# The Geometry Of Spacetime

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the geometry of spacetime

The presence of a massive object (compact or otherwise) would deform the ambient Minkowski geometry of spacetime in accordance with the Einstein equation. The gravitational ﬁeld is described by the metric tensor gµν of the manifold. On any region of the manifold we can place a coordinate system (t, x1 , x2 , x3 ) such that t is a timelike coordinate, and xi are spacelike for i = 1, 2,The metric tensor can then be written in the form g = gtt dt ⊗ dt + gti dt ⊗ dxi + git dxi ⊗ dt + gij dxi ⊗ dxj . (2.1)quantum geometry of spacetime

We use the set of Real numbers, for both theories, in fact for all Physics. This is completely wrong, absurd and unnecessary, since it introduces mathematical concepts into Physics. These are not measurable (Physical) such as moment, point, infinitely small, infinite. We should remember that R is an “actual infinite” set (Cantor), that is to say that it fulfils the following:Its elements lack “good order”, that is, an ordinal number (N) associated with each element of R, which would indicate your order .geometry of spacetime - einstein theory of gravity ii

. of gravity that presumes a deterministic concept of motion within spacetime, and inherently disagrees with currently accepted concepts of Quantum Mechanics.notes geometry and spacetime university california, irvine

It is one of the assumptions behind this course that a relatively modest investment in abstract mathematics pays signiﬁcant dividends for the understanding of the special theory of relativity and recent debates among philosophers concerning its foundations. It provides the resources with which to pose and answer precise questions that bear on those debates. We begin the investment in this ﬁrst part of the course. Here we review certain facts about: (i) aﬃne spaces, (ii) metric aﬃne spaces, and (iii) .
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