?" The answer is that we don't know the answer. Like QM, TEW tells you amplitudes and probabilities, it does not tell you "How?" or "Why?"  What we have accomplished so far is to define and describe these elementary waves that are the focus of this article.
We turn now to the work for which TEW is famous, namely its ability to banish weirdness from quantum experiments.
We will apply elementary waves to the analysis of experiments published in physics journals and accepted as valid by the scientific community. The experiments below are not thought to be controversial. Our re-interpretation of the results might be controversial if anyone knew about them, but mostly they are unknown.

A quantum eraser experiment that allegedly "proves" that the quantum world is weird
There is a famous experiment that QM experts say "proves" that the quantum world is weird. This experiment was published by Kim, et.al. in the year 2000. After we explain the QM viewpoint, we will re-analyze this experiment to show the TEW viewpoint. [36,43] A quick summary is that QM claims that wave function collapse occurs at the detectors, whereas TEW claims wave function collapse occurs a dozen nanoseconds earlier, at the laser. That dozen nanoseconds means that the conclusions we draw from this experiment are totally different.

The experiment as explained by QM
In a double slit experiment you see an interference fringe pattern on the target screen if and only if you are ignorant of which slit was used by the particle. This is called "complementarity." If you discover which slit was used, then the pattern vanishes. John Wheeler wondered whether the same thing would be true if there were delayed choice. In other words, suppose you build an experiment in which an interference fringe pattern is etched on the target screen at a time when you do not know which slit was used. But then at a later time you discover that slit A was used. Wheeler's hypothesis was that the interference fringe pattern on the target screen would be erased, backwards in time.
The experiment by Kim, et. al. appears to confirms Wheeler's idea about backwards-in-time erasure of data ( Fig. 10).
In the experiment each photon goes through a double slit barrier, then immediately encounters a BBO Crystal (β − BaB 2 O 4 ) which splits it into two identical photons. One of these photons is sent up into a double slit experiment ( Fig. 11) where an interference fringe pattern is made on the screen. That photon goes less distance, so the pattern on the screen is established BEFORE the lower photon randomly chooses to "click" another detector. If a red and blue When the computer assembles data, it connects data from two detectors: from D 0 paired with one of the other detectors. The final results show that if the lower photon subsequently "clicked" D 1 or D 2 then there is an interference fringe pattern visible on the target screen (in the upper area). But if the lower photon subsequently "clicked" detector D 3 then the interference fringe pattern on the target screen is erased and the screen is blank. The experimenters are confident that this means that data can be erased backwards in time if you discover at a later date which slit was used in a double slit experiment. "Backwards in time" means a nanosecond earlier.
If you limit yourself to the mathematics of QM then you are forced to say that this experiment proves that data can be erased backwards in time. That is an example of "quantum weirdness." You know you have encountered quantum weirdness when you get a migraine. Fortunately, if we view the experiment with the mathematics of TEW, then the same experiment reaches different conclusions. According to TEW this is a simple experiment (Fig. 12). All decisions are made at the Laser, 20± nanoseconds earlier than QM believes that decisions were made. Time does not go backwards. Data are not erased from the target screen.

TEW explanation of the quantum eraser experiment
The target screen is a picture of wave interference in proximity to the laser. What is reported on the target screen is reality. You cannot erase reality. The reality is that there is interference of two Elementary Waves at the laser iff there are two waves (red and blue) impinging on the laser. If there is only one Elementary Wave impinging on the laser, then of course there will be no wave interference to report on the target screen, because you cannot have wave interference with only one wave impinging on the laser.
So how could there be an interference pattern on the target screen at one time, and then it is erased? The answer is, that does not happen. What happens is that if data from the target screen is paired with data from detectors D 1 or D 2 , then there are both red and blue Elementary Waves impinging on the laser (Fig. 13), and therefore there is wave interference at the laser. But if data from detector D 0 is paired with data from detector D 3 , then only a blue wave (see TEW proposes that the data describe reality. We ask the following question of these researchers. If you don't believe that your detector tells you the truth, then why bother doing research? We also ask a second question: If you claim that data from the target screen were erased, why didn't you design the experiment in such a way as to give us a picture of those data before they were erased? We claim the screen in blank (if Detector D 3 is involved) because there never was any data on that screen. When the photon makes that choice the Schrődinger wave packet mechanism is triggered and that wave packet sweeps the photon off its feet and carries it away from the laser. When the wave packet reaches the BBO crystal it splits into two wave packets. Once the photon leaves the laser the ball game is over. The final data are determined. Nothing changes from that moment on. The photons simply follow their Schrődinger waves packet, which follow the elementary waves backwards to the detectors from which those waves are coming.
If the photon randomly chooses # 1 or # 2 (from the list above) then the final data will show an interference pattern on the target screen (D 0 ). If the photon randomly chooses # 3 (from the list above), then the final data will show no interference pattern on the target screen (D 0 ).

