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Better and Deeper Quantum Mechanics! Thoughts on a New Definition of Momentum That Makes Physics Simpler and More Consistent

Espen Gaarder Haug

Published Dec 1, 2018• 0 citations
OpenAlex

Abstract

We suggest that momentum should be redefined in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy–momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation leads us to a new relativistic wave equation and a new and likely better QM. Further, we show that Minkowski space-time is unnecessarily complex and that a simplified, special case of Minkowski space-time is more consistent with the quantum world. Also, we show how the Heisenberg principle breaks down at the Planck scale, which opens this area of physics up for hidden variable theories once again. Many of the mystical interpretations in modern QM are rooted in the development of an unnecessarily complex theory that drives much speculation and is therefore subject to many different and even conflicting interpretations.

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Better Quantum Mechanics ? Thoughts on a New Definition of Momentum That Makes Physics Simpler and More Consistent

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We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.

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We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.

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We will here show that there is one more relativistic wave equation rooted in the relativistic energy Compton moment relation, which should not be confused with the standard relativistic energy momentum relation. The standard momentum is, from a quantum perspective, rooted in the de Broglie wave. The de Broglie wave is not mathematically defined for rest-mass particles and has strange properties such as converging to infinity when the particle is almost at rest. As mentioned in the previous paper, the de Broglie wave is likely just a mathematical derivative of the true matter wave, which we have good reasons to think is the Compton wave. A wave equation that satisfies the relativistic energy Compton momentum relation will, in addition automatically satisfy the standard relativistic energy momentum relation, so there is no conflict between these two relations. The new one related to Compton is just the deeper reality and help explain why it gives simpler and more elegant relativistic wave equations, which are likely easier to interpret in terms of the physical reality.

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In this paper, we discuss in brief the most common wave equations in quantum mechanics and some recent development in wave mechanics. We also present two new quantum wave mechanics equations based on the Compton momentum. We also question the idea that energy and mass are scalars, and we claim they are vectors instead. We have good reasons to think that the standard momentum is a mathematical derivative of the more fundamental Compton momentum. This will hopefully simplify interpretations of quantum mechanics significantly; our new relativistic wave equations look promising, but need further investigation into what they predict. This way of looking at quantum mechanics in new light is not in conflict with existing equations, but they are supplemental to the collection of existing wave equations. We prove mathematically that if one satisfies our new relativistic energy Compton momentum relation, one also satisfies the standard relativistic energy momentum relation automatically. They are two sides of the same coin, where the relations to the Compton wavelength likely represent the deeper reality, so we have reasons to think our new wave mechanics addresses a deeper level of understanding than the existing conception. We also look at our new wave equation in relation to hydrogen-like atoms; we follow the “standard approach” used for the Schro dinger equation of putting it in polar coordinate form and, by change of variables, finding three ODEs and their solutions. We give a table summary of our new ODEs and their solutions compared to the well-known solutions of the Schro dinger equation.

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Espen Gaarder Haug

We demonstrate that the Compton wavelength mathematically corresponds exactly to the photon wavelength of rest mass energy. On the other hand, the de Broglie wavelength is not defined for a rest-mass particle, but if the particle is nearly at rest, then the de Broglie wavelength approaches infinity, and the corresponding photon wavelength of the rest-mass energy is then this length times \(\frac{v}{c}\) again, that is it approaches zero when \(v\) approaches zero. Our analysis indicates that the de Broglie wavelength appears to be a pure mathematical derivative of the Compton wavelength. Everything that can be expressed with the de Broglie wavelength can essentially be expressed by the Compton wavelength. We also demonstrate how spectral lines from atoms and chemical elements are linked to the Compton wavelength of the electron and that the Rydberg constant is not needed. Furthermore, we demonstrate that the Compton frequency is embedded in the Schrödinger equation, the Dirac equation, and the Klein-Gordon equation, where the Planck constant actually cancels out, and the de Broglie wavelength is not present in these equations. The Compton frequency seems to be linked to the quantization in quantum mechanics rather than the Planck constant. Additionally, we discuss recent literature that shows a remarkably simple but overlooked way to quantize Newton’s and General Relativity theories, as well as other gravity theories, and also how to link them to the Planck scale. This, once again, leads to the conclusion that the Compton wavelength and Compton frequency are related to the quantization of matter and, thereby, the quantization of gravity. In addition, the Planck length plays a crucial role in quantum gravity, as demonstrated. Viewing physics through the de Broglie wavelength is like looking at the world through a distorted lens; switch to the Compton wavelength, and the distortion is removed, allowing us to see simplicity and clarity even in complex phenomena such as quantum gravity. Remarkably, Heisenberg’s uncertainty principle seems to need modification to a Certainty-Uncertainty Principle when one understands that the Compton wavelength is the true wavelength of matter. Gravity is related to the Planck mass particle and is again related to absolute rest, which lasts for the Planck time. This certainty-uncertainty principle leads to the unification of gravity and quantum mechanics.

