Abstract-algebraic interpretations of the energy–time uncertainty relation prove quantization of time

Abstract

In modern physics, the general theory of relativity (GTR) successfully predicts the vital structure of gravity. The GTR confirmed that gravity is the distortion of four-dimensional spacetime [Formula: see text] by massive bodies. Such a prediction of the GTR is one of the vital successes towards the development goals of modern physics. Though, the central foundation for all the calculations of the GR is the hypothesis of continuum spacetime. In this paper, the author introduces a theorem of the quantum mechanical theory of time (QMT) to test whether the metric time is discrete or continuous. To prove the theorem, the author applied the set theory of cardinal numbers on the energy–time uncertainty relationship. The proof of the theorem confirmed that the metric time is discrete, and has an intrinsic quantum nature. The result implied that the continuum spacetime assumption of the GTR is found fundamentally erroneous. Therefore, spacetime is discrete and needs to be analyzed by the principles of quantum mechanics (QM).