When do you pay the "weirdness tax"?
In summary, we have just showed how the conclusions drawn from a quantum eraser experiment are different if we adopt the TEW mathematics. If this experiment says something unbelievable when you look at it through QM mathematical glasses, but says nothing remarkable when you look at it through TEW mathematical glasses, then the "weirdness" is located in the glasses, not in the quantum world.
When people reject TEW it is often because our starting assumption is "too bizarre": namely our claim that a particle can only strike a detector if the particle was previously invited to do so by the detector. This "invitation" consists of a zero energy elementary wave that traveled first from the detector to the Laser, before any photon was fired. It means we live in a different world than we thought we lived in. It is a world where things are more interconnected than we realized! QM says the same thing. They use the word "non-local" to describe this interconnectedness. We claim that "non-local" is too vague a term. "Elementary wave" is more specific. You know a tree by its fruit. The fruit of QM is that data can be erased backwards in time. The fruit of TEW is that data cannot be erased backwards in time.
https://rajpub.com/index.php/jam Both QM and TEW say the quantum world is weird. But TEW pays the "weirdness tax" up front in the form of the doctrine that before a particle strikes a detector, the detector has to invite it. QM starts with more pedestrian and flat footed assumptions and ends up paying a tax penalty forever, in the form of a permanent wrong doctrine that the quantum world cannot be understood by humans. In the quantum world data can be erased backwards in time; in the human world this does not happen. That misperception is a scientific error, which is a heavy tax that QM must pay forever.
We advocate paying your "weirdness tax" right away. Life is easier that way. It allows you to see that the world of everyday experience (the classical world) is like a plate glass window. When you look at the quantum world through that window, it looks like what you would expect.

An attenuated laser experiment disproves wave particle duality
An obvious weirdness in the quantum world, the experts tell us, is that when a single particle is fired from a gun in a double slit experiment, it is a wave-particle that goes through both slits and interferes with itself It is well known that when laser beams cross there can be an interference fringe pattern (Fig. 15). In this case a photon only travels through one slit (i.e. from one of the two lasers) so it cannot interfere with itself. The question is whether this effect would persist if you turn down the intensity of the light to such an extent that there is no photon from either laser in the experiment most of the time. In other words, is the interference pattern caused by the waves even without photons? Obviously you would have to run this experiment for a long time in order to accumulate enough photons to see anything because it takes a photon to make a detector "click." In the Pfleegor and Mandel experiment they did exactly that. They used two "attenuated" laser beams, such that every photon is separated by 200 times as much time when there is no photon. So the photons cannot interfere with each other.
To reiterate, they designed an experiment in which each photon cannot interfere with itself (because it comes from only one laser or the other but not both), nor can it interfere with a photon before or after it. That means that wave interference exists but cannot be attributed to the photons. The experiment shows that zero energy waves from one laser interfere with zero energy waves from the other laser. That contradicts the wave particle duality doctrine.  Data from this experiment force us to say that there are zero energy waves in Nature and that particles, when they happen to come along, follow those waves. Just as a kayak coming down a river encounters standing waves, similarly the bobbing about of the particle in this experiment makes the interfering waves visible. The standing waves in the river are present whether a kayak comes down the river or not.
The experimenters say that variables n 1 and n 2 should be anti-correlated. Any photon must be seen by one detector or the other. If it is seen by one, then it will not be seen by the other. That is the reason for the anti-correlation.

