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RECENT POSTS IN THIS TOPIC

Héctor Gianni: on 8/9/13 at 23:38pm UTC, wrote Dear Sean Gryb: I am an old physician, and I don’t know nothing of...

Thomas Ray: on 8/8/13 at 11:04am UTC, wrote Hi Sean, It's just the difference between algebra and analysis. If one...

Ralph Walker III: on 8/8/13 at 0:32am UTC, wrote Thanks Sean. I know it's extremely late, but even if you don't get a...

Sean Gryb: on 8/7/13 at 20:24pm UTC, wrote Thanks Ben! Hope things are well with you! Sean.

Sean Gryb: on 8/7/13 at 20:22pm UTC, wrote hmmm... I'm still not sure I understand what you're getting at. Of course,...

Thomas Ray: on 8/7/13 at 15:27pm UTC, wrote Thanks, Sean. I won't pretend to speak for Carlo Rovelli, though I think I...

Benjamin Dribus: on 8/7/13 at 15:06pm UTC, wrote Sean, Good to see another fine submission from you! I didn't have time to...

Sean Gryb: on 8/7/13 at 13:27pm UTC, wrote Dear Adel, It is certainly true in shape dynamics that only ratios of...


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FQXi FORUM
July 18, 2019

CATEGORY: It From Bit or Bit From It? Essay Contest (2013) [back]
TOPIC: Is Spacetime Countable? by Sean Gryb [refresh]
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Author Sean Gryb wrote on Jul. 5, 2013 @ 16:14 GMT
Essay Abstract

Is there a number for every bit of spacetime, or is spacetime smooth like the real line? The ultimate fate of a quantum theory of gravity might depend on it. The troublesome infinities of quantum gravity can be cured by assuming that spacetime comes in countable, discrete pieces which one could simulate on a computer. But, perhaps there is another way? In this essay, we propose a picture where scale is meaningless so that there can be no minimum length and, hence, no fundamental discreteness. In this picture, Einstein's Special Relativity, suitably modified to accommodate an expanding Universe, can be reinterpreted as a theory where only the instantaneous shapes of configurations count.

Author Bio

Sean Gryb worked on his PhD at the Perimeter Institute and is now splitting his time during a postdoc between Utrecht and Radboud Universities in the Netherlands. He is working on developing Shape Dynamics and is generally interested in the foundations and experimental tests of quantum gravity.

Download Essay PDF File

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James Lee Hoover wrote on Jul. 5, 2013 @ 21:22 GMT
Sean,

If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, “It’s good to be the king,” is serious about our subject.

Jim

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Manuel S Morales wrote on Jul. 6, 2013 @ 11:49 GMT
Sean,

As of 7-6-13, 7:49 am EST, the rating function for your essay is not available. Sorry I can't help you out right now by rating your essay. NOTE: I have logged in using a PC and a MAC and different browsers but it appears to be a site function issue.

Manuel

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Manuel S Morales replied on Jul. 7, 2013 @ 21:17 GMT
Sean,

I have sent an email requesting that FQXi extend to those of you who had their essay posted on July 5, 2013, be allowed additional days to compensate for the days of not being able to rate these essays.

My experience in conducting the online Tempt Destiny (TD) experiment from 2000 to 2012 gave me an understanding of the complexities involved in administrating an online competition which assures me that the competition will be back up and running soon. Ironically, the inability of not being able to rate the essays correlates with the TD experimental findings, as presented in my essay, which show how the acts of selection are fundamental to our physical existence.

Anyway, I hope that all entrants will be allocated the same opportunity to have their essay rated when they are posted, and if not possible due to technical difficulties, will have their opportunity adjusted accordingly. Best wishes to you with your entry.

Manuel

PS I will be reviewing and rating your entry after this function has been turned back on.

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Giacomo Alessiani wrote on Jul. 6, 2013 @ 19:54 GMT
Mr. Gryb

My compliments , I liked too much the script . Only ,

can You verify this ? I am asking if it is possible to change Your:

phi = phi + 2pi into m2v2-> = m1v1-> + n(pi) ? (page 5)

( -> is for vector, n any number , m mass , v velocity )

This new element , is quite My essay, in its

smallest form.

I am waiting the rating system back.

My Best Regards.

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Author Sean Gryb replied on Jul. 8, 2013 @ 16:21 GMT
Glad that you liked it.

I'm not sure that I would make this change myself. I wouldn't know how to interpret my phi as a momentum.

Cheers,

Sean.

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Giacomo Alessiani replied on Jul. 11, 2013 @ 01:19 GMT
Mr Gryb,

It is possible. I do not know how to show You now.

So good luck and thanks again for the reply.



My Best Regards. Giacomo Alessiani.

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Hoang cao Hai wrote on Jul. 7, 2013 @ 01:41 GMT
Dear Sean

Unfortunately, your essay is too large for automatic translation capabilities of my computer. Anyway,also wish you success.

And to change the atmosphere "abstract" of the competition along with demonstrate for the real preeminent possibility of the Absolute theory as well as to clarify the issues I mentioned in the essay and to avoid duplicate questions after receiving the...

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Alan M. Kadin wrote on Jul. 8, 2013 @ 01:00 GMT
Dr. Gryb,

In your essay you present a clear explanation of why QM and GR are generally viewed to be incompatible: quantum indeterminacy inevitably leads to black hole singularities on the microscopic scale. But in my essay ( "Watching the Clock: Quantum Rotations and Relative Time" ), I present a simple picture of real deterministic wave packets of relativistic quantum fields. These same oscillating fields act as local clocks. The presence of a gravitational potential reduces the energy and hence the frequency of these fields, thus slowing local time. This provides a simple, natural basis for GR, but in a way that avoids divergences leading to black holes, which do not exist in this picture. This would seem to provide a promising foundation for a more complete theory of quantum gravity, which avoids the conventional difficulties.

Alan Kadin

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Author Sean Gryb replied on Jul. 8, 2013 @ 16:28 GMT
Dear Alan,

Thanks for pointing this out and for reading the essay. I hope you enjoyed it. I will take a look at your model, your goal is ambitious.

All the best,

Sean.

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Member Carlo Rovelli replied on Jul. 24, 2013 @ 04:27 GMT
Sean,

the "number of degrees of freedom" of a standard QFT is discrete. Not continuous. This is the entire point of the Fock space construction. The one-particle space describes, obviously, a finite number of degrees of freedom, and so the two-particle state space, and so the n-particle space state, so you can associate an integer number to each degree of freedom, which is your definition of a system with a finite number of degrees of freedom.

ciao, carlo

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Antony Ryan wrote on Jul. 10, 2013 @ 08:51 GMT
Dear Sean,

I posted comments yesterday (something obviously went wrong as they aren't here). Great essay. I like the idea that scale becomes meaningless. I worked on similar around simplex geometry away from the contest, which reveals a lot about reality. If you get a chance, please take a look at my essay.

