Discrete or Continuous? The Quest for Fundamental Length in by Amit Hagar

By Amit Hagar

The assumption of infinity performs an important position in our realizing of the universe, with the endless spacetime continuum maybe the best-known instance - yet is spacetime relatively non-stop? during the background of technology, many have felt that the continuum version is an unphysical idealization, and that spacetime can be regarded as 'quantized' on the smallest of scales. Combining novel conceptual research, a clean historic standpoint, and urban actual examples, this precise e-book tells the tale of the quest for the basic unit of size in smooth physics, from early classical electrodynamics to present techniques to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics examine, are offered and defended in an available layout that avoids complicated arithmetic. mixing heritage, philosophy, and theoretical physics, this clean outlook at the nature of spacetime sheds mild on essentially the most thought-provoking themes in smooth physics.

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But as in the debate between Gr¨unbaum and Whitehead, one should distinguish between problems of consistency (logic) and problems of truth (reference). , has any reference, or truth makers, in the real world. Within continuum mechanics the notion of impenetrability (crucial for the above argument against collision) is kinematically defined as a uniqueness constraint on the mapping between the space of configuration of material bodies and physical space: no material point can occupy two spatial points, and no spatial point can be occupied by two material points ([LS74], p.

See [For95], pp. 338–339, and [VB10]. These axioms are Addition and Multiplication, Associativity, Commutativity, Distributivity, Identity, Additive Inverse, Multiplicative Inverse, Trichotomy, Transitivity, Isotony, and Completion. , [Lyn71]. Cantor formulated the CH without proving it in the nineteenth century, and it was listed as one of Hilbert’s celebrated 23 problems for mathematics at the dawn of the twentieth century. , f : S → R,23 where R S is the set of all functions f from S to R. 24 This lacuna can be fixed if we relax the notion of truth so that for functions f which do not have an inverse, the statement “f = z” (“f is the zero function”) will be true.

The Pythagorean theorem in macroscopic space, or the results obtained by standard integral and differential equations), or (2) approximating these results of contemporary theory to a high degree of accuracy. 1 Outline Spatial discreteness – interpreted either as an ontological commitment, or as an epistemological constraint on measurement resolution – cannot be ruled out as a matter of logic; neither can attempts at approximating the continuous with the discrete. This much we have learned from the previous chapter.

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