Equation 31
is derived from a long line of equations: and (n 1 ) 2 = n 1 + 1 2 and n 1 n 2 = n 1 + 1 2  Our interpretation of the experiment is almost identical to that of Pfleegor and Mandel, except for the direction of the zero energy waves. The data in Fig. 17 show wave interference. That interference cannot be attributed to a photon interfering with itself because the photon only came through one slit. Nor can the interference be attributed to two separate photons interfering because the lasers were so attenuated that there was a long elapse of time after one photon was fired, before another one was fired.
The only other possibility is that zero energy waves from one laser were interfering with zero energy waves from the other laser. This contradicts the doctrine of wave particle duality, because the experiment shows that waves can exist without particles.
We have proved therefore that there are some zero energy waves in Nature even when no particles are around, and that these waves can interfere with one another. 6 The double slit experiment allegedly "proves" that a particle can be in two places simultaneously QM experts say the double slit experiment proves wave particle duality (Fig. 19). Einstein decisively proved that the QM model must be wrong.
Einstein proved that Fig. 19 cannot possibly be the explanation of how this experiment works. He said that whenever a dot appears anywhere, the wave particle has been localized to be one discreet dot. At that instant it is necessary that every part of the Schrődinger wave everywhere else vanish faster than the speed of light. If that did not happen then the residual parts of the Schrődinger wave could produce a second dot, which would be impossible. No one has  Young thought wave interference was located to the right of the double slit barrier; TEW says it is located to the left.
We use the word "hundreds" metaphorically to mean a "large finite number." According to TEW elementary waves from every point on the target screen travel to the left, through both slits, interfere as they impinge on the gun, and then the particle randomly triggers one specific wave to produce a Schrődinger wave packet. The wave packet follows the elementary wave trajectory (backwards) through one and only one of the slits (it doesn't matter which) to exactly that point α from which that specific elementary wave is emanating. When the particle leaves the gun the experiment becomes deterministic: the particle is tethered to point α, where it is destined to make a dot. This mechanism will produce exactly the same wave pattern on the target screen, and the same mathematics, as the QM model (Fig. 21). Waves from various points on the target screen refract through the two slits with a phase difference (θ B − θ A ). The phase difference determines whether the wave interference incident to the gun is constructive, intermediate, or destructive. That influences the probability of the particle randomly choosing that particular incident wave. For example, if the point α on the target screen is located such that there is a phase difference of (θ B − θ A ) = π then there will be destructive interference at the gun and therefore no likelihood that a particle will be triggered by that incident wave, and therefore point α will remain black in the final dataset.
On the other hand, the equation describing the Schrődinger wave packet as it moves away from the particle gun (Equation 23), is: Our model (bottom of Fig. 20) differs from the conventional model of the double slit experiment (Fig. 19) in that there are hundreds of such elementary waves, traveling in the opposite direction as expected, and a random decision is made among them by the particle. As we showed elsewhere, this picture involves a concept of Hilbert space and

A question asked by John von Neumann
Von Neumann said that the Schrődinger equation is a deterministic equation. He said that it was therefore a mystery how the randomness got into QM. Our answer is that the randomness can be blamed on the particle. The randomness is not due to the Schrődinger equation. There are hundreds of elementary waves impinging on the particle in the gun.
We know from Brownian motion that particles are intrinsically random. When the particle randomly chooses one elementary wave to respond to, that decision has an impact on the trigger mechanism of that wave. It causes a Schrődinger wave packet to abruptly emerge from that one elementary wave. No other incident wave blossoms a Schrődinger wave packet. Therefore it is the particle that introduces randomness into QM. As we said, the particle's random decision causes one elementary wave to change and be different than all its siblings. Not only is that Schrődinger wave packet deterministic (as von Neumann says), it follows backwards the path of the elementary wave from which it emerged, so that a dot appears on point α on the target screen with a probability of one. We assume that α is that point from which the elementary wave is emanating. Our model provides a simple explanation of complementarity. If you know which slit a particle uses then the interference fringe pattern on the target screen vanishes. With TEW this is no longer a mystery.

