# PDE boundary conditions that eliminate quantum weirdness: a mathematical game inspired by Kurt Gödel and Alan Turing

## DOI:

https://doi.org/10.24297/jam.v20i.9042## Keywords:

worldview, metaphysics, unsolved problems, mathematical enigmas and puzzles## Abstract

Although boundary condition problems in quantum mathematics (QM) are well known, no one ever used boundary conditions technology to abolish quantum weirdness. We employ boundary conditions to build a mathematical game that is fun to learn, and by using it you will discover that quantum weirdness evaporates and vanishes. Our clever game is so designed that you can solve the boundary condition problems for a single point if-and-only-if you also solve the “weirdness” problem for all of quantum mathematics. Our approach differs radically from Dirichlet, Neumann, Robin, or Wolfram Alpha. We define domain Ω in one-dimension, on which a partial differential equation (PDE) is defined. Point **α** on ∂Ω is the location of a boundary condition game that involves an off-center bi-directional wave solution called** Æ**, an “elementary wave.” Study of this unusual, complex wave is called the Theory of Elementary Waves (TEW). We are inspired by Kurt Gödel and Alan Turing who built mathematical games that demonstrated that axiomatization of all mathematics was impossible. In our machine quantum weirdness vanishes if understood from the perspective of a single point **α**, because that pinpoint teaches us that nature is organized differently than we expect.

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## References

J. Baggott, The Quantum Story: a history in 40 moments, Oxford University Press, 2011. ISBN:978–0-19-956684-6

A. Bassi, K. Lochan, S. Satin, T.P. Singh and H. Ulbricht, “Models of wave function collapse,” Reviews of Modern Physics, 85. 471. DOI: 10.1103/RevModPhys.85.471

A. Becker, What Is Real? Basic Books, 2018. ISBN:978–0-19-956684-6

M. Born, “On the quantum mechanics of collisions,” in J. A. Wheeler and W. H. Zurek (eds.), Quantum Theory and Measurement, Princeton, pp.50-55, 1983. ISBN 978-0-691-08316-2.

J. H. Boyd, “Six reasons to discard wave particle duality.” Journal of Advances in Chemistry, 18, 1-29, 2021. DOI: 10.24297/jac.v18i.8948

J. H. Boyd, “6 reasons to discard wave particle duality,” a YouTube video, 2021, at https://www.youtube.com/watch?v=LD4xXl5gMzg&t=2s.

J. H. Boyd, “The Periodic Table needs negative orbitals in order to eliminate quantum weirdness,” Journal of Advances in Chemistry, vol. 17, pp.88-125, 2020. DOI: 10.24297/jac.v17i.8865

J. H. Boyd, “There are two solutions to the equations of Feynman’s Quantum Electrodynamics (QED); the newly discovered solution is free of quantum weirdness,” Journal of Advances in Physics, vol. 18, pp. 39-57, 2020. DOI: 10.24297/jap.v18i.8831.

J. H. Boyd, “If the propagator of QED were reversed, the mathematics of Nature would be much simpler,” Journal of Advances in Mathematics, vol. 18, pp. 129-153, 2020. DOI: 10.24297/jam.v18i.8746

J. H. Boyd, “A tiny, counterintuitive change to the mathematics of the Schrödinger wave packet and Quantum ElectroDynamics could vastly simplify how we view Nature,” Journal of Advances in Physics, vol. 17, pp. 169-203, 2020. DOI: 10.24297/jap.v17i.8696

J. H. Boyd, “New Schrödinger wave mathematics changes experiments from saying there is, to denying there is quantum weirdness,” Journal of Advances in Mathematics, vol. 18, pp. 82-117, 2020. DOI: 10.24297/jap.v17i.8696

J. H. Boyd, “Decrypting the central mystery of quantum mathematics: Part 1. The double slit experiment,” Journal of Advances in Mathematics, 2 vol. 17, pp. 255-282, 2019. DOI: 10.24297/jam.v17i0.8475

J. H. Boyd, “Decrypting the Central Mystery of Quantum Mathematics: Part 2. A mountain of empirical data supports TEW,” Journal of Advances in Mathematics, vol. 17, pp. 283-314, 2019. DOI: 10.24297/jam.v17i0.8489

J. H. Boyd, “Decrypting the central mystery of quantum mathematics: Part 3. A non-Einstein, non-QM view of Bell test experiments,” Journal of Advances in Mathematics, vol. 17, pp. 315-331, 2019. DOI: 10.24297/jam.v17i0.8490

