Is Spacetime Countable? by Sean Gryb

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 express some of my newer conclusions - by themselves, so to speak, and independently of the logic that justifies them; the logic is, of course, outlined in my essay.

I now see the Cosmos as founded upon positive-negative charges: It is a binary structure and process that acquires its most elemental dimensional definition with the appearance of Hydrogen - one proton, one electron.

There is no other interaction so fundamental and all-pervasive as this binary phenomenon: Its continuance produces our elements - which are the array of all possible inorganic variants.

Once there exists a great enough correlation between protons and electrons - that is, once there are a great many Hydrogen atoms, and a great many other types of atoms as well - the continuing Cosmic binary process arranges them all into a new platform: Life.

This phenomenon is quite simply inherent to a Cosmos that has reached a certain volume of particles; and like the Cosmos from which it evolves, life behaves as a binary process.

Life therefore evolves not only by the chance events of natural selection, but also by the chance interactions of its underlying binary elements.

This means that ultimately, DNA behaves as does the atom - each is a particle defined by, and interacting within, its distinct Vortex - or 'platform'.

However, as the cosmic system expands, simple sensory activity is transformed into a third platform, one that is correlated with the Organic and Inorganic phenomena already in existence: This is the Sensory-Cognitive platform.

Most significantly, the development of Sensory-Cognition into a distinct platform, or Vortex, is the event that is responsible for creating (on Earth) the Human Species - in whom the mind has acquired the dexterity to focus upon itself.

Humans affect, and are affected by, the binary field of Sensory-Cognition: We can ask specific questions and enunciate specific answers - and we can also step back and contextualize our conclusions: That is to say, we can move beyond the specific, and create what might be termed 'Unified Binary Fields' - in the same way that the forces acting upon the Cosmos, and holding the whole structure together, simultaneously act upon its individual particles, giving them their motion and structure.

The mind mimics the Cosmos - or more exactly, it is correlated with it.

Thus, it transpires that the role of chance decreases with evolution, because this dual activity (by which we 'particularize' binary elements, while also unifying them into fields) clearly increases our control over the foundational binary process itself.

This in turn signifies that we are evolving, as life in general has always done, towards a new interaction with the Cosmos.

Clearly, the Cosmos is participatory to a far greater degree than Wheeler imagined - with the evolution of the observer continuously re-defining the system.

You might recall the logic by which these conclusions were originally reached in my essay, and the more detailed structure that I also outline there. These elements still hold; the details stated here simply put the paradigm into a sharper focus, I believe.

With many thanks and best wishes,

John

jselye@gmail.com

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, no bit/qbit needs to be deleted, thus no entropy per Laudauer's principle will be generated.

You wrote: "We will now add these two postulates to Einstein's original postulates of Special Relativity: 1. The Laws of physics should take the same form for any inertial observer.2

2. The speed light is defined to be a finite constant, c, for all inertial observers."

Wonderful! Similarly, KQID has the same assumptions.

You wrote: "Just as in Special Relativity, we will assume the existence of idealized rods and clocks which can be perfectly synchronized." KQID relativity ψτ(iLx,y,z, Lm) Multiverse has flexible c-timerod that measures distance, area and volume in terms of time. Time contracts so does length contracts. In contrast, time contracts, the mass as well as the energy increases.

You wrote: "The first ingredient is an assumption of simplicity. If true, then a holistic picture of the world is, at least in principle, possible."

Yes, KQID has "holistic picture" of Existence and has done the theorical framework just to do this.

KQID has contextuality through KQID Ouroboros Equations of Existence that combines Newton, Maxwell, Planck, Boltzmann, Lorentz,Einstein, Laundauer, Wheeler , Feynman, Ssusskind, Hooft, Wilczek, Bousso and others. The Ouroboros Equations mean each interpretation involves every beginning to every ending. Similarly, everything we do involve the Ouroboros action or totality of any action. Nature is such unbelievable phenomena that we are just now starting to peek into its secret that is shockingly simple in the beginning but infinitely complex in the ending that per KQID every absolute digital time ≤ 10^-1000seconds. Interestingly, the mechanism is also simple. See my essay Child of Qbit in time.

