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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.

## By John Gideon Hartnett

Dr John G. Hartnett is an Australian physicist and cosmologist, and a Christian with a biblical creationist worldview. He received a B.Sc. (Hons) and Ph.D. (with distinction) in Physics from The University of Western Australia, W.A., Australia. He was an Australian Research Council (ARC) Discovery Outstanding Researcher Award (DORA) fellow at the University of Adelaide, with rank of Associate Professor. Now he is retired. He has published more than 200 papers in scientific journals, book chapters and conference proceedings.

## 12 replies on “Time As a Geometric Property of Space”

Ericsays:

While this is interesting to me, can someone please clarify the significance of these findings/ideas? Does this fit into a biblical creation model?

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Eric, I posted this article here because it 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. That is all!

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r_speirsays:

I know where you are headed with this. Smart, because it is really all that is left for young earth creationists. If you do not allow for a backward creation of space and time from origin Earth, there is really no way to make a vast universe on day 4 a convincing reality. So on day 4 he basically created our past when he created the universe. But then, not really “our past” because as you say, time is directionless. He just created a vast container of time when he spread out the expanse. Nice. Go for it.

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You are quite correct I would not consider possible “a backward creation of space and time from origin Earth”. When I used the word ‘directionless’ it is in reference to direction in space. We still have the arrow of time seen in many physical processes to deal with. That I see as the scalar irreversible part of time.

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My independent analysis of “Motion” led me to an independent discovery of SR, and an independent deriving of all of the SR equations. This also had led me to the awareness of the existence of a 4 dimensional environment known as Space-Time. It also soon became clear that motion must be confined to being finite, but at the same time this motion must be constant and ongoing within a 4D Space-Time environment. But most of all, this constant motion, no matter what direction it is that it is heading across Space-Time, it occurs with the exact same magnitude of motion as does light as it moves across space.

So what you have in the end, is an objects constant “c” motion that is occurring as it moves across a 4D Space-Time environment, and also 4D rotation will occur whenever any objects direction of travel across Space-Time is being altered.

Again, if you analyze the outcome of this ongoing motion that takes place within a 4 D Space-Time environment, you soon discover SR and you derive the SR equations, and you do so in mere minutes. This brings you back to a 4D Space-Time.
[Ed: Hyperlink deleted. See my response.]
This gives the impression that “Time is NOT a Geometric Property of Space”. YOUR OPINION PLEASE. THANKS.

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Could you please write down you thesis with a logical development of equations? I have not watched all your videos. But I would be very cautious in approach that you don’t implicitly assume time to develop time as a dimension in your ‘spacetime’. We are trying to understand what is most fundamental. So if time is a product of motion (boosts and rotations) then it is derived. Can that then help us understand the true ontology? That is the question.

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Well, I used logic as best as I know how within my videos. Granted I have compressed the big picture to a degree, but overall, it is all there. Trying to explain what goes on within my brain to the full extent, is not an easy chore.

The point is that back in grade nine I noticed a peculiarity concerning “motion”, a peculiarity that no one else seemed to notice at all. My science teacher thought of it as just pure rubbish. Overall, all my teachers thought that whatever came out of my mouth was pure rubbish, and proceeded to classify me as a hopeless case, or just pure rubbish myself. All this simply because I looked at things in a different manner. But thanks to the teachers seeing it as a sign of stupidity rather than difference, along with the recommendations they therefore gave to my parents, my parents pulled me out of school. So a chance to receive a physics education, further math education, etc., was not to be.

But, years later, during my spare time, I when back to analyzing that peculiarity that I had noticed about motion.

The eventual outcome was what is shown within the videos. I just thought that the method in which I discovered SR, and the way in which I derived the SR equations, which uses geometry via the combination of stacking motion vectors and length scalars, might be of some help since both methods are unique and are not found elsewhere in the world of physics, be that the world of physics of today, or within the physics history books.

Overall, what is shown within my videos, is that if you have an “Absolute” ongoing motion of all objects, motion whose magnitude is the same as the magnitude of motion of which light has as it moves across space, motion that is constantly ongoing within an “Absolute” 4 dimensional Space-Time environment, the outcome is all the entire list of strange phenomena that is described via SR.

Thus, absolute constant “c” motion taking place within an absolute 4D Space-Time environment, produces relativity.

