Is Spacetime Countable? by Sean Gryb

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

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 effect of their interactions, of forces between them, never mind Higgs. This means that a force cannot be either attractive or repulsive, always, agreeing with Newton's action = reaction law which says that a force never can be stronger or weaker than the counter force it is able to evoke. As Spring Theory starts from the assumption that particle properties only are the cause of interactions, forces, i.e. that a force either is attractive or repulsive, it cannot ever unify forces but instead is part of the problem itself: of the classical idea that the mass of particles is an unchangeable, intrinsic, privately owned quantity, an absolute, interaction/observation-independent property, something which but for practical difficulties can be measured even from without the universe.

This same misunderstanding has led to the belief that the Planck constant is the minimum energy quantum, the Planck length the minimum distance in the universe. If in blackbody radiation there are more energy levels per unit energy interval at higher energies so we need more decimals to distinguish successive energy levels at higher energies, then the energy gap between subsequent levels can become arbitrarily small: though energy is quantified, there is no minimum limit to the size of the quantum. The Planck constant h then is like the number 1 in arithmetic: 0.5 < 1 < 1.5. If we can measure h more accurately, add another decimal at a higher energy, then we can write that number as 0.95 < 1.0 < 1.05. So if in our equations we again set h = 1, then every time we improve its accuracy by another decimal, we increase the magnifying power of our microscope with a factor 10. In other words, the extent to which spacetime is defined, detailed somewhere, depends on the local energy density, so space is not built from discrete unit volumes which have the same minimum size everywhere, 'cells' which contain the same energy, which would lead to an absurd high zero-point energy. The higher the energy density somewhere, the more detailed spacetime is, the greater the physical difference (observed lengths of rods, pace of clocks) is between adjacent positions, whereas the farther from masses, the emptier spacetime is, the less positions over a larger area differ physically to a massive observing (test) particle. So the Planck constant and Planck length have no special significance whatsoever. Indeed: ''A ''meter" doesn't have any meaning on its own unless it is compared against the length of another object''. So the fact that the meter, second, gram and joule aren't defined outside the universe means that the size of any energy or length quantum must be relative, an interaction/observation-dependent quantity, and hence the mass of objects, so the flaw of GR is that it isn't relative enough.

In the seemingly innocuous assumption of Big Bang Cosmology that we may regard the universe as an ordinary object which has particular properties as a whole, as an object which in its entirety changes in time, BBC unwittingly but implicitly asserts that there's something outside the of it the universe interacts with, owes its properties to: that it has been created by something outside of it. Evidently, this attitude can be justified only if particles would only be the cause of interactions, not if we have to concede that they also must be the product of their interactions. BBC, in the concept of cosmic time, if fact states that the universe lives in a time realm not of its own making. Though it is said that time only stars at the bang, if a universe can create itself, then it must always have been able to do so, in which case it cannot, as a whole, have a beginning: a beginning requires something with respect to which it begins. I'm afraid that never in the history of physics has there been a 'theory' which has wrought more havoc upon physics as the big bang tale. And, no, as I argue in my blog and 2012 FQXi essay, observations which are thought to prove that we live in a big bang universe are far less unequivocal than is assumed.

Regards, Anton

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 interested in reading it. ( most people don't understand it, and is not just because of my bad English). Hawking, "A brief history of time" where he said , "Which is the nature of time?" yes he don't know what time is, and also continue saying............Some day this answer could seem to us "obvious", as much than that the earth rotate around the sun....." In fact the answer is "obvious", but how he could say that, if he didn't know what's time? In fact he is predicting that is going to be an answer, and that this one will be "obvious", I think that with this adjective, he is implying: simple and easy to understand. Maybe he felt it and couldn't explain it with words. We have anthropologic proves that man measure "time" since more than 30.000 years ago, much, much later came science, mathematics and physics that learn to measure "time" from primitive men, adopted the idea and the systems of measurement, but also acquired the incognita of the experimental "time" meaning. Out of common use physics is the science that needs and use more the measurement of what everybody calls "time" and the discipline came to believe it as their own. I always said that to understand the "time" experimental meaning there is not need to know mathematics or physics, as the "time" creators and users didn't. Instead of my opinion I would give Einstein's "Ideas and Opinions" pg. 354 "Space, time, and event, are free creations of human intelligence, tools of thought" he use to call them pre-scientific concepts from which mankind forgot its meanings, he never wrote a whole page about "time" he also use to evade the use of the word, in general relativity when he refer how gravitational force and speed affect "time", he does not use the word "time" instead he would say, speed and gravitational force slows clock movement or "motion", instead of saying that slows "time". FQXi member Andreas Albrecht said that. When asked the question, "What is time?", Einstein gave a pragmatic response: "Time," he said, "is what clocks measure and nothing more." He knew that "time" was a man creation, but he didn't know what man is measuring with the clock.

