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January 23, 2018

CATEGORY: Wandering Towards a Goal Essay Contest (2016-2017) [back]
TOPIC: How a Minimum time step Leads to the Construction of the Arrow of Time and the Formation of Initial Causal structure in space-time by Andrew Walcott Beckwith [refresh]
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Author Andrew Beckwith wrote on Feb. 27, 2017 @ 17:36 GMT
Essay Abstract

Our view point is to assume that the cosmological constant is indeed invariant. And also done where we use an inflaton value due to use of a scale factor if we furthermore use g(t.t) as the variation of the time component of the metric tensor in Pre-Planckian Space-time up to the Planckian space-time initial values. In doing so, we come up with a polynomial expression for a minimum time step, we can call which leads to a development of the arrow of time, and the preservation of information, of essential type, in cosmological early universe dynamics. In doing so we delineate where Causal structure as outlined by Dowker is relevant to Space-time, which is integral to where we examine a nonsingular beginning of space-time, albeit with a very small initial radii, of the order or smaller than Planck’s length in radii. We show an inter relationship between the formation of the Arrow of time, and Causal structure, assuming developments which are from the setting of H = 0 in the Friedman equation as a starting point and systematically allows delineation of where we can meaningfully discuss creation of Causal structure.

Author Bio

PhD in 2001, from the Device development laboratory. Works part time in China, in Chongqing University as a visiting professor since 2010 with Dr. Fangyu Li and Wen Hao. Otherwise, I live in the East Coast of the USA, in the New York area.

Download Essay PDF File

Lawrence B. Crowell wrote on Feb. 27, 2017 @ 21:32 GMT

I read your paper. It looks like a conformal sort of causal set. The running scale on the discrete set is what gives rise to time increments. This is if I understand what you have done here. Anyway I invite you to look at my essay to see if it make sense to you.

Cheers LC

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Edwin Eugene Klingman wrote on Feb. 27, 2017 @ 22:37 GMT
Andrew Beckwith,

If I understand your essay, you assume the scale factor proportional to the power of time and the time dilation component g(t,t) proportional to the square of the initial scale acting on an initial field phi. This apparently leads to a polynomial expression for a minimum time step, delta-t, and implies an arrow of time (better than the converse!). I do not understand causal issues, be it Dowker, or anyone else, but I do note that you appear to obtain an early 'bubble' of space-time versus the singularity of the black hole variety. Does this map into Steven Kauffmann's g(t,t)-based expanding universe model? I also note that you appear to replace the mass density in your equation 9 with the energy density, which I assume can imply gravitational self-energy, with which I concur. While I very much like the way in which you distinctively label your terms, instead of simple indices, nevertheless, your failure to define many of the terms in your equations will limit appreciation of your essay to those who are already familiar with such.

You end by observing that you've answered FQXi's question. Another sentence or two explaining how you have done so would not be inappropriate. Incidentally, that is one of the nice features of FQXi comments page per author, i.e., we get to augment our essays for various 'customers'.

Best regards,

Edwin Eugene Klingman

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Jonathan J. Dickau wrote on Feb. 28, 2017 @ 02:47 GMT
Interesting premise Dr. Beckwith..

I like the idea that a minimum time step would lead to emergent causal structure. Indeed; such a feature is evident in some octonionic inflationary scenarios, as Ray Munroe and I wrote about, prior to his passing. It is also a feature of the ideas described in my contest essay. But while Dowker appears to be working from causal set theory; causal structure is a broad movement within the quantum gravity field.

Lee Smolin spoke about energetic causal sets at GR21, which are worth checking out, but Causal Dynamical Triangulations, as formulated by Ambjörn, Loll, and Jurkiewicz, also satisfies the premise of causal structure theories. Exactly what causal structure flies is currently a matter of debate. But it appears that any theory where geometry becomes non-commutative or non associative in the microscale is automatically one of spacetime emergence.

So there is a lot to talk about. I am needing to give you half credit in some grading criteria, which requires me to read your essay again before rating it.

All the Best,


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Jonathan J. Dickau replied on Feb. 28, 2017 @ 04:30 GMT
After some consideration,

It definitely looks like something worth investigating further. While it does not completely address the FQXi topic notion of directed evolution vs aimlessness, your demonstration of a simple basis for the emergence of causal structure is impressive. Since I think that ideas about emergent spacetime are germane to the intended topic; I have given you partial credit. It appears someone else did not share in my high opinion of this work, however.