Definitely on the right track in my opinion!

Well done,

Antony

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Author Sean Gryb replied on Jul. 11, 2013 @ 11:40 GMT
Dear Antony,

Thanks for the encouraging remarks. There definitely seems like scale invariance is an interesting avenue to pursue. Who knows where it could lead, but the journey might be interesting. Thanks for taking a look at my essay. I will try to return the favour.

Cheers,

Sean.

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Antony Ryan replied on Jul. 12, 2013 @ 17:14 GMT
Dear Sean, No panic - I know how tough it is getting through them all.

Glad there are more out here who think like this, as scale invariance is so intuitively fitting for Quantum Gravity.

Well done with your essay and best wishes for the contest,

Antony

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Cristinel Stoica wrote on Jul. 10, 2013 @ 10:38 GMT
Dear Sean,

It was a pleasure to read your wonderful essay, on the role of scale invariance. This is particularly important for Shape Dynamics. (For different reasons - singularities - I argued in favor of scale invariance, in my "digital vs. analogic" FQXi essay, Infinite Resolution. At that time I did not consider the problems of quantum gravity, but soon I found that singularities exhibit geometric dimensional reduction, and there is data supporting the view that this make quantum gravity perturbatively renormalizable). It is beautiful how you interpret inertial trajectories in de Sitter space as Shape Dynamics.

Best regards,

Cristi Stoica

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Author Sean Gryb replied on Jul. 11, 2013 @ 11:37 GMT
Dear Cristi,

Thanks for reading and for your positive comments. I will definitely have a look at your essay. I'm very much interested in the idea of dimensional reduction, which seems to play a role in many non-perturbative approaches to quantum gravity such as Causal Dynamical Triangulations, Horava gravity, and Asymptotic Safety scenarios. Even if you already know this, it is worth repeating: the magical dimension seems to be 2. This is, perhaps, not surprising since 2 is the dimension where gravity becomes conformal. Again, scale invariance seems to be playing an important role.

't Hooft also has some ideas about conformal invariance and black holes. He is convinced that the latter imply the former, but he doesn't have dimensional reduction in mind. Anyway, he is a very cleaver man and it seems like an interesting program.

Take care,

Sean.

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Lawrence B Crowell wrote on Jul. 11, 2013 @ 02:34 GMT
Sean,

Your paper is rather interesting. I will probably have to give it a second reading. What thought did come to mind is that a closed timelike curve in Lorentz spacetime have a nontrivial fundamental form π^1(L,M) = Z. There is a similar nontrivial topology for a sphere in Lorentz spacetime, and it is easy to see that the 2-sphere contains CTCs. Of course de Sitter spacetime is contained in a Minkowski spacetime of one dimension. Your projection based on the Mobius transformation, which in deeper levels is a categorical system based on [0, 1, ∞].

Cheers LC

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Author Sean Gryb replied on Jul. 11, 2013 @ 11:43 GMT
Dear Lawrence,

Glad to see you in this competition and thanks for your comments!

I'm not sure how relevant CTCs would be to what I am trying to do since deSitter is globally hyperbolic, so admits no CTCs. Interesting comments nonetheless.

Thanks!

Sean.

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Lawrence B Crowell wrote on Jul. 11, 2013 @ 13:13 GMT
The CTC does not of course exist in the dS spacetime, but in the embedding space of one dimension larger. More to the point these spheres only “kiss” the dS along a spacelike circle, or sphere S^n for n = dim(dS), at a t = constant, which is also contained n the embedding space. A CTC is then only contained in the dS within some subspace of n-1 dimensions. In the case of the diagrams the CTC is contained in the dS at two disconnected points.

I am not claiming these CTCs are physical geodesics. Yet as cochains in these spheres are not contractible to a point. The paper H. Monroe, "Are Causality Violations Undesirable?". Foundations of Physics 38 (11): 1065–1069 (2008) illustrates some of this. The topological quantum number then appears to be mapped into some information when the closed curve is mapped into an open curve on the dS spacetime. There may be some deep topological aspect to this construction. This could be worth some analysis and a short paper.

Overall I find your paper to be one of the better ones in the FQXi context.

Cheers LC

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Author Sean Gryb replied on Jul. 11, 2013 @ 14:41 GMT
That is interesting, I didn't know about these properties of CTC. Thanks for alerting me. And definitely thanks for the compliment!

Cheers,

Sean.

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Lawrence B. Crowell replied on Jul. 12, 2013 @ 02:20 GMT
I gave your paper a bit of a boost today.

I am rethinking a bit of my conjecture. These sphere have closed curves, but they are not closed timelike curves. However a circle with timelike parts, say a curve that loops over the top and bottom of the sphere as oriented with respect to the hyperboloid, is mapped to the hyperbold as one or two timelike curves. So we might think of the longitudinal lines on the sphere as mapped from CTCs from another space. This is so these curves on the two-spheres contain the same data as the geodesics on the hyperboloid.

I'll need to dwell on this for a while to see if it makes sense.

Cheers LC

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Yuri Danoyan wrote on Jul. 11, 2013 @ 23:08 GMT
Sean

I would like to show my short question about spacetime to Stephen Weinberg

Fri 8/1/2008 1:21 PM

Quoting Yuri Danoyan :

"Dear Dr Weinberg

If space is discrete and time is continue,does 4-dimensional space-time

lost its sense?

Sincerely

Yuri Danoyan"

from

weinberg@physics.utexas.edu

to Yuri Danoyan

"Yes"

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Satyavarapu Naga Parameswara Gupta wrote on Jul. 12, 2013 @ 00:06 GMT
Dear Sean,

Thank you for presenting your nice essay. I saw the abstract and will post my comments soon. So you can produce matter from your thinking or from information description of that matter? Why don't you take space as space an time as time. . . . ?

I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on...

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Harlan Swyers wrote on Jul. 12, 2013 @ 13:04 GMT
Interesting essay, I would like to point out that one thing that has not really been explored in physics are irrational basis of counting, which in some sense are more practical when one considers the full continuum.

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Author Sean Gryb replied on Jul. 15, 2013 @ 14:18 GMT
Indeed.

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Anton Biermans wrote on Jul. 14, 2013 @ 03:13 GMT
Hi Sean,

As far as I'm aware of, the universe either has been created by some outside intervention or it creates itself out of nothing, without any such interference. If in the last analysis in a self-creating universe particles have to create themselves, each other, then we cannot avoid the conclusion that particles, particle properties, like their mass, must be as much the cause as the...