J. H. Boyd, “Decrypting the central mystery of quantum mathematics: Part 4. In what medium do Elementary Waves travel?” Journal of Advances in Mathematics, vol. 17, pp. 332-351, 2019. DOI: 10.24297/jam.v17i0.8491

J. H. Boyd, “The quantum world is astonishingly similar to our world,” Journal of Advances in Physics, vol. 14, pp. 5598-5610, 2018. DOI: 10.24297/jap.v14i2.7555

J. H. Boyd, “The von Neumann and double slit paradoxes lead to a new Schrödinger wave mathematics,” Journal of Advances in Physics, vol.14, pp. 5812-5834, 2018. doi.org/10.24297/jap.v14i3.7820

J. H. Boyd, “The Boyd Conjecture,” Journal of Advances in Physics, vol. 13, pp. 4830-4837, 2017. DOI: 10.24297/jap.v13i4.6038

J. H. Boyd, “A symmetry hidden at the center of quantum mathematics causes a disconnect between quantum math and quantum mechanics,” Journal of Advances in Mathematics, vol. 13, pp. 7379-7386, 2017. DOI: 10.24297/jam.v13i4.6413

J. H. Boyd, “Paul Dirac’s view of the Theory of Elementary Waves,” Journal of Advances in Physics, vol. 13, pp. 4731-4734, 2017. DOI: 10.24297/jap.v13i3.5921

J. H. Boyd, “A paradigm shift in mathematical physics, Part 1: The Theory of Elementary Waves (TEW),” Journal of Advances in Mathematics, vol. 10, pp. 3828-3839, 2015. DOI: 10.24297/jam.v10i9.1908

J. H. Boyd, “A paradigm shift in mathematical physics, Part 2: A new local realism explains Bell test & other experiments,” Journal of Advances in Mathematics, vol. 10, pp. 3828-3839, 2015. DOI: 10.24297/jam.v10i9.1884

J. H. Boyd, “A paradigm shift in mathematical physics, Part 3: A mirror image of Feynman’s quantum electrodynamics (QED),” Journal of Advances in Mathematics, vol. 11, pp. 3977-3991, 2015. DOI: 10.24297/jam.v11i2.1283

J. H. Boyd, “A paradigm shift in mathematical physics, Part 4: Quantum computers and the local realism of all 4 Bell states,” Journal of Advances in Mathematics, vol. 11, pp. 5476-5493, 2015. DOI: 10.24297/jam.v11i7.1224

J. H. Boyd, “The Theory of Elementary Waves eliminates Wave Particle Duality,” Journal of Advances in Physics, vol. 7, pp. 1916-1922, 2015. DOI: 10.24297/jap.v7i3.1576

J. H. Boyd, “A new variety of local realism explains a Bell test experiment,” Journal of Advances in Physics, vol. 8, pp. 2051-2058, 2015. DOI: 10.24297/jap.v8i1.1541

J. H. Boyd, “A proposed physical analog of a quantum amplitude,” Journal of Advances in Physics, vol. 10, pp. 2774-2783, 2015. DOI: 10.24297/jap.v10i3.1324

J. H. Boyd, “Re-thinking a delayed choice quantum eraser experiment: a simple baseball model,” Physics Essays, vol. 26, pp. 100-109, 2013. DOI: 10.4006/0836-1398-26.1.100

J. H. Boyd, “Re-thinking Alain Aspect’s 1982 Bell test experiment with delayed choice,” Physics Essays, vol. 26, pp. 582-591, 2013. DOI: 10.4006/0836-1398-26.1.100 10.4006/0836-1398-26.4.582

J. H. Boyd, “Rethinking a Wheeler delayed choice gedanken experiment,” Physics Essays, vol. 25, pp. 390-396, 2012. DOI: 10.4006/0836-1398-25.3.390

B. Carlson, “Boundary conditions in the time independent Schrödinger equation,” 2013, https://www.youtube.com/watch?v=dWDJIMjWxlM

J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, “Proposed experiment to test local hidden-variable theories.” Physical Review Letters 23, 880-884, 1969. DOI: 10.1103/PhysRevLett.23.880

L. de Broglie, Research on the Theory of Quanta, translated by André Michaud and Fritz Lewertoff, Montreal: Minkowski Institute Press, 2021. ISBN: 1-927763-99-5.

H. Everett, J. A. Wheeler, B.S. DeWitt, L.N.Cooper, D. Van Vechten, and N. Graham, “Theory of the Universal Wave-Function,” pp. 1-150, in DeWitt, B.S., and N. Graham, editors, The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press (1973). ISBN: 0-691-88131-X

C. A. Fuchs, N. D. Mermin, and R. Schack, "An introduction to QBism with an application to the locality of quantum mechanics," arXiv: 1311.52531v1, November 20, 2013.