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Author Andrew Beckwith wrote on Feb. 28, 2017 @ 05:21 GMT
Edwin Eugene Klingman

How I answered the question. It was to use a random root finding protocol in order to ascertain a highly structured result, namely the existence of causal structure.

The process of root finding is in many cases as random and as unpredictable as it gets.

As was discussed by Lawrence Crowell, the idea was a conformal sort of causal set, and he guessed as to the intentions of my essay. I will explain the input into the variables I used next time.


Satyavarapu Naga Parameswara Gupta wrote on Mar. 2, 2017 @ 08:05 GMT
Dear Beckwith,

Thank you for the nice essay on “Bigbang based Expanding Universe Models"

Your equations are developed excellently on cosmological constant Introduced by Einstein.

I request you to please consider other Galaxies such as Blue shifted Galaxies and Quasars which will be totalling to 60 percent of total number of Galaxies universe. You developed the whole theory...

view entire post

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Joe Fisher wrote on Mar. 2, 2017 @ 17:03 GMT
Dear Professor Andrew Walcott Beckwith

Please excuse me for I have no intention of disparaging in any way any part of your essay.

I merely wish to point out that “Everything should be made as simple as possible, but not simpler.” Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

Only nature could produce a reality so simple, a single cell amoeba could deal with it.

The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

Joe Fisher, Realist

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Christian Corda wrote on Mar. 7, 2017 @ 09:39 GMT
Hi Andy,

Nice work, intriguing and original. Congrats, I enjoyed a lot in reading it. On the other hand, you know that I appreciate your research work. I will give you the highest score. Good luck!

Cheers, Ch.

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Bayarsaikhan Bayarsaikhan Choisuren wrote on Mar. 14, 2017 @ 13:46 GMT
Dear Beckwith,

Thank you for the nice essay.

Bubble of space-time being of the order of magnitude of Planck Length and its equations are very interesting for me.

The bubble of space-time should be developed into spatial fluid sink flow.



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Steve Dufourny wrote on Mar. 16, 2017 @ 18:57 GMT
Hello Mr Beckwith,

I liked your papper and I congratulate you.Personally I think that expansion is gravitational and spherical and that the Big Bang is not correct because we consider a luminiferous aether instead of this gravitational aether with particles of gravitations which are not baryonic nor relativistic.The Works of Lemaître in the past was inserted in my theory of spherisation with quant and cosm 3D sphères and the spherisation is a reality so I have suggested an universal sphere with the parameters of Lemaître due to increasing mass.But after some years of irmpovement of my theory and in inserting this quantum gravity and my equation E=m(b)c²+m(nb)l²,the photonic sphere is just a photonic sphere after all.The gravitational cold sphere is more important, that is why the waves of gravity are speeder than c.

Thanks for sharing your papper ,good luck in this contest :)

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Bayarsaikhan Bayarsaikhan Choisuren wrote on Mar. 19, 2017 @ 10:19 GMT
Dear Dr. Beckwith,

The speed of light in vacuum is constant relative to ‘Space’ itself, instead of relative to a material object. Therefore, the speed of electromagnetic wave is not only a speed but also a fundamental property of nature, which can be a key property to generate gravitational and inertial forces.

With Best Regards


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Bayarsaikhan Bayarsaikhan Choisuren wrote on Mar. 25, 2017 @ 10:53 GMT
Dear Dr. Andrew Walcott Beckwith,

Your (spatial bubble) bubble of space-time being of the order of magnitude of Planck Length in Pre-Planckian Space-time up to the Planckian space-time initial values is to be primordial elementary particles. I think it can be a bubble of spatial fluid having extremely strong gravitational strength.

Also the bubble is to be considered as a singular point in a Space-Time. Then it may be needed to apply a particular mathematics in the fields of dynamical systems and geometric topology including Anosov flow on (tangent bundles of) Riemann surfaces.

With Best Regards,


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Peter Jackson wrote on Mar. 25, 2017 @ 21:43 GMT

Very interesting essay and approach, seemingly somehow deriving time steps and causality virtually from 'nothing'! I'd be interested motivations for setting the Planck length to zero as I find this a perfectly acceptable philosophy. Indeed it seems consistent with Wheelers view that there's unlimited space for physics smaller scales.

Do please correct or expand on that. (As I'm no mathematician I couldn't work through your equations) I did have to read it 3 times, but being concise that was easy!

I hope you read mine, parts of which you may also have to read more than once though I'm afraid it forms a rather long and complex ontological construction.

Very best


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