Complementarity explained
In order to know which slit we need to introduce a lamp (or low energy source) into the experiment, along with a detector as shown in Fig. 22. Whenever the light is switched "ON" that energy is much more than the zero energy elementary waves. The light's energy destroys the superposition additivity of the elementary waves. If two waves cannot be added together into a superposition, then two waves cannot interfere with one another. Therefore waves from point α on the target screen, when they travel through slit A will not interfere with waves from point α that travel through slit B. What the final data on the target screen gives us is a picture of wave interference incident to the gun. There would be no such interference if the light were turned on.
The final data on the target screen simply tell us the truth, which is "You have destroyed the wave interference at the gun." There is nothing mysterious about it.
Empirically we observe that sometimes elementary waves possess, and other times they do not possess superposition additivity. Mostly they lack that capability. For example, if two adjacent points α and β on the target screen send elementary waves towards the two slits and the light is off, the waves from α cannot be added to the waves from β. We don't know why this is true. We simply observe Nature and tell you what we see.

The Bell test experiments allegedly "prove" quantum weirdness
The Bell test experiments are alleged to be a fountain of quantum weirdness. That weirdness disappears when we apply TEW technology to the experiments. [7,27,33] It is well known that when Alice and Bob test their entangled photons at random angles θ 1 and θ 2 , their results obey this equation: P = cos 2 (θ 2 − θ 1 ) where P is the probability of both Alice and Bob seeing a photon simultaneously.
That equation contradicts Einstein's prediction. We will use the word "probability" instead of "coincidence rate," which is the word used in QM discussions of this phenomenon.

Bi-Rays defined
TEW can explain the results based on Bi-Rays which consist of two elementary rays traveling coaxially in opposite directions (Fig. 23). A pair of photons, when emitted, is already embedded in such a Bi-Ray that extends from Alice's equipment, across fiberoptic cable to Bob's equipment. The relationship P = cos 2 (θ 2 − θ 1 ) is intrinsic to that Bi-Ray.
Therefore Alice's equipment does not send a "signal" to Bob's equipment. The experimental results are explained with a small number of starting assumptions, and with no evidence of quantum weirdness.
Here is a more detailed explanation of what we just said.
Einstein proposed in 1935 that something was missing from QM. His thought experiment was to imagine that an atom produces two particles with equal but opposite spin traveling in opposite directions. If you do an experiment on one, you learn something about the other. The term "local realism" has become a code word meaning "Einstein's idea of how the Nature works."  As we said before, TEW implies that everywhere in Nature there are an infinite number of zero energy elementary waves traveling at the speed of light in all directions and at all frequencies. The vast majority of them are attached to no particle, and are therefore invisible to our detectors.
That implies that every elementary ray has a mate, namely an identical ray traveling coaxially in the opposite direction.
This pair forms of "Bi-Ray." Two particles are entangled if they follow the same Bi-Ray in opposite directions. The probability of a particle following a Bi-Ray is the amplitude of it following one of the rays, times the amplitude of it following the other. Think of a railroad engine. It has an amplitude for following each of the two tracks.
What makes the countervailing rays coherent is the particle following them. It would be as if two rails were held together by a locomotive, not by the railroad ties.

Bi-Ray trigonometry
The key to understanding why Bi-Rays explain the Bell test experiments is that the two mono-rays relate to each other in complex ways. There are four eigenstates of the elementary rays individually ("V"=Vertical and"H"= Horizontal) . We use the color red to signify that a ray is moving to the right; and blue means left. Bi-Rays are more complicated than monorays and have these four Eigenstates: Fig . 24 shows the complicated situation that exists inside a Bell test experiment. On the left is Alice who randomly sets her polarizer to angle θ 1 . On the right is Bob who randomly sets his polarizer to angle θ 2 . Between Alice and Bob is fiberoptic cable and a 2-photon-source (see yellow rectangles). The research question is, "What is the probability of Alice and Bob both seeing a photon simultaneously?" QM asks that same question but uses the term "coincidence rate" instead of "probability."  A law of probability is that the probability of Alice and Bob both seeing a photon is a product of the probability of each of them seeing a photon in Eigenstate A. Therefore the top layer of Fig. 24 will give us: The probability of both people seeing a photon simultaneously is the sum of the probabilities in each of the four Eigenstates. When we turn the crank of the trigonometry machinery the trigonometry does the work for us. The probability of both Alice and Bob seeing a photon simultaneously is: If we use polar coordinates, so the angle V is zero, and H is π/2, then we get: which can be factored: for which there is a trigonometry equation, which gives us: The result, P = cos 2 (θ 2 − θ 1 ), is the probability of both Alice and Bob seeing a photon simultaneously. In the literature about Bell test experiments, this is called a "Coincidence Rate." It is exactly the answer found by QM if the two photons are emitted with the same orientation. Figs. 25 and 26 show that for any value of θ 1 chosen by Alice, if Bob chooses a random angle θ 2 , then the height of the graph will give the probability that they will both simultaneously see a photon at angles θ 1 and θ 2 .
The results reported so far are based on a 2-photon source that emits photons with a correlated polarization. For example, the famous Aspect, Dalibard and Roger experiment of 1982 used a calcium-40 source that produced two photons with correlated polarization and obtained similar results as ours. [7,27] There would be different results if the two photons were orthogonal to one another at birth. That would happen for example if the pair of photons was produced by a Wollaston prism. Then the final probability would be Z = sin 2 (θ 2 − θ 1 ).

