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January 20, 2018

CATEGORY: FQXi Essay Contest - Spring, 2017 [back]
TOPIC: Using Klauder’s Enhanced Quantization to set a bound to the Cosmological constant, in Pre Planckian space- as a way to ascertain the most important fundamental physics question. by Andrew Beckwith [refresh]
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This essay's rating: Community = 6.3; Public = 5.0

Author Andrew Beckwith wrote on Dec. 21, 2017 @ 21:02 GMT
Essay Abstract

We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). In FFP 15, in the Author’s presentation, one of the two compared action integrals was from Hambler’ Quantum Gravity reference, while another was given as similar to the action principle of the Hilbert idea of General Relativistic derivation of the Einstein Field Equations. What we have done is to replace the Hambler Quantum gravity reference based action integral with a result straight from John Klauder’s “Enhanced Quantization” tome. In doing so, with also a nod to Thanu Padamabhan’s treatment of the inflaton, we then commence to initiate an explicit bound upon the cosmological constant. The further approximation is to use the inflaton results, and conflate them with John Klauder’s Action principle for a way to , if we have the idea of a potential well, generalized by Klauder, with a wall of space time in the Pre Planckian regime to ask what bounds the Cosmological constant prior to inflation. We argue this is the most important fundamental question in physics today, for reasons we elaborate upon in the conclusion. Section 6 details my actual answers to the essay’s ideas, in lieu of the creation of this answer to the cosmological constant due to enhanced quantization.

Author Bio

Live in New York state part of the year with trips as a guest instructor to Chongqing, PRC, where I perform the duties of a visiting professor and researcher in gravitational physics. Received PhD in 2001 at the U of Houston, and a frequent visitor to conferences, the last being Frontiers in Fundamental physics 15 in Spain this last November, 2017

Download Essay PDF File

Author Andrew Beckwith wrote on Dec. 21, 2017 @ 21:23 GMT
I wish to add a note to this essay

1st. there is an error which I already pointed out to FQXI admins which was not corrected

It is, to read section 7 as follows


7 . Acknowledgements

This work is supported in part by National Nature Science Foundation of China grant No. 11375279. We also thank Dr. Christian Corda for recommending that this author be allowed...

view entire post

Author Andrew Beckwith wrote on Dec. 21, 2017 @ 21:26 GMT
individuals reading my essay should be aware that the prior version of section 7 had an INCORRECT [4] instead of [3] put in. What I have done is to append and correct this error

I asked for a substitution of a corrected document for the FQXI contest, but this evidently was denied

I hope that these two posts, as made will re focus the evaluators upon the intended flow of ideas.

Anonymous wrote on Dec. 22, 2017 @ 00:03 GMT
Hi Andrew, Your knowledge in math and physics is very apparent from this paper. You state the cosmological constant is fundamental. Have you derived our universe from just this constant? Did you derive the additional basic physical parameters from the cosmological constant? Don't the physical constants have to be associated with some physical reality. Would those physical realities be considered fundamental also?

Also it seems unusual that the most fundamental parameter would be the cosmological constant - why not the speed of light?

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Author Andrew Beckwith wrote on Dec. 22, 2017 @ 00:56 GMT
The reason why I picked the cosmological constant is because the speed of light can vary in materials. I.e.the speed of light is not quite what people think it is

Next, see

The learned paper referenced from the article is here:

But be sure also to see a follow-up paper here: »

The single sentence summary of the follow-up paper "says it all":

"We show that even spatially structured photons travel at the speed of light and the measurement of D. Giovannini et al. only provided the projection of this velocity onto the axis of beam propagation."

In fact, the original paper even acknowledges this, in at least a few places.

It's as simple as comparing a beam traveling straight with one reflecting back and forth along some beam path: simply add up the extra path-length travelled.

IMO if we go by what is MEASURED, we have to use data collection and the speed of light has some measurement issues

Whereas the Cosmological constant is tied into the question of Dark Energy

i.e. setting the cosmological constant gets into the fate of tthe universe which is why I picked it

Author Andrew Beckwith wrote on Dec. 22, 2017 @ 00:58 GMT
setting the cosmological constant leads to some very huge components as to the fate of the universe as related here:

Author Andrew Beckwith wrote on Dec. 22, 2017 @ 01:04 GMT
To paraphrase my point. the speed of light, as Measured , has some obvious and subtle issues, as brought up above.