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Héctor Daniel Gianni wrote on Jul. 14, 2013 @ 20:59 GMT
Dear Sean Gryb:

I am an old physician, and I don’t know nothing of mathematics and almost nothing of physics, but after the common people your discipline is the one that uses more the so called “time” than any other.

I am sending you a practical summary, so you can easy decide if you read or not my...

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M. V. Vasilyeva wrote on Jul. 15, 2013 @ 04:03 GMT
Sean,

I loved your clear, so well-written and so well-explained essay. You have an amazing gift for introducing complex ideas in a readily accessible even to the non-specialists like myself way. You present your idea with such clarity that in the end it appears self-evident. Which naturally rises the question in my mind: why would not the rest of your colleagues immediately drop whatever they are pursuing and join you under the banner of Shape Dynamics? What are their main objections and how do you rectify them?

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Author Sean Gryb replied on Jul. 15, 2013 @ 17:32 GMT
Dear Ms. Vasilyeva,

Thank you for the very flattering comments on the essay. I'm glad that you found it interesting.

I'm not really sure if I can completely answer your question. The short answer is that "quantum gravity" is a really big, really hard problem, and there are many excellent ideas out there that should be pursued. It's important to have a variety of different opinions...

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M. V. Vasilyeva replied on Jul. 17, 2013 @ 07:22 GMT
Thank you Dr. Gryb for your explanation. Again I leave your blog with enriched understanding of physics and its current problems. Good luck at the conference!

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:20 GMT
Thanks! And good luck to you in this competition!

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Joe Fisher wrote on Jul. 15, 2013 @ 16:16 GMT
Dr. Gryb,

I am an unschooled decrepit realist so I am afraid I could not quite understand most of your excellent essay. I did think that Dr. Ngui’s graphics were superbly rendered and adequately explained.

Joe

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Author Sean Gryb wrote on Jul. 15, 2013 @ 17:35 GMT
I will pass on the message to Marc that you appreciated his graphics!

I agree that he did a really great job with the pictures. Then even helped me a lot to understand certain subtleties of the project.

Cheers,

Sean.

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Jeff Baugher wrote on Jul. 15, 2013 @ 19:35 GMT
Dr. Gryb,

Interesting take on Shape Dynamics, but I would argue that including in the Cosmological Constant without understanding why the parameter mathematically appears would run counter to your postulate on the assumption of simplicity. I have a different take on what the Cosmological Constant is through a modification to Gunnar Nordstroem's theory . Even if you don't find my own idea appealing but are not familiar with this pre-GR theory, I do recommend it for a different viewpoint.

Kind Regards,

Jeff

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:24 GMT
Dear Jeff,

Thanks for letting me know about your essay. I am familiar with the Nordstrom theory of course, but it is always good to learn more.

Sean.

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Richard N. Shand wrote on Jul. 16, 2013 @ 07:35 GMT
Dear Sean,

You explanation of scale invariance is very clear and well illustrated. Well done!

When I was writing my essay I had shape dynamics in the back of my mind. Scale can also be approached as a measure of entropy using Eddington's phase dimension (see my essay "A Complex Conjugate Bit and It").

You write that ultimately "scale is a matter of your point of view." This also relates to the conditional entropy of the observer, without whom the mental constructs of space and time would not exist.

Best wishes,

Richard Shand

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:29 GMT
Dear Richard,

I'm glad that we share the same kinds of intuitions about shapes. The idea of approaching scale from the point of view of entropy is an incredibly interesting one. I agree that there could be a lot of value in doing so. I'm interested to see what you say about it in your essay.

Sean.

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Hugh Matlock wrote on Jul. 16, 2013 @ 08:31 GMT
Hi Sean,

An excellent presentation and argument!

Starting from different premises (the simulation paradigm) I have come to a similar conclusion: that the 3-sphere is a key structure in several ways. I hope you get a chance to look at my essay Software Cosmos as I think it nicely complements your essay with some additonal observational evidence for this viewpoint.

Hugh

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:30 GMT
Dear Hugh,

Observational evidence is always important. Thanks for pointing out this work.

Sean.

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Peter Jackson wrote on Jul. 17, 2013 @ 15:20 GMT
Sean,

An excellently crafted description of a very complex and non-intuitive concept, which I now understand far better. But like others above my understanding is still incomplete, seeing many apparent loose ends and new propositions and concepts not yet justified.

Your introductory overview was one of the best I've read, but broke down with the misquoting of Einstein's; "original...

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:35 GMT
Dear Peter,

Thanks for you flattering remarks and the detailed comments. I'm glad you enjoyed the explanations and are happy for the critiques on the content.

Your approach sounds interesting, but I will have to look more closely at the details to be able to make an educated opinion.

Good luck in the competition!

Sean.

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Akinbo Ojo wrote on Jul. 17, 2013 @ 19:34 GMT
Hi Sean,

Is space-time countable, my answer is YES. I would be glad for you to read my essay and fault the logic. Further exchanges are warranted. Meanwhile...

As the contest in Wheeler's honor draws to a close, leaving for the moment considerations of rating and prize money, and knowing we cannot all agree on whether 'it' comes from 'bit' or otherwise or even what 'it' and 'bit' mean, and as we may not be able to read all essays, though we should try, I pose the following 4 simple questions and will rate you accordingly before July 31 when I will be revisiting your blog.

"If you wake up one morning and dip your hand in your pocket and 'detect' a million dollars, then on your way back from work, you dip your hand again and find that there is nothing there…

1) Have you 'elicited' an information in the latter case?

2) If you did not 'participate' by putting your 'detector' hand in your pocket, can you 'elicit' information?

3) If the information is provided by the presence of the crisp notes ('its') you found in your pocket, can the absence of the notes, being an 'immaterial source' convey information?

Finally, leaving for the moment what the terms mean and whether or not they can be discretely expressed in the way spin information is discretely expressed, e.g. by electrons

4) Can the existence/non-existence of an 'it' be a binary choice, representable by 0 and 1?"

Answers can be in binary form for brevity, i.e. YES = 1, NO = 0, e.g. 0-1-0-1.

Best regards,

Akinbo

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:39 GMT
Dear Ojo,

I'm curious to hear why you think spacetime is countable. However, I hope that you judge the essays by their content alone.

Sean.

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James Lee Hoover wrote on Jul. 17, 2013 @ 22:29 GMT
Sean,

"Perhaps it suggests that there is a way to think of quantum gravity in fully scale-invariant terms. If true, this would provide a new mechanism for being able to deal with the uncountably infi nite number of degrees of freedom in the gravitational field without introducing discreteness at the Plank scale."