What do the Bell test experiments tell us about the quantum world?
In experiment after experiment QM has asserted that the quantum world is weird. Yet when we change to the TEW mathematics we find that the quantum world is not weird. The quantum world is very similar to the classical world of  For example, in the Bell test experiments QM asserts that wave function collapse occurs when something is measured.
Thus when Alice observes her photon at angle θ 1 , that reality comes into existence. Prior to her observation that photon had no specific characteristics or attributes. When Bob observes his photon at angle θ 2 that reality also comes into existence. So how quickly would we expect there to be an equation showing that the correlation rate of Alice and Bob's observation is cos 2 (θ 2 − θ 1 )?
From the viewpoint of QM it is astonishing that this result emerges instantaneously, without time for a signal from Alice's equipment to reach Bob at the speed of light. That is why they conclude that instantaneous communication has occurred. As Franco Selleri said, "With QM a lot of miracles happen!" When we shift to the TEW mathematics, things look entirely different. The fact that the correlation rate between Alice's data and Bob's data is P = cos 2 (θ 2 − θ 1 ) is what we would expect, once we know that there is a Bi-Ray stretching from Alice to Bob. Nothing else could happen, unless you change the 2-photon source. In TEW nothing travels faster than the speed of light, and wave function collapse occurs before you measure something. Wave function collapse happens when a pair of photons is born into that bi-ray environment instead of another bi-ray environment.
We have demonstrated in an earlier publication that TEW is able to explain quantum computers. [10] Thus the alleged deep mysteries of the quantum world vanish if we adopt TEW technology.

The Purcell effect shows that quantum experts already know about elementary waves
Many experiments have established the Purcell effect, which is that an excited atom will decay more rapidly and emit a photon (to carry off the excess energy) if the excited atom is in a micro-cavity whose diameter is a multiple of λ/2 where λ is the wavelength of the photon about to be emitted. [42] Information about the size of the cavity must be carried somehow into the excited atom, before it decays and emits a photon. Otherwise how does the atom know that it is a hospitable environment? That information enters the atom with zero energy. QM experts give this phenomenon the names "available states" or "modes of the cavity." TEW agrees and simply uses a different word. What the experts call an "available state," we call an "elementary wave." For example, if a Rydberg atom (such as sodium, cesium, beryllium, magnesium or calcium) is heated in an oven, then a laser is used to excite the outer electron to a higher energy state, and the excited atom is put into a resonant cavity (•), the excited atom will decay hundreds of times faster and lose its excess energy (as a photon) if the width of the cavity is a multiple of the wavelength λ of the photon which the atom wants to emit. This was discovered in the 1946 by Edward Purcell. [42] This experiment demonstrates that quantum experts are familiar with elementary waves. They simply give them a different name than we do. What we call "elementary waves" in resonant cavities, QM experts call "available states" or "modes of the cavity." 9 Conclusion: Where did these ideas come from?
Einstein and dozens of other geniuses searched for the past century to try to find the solution to the quantum enigma, and didn't find it. [5,6] Yet here it is, given to you free of charge in this article. How is that possible? How did it happen?