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I am sorry I really don’t follow. You describe ‘absolute’ motion and special relativity (SR). There is no way to determine absolute motion; that is the whole point of Einstein’s theory. The speed of light is an absolute universal constant; it is the same for all observers regardless of their motion. But I don’t agree with any concept of absoluteness in space and time. I don’t say that our galaxy might not be in a privileged location but physics has shown that the idea of absolute space and time to be problematic.

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What you speak of is just the same as that which is mentioned within my video, “There is no way to detect absolute motion”.

However, the point is that if you set up an environment in which you always have ongoing “c” motion taking place within a 4 dimensional Space-Time environment, the outcome is SR.

Under such conditions, anyone, anywhere, moving at any velocity across space (with speed of light being the boundary), all will still measure the speed of light as being the speed of light. Also, any observer will observe length contraction if viewing another object that appears to be in motion relative to the observer, and this works both ways. Also, any observer will observe time dilation if viewing another object that appears to be in motion relative to the observer, and this also works both ways. Also, this ongoing “c” motion taking place within a 4 dimensional Space-Time environment also causes a strange form of velocity addition. And so on and so on.

Meaning, the condition of there being absolute ongoing “c” motion taking place within an absolute 4 dimensional Space-Time environment, produces every effect described via special relativity, and if this concept is converted into math equations, via the use of a geometric representation of this ongoing “c” motion taking place within a 4 dimensional Space-Time environment, it produces each and every SR mathematical equation.

To see a similar point of view, Google “The Elegant Universe pdf” and view pages 26 & 27. Here within the popular physicist Brian Greene’s book, is the statement “all objects in the universe are always traveling through spacetime at one fixed speed, that of light.”. I was glad to find at least someone else who shared my point of view to some degree.

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From what I can understand of what you write it would appear you are saying if one assumes that all observers measure the same value for the speed of light regardless of their relative motion then one gets Einstein’s special relativity theory. I agree.

I looked up your Brian Greene quote which I found on page 41 of the PDF under the heading of “Motion through spacetime”. The quote in context is this

When an object moves through space relative to us, its clock runs slow compared to
ours. That is, the speed of its motion through time slows down. Here’s the leap: Einstein proclaimed
that all objects in the universe are always traveling through spacetime at one fixed speed—that of
light
. This is a strange idea; we are used to the notion that objects travel at speeds considerably less
than that of light. We have repeatedly emphasized this as the reason relativistic effects are so
unfamiliar in the everyday world. All of this is true. We are presently talking about an object’s
combined speed through all four dimensions—three space and one time—and it is the object’s speed
in this generalized sense that is equal to that of light.

I have bolded the excerpt you quoted. Greene is totally correct in what he has written. All objects travel through spacetime at the canonical speed of light c, but they do not travel through space at speed c; only massless particle do that.

If anyone starts with Einstein’s relativity principle they can easily derive the mathematical formalism of special relativity. The special principle of relativity states that physical laws are the same in every inertial frame of reference. Any inertial (freely falling, non-accelerating) observer will determine the same laws of physics. This is called Lorentz invariance. The speed of light therefore will be measured to be the same regardless of the motion of any inertial observer. I would guess that you have done just that in your own “independent” analysis. But it is not new.

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Like I have stated, I had not received any education in physics. Thus I had only heard of some of the bizarre outcomes associated with Special Relativity via watching some science TV shows decades ago. In turn, SR made no sense to me at all. Bizarre meant incomplete. That was why I went back to performing a simple step by step analysis of “motion” instead. So since I had no knowledge of Newtonian physics, I think that made things a lot easier. Standing upon the shoulders of the errors of others, is a big hold back. Starting from scratch, eliminates that problem.

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It shows that you have no knowledge of physics, Newtonian or otherwise. I would suggest that if you want to genuinely present a theory that you go back to basics and learn some basics physics from a fundamental level. Newton was probably the greatest physicist of all time, and he was a biblical creationist as well. Einstein certainly was a genius and made some amazing insightful steps to help us understand the nature of the physical world. Believe me you are not advantaged by lacking a basic knowledge of what these men discovered and taught. And I mean their way of thinking which necessarily involved a mathematical description. I suggest you read “Is mathematics intrinsic to the Universe?”

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