Both Albert Einstein and Louis de Broglie were dissatisfied with the type of quantum probabilities found in standard quantum mechanics. We have recently introduced a new formulation of quantum mechanics in which the quantum gravity probabilities are more closely aligned with what de Broglie was seeking and hoping for. We show that if energy is conserved, then the corresponding total aggregate collision-event count is also conserved. Furthermore, we suggest that there must exist a probability gap above zero, that is, a lowest non-zero individual probability. Individual quantum gravity probabilities are therefore not continuous from zero to one, but instead exhibit a finite probability gap. Quantities larger than one are not single probabilities; they are aggregate collision-event counts obtained by summing many bounded individual probabilities.
References
[1]
Born, M. (1926) Zur quantenmechanik der Sto?vorg?nge. Zeitschrift für Physik, 37, 863-867. https://doi.org/10.1007/bf01397477
[2]
Gudder, S. (1990) Quantum Probability and Operational Statistics. Foundations of Physics, 20, 499-527. https://doi.org/10.1007/bf01883237
[3]
Barnett, S.M., Cresser, J.D., Jeffers, J. and Pegg, D.T. (2014) Quantum Probability Rule: A Generalization of the Theorems of Gleason and Busch. New Journal of Physics, 16, Article 043025. https://doi.org/10.1088/1367-2630/16/4/043025
[4]
Yukalov, V.I., Yukalova, E.P. and Sornette, D. (2014) Quantum Probabilities and Entanglement for Multimode Quantum Systems. Journal of Physics: Conference Series, 497, Article 012034. https://doi.org/10.1088/1742-6596/497/1/012034
[5]
Yukalov, V.I. and Sornette, D. (2016) Quantum Probability and Quantum Decision-making. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374, Article 20150100. https://doi.org/10.1098/rsta.2015.0100
[6]
Han, Y.D. and Choi, T. (2016) Quantum Probability Assignment Limited by Relativistic Causality. Scientific Reports, 6, Article No. 22986. https://doi.org/10.1038/srep22986
[7]
Khrennikov, A., Basieva, I., Pothos, E.M. and Yamato, I. (2018) Quantum Probability in Decision Making from Quantum Information Representation of Neuronal States. Scientific Reports, 8, Article No. 16225. https://doi.org/10.1038/s41598-018-34531-3
[8]
Helland, I.S. (2025) Quantum Probability for Statisticians; Some New Ideas. Methodology and Computing in Applied Probability, 27, Article No. 84. https://doi.org/10.1007/s11009-025-10214-1
Haug, E.G. (2021) Quantum Gravity Hidden in Newton Gravity and How to Unify It with Quantum Mechanics. In: Krasnoholovets, V., Ed., The Origin of Gravity from the First Principles, NOVA Publishing, 133-216.
[11]
Planck, M. (1899) Natuerliche Masseinheiten. Der K?niglich Preussischen Akademie Der Wissenschaften.
[12]
Planck, M. (1906) Vorlesungen über die theorie der w?rmestrahlung. J.A. Barth, p. 163.
[13]
Haug, E.G. (2020) Finding the Planck Length Multiplied by the Speed of Light without Any Knowledge of g, c, or ?, Using a Newton Force Spring. Journal of Physics Communications, 4, Article 075001. https://doi.org/10.1088/2399-6528/ab9dd7
[14]
Haug, E.G. (2022) Planck Units Measured Totally Independently of Big G. Open Journal of Microphysics, 12, 55-85. https://doi.org/10.4236/ojm.2022.122004
[15]
Haug, E.G. (2023) Planck Scale Fluid Mechanics: Measuring the Planck Length from Fluid Mechanics Independent of G. Open Journal of Fluid Dynamics, 13, 250-261. https://doi.org/10.4236/ojfd.2023.135019
[16]
Compton, A.H. (1923) A Quantum Theory of the Scattering of X-Rays by Light Elements. Physical Review, 21, 483-502. https://doi.org/10.1103/physrev.21.483
[17]
Cornu, A. and Baille, J.B. (1873) Détermination nouvelle de la constante de l’attraction et de la densité moyenne de la terre. Comptes Rendus de l’Académie des Sciences de, 76, 954.
[18]
Haug, E.G. (2017) The Ultimate Limits of the Relativistic Rocket Equation. The Planck Photon Rocket. Acta Astronautica, 136, 144-147. https://doi.org/10.1016/j.actaastro.2017.03.011
[19]
Haug, E.G. (2022) Planck Speed: The Missing Speed of Physics? Absolute Still without Breaking Lorentz Symmetry! European Journal of Applied Physics, 4, 11-18. https://doi.org/10.24018/ejphysics.2022.4.1.144
[20]
Einstein, A. (1916) N?herungsweise integration der feldgleichungen der gravitation. Sitzungsberichte der K?niglich Preussischen Akademie der Wissenschaften Berlin.
[21]
De Broglie, L. (1925) Recherches sur la théorie des quanta. Annales de Physique, 10, 22-128. https://doi.org/10.1051/anphys/192510030022
[22]
de Broglie, L. (1930) An Introduction to the Study of Wave Mechanics. Metheum & Co.
[23]
Haug, E.G. (2023) The Compton Wavelength Is the True Matter Wavelength, Linked to the Photon Wavelength, while the de Broglie Wavelength Is Simply a Mathematical Derivative, Understanding this Leads to Unification of Gravity and New Quantum Mechanics. Qeios.
Lema?tre, G. (1927) Un univers homogétne de masse constante et de rayon croissant rendant compte de la vitesse radiale des nétbuleuses extra-galactiques. Annales de la Sociétét Scientifique de Bruxelles, 47, 49.
[26]
Haug, E.G. (2022) Progress in the Composite View of the Newton Gravitational Constant and Its Link to the Planck Scale. Universe, 8, Article 454. https://doi.org/10.3390/universe8090454
[27]
Haug, E.G. (2024) The Extremal Universe Exact Solution from Einstein’s Field Equation Gives the Cosmological Constant Directly. Journal of High Energy Physics, Gravitation and Cosmology, 10, 386-397. https://doi.org/10.4236/jhepgc.2024.101027
[28]
Haug, E.G. (2024) The Planck Computer Is the Quantum Gravity Computer: We Live Inside a Gigantic Computer, the Hubble Sphere Computer? Quantum Reports, 6, 482-492. https://doi.org/10.3390/quantum6030032
[29]
Newton, I. (1686) Philosophiae Naturalis Principia Mathematica. Jussu Societatis Regiae ac Typis Josephi Streater. Prostat Apud Plures Bibliopolas. https://doi.org/10.5479/sil.52126.39088015628399
[30]
Schwarzschild, K. (1916) über das gravitationsfeld eines massenpunktes nach der Ein-stein’schen theorie. Sitzungsberichte der Deutschen Akademie der Wissenschaften zu Berlin, Klasse fur Mathematik, Physik, und Technik, p. 189.
[31]
Schwarzschild, K. (1916) über das gravitationsfeld einer kugel aus inkompressibler flus-sigkeit nach der Einstein’schen theorie. Sitzungsberichte der Deutschen Akademie der Wissenschaften zu Berlin, Klasse fur Mathematik, Physik, und Technik, p. 424.