A brief history of TEW
The ideas presented in this article evolved over five decades. That evolution did not occur at the major academic centers such as CERN, Stanford research park, the Institute of Advanced Studies, the University of Innsbruck, nor MIT. It occurred outside the horizon of mainstream science. When it peeked up from obscurity the leaders of science did not recognize it and rejected it, much as what happened to Alfred Wegener (see below) First there was the counter-intuitive idea that particles follow zero energy waves backwards. After working alone for thirty years a physicist named Lewis E. Little discovered that idea in March 1993.
Twenty seven years later, in the year 2020, there was a refinement of that idea that emerged for the first time in the article you are now reading. Particles don't follow waves backwards. There are Schrődinger waves that represent the particle, and the Schrődinger waves travel in the expected direction. But Schrődinger wave packets are part of a larger elementary wave traveling in the opposite direction as the particle.
These two colorful people, Lewis Little and myself, are cousins who have been in dialog for 60 years. To understand where TEW came from, you need a thumbnail sketch of that relationship. Seven years ago we had a fight and are no longer speaking to each other. Here is a sketch of how TEW emerged from our turbulent relationship.
In high school Lewis Little's IQ was tested and found to be 196. He was a lot smarter, and two years older than me.
We would sit on the living room floor at my grandmother's house on holidays, playing 3 dimensional tic-tack-toe (on a cube that was 4 x 4 x 4). The problem with 3 dimensional tic-tack-toe is that whoever goes first can always win. So we designed and played 4 dimensional tic-tack-toe (on a 5 x 5 x 5 x 5 hypercube). The diagonals were difficult to picture.
I don't remember who won.
I went to Brown University to study mathematics based on Lewis's recommendation of Brown. I think he graduated summa cum laude in physics three years before I graduated in math. When he graduated he said to me, "Either QM is crazy, or I am." I thought at the time, "Lewis, you argue with everyone about everything!" Although Little had a huge impact on my life, his love of arguing was annoying.

Why QM inflicts suffering on anyone who is logical
What did Little mean when he said that QM "was crazy"? QM is the most powerful and accurate science that humans have ever had, and is the basis of our entire high tech economy. As a mathematics it works well. But rarely can we picture what the quantum world looks like. That missing picture can be called "metaphysics." Since it is a jumble of incoherent images, each of which is out-of-focus, "metaphysics" has a bad reputation in QM. Experts say it should be avoided. David Mermin said, "Shut up and calculate!" What he meant when he said said, "Shut up" was: "Stop thinking. Stop using the non-mathematical parts of your brain! Stop using images to picture things." What Lewis Little hated about QM was the metaphysics, or rather the lack of a metaphysics. He could not bring himself to stop thinking. "I think in images," he once said. A man whose brain was ruled by a tyranny of hyper-logic, That is what he meant when he said, "Either QM is crazy, or I am."

Thirty years in isolation
Little went to graduate school at Princeton University to answer the question about whether he or QM "was crazy.' He concluded that it was QM and not he who was crazy. At the time, I thought, "Are you SURE that it is not you that is crazy? It could be BOTH!" His PhD in physics was from New York University in 1974.
Many people with a PhD in physics end up in Wall Street, investing in the stock market. Little developed a career trading in commodities. That was his daytime job. Nights and weekends were devoted to his passion, which was to rethink QM so as to discover a theory without weirdness.
He read physics and drilled down in QM for thirty years, working in isolation, talking to no one. Aristotle's thinking was one of his guides. Little told me that his notebooks show a pattern: every five years he would cover about the same territory, without any progress. He went around in circles six times. "I kept making the same mistake Einstein made, which was to believe in wave particle duality," he said.
After thirty years working alone he had the peculiar thought in 1993 that, "Could it be that the wave is traveling in the opposite direction as the particle?" That was a "Eureka!" moment, when all the pieces of the puzzle fell into place. It was the happiest day of his life. He believed that he had triumphed, that he would now become a professor of physics, fabulously wealthy and famous. Unfortunately that did not happen.
When he sent a scholarly paper to leading physics journals, he expected that he would be applauded. That did not happen. His manuscript was repeatedly rejected. Journals would send it back without peer review, perhaps with "This isn't science" written on the front page, or with no comment other than, "Not appropriate for this journal." After years of universal rejection it was finally published in Physics Essays in 1996, [37] and he was invited to give a talk at the Jet

