Roasted Broadcast

M.Sc student in Maths. B.Sc in Maths and Physics. Classical Liberal. Anglophile. Optimist.

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Showing posts with the label Consistent

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Consistency, Measurement and Decoherence

on October 21, 2019

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Set Theory

This post is a very brief introduction to some of the basic concepts of set theory. Set theory is a branch of mathematical-logic, that has wide applications across disciplines. Its not just used in the obvious way of studying the foundations of mathematics by mathematicians but also in physics, social science and even in philosophey. I'm only going to cover in this post what's needed for predicate logic (although you can do propositional logic without set theory) but it has for many other applications. A set is a collection of elements, or members; the notation for a set is specified by listing its components. So the set of even numbers can be represented as $E: \left \{ 2,4,6,8 ... \right \}$ $E: \left \{ x: x > 0 \wedge even\right \}$ Either of these notations is valid. Further, elements of a set can only be in that set once. $E: \left \{ 2,2,2,4,4,6,8 ... \right \} = E: \left \{ 2,4,6,8 ... \right \}$ The notation used to indicate that somethin...

William Lane Craig and the Hartle-Hawking No Boundary Proposal

Standard hot Big Bang cosmology represents the universe as beginning from a singular dense point, with no prior description or explanation of classical spacetime. Quantum cosmology is different in that it replaces the initial singularity with a description in accord with some law the "quantum mechanical wave function of the universe", different approaches to quantum cosmology differ in their appeal either to describe the origin of the material content of the universe e.g., Tyron 1973, Linde 1983a, Krauss 2012 or the origin of spacetime itself e.g., Vilenkin 1982, Linde 1983b, Hartle-Hawking 1983, Vilenkin 1984. These last few proposals by Vilenkin, Hartle-Hawking and others are solutions to the Wheeler-DeWitt equation come under a category of proposals called "quantum gravity cosmologies" which make cosmic applications of an approach to quantum gravity called "closed dynamic triangulation" or CDT (also known as Euclidean quantum gravity). I've n...

Creation Of Universes from Nothing

The above paper " Creation of Universes from Nothing " was published in 1982, which was subsequently followed up in 1984 by a paper titled " Quantum Creation of Universes ". I decided it would be a good idea to talk about these proposals, since last time I talked about the Hartle-Hawking model which was, as it turns out, inspired by this work. Alexander Vilenkin also explains in a non-technical way the essential idea in his book; Many World's in One (one of the best books I've ever read), it mostly covers cosmic inflationary theory but the 17th chapter covers how inflation may have started. In fact Vilenkin is one of the main proponents who helped develop inflation along with Steinhardt, Guth, Hawking, Starobinsky, Linde and others. Although I won't talk about it here, Vilenkin is also known for his work on topological defects at GUT scales and in developing cosmic strings, a topic which is also connected to inflation. In explain...

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