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Chapter 13, "The Universe on a Brane", expands on ideas from chapter 12, particularly on M-theory, of which string theory is a branch. This chapter is devoted to speculations on space and time. The insights of a number of physicists, including Edward Witten and Paul Dirac, are presented. The focus of the chapter becomes gravity and its ...
Quantum foam (or spacetime foam, or spacetime bubble) is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at this small scale, particles of matter and antimatter are constantly created and destroyed. These subatomic objects are called virtual particles. [1]
This is done in "3+1" formulations, where spacetime is split into three space dimensions and one time dimension. The best-known example is the ADM formalism . [ 174 ] These decompositions show that the spacetime evolution equations of general relativity are well-behaved: solutions always exist , and are uniquely defined, once suitable initial ...
A spacetime diagram is typically drawn with only a single space and a single time coordinate. Fig. 2-1 presents a spacetime diagram illustrating the world lines (i.e. paths in spacetime) of two photons, A and B, originating from the same event and going in opposite directions. In addition, C illustrates the world line of a slower-than-light ...
With the help of Riemannian geometry, Einstein formulated a geometric description of gravity in which Minkowski's spacetime is replaced by distorted, curved spacetime, just as curved surfaces are a generalization of ordinary plane surfaces. Embedding Diagrams are used to illustrate curved spacetime in educational contexts. [13] [14]
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time.In Albert Einstein's 1905 paper, On the Electrodynamics of Moving Bodies, the theory is presented as being based on just two postulates: [p 1] [1] [2]
In Einstein's theories, the ideas of absolute time and space were superseded by the notion of spacetime in special relativity, and curved spacetime in general relativity. Absolute simultaneity refers to the concurrence of events in time at different locations in space in a manner agreed upon in all frames of reference.
Spacetime algebra is a type of geometric algebra that is closely related to Minkowski space, and is equivalent to other formalisms of special relativity. It uses mathematical objects such as bivectors to replace tensors in traditional formalisms of Minkowski spacetime, leading to much simpler equations than in matrix mechanics or vector calculus.