All “interpretations” of Quantum Mechanics (QM) are predicated on the assumption that quantum mathematics is correct. We disagree. The Born rule implies that nature may have a hidden symmetry: |+ψ|2 = |–ψ|2 = probability. If nature uses –ψ then physicists would not recognize that their math is 100% wrong. This hypothesis could explain the mystery that quantum math appears to be the most accurate and productive mathematics humans ever possessed, the source of our high-tech economy, yet scientists cannot agree on what the quantum world is like: does it exist, are there infinitely many worlds, etc. If we change our wave-function from +ψ to –ψ, that will mean that quantum particles follow zero-energy “Elementary Waves” backwards. This symmetry does not conform to Noether’s Theorem because it does not involve physical space, rather an error in the human imagination. Wave-function collapse no longer occurs when a quantum particle is observed. It occurs when a free particle is emitted: when the particle selects which in-coming Elementary Wave to follow backwards. This undermines the foundations of the many-worlds theory. A superposition of states collapses as a particle is emitted, becoming only one state, located in only one world, not many. Type (Method/Approach): No one previously recognized the Born rule could hide a “Born Symmetry”: |+ψ|2 ≡ |–ψ|2. If so, it would be so immense, pervasive, insidious, and invisible that it could explain all quantum “weirdness” even though quantum math is the most accurate and productive science ever.
All “interpretations” of Quantum Mechanics (QM) are predicated on the assumption that quantum mathematics is correct. We disagree. The Born rule implies that nature may have a hidden symmetry: |+ψ|2 = |–ψ|2 = probability. If nature uses –ψ then physicists would not recognize that their math is 100% wrong. This hypothesis could explain the mystery that quantum math appears to be the most accurate and productive mathematics humans ever possessed, the source of our high-tech economy, yet scientists cannot agree on what the quantum world is like: does it exist, are there infinitely many worlds, etc. If we change our wave-function from +ψ to –ψ, that will mean that quantum particles follow zero-energy “Elementary Waves” backwards. This symmetry does not conform to Noether’s Theorem because it does not involve physical space, rather an error in the human imagination. Wave-function collapse no longer occurs when a quantum particle is observed. It occurs when a free particle is emitted: when the particle selects which in-coming Elementary Wave to follow backwards. This undermines the foundations of the many-worlds theory. A superposition of states collapses as a particle is emitted, becoming only one state, located in only one world, not many. Type (Method/Approach): No one previously recognized the Born rule could hide a “Born Symmetry”: |+ψ|2 ≡ |–ψ|2. If so, it would be so immense, pervasive, insidious, and invisible that it could explain all quantum “weirdness” even though quantum math is the most accurate and productive science ever.
Is the quantum world as strange as they say? If this were an unsolved mathematics question, we might try a new angle of attack. We know quantum mechanics (QM) is the most accurate and productive science humans ever had, meaning its probability predictions are accurate. Every probability has two square roots. The Born rule says either would produce the same probability. Assume nature uses the negative of QM’s equations. What could that mean? We’d need to revise Feynman’s path-integrals and Schrödinger’s equation. If waves travel in the opposite direction as what QM believes, that could produce the negative equations. No wave-particle duality. Free particles would follow backwards zero-energy waves coming from detectors. This, surprisingly, gets rid of quantum weirdness. Our proposal is that nature uses the negative of QM’s equations because particles follow zero-energy waves backwards. Considerable evidence fits this model, including a neutron-interferometer and the Davisson-Germer experiments, a quantum-eraser experiment, Wheeler-gedanken and double-slit experiments, Bell-test experiments, Stern-Gerlach, and high-energy scattering experiments. Finally, we propose a plan for how to motivate students to want to study quantum technologies, thereby addressing the most prominent problem in QM today: the shortage of an educated workforce, the scarcity of aspiring students.
The quantum world is allegedly strange. But is it? What if there’s a simple mathematical explanation, and a simple solution? The success of quantum mechanics (QM) arises from the accuracy of its probability predictions, which are obtained by squaring amplitudes (the Born rule). Suppose for a moment that nature uses the negative of QM’s equations. When squared they would yield the same probabilities, confirmed by the same experiments and technological triumphs. If that were true, if nature uses the negative of QM’s equations, then the quantum world would become transparent, easy to understand. No more Schrödinger’s-cat. No quantum-eraser. No backwards-in-time cause-and-effect. No paradoxes nor enigmas. But, what’s a negative quantum equation? It could mean that particles follow zero-energy waves backwards, instead of forwards. That’s still an eccentric idea, a residual strangeness. Overall, it’s a bargain. We could swap one odd idea for another, because wave-particle duality is odd. We are accustomed to wave-particle duality. But we’ll show that experiments support the other arrangement: quantum particles follow zero-energy waves backwards. How could that possibly be true? We present substantial experimental evidence, new mathematics, and six dozen colorful illustrations. This is the Theory of Elementary Waves (TEW).