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Espen Gaarder Haug

We demonstrate that the Compton wavelength mathematically corresponds exactly to the photon wavelength of rest mass energy. On the other hand, the de Broglie wavelength is not defined for a rest-mass particle, but if the particle is nearly at rest, then the de Broglie wavelength approaches infinity, and the corresponding photon wavelength of the rest-mass energy is then this length times \(\frac{v}{c}\) again, that is it approaches zero when \(v\) approaches zero. Our analysis indicates that the de Broglie wavelength appears to be a pure mathematical derivative of the Compton wavelength. Everything that can be expressed with the de Broglie wavelength can essentially be expressed by the Compton wavelength. We also demonstrate how spectral lines from atoms and chemical elements are linked to the Compton wavelength of the electron and that the Rydberg constant is not needed. Furthermore, we demonstrate that the Compton frequency is embedded in the Schrödinger equation, the Dirac equation, and the Klein-Gordon equation, where the Planck constant actually cancels out, and the de Broglie wavelength is not present in these equations. The Compton frequency seems to be linked to the quantization in quantum mechanics rather than the Planck constant. Additionally, we discuss recent literature that shows a remarkably simple but overlooked way to quantize Newton’s and General Relativity theories, as well as other gravity theories, and also how to link them to the Planck scale. This, once again, leads to the conclusion that the Compton wavelength and Compton frequency are related to the quantization of matter and, thereby, the quantization of gravity. In addition, the Planck length plays a crucial role in quantum gravity, as demonstrated. Viewing physics through the de Broglie wavelength is like looking at the world through a distorted lens; switch to the Compton wavelength, and the distortion is removed, allowing us to see simplicity and clarity even in complex phenomena such as quantum gravity. Remarkably, Heisenberg’s uncertainty principle seems to need modification to a Certainty-Uncertainty Principle when one understands that the Compton wavelength is the true wavelength of matter. Gravity is related to the Planck mass particle and is again related to absolute rest, which lasts for the Planck time. This certainty-uncertainty principle leads to the unification of gravity and quantum mechanics.