Certainly this is a perception that could help unify QM and relativity -- gravity universal and complete regardless of scale? Thinking outside the anthropomorphic box is quite necessary in dealing with a unified theory and solving the mystery of gravity. My ideas are somewhat feeble w/o such grand theories.

Jim

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:43 GMT
Dear Jim,

Agreed.

Best of luck in the competition,

Sean.

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Don Limuti wrote on Jul. 18, 2013 @ 18:46 GMT
Hi Sean,

I like your work and rated it highly. Shape dynamics may be a productive path.

You have suggested two means of uniting gravity and QM.

1. Change the conception of gravity

2. Abandon the continuity of space-time

It may also be productive to also consider keeping the continuity of space-time while

keep a discreteness to velocity. Check my essay, you may find it interesting.

Thanks,

Don Limuti

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:48 GMT
Dear Don,

Thanks for the rating.

That sounds like an interesting idea. Certainly discretizing the momentum could be a path to helping solve some issues. That you for pointing this out.

Best of luck in the competition,

Sean.

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Sreenath B N wrote on Jul. 19, 2013 @ 02:21 GMT
Dear Sean,

I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

Regards and good luck in the contest,

Sreenath BN.

http://fqxi.org/community/forum/topic/1827

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Hoang cao Hai wrote on Jul. 19, 2013 @ 09:51 GMT
Dear Sean

I tried to read your essay .

You probably need to add a specific definition (for the equations in the essay) on two concepts - are thought to be very vague - that is: time and gravity, then the result of the equation that will be more practical value.

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Jayakar Johnson Joseph wrote on Jul. 19, 2013 @ 11:02 GMT
Dear Sean,

In particle scenario, quantisation is imperative to measure infinite space-time continuum in that uncertainty exists with the observations of observational information, while the nature of information is not considered as continuum in this scenario. Thus, space-time is a countable set in continuum whereas information is countable only as discrete, as the observational information in this scenario is probabilistic rather than realistic. Thus the observational information on space-time is not realistic though countable.

As the ‘Informationalism’ expressional with Information science is indicative of information continuum, a pragmatic definition for information may be ascribed as the transfer of matter with energy in continuum and thereby we may consider for an alternative cosmological model in that a string-matter continuum scenario is descriptive.

With best wishes

Jayakar

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Member Ken Wharton wrote on Jul. 19, 2013 @ 13:33 GMT
Hi Sean,

Fantastic Essay! You really have a knack for this level of explanatory writing; you should do more of it. (George Musser, if you're reading this, go commission an article by Sean post-haste!)

What really came through for me was the first argument that I've really bought/understood as to why scale invariance is so attractive. Sure, I've always disliked the idea of some fundamental Planck length and prefer the continuum, but mainly because I have too much respect for Lorentz and Poincare invariance, not because of this type of argument. Beautiful stuff.

I vaguely remember that the only non-scale-invariant piece of the standard model is the Higgs...? Any thoughts on how that might play out in this story?

Am I right that your clock variable \varphi is what would be measured by a conformal clock? (Meaning, say, Einstein's light clock where the two mirrors are changing their relative distance along with the expansion of the universe.) That almost fits with my limited understanding of these things, except that I had thought the universe was of finite duration as measured by such a clock, while your clock parameter still (logarithmically) diverges as t->\infty. Does the small cosmological constant limit this to a finite \varphi even as t->\infty?

And if I'm right that the universe *is* of finite duration (as measured by such a clock), does this imply anything in particular for the way you see cosmological boundary conditions as coming into the story? (Would one have a future boundary condition at the final conformal-time boundary?)

Again, excellent job! (Arguably 2 contests too late, but I, for one, am very glad you fit it into this year's topic.) Keep it up and you might even strong-arm me into seriously thinking about cosmology again... :-)

Best,

Ken

PS -- Looking forward to catching up in Munich!

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Author Sean Gryb replied on Jul. 20, 2013 @ 11:53 GMT
Dear Ken,

Thanks so much for your very generous comments on the essay! I really enjoy this kind of writing and would be happy to do more of it (do you know how I could look into doing this??).

Yes, conformal invariance is a really important thing to look for in a quantum field theory because this is the definition of a fixed-point of the RG flow. I'm not sure why this point is not...

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Willard Mittelman wrote on Jul. 19, 2013 @ 17:16 GMT
Hello,

I liked your essay and found it interesting, but I'm wondering if the scale-invariance that you describe is really opposed to fundamental discreteness. I believe that the paper "Regular black holes in UV self-complete quantum gravity," by E. Spallucci and S. Ansoldi (arXiv:1101.2760), is illuminating in this regard. (As an aside, I've already discussed this paper with Douglas Singleton over at his essay; you might find his paper (co-authored with Elias Vagenas & Tao Zhu), with its use of self-similarity, relevant to your own perspective.) Spallucci & Ansoldi argue (drawing on earlier ideas of G. Dvali)that the Planck scale is a scale-invariant limit, or "anchor," of the very kind that you describe on p. 2 (section 2) of your essay. Yet they also take the Planck length to be a minimal length - in the sense that it is impossible to probe shorter distances - so that it sets a fundamental discreteness scale.

So, I'm not sure that discreteness needs to be rejected, even if one accepts scale-invariance. Admittedly, there is the objection you mention about it being impossible to prove that a given discrete theory T is truly fundamental; but to me, the mere possbility of a more fundamental theory is hardly a devastating objection to such a T.

Anyway, best wishes and good luck in the contest,

Willard Mittelman

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Author Sean Gryb replied on Jul. 20, 2013 @ 11:21 GMT
Dear Willard,

I appreciate the reflective comments and will have a look at the work you recommend.

I would not deny that it is impossible to have a form of discreteness while still having scale invariance. For example, it could be possible that there is a kind of "minimum" ratio instead of an absolute minimum length or it may be that the scale invariant degrees of freedom come in countable discrete packets. I wouldn't be surprised if there exists models that exhibit this kind of behaviour so I do take your point.

The point I was trying to make was that scale invariance could provide an interesting alternative to fundamental discreteness as a resolution of the non-renormalizability of General Relativity. Postulating a fundamental minimum length is a quite a traumatic thing to do to spacetime. I think it's valuable to explore alternatives.

Re: your last comment, I would mainly object to the use of the word *fundamental*, which I think is widely and deceptively overused in physics - especially in this case.

All the best in the essay. I am eager to have a look at your paper, but please have patience: I am travelling and am very busy with the Loop conference right now, so it might take me a bit of time to get to it.

Best of luck with the competition!

Sean.