If the Cosmological constant is in a 1 relationship with respect to dark energy, this may be a way to explain the speed up of acceleration of the universe, and also of other things, in a macro scale

I.e. see the following


The only thing that could be accelerating the expansion (i.e. more than countering the braking force of the mutual gravitational pull of the galaxies) is space itself, suggesting that perhaps it is not empty after all but contains some strange “dark energy” or “antigravity” currently unknown to science. Thus, even what appears to be a complete vacuum actually contains energy in some currently unknown way. In fact, initial calculations (backed up by more recent research such as that on the growth of galaxy clusters by NASA's Chandra x-ray space telescope and that on binary galaxies by Christian Marinoni and Adeline Buzzi of the University of Provence) suggest that fully 73 - 74% of the universe consists of this dark energy.

John R. Cox replied on Dec. 27, 2017 @ 15:02 GMT
Dr. Beckwith,

To say, "The only thing that could be accelerating the expansion... is space itself," suggests that space (along with time) is continuously coming into being. That in turn could be the origin of energy. This would be a violation of conservation laws in a naïve sense, but would be an argument for the Cosmological Constant expressing a fundamental property of creational equilibrium. I'd buy that. GR isn't a complete theory, and while being causal and realistic, it is dependent on the Gravitational Constant which has yet to be rationalized, and cannot unify with the quantum realm because it treats ponderable bodies by *mass average* in an observable horizon without an empirical density bound established by theoretical premise. jrc

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Author Andrew Beckwith wrote on Dec. 22, 2017 @ 01:08 GMT
Here is a popular science exposition as to how Dark energy and the cosmological constant may have a 1-1 relationship

this identification is correct, and I am suggesting it is, then that is why I have made the identification I have made, about the cosmological constant being so fundamental.

I hope this answers your question, from an OBSERVATIONAL stand point.

Scott S Gordon replied on Dec. 22, 2017 @ 01:48 GMT
I agree with all you said about dark energy and its relationship with the cosmological constant.

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Author Andrew Beckwith wrote on Dec. 22, 2017 @ 01:50 GMT
And that, from an observational stand point is the reason for the huge importance of the cosmological constant, Scott, from an OBSERVATIONAL stand point

Scott S Gordon replied on Dec. 25, 2017 @ 00:08 GMT
Hi Andy - I just want to state for the record that what we "observe" will not unlock the actual true physical model (our eyes and instruments deceive us!). My theory shows that the speed of light is the first and most fundamental constant and even the speed of light is not an "absolute" constant - It is a "relative constant" (a term I coined from my theory) and it is the reason why all physical constants are the same in all inertial reference frames.

One more thing - The cosmological constant is a misnomer... it was never a constant in time or place in the universe.

I know you will not believe me now but time will tell... I like your original thinking on the topic and wish you the best of luck.

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Author Andrew Beckwith replied on Dec. 25, 2017 @ 00:42 GMT
Why I do not believe you, and this is not personal

Now for falsification of quinessence


review the last link, i.e. it kills a time varying cosmological constant


I was asked to present the status of the...

view entire post

Author Andrew Beckwith replied on Dec. 25, 2017 @ 00:43 GMT
in short, no need for quinessence

Author Andrew Beckwith wrote on Dec. 22, 2017 @ 03:18 GMT
See page 59 of "Faster than light" by Nick Herbert for fourteen things moving faster than the speed of light

Issue is of information transfer, and communication

Scott S Gordon wrote on Dec. 25, 2017 @ 01:30 GMT
No Problem Andy - Like I said - I stated it for the record!

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John R. Cox wrote on Dec. 26, 2017 @ 16:31 GMT
Dr. Beckwith,

any thoughts on why the Gravitational Constant is what it is, and why it apparently exists as a fundamental property of action? jrc

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Author Andrew Beckwith replied on Dec. 26, 2017 @ 17:19 GMT
preserving the consistency of physical law from cycle to cycle

avoiding having a collapsing universe

Author Andrew Beckwith replied on Dec. 26, 2017 @ 17:21 GMT
otherwise one would have the cascade of baby universes with most of them non viable

Philip Gibbs wrote on Dec. 29, 2017 @ 15:00 GMT
Andrew, It is good to see someone tackling inflation and the cosmological constant together. I agree that these things are of fundamental importance and considerations such as this could lead to a real breakthrough in understanding.

Does the analysis lead to the conclusion that there should be a bounce or is that an assumption of the theory?