Furthermore, KQID has done that no other theories that I know has done so far:

First, KQID Qbit is (00,1,-1) which is singularity Qbit Multiverse in zeroth dimension at absolute zero temperature that computes and projects Einstein complex coordinates (Pythagoras complex triangles or Fu Xi's gua or Fibonacci numbers!) onto the 2D Minkowski Null geodesic and then instantaneously into the 3D in Lm, our Multiverse timeline to allows Existence to move around 360 degree and its arrows of time as you described below. As you also agree below, no information is ever deleted. See my essay Child of Qbit in time. KQID is the only theory out there that can calculate the dark energy of our Multiverse ≤10^-153Pm/Pv and the minimum bits as the lower bound ≥ 10^153 bits in our Multiverse. KQID is the only theory that I knows here that proves bit = it, and KQID calculates Sun lights into Sun bits; calculates electron, proton and neutron in terms of bits; set up equivalent principle of bits with energy and matter. Therefore, Wheeler's it from bit and bit from it. Correct me if I am wrong. Furthermore, KQID is the only theory in this universe has the mechanism on how Holographic Principle works. Also answer the mother of all questions, the why, how and what Existence.

Pythagoras famously summarized: "All things are numbers." KQID rephrase it that all thing are one Qbit: Qbit is all things and all things are Qbit. Thus, Wheeler's it from bit and bit from it because bit = it.

You are definitely a serious original thinker. Let us share our thoughts.

Best wishes,

Leo KoGuan

Why dis you stop answering the posts on your thread ?

holidays ?

best regards

Wilhelmus

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 drives cosmic expansion. This is exactly what motivated my PhD thesis, and at one point I picked up Eddington's 'Expanding Universe' and found that it was really the idea he had in mind, too. Throughout the 1920s, guys like him and Weyl had been thinking about cosmic expansion in terms of this 'cosmical repulsion' due to Lambda; and in 1924, Weyl even wrote a dialogue between 'Petrus' and 'Paulus' (Saints Peter and Paul), who presented Einstein's views and his own, respectively. The dialogue presents an obvious reaction to the postcard that he got from Einstein in 1923 (dated something like a week prior to Einstein posting his retraction to what he originally wrote about Friedman's paper, which he now called "correct" and "clarifying"), where he famously said "If there is no quasi-static world, then away with the cosmological term." The interesting thing in Weyl's paper, though, is that he didn't know what the hell Einstein was talking about, because he had never heard of Friedman's "correct" and "clarifying" paper, so when he received the post card he clearly though Einstein was saying he wanted to go back to special relativity, which obviously makes no sense if the Universe is expanding. 'Paulus' aka Weyl replied to 'Petrus' aka Einstein at this point in the dialogue, by saying something like, 'but all the spiral nebulae are receding, so the Universe is probably expanding, so dS space-time is the best bet that we know of'.

So anyway, guys like Weyl and Eddington had this idea of a 'cosmical repulsion' that drives expansion in their minds throughout the 1920s. And in Eddington's 'Expanding Universe' (1933), he did not hide the fact that he was really really upset that Einstein, after pretty much remaining silent on the issue of expansion, and not saying anything to anyone about Friedman's paper throughout the 1920s (everyone else learned about it in like 1930 or 1931, after Hubble confirmed the expansion with his redshift-distance relation in 1929), chose Friedman's solution with no cosmological constant (in the Einstein-de Sitter 1932 paper), where the cosmical repulsion can play no fundamental role in explaining the cosmical expansion. The reason is that near to the big bang, the cosmical repulsion is negligible, so the expansion is, to begin with, always less than it was, with Lambda driving accelerated expansion later on.

