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Time As a Geometric Property of Space

This is the title of a new paper just published in the journal Frontiers in Physics.1 There 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 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. (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.

References

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.

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—John Gideon Hartnett and James Chappell

What is time? This seems to be a particularly intractable question!

Also, while space appears quite tangible and easy to visualise, time on the other hand seems an extremely elusive concept.  Some theorists have thereby concluded that time is perhaps merely a human invention and that only space is real.  However, many authors have also concluded1  that all mathematical concepts are freely created and so it is therefore invalid to single out time in this way.

Similarly, some scientists say that while time is not real the laws of physics are perfect and unchanging. This is part of what is referred to as the Newtonian paradigm.  Time becomes merely a parameter to calculate kinematical and dynamical processes. However, how can we say that the laws of physics do not change with time when we do not have a rigorous definition of time?

Sir Isaac Newton said that he was searching for the way God made the Universe, in the laws of physics.

“The True God is a living, intelligent, and powerful being: His duration reaches from eternity to eternity.”2

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The Unreality of Time

In their book “The Singular Universe and the Reality of TimeRoberto Mangabeira Unger and Lee Smolin argue for the reality of time in the same way Lee Smolin does in his book “Time Reborn2. Smolin is a theoretical physicist and Unger a philosopher. Unger presents in the language of natural philosophy. His terminology is a bit opaque at times, which makes him sometimes difficult to follow but Smolin is much clearer, certainly from a physicist’s point of view. He uses the language of physics, though his naturalistic belief system is strongly evident.

In “Time Reborn” Smolin cannot conceive of a universe created by an extant Creator, who imbued it with immutable laws. His mindset seems to be one that is shocked by the idea that this universe was prepared in a just-right state such that we can exist in it. And this occurs even when he is thinking in evolutionary terms. So to him the idea that the universe occurred just once with initial conditions and laws that allow life to exist is too shocking to contemplate. His answer is ‘evolution’. This universe evolved from a prior universe and its laws evolved along with it.