Is Spacetime Countable? by Sean Gryb

Sean Gryb

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

James Hoover

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

Manuel Morales

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

Manuel Morales

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.

Giacomo Alessiani

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.

Sean Gryb

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.

Giacomo Alessiani

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.

Alan Kadin

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

Sean Gryb

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.

Carlo Rovelli

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

Antony Ryan

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

Sean Gryb

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.

Antony Ryan

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

Cristinel Stoica

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

Sean Gryb

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.

Lawrence Crowell

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

Sean Gryb

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.

Lawrence Crowell

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

Sean Gryb

That is interesting, I didn't know about these properties of CTC. Thanks for alerting me. And definitely thanks for the compliment!

Cheers,

Sean.

[deleted]

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

Yuri Danoyan

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"

Satyavarapu Gupta

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 experimental results.

I failed mainly because I worked against the main stream. The main stream community people want magic from science instead of realty especially in the subject of cosmology. We all know well that cosmology is a subject where speculations rule.

Hope to get your comments even directly to my mail ID also. . . .

Best

=snp

snp.gupta@gmail.com

http://vaksdynamicuniversemodel.blogspot.com/

Pdf download:

http://fqxi.org/community/forum/topic/essay-download/1607/__details/Gupta_Vak_FQXi_TABLE_REF_Fi.pdf

Part of abstract:

- -Material objects are more fundamental- - is being proposed in this paper; It is well known that there is no mental experiment, which produced material. . . Similarly creation of matter from empty space as required in Steady State theory or in Bigbang is another such problem in the Cosmological counterpart. . . . In this paper we will see about CMB, how it is generated from stars and Galaxies around us. And here we show that NO Microwave background radiation was detected till now after excluding radiation from Stars and Galaxies. . . .

Some complements from FQXi community. . . . .

Anton Lorenz Vrba wrote on May. 4, 2013 @ 13:43 GMT

....... I do love your last two sentences - that is why I am coming back.

Author Satyavarapu Naga Parameswara Gupta replied on May. 6, 2013 @ 09:24 GMT

. . . . We should use our minds to down to earth realistic thinking. There is no point in wasting our brains in total imagination which are never realities. It is something like showing, mixing of cartoon characters with normal people in movies or people entering into Game-space in virtual reality games or Firing antimatter into a black hole!!!. It is sheer a madness of such concepts going on in many fields like science, mathematics, computer IT etc. . . .

Francis V wrote on May. 11, 2013 @ 02:05 GMT

Well-presented argument about the absence of any explosion for a relic frequency to occur and the detail on collection of temperature data......

Robert Bennett wrote on May. 14, 2013 @ 18:26 GMT

"Material objects are more fundamental"..... in other words "IT from Bit" is true.

Author Satyavarapu Naga Parameswara Gupta replied on May. 14, 2013 @ 22:53 GMT

1. It is well known that there is no mental experiment, which produced material.

2. John Wheeler did not produce material from information.

3. Information describes material properties. But a mere description of material properties does not produce material.

4. There are Gods, Wizards, and Magicians, allegedly produced material from nowhere. But will that be a scientific experiment?

Hoang cao Hai wrote on Jun. 16, 2013 @ 16:22 GMT

It from bit - where are bit come from?

Author Satyavarapu Naga Parameswara Gupta replied on Jun. 17, 2013 @ 06:10 GMT

....And your question is like asking, -- which is first? Egg or Hen?-- in other words Matter is first or Information is first? Is that so? In reality there is no way that Matter comes from information.

Matter is another form of Energy. Matter cannot be created from nothing. Any type of vacuum cannot produce matter. Matter is another form of energy. Energy is having many forms: Mechanical, Electrical, Heat, Magnetic and so on..

Antony Ryan wrote on Jun. 23, 2013 @ 22:08 GMT

.....Either way your abstract argument based empirical evidence is strong given that "a mere description of material properties does not produce material". While of course materials do give information.

I think you deserve a place in the final based on this alone. Concise - simple - but undeniable.

===============

Please try Dynamic Universe Model with some numerical values, give initial values of velocities, take gravitation into consideration( because you can not experiment in ISOLATION). complete your numerical experiment.

later try changing values of masses and initial values of velocities....

Calculate with different setups and compare your results, if you have done a physical experiment.

I sincerely feel it is better to do experiment physically, or numerically instead of breaking your head on just logic. This way you will solve your problem faster.....

Best

=snp