Time As a Geometric Property of Space

This is the title of a new paper just published in the journal Frontiers in Physics.1 fipThere we explore the notion that time results from properties of space itself. This comes about when one properly use the higher dimensional formalism afforded by Clifford’s geometric algebra.2

Abstract: 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 clockinsights 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. (emphases added)

This work leads to the idea that time can be represented by both a scalar irreversible component and a vector reversible component. We are very familiar with the forward arrow of time seen in irreversible non-directional processes like entropy increase but also there are spin-like processes where time is reversible. We show this can be derived from a property of space when viewed in a higher dimensional world than normally considered. For details please read the paper.

Why is this article posted here? The paper shines a light on a different way of understanding time. Since time is an important issue in biblical creation studies it could be that some research along this line might lead to a better cosmogony for our understanding of the Universe. This may be a starting point. I would encourage those who might be interested to explore the possibilities. Afterall space3 is the result of creation of the material content of the Universe. It is intriging to think that time is a cocomitant property of space.


  1. James M. Chappell, John G. Hartnett, Nicolangelo Iannella, Azhar Iqbal and Derek Abbott, Time As a Geometric Property of Space, Front. Phys., 17 November 2016 | http://dx.doi.org/10.3389/fphy.2016.00044
  2. J.G. Hartnett, Is mathematics intrinsic to the Universe?, May 11, 2015.
  3. J.G. Hartnett, Expansion of space — A dark science, November 13, 2014.

Additional Reading