Is Spacetime Countable? by Sean Gryb

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

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

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"

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. . . . .

A

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. . . .

B.

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......

C

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?

D

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..

E

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

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

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.

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