The Principle of Commensurability of Conserved Quantities as a Basis
1The Principle of Commensurability of Conserved Quantities as a Basis for Solving Quantum Mechanics Problems Using Integer Theory
Layman Abstract : This paper presents a new way to describe how the physical world works using a special area of mathematics called integer theory (which deals with whole numbers). This approach becomes possible by introducing a new rule — called the principle of commensurability — which means that when physical objects interact (like particles colliding), the amounts of energy, momentum, and other properties they exchange must fit together in a way that can be measured using a common unit, both before and after the interaction.
By using this method, the paper helps solve two classic physics problems:
The radiation spectrum of hydrogen-like atoms (how atoms give off light).
The scattering problem (how particles bounce off each other).
The results confirm known scientific findings but also provide new insights. One key conclusion is that the allowed energy levels of atoms — a central idea in quantum physics — happen because these energy levels must fit together according to this new commensurability rule. This gives a new mathematical explanation for Bohr’s quantum theory, which previously lacked a clear physical explanation. The paper also shows that cause-and-effect relationships (causality) apply even in the quantum world, meaning quantum events may not be as random as once thought.
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Original Abstract : The paper proposes a new method of describing physical reality using the mathematical apparatus of integer theory. Applying this apparatus becomes possible after introducing the principle of commensurability of conserved quantities into physics. It states that at the interaction of physical objects, only such exchanges of conserved quantities (energies, momentums, etc.) are possible so that these quantities have a common measure before and after the interaction of objects. Methods of integer theory solve two classical problems of physics: the radiation spectrum of a hydrogen-like atom and the scattering problem. The known results of such solutions are obtained, and new data are also obtained. It follows from the obtained that the physical reason for the ‘allowed’ states of atomic systems is the necessity of commensurability of the excited states of the atom with its ground state in all conserved quantities. This gives physical foundations to the quantum hypothesis of N. Bohr, which it has not had so far. The strict causal relation between stationary quantum states of atomic systems is also established, i.e. the principle of causality in the quantum world is restored.
View Book: https://doi.org/10.9734/bpi/crpps/v7/4113
#The_principle_of_commensurability_of_conserved_quantities #radiation_spectrum_of_a_hydrogen_like_atom #Bohr_quantization_hypothesis #integer_theory #allowed_states_of_quantum_systems #the_principle_of_causality