Introduction to special relativity: Difference between revisions

Revision as of 20:29, 13 June 2013

Revision as of 02:07, 25 June 2013

Line 80:

==The Minkowski formulation: introduction of spacetime==

{{Main|Spacetime}}

After Einstein derived special relativity formally from the (at first sight counter-intuitive) assumption that the speed of light is the same to all observers, [[Hermann Minkowski]] built on mathematical approaches used in non-euclidean geometry<ref>Walter, S.(1999) The non-Euclidean style of Minkowskian relativity. The Symbolic Universe, J. Gray (ed.), Oxford University Press, 1999 http://www.univ-nancy2.fr/DepPhilo/walter/papers/nes.pdf</ref> and on the mathematical work of Lorentz and Poincaré. Minkowski showed in 1908 that Einstein's new theory could also be explained by replacing the concept of a separate ''space and time'' with a four-dimensional continuum called ''spacetime''. This was a groundbreaking concept, and [[Roger Penrose]] has said that relativity was not truly complete until Minkowski reformulated Einstein's work.<ref name="road to reality">{{cite book|last=Penrose|first=Roger|title=The Road to Reality|year=2004|publisher=Vintage|isbn=978009944068 {{Please check ISBN|reason=Invalid length.}}9780099440680|page=406|url=http://books.google.com/books?id=coahAAAACAAJ}}</ref>

The concept of a four-dimensional space is hard to visualise. It may help at the beginning to think simply in terms of coordinates. In three-dimensional space, one needs three real numbers to refer to a point. In the [[Minkowski space]], one needs four real numbers (three space coordinates and one time coordinate) to refer to a point at a particular instant of time. This point, specified by the four coordinates, is called an event. The distance between two different events is called the spacetime interval.