We present an alternative formalism for modeling spin. The ontological elements of this formalism... more We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length n. The machinery necessary to model physics is then developed by considering correlations between base-2 sequences. Upon choosing a reference base-2 sequence, a relational system of numbers can be defined, which we interpret as quantum numbers. Based on the properties of these relational quantum numbers, the selection rules governing interacting spin systems are derived from first principles. A tool for calculating the associated probabilities, which are the squared Clebsch–Gordan coefficients in quantum mechanics, is also presented. The resulting model offers a vivid information theoretic picture of spin and interacting spin systems. Importantly, this model is developed without making any assumptions about the nature of space-time, which presents an interesting opportunity to study emergent space-time models.
In this paper, an alternative formalism for modeling physics is proposed. The motivation for this... more In this paper, an alternative formalism for modeling physics is proposed. The motivation for this approach arises from the tension between the countable (discrete) nature of empirical data and the uncountable sets (continuous functions) that form the foundations of modern physical theories. The foundation of this alternative formalism is the set of all base-2 sequences of length n. While this set is countable for finite n, it becomes uncountable in the limit that n goes to infinity, providing a viable pathway to correspondence with current theories. The mathematical construction necessary to model physics is developed by considering relationships among different base-2 sequences. Upon choosing a reference base-2 sequence, a relational system of numbers can be defined. Based on the properties of these relational numbers, the rules of angular momentum addition in quantum mechanics can be derived from first principles along with an alternative representation of the Clebsch-Gordan coeff...
We present an alternative formalism for modeling spin. The ontological elements of this formalism... more We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length n. The machinery necessary to model physics is then developed by considering correlations between base-2 sequences. Upon choosing a reference base-2 sequence, a relational system of numbers can be defined, which we interpret as quantum numbers. Based on the properties of these relational quantum numbers, the selection rules governing interacting spin systems are derived from first principles. A tool for calculating the associated probabilities, which are the squared Clebsch–Gordan coefficients in quantum mechanics, is also presented. The resulting model offers a vivid information theoretic picture of spin and interacting spin systems. Importantly, this model is developed without making any assumptions about the nature of space-time, which presents an interesting opportunity to study emergent space-time models.
In this paper, an alternative formalism for modeling physics is proposed. The motivation for this... more In this paper, an alternative formalism for modeling physics is proposed. The motivation for this approach arises from the tension between the countable (discrete) nature of empirical data and the uncountable sets (continuous functions) that form the foundations of modern physical theories. The foundation of this alternative formalism is the set of all base-2 sequences of length n. While this set is countable for finite n, it becomes uncountable in the limit that n goes to infinity, providing a viable pathway to correspondence with current theories. The mathematical construction necessary to model physics is developed by considering relationships among different base-2 sequences. Upon choosing a reference base-2 sequence, a relational system of numbers can be defined. Based on the properties of these relational numbers, the rules of angular momentum addition in quantum mechanics can be derived from first principles along with an alternative representation of the Clebsch-Gordan coeff...
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