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Author Andrew Beckwith replied on Dec. 29, 2017 @ 15:29 GMT
It leads to a bounce. Good question. That is part of the implied conclusion

Georgina Woodward wrote on Jan. 3, 2018 @ 21:24 GMT
Hi Andrew, thank goodness for section 6 : ) Fascinating to me that you have chosen this subject as fundamental. Wouldn't be my pick but it is the variety of opinions that makes the contest all the more interesting. I do hope you get lots of readers who can comprehend and appreciate what you have presented. Kind regards Georgina

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Stefan Weckbach wrote on Jan. 6, 2018 @ 13:21 GMT
Hi Andrew, i read your essay and it seems you have found a way to mathematically further underpin an oscillating universe (as I infer from your answers to John Cox and Philip Gibbs above), bouncing off from a collapsing one. Don’t misunderstand me, I fully appreachiate such further underpinnings as important and well done.

Correct me where I am wrong, I conclude that bounce and collapse refer to the same ‘universe’, hence a universe transforms itself into another structure (into a big bang).

My question is whether or not this transformative dynamics is eternal or can come to an end.

Another question to you is whether or not you consider your approach (which I label for the sake of my question as fully consistent and complete in reference to what we know today about physics) as being necessarily the only one that is able to capture the correct ontology of the universe?

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Author Andrew Beckwith replied on Jan. 8, 2018 @ 09:07 GMT
The process of transformative dynamics as modeled is eternal if the initial entropy problem can be fixed

Richard Tolman in " Relativity, Thermodynamics and Cosmology" which is now available in dover book press is a 1934 dated Clareon press release which stated that entropy from cycle to cycle would increase.

If a bouncing universe exists , then some means of avoiding incremental...

view entire post

Stefan Weckbach replied on Jan. 8, 2018 @ 17:52 GMT
Thanks also to you for the elaborate answer.

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Author Andrew Beckwith replied on Jan. 8, 2018 @ 18:04 GMT

Another question to you is whether or not you consider your approach (which I label for the sake of my question as fully consistent and complete in reference to what we know today about physics) as being necessarily the only one that is able to capture the correct ontology of the universe?

end of quote

An answer which solves the build up of entropy problem identified by Tolman will suffice.

The answer I gave is a means to average out different contributions to entropy levels in the start of a non singular universe. I.e. the average level of entropy per cycle at the start of expansion would be zero.

If one believes the Penrose singularity theorem ( I don't) then (entropy) is set to zero at the start by certain conventions.

Needless to say, the problem Tolman identified with cyclical models is very serious.

Steinhart has his own repeating universe model, which has been partly falsified on the basis of recent observations. But it also tried to solve the build up of entropy problem identified by Tolman in 1934

IMO an answer which fixes the build up of entropy per cosmological cycle will suffice.

As it is, I am going to try to present my own findings in Marcel Grossman 15, and also in Dice, in 2018 in Pisa, Italy.

Any MODEL which solves that problem is worthy of analysis, Stefan

Author Andrew Beckwith wrote on Jan. 8, 2018 @ 18:24 GMT
oops I made an error.

Non singular start points to a universe as far as expansion would imply non zero initial entropy.

Singularity, at the start of a universe (Penrose theorem) would IMPLY NO entropy at the start of expansion.

I have some real problems with the Penrose theorem as well as what Hawkings and Ellis said in 1973, in their cambridge university monograph, and will address them in part in Marcel Grossman 15.

Needless to say, if one has a NON singular start to expansion, one has initial non zero entropy, and the Tolman problem of initial increasing entropy levels, is de facto and one has to solve it.

All I am doing, in research is to try to give A SOLUTION to the very real Tolman problem of initial entropy build up, per cosmological cycle.

I salute Steinhardt of Princeton University for his very well thought out attempt to do the same, Stefan.

Any model which solves the initial build up of entropy per cycle, Stefan, is worthy of serious analysis.

I did not say it in my 6 page paper, but I chose the Klauder ENHANCED QUANTIZATION procedure for a cosmological constant, in part, as to how to address the build up of entropy inherent in cyclical universe models

Stefan Weckbach replied on Jan. 9, 2018 @ 08:59 GMT
"Any model which solves the initial build up of entropy per cycle, Stefan, is worthy of serious analysis."

That's my point of view too, since we all are working on some solutions that could bring us all together closer to truth.

Good look for your attempt!

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Stefan Weckbach replied on Jan. 9, 2018 @ 09:01 GMT
ups, should be read as - good luck!!!