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Willard Mittelman replied on Jul. 24, 2013 @ 00:01 GMT
Hi Sean,

Thanks for your helpful response. I don't want to make too big an issue of this -- and given your busy schedule, please don't feel a need to respond -- but when you say (on p. 2 of your essay) that scale-invariance implies that a theory stops changing as we make our measurements more precise, this raises the question of whether there are any limits on how precise our measurements...

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Willard Mittelman replied on Jul. 24, 2013 @ 00:12 GMT
In re-reading the comment I just made, I see that, in the final sentence of my second paragraph, the clause following the semicolon should be deleted as irrelevant, since you're not claiming that there's an inherent opposition between scale-invariance and discreteness. I apologize for my carelessness.

-Willard

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Héctor Daniel Gianni wrote on Jul. 19, 2013 @ 23:00 GMT
Dear Dr.Sean Gryb:

You didn't read my post of july 14. Maybe you would like to read Einstein unic short verbal "space-time" description in Einstein "ideas and Opinions" page 365.

With my very best whishes

Héctor

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Author Sean Gryb replied on Jul. 20, 2013 @ 10:57 GMT
Dear Hector,

My apologies. I am travelling extensively right now and haven't had much time to respond to posts. I did read your post though. Thanks for the description.

Cheers,

Sean.

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Patrick Tonin wrote on Jul. 20, 2013 @ 09:19 GMT
Dear Sean,

You said:

"a. That space is closed and has the shape of a 3 dimensional sphere. This means that an observer can head in the same direction and (eventually) come back to their original location.

b. That space is expanding and that this expansion if fueled by a very small, positive parameter called the cosmological constant, which we will discuss briefly."

This is exactly what I describe in my essay . I have also come up with a scale invariant theory in which I show that the proton's diameter is a scaled up version of the Planck length and that the proton's mass is a scaled down version of the Planck mass.

If you take the Planck length and multiply it by 1020 (the scale factor) and divide it by 1-1/8Pi, you get the exact value of the proton's diameter measured with a muon. If you divide that SAME value again by the SAME 1-1/8Pi, you get the exact value of the proton's diameter measured with an electron (solving the proton radius measurement problem ). This 1-1/8Pi is explained in my theory (it is (8Pi-1)/8Pi).

If you take the Planck mass and multiply it by 10-20(the scale down factor) and multiply it by 8-1/Pi, you get the exact value of the proton's mass. Again, 8-1/Pi is explained in my theory (it is (8Pi-1)/Pi).

The 8Pi-1 also appears in the proton/electron mass ratio formula that I present in my essay but also in a lot more formulae that I won't describe here but that you can find here.

I would love to have your expert opinion on my findings, I hope that you will take the time to read my essay.

Patrick

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Author Sean Gryb replied on Jul. 20, 2013 @ 11:00 GMT
Dear Patrick,

Sounds interesting, but I will have to look more closely at the details to judge.

Good luck in the competition.

Sean.

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Yuri Danoyan wrote on Jul. 22, 2013 @ 14:43 GMT
Dear Sean

You wrote "...so that there can be no minimum length"

I agree but on other reason

http://vixra.org/abs/1301.0191

Good luck

Yuri

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Member Howard N Barnum wrote on Jul. 22, 2013 @ 22:54 GMT
Nice essay, well-written and clearly explaining its topic. It does seem less deeply connected to the question of "It from bit" than some of the other essays I've read, though. I guess countability could be related to the notion of an exact description via a sequence of bits... but if one can imagine eliciting an infinite such sequence, the space of possible sequences could be uncountable...

I"ll be interested to see how this stereographic/de Sitter duality is or isn't useful in future physics... curious on how you view its relation to the conformal/anti-de Sitter duality that is talked about a lot by string theorists?

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:00 GMT
Dear Howard,

Sorry for the delay in my reply. I've just finished 2 intense conferences and then a couple of days of hiking through the Alps. I hope you'll forgive my silence.

To answer your question, there is definitely some relevance to the usual ads/cft correspondence here. Me and a couple of coauthors have been investigating the link between the ads/cft correspondence and shape dynamics in a couple of papers (the most recent being: http://arxiv.org/abs/1305.6315).

Indeed, I think there are more direct connections with the dS/cft correspondence being explored by Skenderis and collaborators over the past few years. I'm working on a paper right now that will compliment the essay and try to make these connections more clear.

Glad you enjoyed the essay and best of luck in the competition!

Sean.

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Stephen James Anastasi wrote on Jul. 23, 2013 @ 11:38 GMT
Hello Sean

I agree with Howard. A lovely essay. I wonder how your concept of there being no minimum length would play out in the context of a proof I created in a Master's thesis (see attached).

Please read my essay on what I call the Armchair Universe which provides a foundation for spacetime, which arose initially after considering scaling bothers. I would be very interested to see how your work might be connected to mine.

Best wishes

Stephen Anastasi

attachments: 1_A_problem_for_geometry_1.pdf

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:04 GMT
Dear Stephen,

Apologies for the delay in the response. I will try to read through this and send some comments if I have any.

Best of luck in the competition!

Sean.

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Paul Borrill wrote on Jul. 23, 2013 @ 21:43 GMT
Very interesting. I also enjoyed your previous paper I found on the arXiV (Right about Time). I had not previously made the connection between countability (one to one relation with the integers) and the continuum problem. Of course, you are right, its all about manifesting discreteness.

However, I would appreciate your opinion other aspects of countability. Consider, for example, the distinction between identity and indistinguishability. If we can identify particles as being discrete, but they are indistinguishable (for example in a Bose-Einstein condensate), then are they countable? More generally, do we need "identity" before the notion of countability is valid?

Also, what about recurrence? Imagine a pendulum (or other simple harmonic oscillator). If there is no physical mechanism to count beyond a modulo (in this case 2), then there could be an infinite number of recurrences (cycles of oscillation) before the event we observe, and after the event we observe. Can we refer to them as countable?

More importantly, if you are asleep, and someone wakes you, and you see the oscillator make a few cycles (you can even count them), and then you sleep for a while, but you don't know how long you have slept and someone wakes you again, can you still say that the number of cycles is countable -- if you have absolutely no external mechanism whatsoever to count the cycles that went by when you were asleep -- can you still say that the cycles are countable?

These may be easy questions for you to answer, nonetheless, they are interesting questions to me regarding "Is Spacetime Countable". For example, we could just as easily say "are cycles countable in the quantum domain"?

Kind regards, Paul

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:11 GMT
Dear Paul,

I'm glad you enjoyed this essay and the last one.

