By Amit Hagar

ISBN-10: 1107062802

ISBN-13: 9781107062801

The belief of infinity performs a vital position in our realizing of the universe, with the limitless spacetime continuum probably the best-known instance - yet is spacetime rather non-stop? in the course of the historical past of technological know-how, many have felt that the continuum version is an unphysical idealization, and that spacetime might be regarded as 'quantized' on the smallest of scales. Combining novel conceptual research, a clean ancient standpoint, and urban actual examples, this precise ebook tells the tale of the quest for the basic unit of size in smooth physics, from early classical electrodynamics to present ways to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics learn, are provided and defended in an obtainable layout that avoids advanced arithmetic. mixing heritage, philosophy, and theoretical physics, this fresh outlook at the nature of spacetime sheds gentle on some of the most thought-provoking themes in smooth physics.

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Extra resources for Discrete or Continuous: The Quest for Fundamental Length in Modern Physics

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The consequence of Gr¨unbaum’s analysis of this paradox, recall, is that if infinite divisibility is allowed, then a consistent structure of the line interval must have cardinality ℵ1 . Since sense awareness cannot suggest an interval structure whose cardinality exceeds ℵ0 , it follows that if the actual structure of the interval is ℵ1 , then sense awareness cannot perceive it. And since one of the necessary conditions of Whitehead’s method is that points must have to each other the kind of relations which geometry demands, then if space does form an actual continuum of cardinality ℵ1 , Whitehead’s method fails.

Their work, inspired by an earlier treatment by J. T. Hjelmslev from 1923, sought to replace the mathematical representation of the infinite plane as a mapping to the Cartesian product of the real numbers, with a mapping from the plane to a finite number field (see [VB10] for more details). Early on it became clear that this replacement was not problem-free: for example, not all finite fields will do; the admissibility depends on the size of the field. , a range between 10−13 and 1027 (the range between one Fermi and the distance to the farthest known object in the universe).

Admittedly, the microstructure that real-world bodies have is quantum mechanical, and not the structure attributed by continuum mechanics; bodies are not continuous, and their interaction is not described with classical trajectories. Nonetheless, continuum mechanics is still an active area of research with many applications in applied math and engineering, for example, fluid flow, gas dynamics, and deformation of elastic and plastic bodies. But as in the debate between Gr¨unbaum and Whitehead, one should distinguish between problems of consistency (logic) and problems of truth (reference).

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Discrete or Continuous: The Quest for Fundamental Length in Modern Physics by Amit Hagar

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