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Author Andrew Beckwith replied on Jan. 10, 2018 @ 03:39 GMT
the statement that there is a requirement for a cessation of monotonic increases in the state, initially, of entropy, at the start of repeated cosmological cycles, is a necessary condition as to avoiding the catastrophe as given by Tolman's 1930s cosmology tome which specified that repeating cycles of cosmological rebirth would by necessity create an ever increasing entropy load for successive universes to co exit with, as far as evolution dynamics. The end result is that if there was a perpetual increase in entropy, per cosmological cycle, that , God forbid, the Friedman evolution equations would no longer work.

I.e. there would be no sense in talking of eternal time.; I.e. cosmological existence would, if there was a cyclical universe, be not a dynamic process.

The alternative to big crunch, and then steadily increasing levels of entropy, at the start of a new universe cycle, is that there would be an averaging out of entropy, at the start of a new cosmological expansion, as I specified in the multi verse generalization of the cyclic cosmology picture.

Not specified, though, but one huge issue, to parse would be if the multi verse existed, with different universes contributing to an initial partition function of a newly expanding universe, is do we have constancy in physical law per cycle, and what does that say about the speculation as to if there is a Darwinian process as to creation of new universes?


as given by Vaas

I will spend a lot of time trying to fine tune an answer to this speculation and to come up with a procedure which coheres and admits the possibility of an eternal multiverse, where as considering that individual universes may have a different fate

I.e. invariance of a Multiverse of perhaps up to an infinite number of different constituent evolving universes.

Steve Dufourny wrote on Jan. 8, 2018 @ 22:11 GMT
Hello Mr Beckwith,

I loved yur barrier between the pre planckian and planckian bubble.It is relevant when we consider that gravitation is the main chief orchetra.

I don't consider a Big Bang in my model of spherisation with quant and cosm sphères Inside the universal sphere.I consider even a gravitational aether.The dark energy I see it like a simple anti gravitational spherical push. This gravitational aether is probably the answer to tnhis quantum gravitation, and there is a link with your preplanckian era when we consider this gravitation.I ask if the cold is the answer ? have you an idea about this zero absolute and this gravitation ?

congratulations for your essay, best regards

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Author Andrew Beckwith replied on Jan. 9, 2018 @ 04:09 GMT
I am thinking of gravitation in terms of an emergent field analogy. It is not the same as your suggestion, but you are motivationally not too far off from what started my inquiry

Also look at this business of NLED (non linear electrodyamics) and GR

also see work done by Camara

they consider if the cosmological constant is time independent or time dependent, and go to the regime of a quantum bounce at the start of nucleation of a new universe

The aether in terms of gravitation may be, as you described it, partly described by

My work is roughly congruent to when one has a time independent cosmological constant, as they describe it

You may wish to consider if your gravitational aether model is congruent with their work.

Thanks for your view point and outlook.

As to the matter of "cold" and an anti gravitational push, all I can say is that various models of the cosmological constant. Dependent upon the initial sign of the cosmological constant, it conceivably could be connected initially as an "anti gravitational" push as you referred to it. That if the sign of the cosmological constant were negative.

As I diagrammed it out, using enhanced quantization, the cosmological constant initially has a positive sign.

If the sign were, instead negative, then the idea you have of an anti gravitational push could be entertained.

That is a matter of further research and speculation though.

Thanks for your contribution to this discussion

austin fearnley wrote on Jan. 12, 2018 @ 16:03 GMT
An interesting paper, but your formulae are beyond me (as I have only met the standard FRW formulae) so I cannot comment on them. However, you have also made useful explanatory points in your posts which interest me in relation to Penrose's CCC model. May I ask if there is a simple reason why you do not agree with the Penrose resetting of entropy to zero? I ask because I accept it as reasonable, but of course I could very easily be wrong.

I imply my acceptance of Penrose's CCC in my contest paper and although CCC is important to me it is only a side issue in my paper. It seems to me that there are two ideas at the CCC node of 1) losing the metric and 2) losing the entropy.

I came late to physics after retirement and my background is in psychometrics. What I knew about making metrics in psychometrics readily led me to accept Penrose's method for losing the metric. I will gladly write more about that if you are interested and not familiar with the Rasch Method of making metrics and also the havoc played by a Guttmann structure of data when trying to make metrics. I am not 100% accepting of when the metric is lost. I think that it could degrade in stages before reaching the node. The issue of the metric in my opinion also affects the entropy issue.