Yes, these are definitely interesting questions. As I said in my essay though, I was using a definition of countability that is completely ignorant to practical issues. You're very right that some things things that are, in principle, countable may, in practice, not be possible to count or one may just go on counting forever. For my purposes, all these things are "countable" (at least in principle). However, it is very interesting to consider the more realistic case of things that are practically countable.

Take care,

Sean.

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Anonymous wrote on Jul. 24, 2013 @ 09:05 GMT
Dear Sean,

Very good essay that, in my opinion, that tackles the ambitious task of unifying QM and GR in the right way.

My topic has to do with "dessins d'enfants" and contextuality. In the wikipedia paper you have a picture of the triangulated hyperbolic plane.

http://en.wikipedia.org/wiki/Dessin_d'enfant

In his book "The icosahedron and the solutions of equations of the fifth degree" (Dover, NY, 1956), Klein's antcipates the Belyi functions for platonic solids by using the stereographic projection.

My essay is here

http://www.fqxi.org/community/forum/topic/1789

I don't look at scale invariance, I don't look at the large scale universe but strangely there are closely related mathematical objects at the starting point.

Good luck,

Michel

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:12 GMT
Dear Michel,

Sounds interesting. Thanks for pointing my attention to this.

Sean.

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Than Tin wrote on Jul. 24, 2013 @ 21:46 GMT
Hello Sean

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19
65/feynman-lecture.html)

said: “It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don’t know why that is – it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn’t look at all like the way you said it before. I don’t know what the reason for this is. I think it is somehow a representation of the simplicity of nature.”

I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

The belief that “Nature is simple” is however being expressed differently in my essay “Analogical Engine” linked to http://fqxi.org/community/forum/topic/1865 .

Specifically though, I said “Planck constant is the Mother of All Dualities” and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism … and so on.

Taken two at a time, it can be read as “what quantum is to classical” is similar to (~) “what wave is to particle.” You can choose any two from among the multitudes that can be found in our discourses.

I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

Since “Nature is Analogical”, we are free to probe nature in so many different ways. And you have touched some corners of it.

Best

Than Tin

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Torsten Asselmeyer-Maluga wrote on Jul. 25, 2013 @ 13:27 GMT
Dear Dr. Gryb,

interesting essay. I like the idea of shape dynamics. One point is especially interesting. You wrote about scale invariance and I think this point of view has something to do with my approach using exotic smoothness. In my essay, I also discuss the question about the countability of the spacetime. I came to the same conclusion, in particular I do not put the smooth manifold away. There is another possibillity to kill the infinities (I believe). All relevant structures in 3D and 4D are very rigid, for instance one has Mostow rigidity for hyperbolic 3-manifolds etc.

I certainly have to read your other papers.

Good luck for the contest

Best

Torsten

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:15 GMT
Dear Torsten,

Thanks for your interest in my essay and my other work.

I don't know much about Mostow rigidity but it sounds like an interesting idea to pursue. I'll try to take a look at your essay.

Good luck in the competition!

Sean.

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William Amos Carine wrote on Jul. 26, 2013 @ 16:47 GMT
Dear S. Gryb,

The reduction of dimensions like the use of meter defined in S. R. simultaneity and time as nothing inherently more than the ticks of hands pointing to positions on a dial indicate a departure form dimension of some if not all quantities by a type of foreshadowing.

Thankful for the good read,

Amos.

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Akinbo Ojo wrote on Jul. 26, 2013 @ 19:48 GMT
Dear Sean,

Please pardon my straying from subject matter. As I am not a professional physicist and just for me to be clear and learn from the experts, especially those with a relationist leaning: Is it being implied by the relational view of space and as suggested by Mach's or other relational principle that what decides whether a centrifugal force would act between two bodies in *constant relation*, would not be the bodies themselves, since they are at fixed distance to each other, nor the space in which they are located since it is a nothing, but by a distant sub-atomic particle light-years away in one of the fixed stars in whose reference frame the *constantly related* bodies are in circular motion? Or in which other relational reference frame can such circular motion be described?

You can reply me here or on my blog. Much appreciated. And please pardon my naive view of physics.

Accept my best regards,

Akinbo

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:20 GMT
Dear Akinbo,

I think there is certainly a sense in which Mach would have agreed that the motions and forces felt by a body should be thought of as being influenced by the relations between everything in the Universe. However, Mach didn't know that things and information can't travel faster than light, so this changes the story slightly.

Hope that helps answer your question.

Sean.

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Ram Gopal Vishwakarma wrote on Jul. 28, 2013 @ 21:43 GMT
Dear Sean,

You propose to trade the scale-invariance of special relativity to explain the real universe in a way that its expansion is not influenced by any form of matter and energy. In fact, there already exists one such theory – the Milne’s model which is a kinematic theory based on the cosmological principle.

It has recently been shown [Phys. Scripta, 5, 055901, (2013)] that this theory explains all the cosmological observations without even requiring the speculative dark matter, dark energy and inflation. Moreover, this theory evades the long-standing problems of the standard cosmology. It would not be correct to say, as is generally (mis)believed, that the Milne model represents an empty universe.

As the Milne’s model appears as a homogeneous, isotropic solution of equations R^{ik}=0 (see my essay in the present contest), and as equations R^{ik}=0 present an scale-invariant theory, it appears that your holy grail is the theory I have presented! I would appreciate your comments on my essay.

Best Regards.

___Ram

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:21 GMT
Dear Ram,

Thanks for bringing this to my attention.

Sean.

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eAmazigh M. HANNOU wrote on Jul. 29, 2013 @ 02:54 GMT
Dear Sean,

One single principle leads the Universe.

Every thing, every object, every phenomenon

is under the influence of this principle.

Nothing can exist if it is not born in the form of opposites.

I simply invite you to discover this in a few words,

but the main part is coming soon.

Thank you, and good luck!

I rated your essay accordingly to my appreciation.

Please visit My essay.

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Douglas Alexander Singleton wrote on Jul. 29, 2013 @ 06:07 GMT
Dear Dr. Gryb,

A clear and nicely illustrated essay (the pictures help). If I understand correctly you are proposing scale invariance as a guiding principle to give a small scale structure for space-time which is smooth rather than foamy or discrete. This is done in the context of dS space-time rather than Minkowski space-time. This is a nice idea and may have some connection with an...

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:35 GMT
Dear Doug,

Thank you for your thoughtful comments. I wasn't aware of the Aldrovandi and Pereira paper but it certainly looks relevant to what we are trying to do. Thanks for the reference. I was aware of the Fermi data which I think everyone working on quantum gravity should be following closely. Experimental probes of quantum gravity effects are rare and you are very right that experiments are really the correct way to settle these kinds of issues.