Qeios•Nov 28, 2024•3 citations
We suggest that momentum should be redefined in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy–momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation leads us to a new relativistic wave equation and a new and likely better QM. Further, we show that Minkowski space-time is unnecessarily complex and that a simplified, special case of Minkowski space-time is more consistent with the quantum world. Also, we show how the Heisenberg principle breaks down at the Planck scale, which opens this area of physics up for hidden variable theories once again. Many of the mystical interpretations in modern QM are rooted in the development of an unnecessarily complex theory that drives much speculation and is therefore subject to many different and even conflicting interpretations.
We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.
We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.
We will here show that there is one more relativistic wave equation rooted in the relativistic energy Compton moment relation, which should not be confused with the standard relativistic energy momentum relation. The standard momentum is, from a quantum perspective, rooted in the de Broglie wave. The de Broglie wave is not mathematically defined for rest-mass particles and has strange properties such as converging to infinity when the particle is almost at rest. As mentioned in the previous paper, the de Broglie wave is likely just a mathematical derivative of the true matter wave, which we have good reasons to think is the Compton wave. A wave equation that satisfies the relativistic energy Compton momentum relation will, in addition automatically satisfy the standard relativistic energy momentum relation, so there is no conflict between these two relations. The new one related to Compton is just the deeper reality and help explain why it gives simpler and more elegant relativistic wave equations, which are likely easier to interpret in terms of the physical reality.
In this paper, we discuss in brief the most common wave equations in quantum mechanics and some recent development in wave mechanics. We also present two new quantum wave mechanics equations based on the Compton momentum. We also question the idea that energy and mass are scalars, and we claim they are vectors instead. We have good reasons to think that the standard momentum is a mathematical derivative of the more fundamental Compton momentum. This will hopefully simplify interpretations of quantum mechanics significantly; our new relativistic wave equations look promising, but need further investigation into what they predict. This way of looking at quantum mechanics in new light is not in conflict with existing equations, but they are supplemental to the collection of existing wave equations. We prove mathematically that if one satisfies our new relativistic energy Compton momentum relation, one also satisfies the standard relativistic energy momentum relation automatically. They are two sides of the same coin, where the relations to the Compton wavelength likely represent the deeper reality, so we have reasons to think our new wave mechanics addresses a deeper level of understanding than the existing conception. We also look at our new wave equation in relation to hydrogen-like atoms; we follow the “standard approach” used for the Schro dinger equation of putting it in polar coordinate form and, by change of variables, finding three ODEs and their solutions. We give a table summary of our new ODEs and their solutions compared to the well-known solutions of the Schro dinger equation.
We demonstrate that the Compton wavelength mathematically corresponds exactly to the photon wavelength of rest mass energy. On the other hand, the de Broglie wavelength is not defined for a rest-mass particle, but if the particle is nearly at rest, then the de Broglie wavelength approaches infinity, and the corresponding photon wavelength of the rest-mass energy is then this length times vc\frac{v}{c}cv​ again, that is it approaches zero when vvv approaches zero. Our analysis indicates that the de Broglie wavelength appears to be a pure mathematical derivative of the Compton wavelength. Everything that can be expressed with the de Broglie wavelength can essentially be expressed by the Compton wavelength. We also demonstrate how spectral lines from atoms and chemical elements are linked to the Compton wavelength of the electron and that the Rydberg constant is not needed. Furthermore, we demonstrate that the Compton frequency is embedded in the Schrödinger equation, the Dirac equation, and the Klein-Gordon equation, where the Planck constant actually cancels out, and the de Broglie wavelength is not present in these equations. The Compton frequency seems to be linked to the quantization in quantum mechanics rather than the Planck constant. Additionally, we discuss recent literature that shows a remarkably simple but overlooked way to quantize Newton’s and General Relativity theories, as well as other gravity theories, and also how to link them to the Planck scale. This, once again, leads to the conclusion that the Compton wavelength and Compton frequency are related to the quantization of matter and, thereby, the quantization of gravity. In addition, the Planck length plays a crucial role in quantum gravity, as demonstrated. Viewing physics through the de Broglie wavelength is like looking at the world through a distorted lens; switch to the Compton wavelength, and the distortion is removed, allowing us to see simplicity and clarity even in complex phenomena such as quantum gravity. Remarkably, Heisenberg’s uncertainty principle seems to need modification to a Certainty-Uncertainty Principle when one understands that the Compton wavelength is the true wavelength of matter. Gravity is related to the Planck mass particle and is again related to absolute rest, which lasts for the Planck time. This certainty-uncertainty principle leads to the unification of gravity and quantum mechanics.
We demonstrate that the Compton wavelength mathematically corresponds exactly to the photon wavelength of rest mass energy. On the other hand, the de Broglie wavelength is not defined for a rest-mass particle, but if the particle is nearly at rest, then the de Broglie wavelength approaches infinity, and the corresponding photon wavelength of the rest-mass energy is then this length times vc\frac{v}{c}cv​ again, that is it approaches zero when vvv approaches zero. Our analysis indicates that the de Broglie wavelength appears to be a pure mathematical derivative of the Compton wavelength. Everything that can be expressed with the de Broglie wavelength can essentially be expressed by the Compton wavelength. We also demonstrate how spectral lines from atoms and chemical elements are linked to the Compton wavelength of the electron and that the Rydberg constant is not needed. Furthermore, we demonstrate that the Compton frequency is embedded in the Schrödinger equation, the Dirac equation, and the Klein-Gordon equation, where the Planck constant actually cancels out, and the de Broglie wavelength is not present in these equations. The Compton frequency seems to be linked to the quantization in quantum mechanics rather than the Planck constant. Additionally, we discuss recent literature that shows a remarkably simple but overlooked way to quantize Newton’s and General Relativity theories, as well as other gravity theories, and also how to link them to the Planck scale. This, once again, leads to the conclusion that the Compton wavelength and Compton frequency are related to the quantization of matter and, thereby, the quantization of gravity. In addition, the Planck length plays a crucial role in quantum gravity, as demonstrated. Viewing physics through the de Broglie wavelength is like looking at the world through a distorted lens; switch to the Compton wavelength, and the distortion is removed, allowing us to see simplicity and clarity even in complex phenomena such as quantum gravity. Remarkably, Heisenberg’s uncertainty principle seems to need modification to a Certainty-Uncertainty Principle when one understands that the Compton wavelength is the true wavelength of matter. Gravity is related to the Planck mass particle and is again related to absolute rest, which lasts for the Planck time. This certainty-uncertainty principle leads to the unification of gravity and quantum mechanics.