TL;DR
This paper explores a model where space dimension dynamically evolves over time using fractional calculus, suggesting a threshold for interaction with particles and potential cosmological applications.
Contribution
It introduces a novel fractional calculus-based model for space evolution with a variable dimension, deriving boundaries from first principles.
Findings
Space dimension d(t) evolves smoothly from 0 to 3 over time.
A minimum space dimension threshold is necessary for interactions.
Potential implications for cosmology are discussed.
Abstract
Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a model is presented, which describes space generation as a dynamic process, where the dimension of space evolves smoothly with time in the range 0 <= d(t) <=3, where the lower and upper boundaries of dimension are derived from first principles. It is demonstrated, that a minimum threshold for the space dimension is necessary to establish an interaction with external probe particles. A possible application in cosmology is suggested.
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