In regards to your last comment, it is true that, if we find a candidate for a UV fixed point we will need some parameter to break conformal invariance. I'm not really sure at this point how this will ultimately work but, at some point, something like the ratio of the cosmological constant to the Newton constant should emerge from the theory. It's still very early on so I can't give a definite answer right now. Nevertheless, it is a great question and exactly the kind of thing we should be thinking about.

Good luck!

Sean.

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Jacek Safuta wrote on Jul. 30, 2013 @ 12:00 GMT
Hi Sean,

Within so many essays it is very hard to find something so interesting as your essay.

We do not agree in 100% but we are very close. My key concept for the unification in physics is scale invariant metric. I have even proposed a simple spin experiment to find out if that metric exists.

Despite the differences between our views (we could discuss them if you read my concept) your essay deserves the highest rating.

Best regards

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:36 GMT
Thanks! Your topic looks interesting.

Good luck in the competition!

Sean.

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Wilhelmus de Wilde de Wilde wrote on Jul. 30, 2013 @ 15:05 GMT
Dear Sean,

You are proposing the opposite as what I think is the essence of reality, but your proposition is so full of good basic assumptions that I read it twice, also you explain some mathematical techniques very clearly, even for a layman like me. You even handed me some tools to explain my own perceptions, thank you for that.

regarding the process that are leading to your...

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Wilhelmus de Wilde de Wilde replied on Aug. 2, 2013 @ 15:20 GMT
Why dis you stop answering the posts on your thread ?

holidays ?

best regards

Wilhelmus

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:45 GMT
Dear Wilhelmus,

Apologies for the delay in my response. You are very right: I've been hiking through the Alps over the last couple of days and haven't had email access. Also, before that I was extremely busy with two very intense conferences. It is a bad idea to schedule an essay contest in the middle of the summer: it is the height of holiday and conference season!!

In regards to your questions, I am very happy that you were able to read through the essay carefully and gets some ideas for your own thoughts about the world. You're right that many of these mathematical structures are just conventions. In the end, they are only useful if they can be used to model real-world experiments. I will admit that the model Universe that I give here is very idealized. But, I still think it could be interesting to give us some clues as to what our real Universe might be doing. The spheres are meant to stay spheres in the infinite future but this is somewhat of an idealization too.

I am really enjoying my time in Holland. It is a very nice country!

All the best,

Sean.

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Vladimir F. Tamari wrote on Jul. 31, 2013 @ 02:01 GMT
Dear Sean

By the time I finished reading your well-written and illustrated essay I could understand what makes scale invariance attractive to you. The technicalities of your approach are beyond me, but I feel that if one starts from the point of view of particle physics with its very absolute value of (h) scale invariance would apply from the small to the large - but would it apply in the other direction?

I wonder how scale invariance would apply in Loop Quantum Gravity, or in an ordered lattice Universe such as my Beautiful Universe Theory BU also found here. I feel that at some minimum scale invariance does not apply in these discrete theories.

For example the measurement of the Gravitational Constant G would seems scale invariant in a continuous physics - but when it comes down to the attraction (and/or repulsion) between individual nodes of an ordered lattice - such as in BU - G (and hence the Planck scale) would be quite different.

With best wishes

Vladimir

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:48 GMT
Dear Vladimir,

Thank you for the nice comments about the essay.

I think you are right that scale invariance seems to be in conflict with Loop Quantum Gravity and other lattice approaches to quantization.

All the best,

Sean.

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Branko L Zivlak wrote on Jul. 31, 2013 @ 11:48 GMT
Dear Physician,

Mass ratio of neutron/proton is fundamental in physics.

Maybe you do not have time to read essay of unknown authors. I encourage you, therefore, allow you to comment on the very essence of following formula:



Where mathematical constant are:



Physical constants:

[equation]a=1/\alpha=137.035999074, \mu=1836.15267245,m=log(\mu,2)=10.8424703056

p=cy/2-(\mu/a+1)
/(\mu/a+2)-1=265.8107668189[/equation]

An important physicist said it was a coincidence, or perhaps just a curiosity. Perhaps you feel the same. My opinion is opposite. I think that in terms of, such a significant relationship physicist should have an attitude.

Greetings Branko

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Ralph Waldo Walker III wrote on Jul. 31, 2013 @ 16:47 GMT
Sean,

I just read your essay, and I must say that it is one of the very finest I've read. As a non-physicist, I was quite impressed with your exceptionally smooth writing style and the fact that, in my opinion, you took the time to explain your thoughts, concepts, and formulas in such a comprehensible manner. This made it so much more enjoyable for me to read. Also, great credit to your graphic artist - truly incredible graphics as well. I gave you the highest rating possible.

Best to you in the future. You would make (in my humble opinion) an outstanding instructor/teacher because of your remarkable ability to convey complex information that is comprehensible to the average person, but I suspect you will be very successful at whatever you choose to do.

Sincerely,

Ralph

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:57 GMT
Dear Ralph,

Thank you for these very flattering remarks. I am really happy that you were able to take something useful out of the essay. You are too kind.

All the best,

Sean.

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Author Sean Gryb replied on Aug. 7, 2013 @ 12:58 GMT
Best of luck in the competition. I will try to take a look at your essay.

Sean.

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Ralph Waldo Walker III replied on Aug. 8, 2013 @ 00:32 GMT
Thanks Sean. I know it's extremely late, but even if you don't get a chance to look at it before the deadline I would appreciate you reviewing it at some point in the future. You seem to have an open mind, so I would value your thoughts.

Best of luck to you in the finals.

Ralph

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john stephan selye wrote on Aug. 1, 2013 @ 22:27 GMT
Having read so many insightful essays, I am probably not the only one to find that my views have crystallized, and that I can now move forward with growing confidence. I cannot exactly say who in the course of the competition was most inspiring - probably it was the continuous back and forth between so many of us. In this case, we should all be grateful to each other.

If I may, I'd like to...

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KoGuan Leo wrote on Aug. 2, 2013 @ 05:26 GMT
Dear Sean,

You wrote: "However, there is an even more basic reason for wanting fundamental scale invariance in your theory: only dimensionless quantities have objective meaning." I am not sure to agree or disagree, however, in KQID, Qbit is that dimensionless objective meaning in itself as Planck's matrix of all matter and Maxwell's infinite being that has unlimited storage capacity thus,...

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Author Sean Gryb replied on Aug. 7, 2013 @ 13:02 GMT
Dear Leo,

Thank you for these thoughtful comments.

I will have to look into this in more detail before making a definite opinion of how my work might relate to yours.

Best of luck in the competition!

Sean.

