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Angular Displacement as a Temporal Coordinate: A Geometric Framework for Rotational Dynamics
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DOI：10.1134/s1028335825600701.png)
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Abstract
En 中文
Traditional special relativity (SR) exhibits limitations in describing rotating reference frames, particularly due to ambiguities in the definition of simultaneity and the inapplicability of Lorentz transformations. While general relativity (GR) addresses rotational effects through metric theory, its complexity and focus on point-mass systems render it less accessible for engineering applications. To overcome these challenges, an alternative framework [1] has systematically defined angular displacement space-time (phi(tau)), where phi denotes angular displacement (in radians) and tau represents temporal progression. This framework introduces an alternative Lorentz transformation tailored to rotational physical laws and establishes a universal rotational speed limit, Omega(max) = c/(2 pi), analogous to the universal speed limit c. By postulating complex time (Time = t + i tau), where t is linear time and tau is angular time, this theory separates linear and rotational dimensions, forming a kinematic symmetry hypothesis. The angular displacement space-time (phi(tau)) framework offers a concise toolkit for analyzing rotational phenomena across disciplines, including rotor dynamics, astrophysics, fluid mechanics, and quantum systems. Its potential lies in bridging relativity and quantum mechanics under rotational contexts. Currently, the theory remains in a kinematic phase, necessitating experimental validation-particularly for the Omega(max) postulate-and mathematical refinement to transition toward dynamic formulations. Should experiments refute Omega(max), the symmetry framework would collapse, yet the exploratory process could still yield novel techniques (e.g., ultra-high-speed rotational measurement) or mathematical constructs (e.g., engineering applications of complex time). Regardless of outcomes, angular displacement space-time (phi(tau)) constitutes a distinct mathematical framework with profound interdisciplinary relevance.
Keywords:
angular displacement space-time (phi(tau))
maximum angular velocity (Omega(max))
complex time
alternative Lorentz transformation
alternative special theory of relativity