Best wishes


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Author Andrew Beckwith replied on Jan. 12, 2018 @ 16:10 GMT
Austin, please doth e bring up the Rasch method



Author Andrew Beckwith replied on Jan. 12, 2018 @ 16:11 GMT
oops, please do bring up the Rasch method. You are correct. I do not know of it



austin fearnley replied on Jan. 12, 2018 @ 18:15 GMT
I am glad you are interested in hearing more on Rasch. The experts are at and at .

I have used some Rasch programs but am not an expert in writing the model or the software.

The Rasch model claims to make rating measurements on a ratio scale equivalent to scales in the physical sciences,...

view entire post

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austin fearnley wrote on Jan. 13, 2018 @ 00:22 GMT
They work for me, but they are two links, rather than one, to two sources of Rasch software and expertise ...


Does that help? If not I will look up more sources.

Best wishes

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Author Andrew Beckwith replied on Jan. 13, 2018 @ 00:36 GMT
yes they do work. Thank you.

Not a criticism, but the links appear to be linked to data analysis, and can you explain the linkage to cosmology?

Pardon me being so tone deaf. I have been ill for 20 hours and have been sleeping most of the time

Tomorrow, I should be able to understand your point

austin fearnley replied on Jan. 13, 2018 @ 03:36 GMT
I sympathise and empathise fully with you and hope you are now getting some sleep. I am in my fourth week of flu. I sent in my contest essay when the flu was at its worst. I went to bed tonight but was too ill to sleep and so am typing this three hours after midnight.

I think I am not explaining myself well. I am possibly the only person who sees any relevance of Rasch analysis to Penrose's CCC. There are no Rasch papers written, as far as I know, pertaining to cosmology. Rasch analysis is used for tasks such as item analysis in examinations and analysing questionnaire scales. Quite often measurements or ratings get added and averaged etc without much care about the nature of the rating scale. The Rasch analysis aims to improve the quality of the scale of the results, for example by adding or averaging modified ratings rather than adding the raw ratings.

Forget the previous links that I listed.

Try the wiki website:

for an overview of the Rasch model.

However, the only Rasch paper that I can show you which is not using Rasch in a standard psychometric context is my own paper at

In that paper you can see a number of metrics made by the Rasch model. Some of these metrics break down. I am suggesting that these metrics break down possibly for the same reason that the metric breaks down at the end of a Penrose CCC cycle. And that reason is the nature of the data is too perfectly Guttman, with too little error in the data. This idea does make a bold assumption that the universe's space metric can somehow be constructed and destructed in a similar manner to running a Rasch analysis! And maybe this is too off-beat a step for you to want to follow it further? If so, that would be understandable.

Best wishes


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Author Andrew Beckwith replied on Jan. 13, 2018 @ 13:58 GMT
quote from your Vixra paper

This paper shows that a Rasch analysis compresses its location parameter space according to the level of

uncertainty in making judgements within that space. The more uncertain the judgements, the more compressed

are the points on the scale. The more uncertain the judgements the more that the location parameters are close to

one another so that uncertainty in making judgements is equivalent to homogeneity in positions of objects.

Dear sir, the point of this appears to be connected to the idea of avoiding space-time singularities.

Is this the interpretation you are seeking?

Thanks for your input

Joe Fisher wrote on Jan. 14, 2018 @ 22:52 GMT
Dear Professor Andrew Beckwith,

My research has concluded that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

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Edwin Eugene Klingman wrote on Jan. 18, 2018 @ 00:32 GMT
Dear Andrew Walcott Beckwith,

I believe you often attempt to bound phenomena, and to herein derive an explicit bound on the cosmological constant, based on Klauder's enhanced quantization.

Your equations are impossible to critique (I pity your reviewers!) but your basic concept seems to be that of a space-time "wall" separating pre-Planckian from Planckian regimes. I have difficulty conceiving of such a wall, but then I have difficulty conceiving of lots of things.

You might wish to read my comment on Klauder's essay page, where I key off of his basis in Dirac to note our friend Steven Kauffmann's paper pointing out nonsense results from the Dirac equation and attributing these to Dirac's consideration of space-time symmetry issues that he used instead of deriving his equation from a corresponding classical Hamiltonian. It is difficult to know just how far this nonsense can or has ricocheted in relativistic quantum field theory.

Which brings me to my essay that treats the historical development of 'space-time symmetry' and raises questions about it. I hope you will read my essay and comment.

My very best regards,

Edwin Eugene Klingman

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