I insist, that for "measuring motion" we should always and only use a unique: "constant" or "uniform" "motion" to measure "no constant motions" "which integrates and form part of every change and transformation in every physical thing. Why? because is the only kind of "motion" whose characteristics allow it, to be divided in equal parts as Egyptians and Sumerians did it, giving born to "motion fractions", which I call "motion units" as hours, minutes and seconds. "Motion" which is the real thing, was always hide behind time, and covert by its shadow, it was hide in front everybody eyes, during at least two millenniums at hand of almost everybody. Which is the difference in physics between using the so-called time or using "motion"?, time just has been used to measure the "duration" of different phenomena, why only for that? Because it was impossible for physicists to relate a mysterious time with the rest of the physical elements of known characteristics, without knowing what time is and which its physical characteristics were. On the other hand "motion" is not something mysterious, it is a quality or physical property of all things, and can be related with all of them, this is a huge difference especially for theoretical physics I believe. I as a physician with this find I was able to do quite a few things. I imagine a physicist with this can make marvelous things.

With my best whishes

Héctor

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?

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

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

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

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

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!

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 postulates of Special Relativity." Here he specified 'propagation speed', as only then did it give the; "compatibility with observations" you note. Do you not agree that, though forced to eschew an 'absolute' background, he reclaimed a background for GR, and re-affirmed that SR is; "Entirely contained within the postulates" in 1952. I point this out as I've found it very important, offering a far simpler solution.

I feel essays shouldn't be judged on 'coincidence of propositions' so yours certainly earns a high score, but can you advise any reason why this simpler proposition may be invalid;

Particles are condensed ('pop up') from the continuum as a symmetry breaking 'phase transition' (i.e. photoionization, the Unruh effect etc) and measuring their position is only possible to their non zero 'diameter', well above planck scale. They are condensed with a 'state of motion (rest frame), and for a purpose; to implement the laws of physics by absorption and scattering of EM fluctuation energy. They instantaneously form the ubiquitous two-fluid plasma and 'surface charge' plasmons.

Now we add one logical quantum ingredient. The only 'c' they re-scatter to is their OWN (rest frame) speed c. Ergo, when all em waves meet all matter they are instantaneously re-scattered to local c each 'side' of the 'fluid' (the TZ between is MHD turbulence). The plasma 'shocks' are then mainly formed by compression of the continuum from the motion of matter.

Now I've tried to test that model to destruction but all it does is resolve anomalies! I can't now see how that simple quantum mechanism doesn't solve ALL the issues that both current theory and shape dynamics are trying to resolve in a far more complex way, plus explain exactly what the Lorentz (Poincare) transformation mechanism really is about.

I discuss the unlimited additional degrees of freedom allowed from orbital angular momentum in my essay, and show it's power in resolving the EPR paradox. (my prev 2 yrs essays also discuss aspects).

I hope you'll point out any apparent logical flaw in my logic. I think all have simple answers, some fundamentals are addressed in my essay which I hope you may find time to read.

Now if only I had your brilliant writing and explanatory skills I'm sure I could have put this 'discrete field' model (DFM) across much better, but I hope those are equalled by your powers of comprehension!

Congratulations, very well written.

And very best of luck for a top finish for us both.

Peter

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!