C. A. Fuchs and A. Peres, "Quantum theory needs no 'interpretation,'" Physics Today, vol. 53, issue 3, p. 70 (March 2000). DOI: 10.1063/1.88304

K. Gödel, “The incompleteness theorem,” in S. Hawkings, editor, 2005. God Created the Integers, Running Press, Philadelphia, ISBN 0-7624-1922-9. Gödel's paper appears starting on p. 1097

A. Harris, “Animating Schrödinger’s equation.” http://https//www.youtube.com/watch?v=cV2fkDscwvY

W. Heisenberg, The Physical Principles of the Quantum Theory, translated by Carl Eckart and Frank C. Hoyt, Dover Publications. Library of Congress Number 49-11952.

D. Hilbert and W. Ackermann, The Foundations of Mathematical Logic, translated by L. M. Hammond, G. G. Leckie, and R.E. Luce, AMS Chelsea Publishing, Providence R.I., USA, (c1958) ISBN-13: 978-0821820247

R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Physical Review Letters, vol. 55, pp. 2137-2140, 1985. https://doi.org/10.1103/PhysRevLett.55.2137

H. Kaiser, R. Clothier, S. Werner, et. al., "Coherence and spectral filtering in neutron interferometry," Physical Review A, vol. 45, pp. 31-42, 1992. DOI: 10.1103/PhysRevA.45.31

T. S. Kuhn, The Structure of Scientific Revolutions, (Chicago: U. of Chicago Press, 1970. ISBN 978-0-226-45803-8.

L. E. Little, The Theory of Elementary Waves, (New Classics Library, Gainsville, GA), 2009. ISBN: 978-0-932750-84-6.

L. E. Little, “Theory of Elementary Waves,” Physics Essays, vol. 9, pp. 100-134, 1996. DOI: 10.4006/1.3029212

L. E. Little, “Theory of Elementary Waves @ JPL, Feb 2000,” https://www.youtube.com/watch?v=3_9LB0RzgWg

L. E. Little “Introduction to Elementary Waves,” 2016. https://www.youtube.com/watch?v=xx5V03iCbAo&t=16s

L. E. Little, “We have seen these waves,” 2016. https://www.youtube.com/watch?v=xWMiNsD_xdM&t=5s

N. D. Mermin, "Is the moon there when nobody looks? Reality and the quantum theory," Physics Today, 38, 38-47 (1985). DOI: 10.1063/1.880968

N. D. Mermin, ““Measured responses to quantum Bayesianism,” Physics Today, 65 (12) (December 2012), pp. 12-13. DOI: 10.1063/PT.3.1803.

J. R. Pierce, Almost All About Waves, New York: Dover Books, 1974. ISBN: 0-486-45302-2.

E. M. Purcell, "Proceedings of the American Physical Society: Spontaneous Emission Probabilities at Ratio Frequencies" Physical Review. American Physical Society 69 (11–12): 681. http://pages.erau.edu/~reynodb2/colloquia/Purcell_1946_SpontaneousEmission.pdf

H. Schlichtkrull, “Boundary value problems for partial differential equations,” 2013,

a. http://web.math.ku.dk/~schlicht/DL/2013/PDE13.pdf

E. Schrödinger, Collected Papers on Wave Mechanics, Montreal: Minkowski Institute Press, 2020, ISBN: 978-1-927763-81-0.

E. Schrödinger, Abhandlunen zur Wellenmechanik, published by Leipzig: Johann Ambrose Barth, 1928.

J. C. Slater, “Physics and the Wave Equation,” the Josiah Willard Gibbs lecture, at the American Mathematical Society and the Mathematical Association of America, in Chicago, IL, USA Nov 23, 1946

a. https://www.ams.org/journals/bull/1946-52-05/S0002-9904-1946-08558-4/S0002-9904-1946-08558-4.pdf

A. Turing, “On computable numbers, with an application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society, Volume s2-42, Issue 1, 1937, Pages 230–265, DOI: 10.1112/plms/s2-42.1.230

ViaScience, “Bell’s inequality II,” YouTube, https://www.youtube.com/watch?v=8UxYKN1q5sI&t=3s

J. von Neumann, Mathematical Foundations of Quantum Mechanics, translated by Robert T. Beyer, (Princeton NJ: Princeton University Press, c1955). ISBN: 0-691-02893-1

S. A. Werner, R. Clothier, H. Kaiser, et.al., “Spectral filtering in neutron interferometry,” Physical Review Letters, vol. 67, pp.683-686, 1991. DOI: 10.1103/PhysRevLett.67.683

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