This is one of a series of articles building a map of elementary waves, based on experimental data and quantum mathematics. Previous articles showed that elementary waves carry no energy. Particles follow them backwards. Why? Elementary rays consist of probability amplitudes, which influence particles because that is what probability amplitudes do. Elementary waves are that part of nature corresponding to quantum mathematics. Since these waves are the physical analogs of quantum equations, those equations provide a roadmap to the world of elementary waves: a map written in hieroglyphs. Quantum math is our Rosetta stone. The quantum world is far, far more similar to the world of everyday experience than quantum experts think. Waves are in a superposition. Particles are not. Wave function collapse does not occur when we measure something. It had occurred much earlier, when the object came into existence. This resolves insoluble problems that stumped John von Neumann. The smooth functioning of a Schrödinger equation abruptly collapses into one specific eigenstate when a gun is fired, not when the bullet hits the target. The bullet that caused World War I is an example. That bullet caused an abrupt collapse of the smooth probabilities of commerce and diplomacy.
A consensus among quantum experts is that the quantum world is not properly understood. It is a mistake to think we can cure quantum weirdness by tinkering with superficial aspects of quantum mechanics (QM). We propose that nature uses (–ψ) as its wave function, whereas QM uses (+ψ). We propose therefore that the Periodical Table should be changed to negative orbitals (–ψ). Surprisingly, this change makes almost no difference to chemistry on a practical level. The Born rule takes the absolute square of an amplitude to obtain a probability to test in chemistry lab P=|–ψ|2=|+ψ|2. We propose a new math based on (–ψ) that is the mirror image of quantum mathematics. We call it the Theory of Elementary Waves (TEW). The negative sign is not an electrical charge. It has nothing to do with Coulomb’s law. Valence electrons are unchanged. Ions, covalent bonds, dipoles, metals, hydrogen bonding and the hydrogen 21 cm line are unchanged. The octet rule and rules for drawing dot structures of molecules do not change. Amino acids, sugars and DNA do not change their handedness. We cite abundant experimental evidence showing that TEW is correct and QM is wrong.
Quantum mechanics is our most successful physical theory. It predicts the behavior of atoms, molecules, and light to ten decimal places. No experiment has ever contradicted it. It also contains a crack at its foundation. The theory’s central equation—the Schrodinger equation—describes a smooth, continuous, perfectly predictable evolution of the quantum state. But whenever anyone performs a measurement, they get a single, definite result. Which result they get appears to be random. The transition from smooth evolution to random outcome is called the “collapse of the wavefunction,” and after nearly a century of analysis, there is no agreed-upon explanation for what causes it, when it occurs, or whether it occurs at all. This is the measurement problem. The measurement problem is not a minor puzzle at the margins of the theory. It is a failure to explain the most basic operation in science: looking at the result of an experiment. Around it cluster other puzzles. Light behaves like a wave in some experiments and like a particle in others—two contradictory descriptions. Two particles that have interacted remain correlated across arbitrary distances, as though communicating faster than light. The probabilities that govern measurement outcomes appear as a postulate—the Born rule—inserted by hand with no deeper justification. And the theory offers no unified picture of reality: quantum mechanics, general relativity, and the standard model of particle physics speak incompatible mathematical languages. A century of effort has produced many interpretations of quantum mechanics. Copenhagen. Many-worlds. De Broglie-Bohm. Objective collapse. Quantum Bayesianism. None has achieved consensus. The measurement problem remains. This document proposes that the source of these puzzles is not quantum mechanics itself. It is a single, invisible assumption made at the very beginning of the theory in 1900—an assumption so deeply embedded that nobody noticed they were making it. Change that assumption, and the puzzles do not get solved. They dissolve. They stop being puzzles. They become predictable consequences of geometry.
In quantum mechanics, the physics of probability amplitudes, that exists in the imaginary and complex mathematical realm, is brought to the measurable realm by the iconic Born rule https://www.w3.org/1998/Math/MathML" display="inline"> | ψ 〉 | ψ 〉 ∗ = | | ψ 〉 | 2 that convert the superposition probability amplitude https://www.w3.org/1998/Math/MathML" display="inline"> | ψ 〉 into a measurable interferometric probability distribution. When Born first introduced his rule, in 1926, he did so in the absence of a physical derivation. In fact, Born never offered a derivation for his most crucial rule. In this chapter a transparent interferometric derivation of Born's rule is given. Furthermore, it is indicated that far from a ‘collapse’ the https://www.w3.org/1998/Math/MathML" display="inline"> | ψ 〉 → | ψ 〉 | ψ 〉 ∗ transition, for interferometric configurations, clearly involves a mathematical expansion . The https://www.w3.org/1998/Math/MathML" display="inline"> | ψ 〉 → | ψ 〉 | ψ 〉 ∗ transition for quantum entanglement is also discussed.