Front. Phys., 17 November 2016 | http://dx.doi.org/10.3389/fphy.2016.00044
Time As a Geometric Property of Space
James M. Chappell1*, John G. Hartnett2, Nicolangelo Iannella3, Azhar Iqbal1 and Derek Abbott1
1School of Electrical and Electronic Engineering, University of Adelaide, Adelaide, SA, Australia
2School of Physical Sciences, Institute for Photonics and Advanced Sensing, University of Adelaide, Adelaide, SA, Australia
3School of Mathematical Sciences, University of Nottingham, London, UK
The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which “flows equably without relation to anything external.” In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that he could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation of 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
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