I do think there is a way around this last problem, which is what I wrote about in my last essay. There are more details about all of this there, if you're interested.

Okay, that's point one, and my comment's already getting long. I think point two is more interesting, though, so I'm still going to post it. It has to do with the motivation for the dS hyperboloid, which you presented in an interesting way in your essay. I wanted to discuss and alternative approach, though, which I think makes fewer assumptions, and provides a really neat way of thinking about this cool geometry that you've presented such an interesting analysis of.

So: what's the one aspect of nature that seems to be physically the most important? Symmetry, right? Symmetry that can be broken, but which is fundamental in nature. So, to begin I want just to assume that reality has an underlying metric, and that it has maximal symmetry. The only other thing I want to require, since relativity indicates that it's a property of nature, is Lorentzian signature of that metric. I don't want to assume that from the outset, though, but will only pick the solution with this property out of the list of possibilities derived from the assumption of maximal symmetry.

The maximally symmetric spaces can all be recovered as constant curvature hypersurfaces of Euclidean space, so begin by writing down the induced metric, [math]ds^2=\sum_{\mu=0}^{4}dx_{\mu}^2,[/math] [math]\sum_{\mu=0}^{4}x_{\mu}^2 =\alpha^2.[/math] This can be re-written in just four coordinates by arbitrarily solving for one of the five, as in [math]x_0=\pm\sqrt{\alpha^2-\sum_{i=1}^{4}x_{i}^2 },[/math] and the result can be neatly written as [math]ds^2=d\mathbf{x}^2\frac{(\mathbf{x}\cdot{d}\mathbf{x})^2}{\alpha^2-\mathbf{x}^2},[/math] where [math]\mathbf{x}=(x_1,x_2,x_3,x_4)[/math] is a real vector, and alpha is now the spherically symmetric space's *intrinsic* "radius of curvature". We can require this x to be real, since we began in E^5, but there's actually no reason that x_0 can't be imaginary, since it's fictitious anyway; i.e., the 4D maxiamlly symmetric spaces are still described in terms of a real Euclidean basis. From this line-element, we can pretty much just read off the components of the metric tensor in this basis, [math]g_{ij}=\frac{1}{\alpha^2-\mathbf{x}^2}\cdot[\alpha^2-(\mathbf{x}^2-{x_i}^2)],~\mathrm{if}~i=j,[/math] [math]g_{ij}=\frac{1}{\alpha^2-\mathbf{x}^2}\cdot{x_i}{x_j},~\mathrm{if}~i\neq{j}.[/math] The eigenvalues of the tensor are all positive except one, which is given by [math]\lambda=\frac{\alpha^2}{\alpha^2-\mathbf{x}^2}.[/math]

The closed sphere is described by setting alpha^2>0 and alpha^2>x^2; hyperbolic space, by setting 0>alpha^2 and x real; and dS space, by setting alpha^2>0 and x^2>alpha^2. If alpha=0, the metric space is degenerate.

So it turns out that just in case alpha^2 is positive (by the way, alpha^2=1/Lambda), and only when x^2>alpha^2 (dS space) does the metric have Lorentzian signature. The two points that are of further interest are that Lambda>0 is what we actually observe anyway, and that this space (actually, all of them) satisfies the vacuum Einstein equation R_ab=Lambda*g_ab.

I think it's pretty cool that with no reference to GR, and with no prior requirement that the metric should be Lorentzian, but only by requiring maximal symmetry to begin with, and an embedding in Euclidean space, it can be shown that dS space is the only one that does have a Lorentzian metric, and the space satisfies the vacuum Einstein equation.

I'm interested to know what you think of all this, because I think there is a lot of overlap in what we're considering.

Best of luck in the contest--and really, a great job done on the essay!

Daryl

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.

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

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

Hi Sean

Are you rated my essay?

Yuri

Hi, votes are vanishing again.