Is Spacetime Countable? by Sean Gryb

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

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

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

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

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

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!

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

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

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