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CS Unnikrishnan wrote on Aug. 3, 2013 @ 11:58 GMT
Dear Sean,

While the title and the beginning sentences (countability) in your paper gave the impression that you would address some aspects of relation ebtween matter and information, it finally was addressing the relation between quantum gravity and scale invariance. I find only a tenous connection, subject to interpretation, with the original question in discussion - do you have an explanation of the connection between what you wrote and the relation between matter and information?

Thanks.

Unnikrishnan

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Author Sean Gryb replied on Aug. 7, 2013 @ 13:10 GMT
Dear Unnikrishnan,

Thanks for the question.

The relation is between space and time and information. Since space and time provide the fundamental arena in which relationships between matter can be described, the essay addresses whether it's possible for matter to be fundamentally describable solely through information. My suggestion is 'no', because the standard arguments for the discretization of spacetime can be replaced by fundamental scale invariance. I thus don't find the arguments that matter can be described primarily by information particularly compelling.

All the best,

Sean.

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Daryl Janzen wrote on Aug. 4, 2013 @ 17:07 GMT
Hi Sean,

It was nice meeting you at the foundations conference in Munich. It was also really nice reading your essay. I really liked you analysis, and the subject matter is very interesting to me. I have a couple of comments which I'd like to hear your thoughts on.

The first one is mostly a remark: you mentioned a few times that you want to think of the cosmological constant as what...

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eAmazigh M. HANNOU wrote on Aug. 5, 2013 @ 22:20 GMT
Dear Sean,

We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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Thomas Howard Ray wrote on Aug. 6, 2013 @ 14:34 GMT
Dear Sean,

I hope you and your group publish a textbook on shape dynamics. You are all such superior geometers that one cannot go away without learning something new, or at the least looking at current knowledge in a new way. I now have a clearer idea of the assumptions underlying your research program.

As much as I thoroughly enjoyed your essay -- and certainly, my high rating will reflect it -- I have to agree with Carlo Rovelli that QFT degrees of freedom are discrete and therefore static, not dynamic. For this reason, I think that attempts to found quantum gravity in a continuum theory favors models like those of 't Hooft and Corda. These models work with scale invariance, too, and at the black hole extreme condition I think better explain the meaning of the time-dependent Schrodinger equation. Nevertheless, in free space, I can see that shape dynamics is a beautiful and useful model.

All best in the competition, and I do hope you can visit my essay before the curtain closes.

Tom

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Author Sean Gryb replied on Aug. 7, 2013 @ 13:22 GMT
Dear Tom,

Thanks for your nice comments on the essay. I will definitely try to have a look (very soon) at your essay.

Regarding Rovelli, I'm not sure I immediately see why QFT degrees of freedom are discrete or what it means for them to be static. After all, things DO HAPPEN in QCD, which seems to me to indicate some sort of notion of dynamics. On the other hand, I do agree that 't Hooft's conformal gravity stuff is very interesting and promising. I'm not too familiar with Corda.

All the best,

Sean.

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Thomas Howard Ray replied on Aug. 7, 2013 @ 15:27 GMT
Thanks, Sean. I won't pretend to speak for Carlo Rovelli, though I think I do understand what he means by degrees of freedom in an n-particle state space (I would say n-dimension state space and use the Hilbert space) where things happen discontinuously because the field assumes t = 1 and time coordinates are therefore constant (static).

In a continuous spacetime field, time changes with space -- dynamically, as you say. So I think what Carlo is saying, is that because a continuum theory such as shape dynamics cannot associate a definite dimensionless integer to a point of the space evolving in time, it is just as, if not more, meaningful to speak of the algebraic (Fock space) degrees of freedom as to speak of finite degrees of freedom in your continuously evolving system -- because the two descriptions, absent a simple time parameter of reversible trajectory, are equivalent.

Personally, I don't agree with Carlo, though I understand the Fock space construction. At the end of the day, I think that if shape dynamics is mathematically complete, it allows relative degrees of freedom; i.e., time reversibility that guarantees conservation of information. That's what the 't Hooft and Corda references are all about.

All best,

Tom

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Author Sean Gryb replied on Aug. 7, 2013 @ 20:22 GMT
hmmm... I'm still not sure I understand what you're getting at. Of course, there is nothing wrong with having a Fock space in Shape Dynamics, but that doesn't mean that the degrees of freedom are discrete: the number of particles can be an integer but their energy spectrum can still be continuous. Just think of a scattering experiment. Perhaps there is something I am missing.

Cheers,

Sean.

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adel sadeq wrote on Aug. 7, 2013 @ 01:16 GMT
Hi Sean,

I read your essay and I finally understood the basics of shape dynamics. Although this is about your essay(very nicely written), I would like to discuss it from my essay point of view. My theory is just like yours is scale invariant of a sort. My theory is both scale invariant for reals and integer for large scale but for small scale the reals and integer diverge.

But the interesting part which I like to ask you if shape dynamics agree with is that although my system is scale free but the constants c,h_bar, charge e are all constant since they are generated from ratios. The same thing is with mass ratios. but not absolute mass.

All this is apparent from the curves that you see for the electron mass from my essay. If you look at them you see the mass of electron in au units which does not make sense. In fact this is just a coincidence because of the scale of the simulations, you can find the proton to electron mass ratio at any scale.

I am sorry for being brief, I will explain more.

http://fqxi.org/community/forum/topic/1877

Thank you.

Adel

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Author Sean Gryb replied on Aug. 7, 2013 @ 13:27 GMT
Dear Adel,

It is certainly true in shape dynamics that only ratios of coupling constants have empirical meaning. However, it's not clear to me how much your ideas could be related to shape dynamics.

Best of luck in the competition!

Sean.

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Yuri Danoyan wrote on Aug. 7, 2013 @ 03:19 GMT
Hi Sean

Are you rated my essay?

Yuri

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Cristinel Stoica wrote on Aug. 7, 2013 @ 07:40 GMT
Hi, votes are vanishing again.

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Member Benjamin F. Dribus wrote on Aug. 7, 2013 @ 15:06 GMT
Sean,

Good to see another fine submission from you! I didn't have time to participate in the present contest, but I enjoyed your essay. Good luck with the contest, and take care,

Ben

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Author Sean Gryb replied on Aug. 7, 2013 @ 20:24 GMT
Thanks Ben!

Hope things are well with you!

Sean.

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Héctor Daniel Gianni wrote on Aug. 9, 2013 @ 23:38 GMT
Dear Sean Gryb:

I am an old physician, and I don’t know nothing of mathematics and almost nothing of physics, but after the common people your discipline is the one that uses more the so called “time” than any other.

I am sending you a practical summary, so you can easy decide if you read or not my essay “The deep nature of reality”.

I am convince you would be...

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