Who is afraid of preposterous ideas, and who isn't
It may be that the scientific community will never grow interested in TEW. Physicists sometimes take me aside and encourage me, saying that no one else can explain these things that TEW can explain. "Don't give up," they tell me, "No one else can explain the double slit experiment, but you can!" These encouraging physicists are timid and afraid of ruining their reputation. No physicists want their name associated with this heresy.
I am convinced that TEW is correct. The greatest disaster I can imagine is when our generation dies of old age, if TEW peters out and vanishes from the face of the earth. It is an idea that might not enter human history again. I owe it to my grandchildren for their generation to have an opportunity to hear about this idea. So I awaken at 4 AM day after day, because 4 AM is when my brain is able to think about the unthinkable, and imagine the unimaginable.
Sometimes I am lazy and sleep in until 5 AM.
is based on each of us encouraging the other one to be who we really are.
In the year 2020 it occurred to me that it was a mistake to say that particles follow elementary waves backwards.
There is a mountain of data saying that particles and Schrődinger wave packets travel in the same direction. This led me to recognize that the apparent contradictions of the quantum world might be embedded in the structure of quantum waves, namely that they travel in opposite directions simultaneously.
I now think Little's insight of 1993 half wrong, and half right. There must be some compromise, some middle ground between TEW and QM. My personal style is one of seeking compromises. Whereas Little prefers "Either-Or," I prefer "Both-And" It dawned on me that elementary waves and Schrődinger waves are two aspects of the same thing. In ancient Rome there was a god named Janus who had two faces (Fig. 30). He/she was the god of doorways, gates, passages, transitions, beginnings and endings, time and duality. He/she was like an elementary wave. Mathematicians live in a world where "bizarre" is an advantage for a new idea. Do mathematicians ever stumble across new ideas that are not "bizarre"? The Taniyama-Shimura-Weil conjecture was bizarre: that there was a relationship between modularity and elliptical curves. Andrew Weil's proof of Fermat's last theorem using deformation theory in Galois representations was bizarre. Bernhard Riemann's geometry was so bizarre that other mathematicians, such as Arthur Cayley rejected it as useless, declaring Euclid's was the only geometry that made sense. A century later Albert Einstein based his general theory of relativity on Riemann.
For me TEW is a clever new idea that explains a mountain of empirical data, and allows us to see that the quantum world is not "weird." As I said before, the quantum world cannot be "weird" because when you open your eyes and see the world of everyday experience, which is transparent, what you are seeing is the quantum world, which is right there, staring back at you.

Plate tectonics compared to TEW
TEW doubled the size of the universe we live in. To the half of Nature that consists of matter and energy, it added the other half that contains neither matter nor energy.
Franco Selleri (1936 -2013) said that history has demonstrated that in science the majority opinion is usually wrong.
When someone proposes a preposterous idea, scientists promptly reject the idea. [34] That is what happened to Alfred Wegener's idea in 1912. [46] He was the first person to ever propose that there had been a continent that he named "Pangea", composed of all the continents. When Pangea split apart the pieces drifted to their present locations. Every reasonable scientist on earth denounced this idea as stupid because there was no force strong enough to move continents across the face of the earth. No map of the seabed existed in 1912. They had no idea there was a mid-Atlantic mountain range. They didn't know that the Indian ocean floor tells us that India moved north from Madagascar and slammed into Siberia, causing the Himalayan mountains to rise. Wegener's ridiculous idea was banned from science for half a century. Then it came back in the form of plate tectonics and has dominated geology ever since.
So you never know. Perhaps my friend David was wrong and a century from now scientists will be interested in TEW.
It is clear that I will not see it during my lifetime. After my 76th birthday it dawned on me that possibly I might not be immortal. That is a startling new thought.

Acknowledgment:
The author thanks Lewis E. Little who taught him the Theory of Elementary Waves, and challenged this author to develop a corresponding mathematics.
Author Biography: The author was raised in the family of a factory worker in New Jersey, USA. He is the first member of his family to graduate from college. In elementary school he and his family were astonished to discover that he had a talent in mathematics. He subsequently graduated with advanced degrees from Harvard, Yale, Brown and Case Western Reserve Universities, and spent a decade on the faculty of the National Institutes of Health in Bethesda, Maryland. He was ordained a priest in the Episcopal Church. He also served as Chairman of Psychiatry at Waterbury Hospital in CT.
His passion was treating indigent patients with severe chronic illnesses. He is now retired. Other aspects of his