Scales Solve the Continuous vs. Discrete Paradox by Ray B Munroe

Dear Ray,

Good to see you in the contest. I have actually read your essay and I am congratulating myself for doing so. It is presented in a clear way, including helpful big diagrams and table, but my non mathematical background, in particular, is as ever a handicap. I wish to congratulate you for making, what is to me something very complex, a little more comprehensible than many of the "conversations" we have had on FQXi blogs, and that you have had with other mathematically competent contributors.

It does not seem foundational to me but I understand that you and others such as Lawrence Crowell do think that these kinds of ideas and mathematics really are promising avenues of investigation, potentially leading to more complete predictive models of the universe. I do not feel qualified to argue with that.

Sometimes it seems that this modeling is a puzzle like "Eternity 2". Some pieces fit easily together but it is never so easy to complete.A board full of linked pieces looks good but so does the empty board that is full with potential.I agree that reality is most probably both digital and analogue and that the wave- particle duality is an important consideration.

I hope you you receive lots of interesting and positive feedback. Good luck and Kind regards, Georgina.

Hi Dr Cosmic Ray,

If we take E=mc².....let's imagine a finite mass and thus let's imagine the last field at the Planck Scale.Thus the fisrt unity of mass and the last field, thus the maximum E.

Now with (c²o²s²)m=E.........We have this constant c²o²s² multiplicates by this smaller unity of mass.

That gives us the real maximum, but we must consider that the entropy increases at all moments due to a polarization mass/light.Thus a parameter of time, constant becomes essential also for a concrete understanding of this universal equation.Now all that can be linked with thermodynamics and mecanics with the rotating spheres.

Regards

Steve

Dear Georgina,

You said "I wish to congratulate you for making, what is to me something very complex, a little more comprehensible than many of the "conversations" we have had on FQXi blogs, and that you have had with other mathematically competent contributors."

Thank you for your comments. I apologize that I have been busy lately and have not read as many essays (including yours) as I would like to read. At least I have another month to read these essays...

These essays gave us an opportunity to explain our ideas better - whether "better" means more diagrams, more references, more analogies, more explainations, or more mathematics than we would ordinarily use on these blog sites.

You also said "It does not seem foundational to me but I understand that you and others such as Lawrence Crowell do think that these kinds of ideas and mathematics really are promising avenues of investigation, potentially leading to more complete predictive models of the universe. I do not feel qualified to argue with that."

The recent results by Coldea et al (attached) have convinced me that a 5-fold "pentality" symmetry, and the related Golden Ratio, are relevant to the origin of mass.

You also said "Sometimes it seems that this modeling is a puzzle like "Eternity 2". Some pieces fit easily together but it is never so easy to complete.A board full of linked pieces looks good but so does the empty board that is full with potential.I agree that reality is most probably both digital and analogue and that the wave- particle duality is an important consideration."

I agree. I kept this essay more basic, and did not include all of my radical ideas, because I am constantly reconsidering those ideas. For example, I think that Fibonacci's sequence is relevant: 1,1,2,3,5,8,... partially because 1*1*2*3*5*8=240 roots of the largest classical exceptional group, E8, and partially because of its relationship with the Golden Ratio and Coldea et al's paper. However, at vixra log:

http://blog.vixra.org/2011/02/12/string-theory-and-partitions-numbers/

Philip Gibbs has presented Ken Ono's ideas about partition numbers: 1,1,2,3,5,7,... which differs from Fibonacci's sequence beginning with the sixth entry (and includes more small prime numbers than Fibonacci). Partition functions occur in Statistical Mechanics and are relevant to concepts such as Information and Entropy which are proportional to N*ln(N). But should partitions be additive, or multiplicative, or a hybrid function of both? To further confuse the picture, I have a 14-fold (G2 or Klein's Chi(7)) symmetry in my TOE models, but I don't think it is a 7-fold symmetry, and I don't think that it exactly supports Ono's ideas.

Questions such as these have caused me to focus more on specific components of a TOE - such as my Quantum Statistcal Grand Unified Theory (new developments in Prespacetime Journal volume 1, issue 9), on the pentality symmetry and Golden Ratio (new developments with Lawrence Crowell in Prespacetime Journal volume 1, issue 7), and on the possible application of Laurent Nottale's Scales.

Have Fun!

Dr. Cosmic RayAttachment #1: Coldea_Golden_Ratio_Mass.pdf

Dear Ray,

I agree with you that our Observable Universe seems to be finite both in spatial and temporal dimensions. My Hole Theory also is based on Finite Universe. The difference is only that you say: We are limited from seeing beyond the Observable Universe by the Relativistic speed-of-light Scale limit. And my theory says that "We are limited from seeing beyond the Observable Universe by the Edge of the Universe. Perhaps, both propositions have the same sense.

Best Regards

Constantin

Dear Constantin,

I think we are saying the same thing in different ways. I consider the speed-of-light to be our upper Scale-limit. As a result, our Observable Universe is finite because a finite age (13.7 billion years) times a finite speed limit (c) is a finite number.

Your quantum holes are probably lattice defects in the Dirac Sea (in the context of Solid State Physics, a "hole" is a quasi-particle lattice defect in a crystal), and therefore, a direct extension of my essay's lattice-based ideas.

Good luck in the essay contest!

Have Fun!

Dr. Cosmic Ray

I also posted this comment on Edwin Eugene Klingman's blog site:

Dear Ed,

Your Master Equation seems to generate the correct types of fields, but I am concerned that these limited fields (G,C,E,M) in 4 dimensions do not contain enough degrees of freedom to account for all known generations of "fundamental particles" - at least an SO(10) of fermions and an SU(5) of bosons. You begin with continuous fields only, and try to insert quantized "fundamental particles", but you omitted talking about Second Quantization, and this is the most accepted method for obtaining quantized particles from continuous fields. I also didn't discuss Second Quantization in my essay, because I proposed that fields and particles are both necessary complementary inverse scales.

Tajmar's explaination of a mass increase in Niobium Cooper-pairs is interesting. Superconductivity has also been implied to be the bridge between electromagnetism and gravitation by Chiao's and Podkletnov's research teams. You mention a kappa ~ 10^31, but Chiao says that a gravitational wave should have an effect of 42 orders in magnitude. I agree with Chiao because this is of order Dirac's Large Number ~ 10^41, which is one of my scale numbers (please see Equation 15 of my book for the relationship between electromagnetic and gravitational couplings). Now we can explain the Cosmological constant of Lambda ~ 10^(-123) ~ (10^41)^(-3) by the fact that we have three spatial dimensions (you said "If scale invariant is motion invariant, time has no obvious meaning"). I think that your inverse square-roots (~10^61) and inverse fourth-roots (~10^31) of Lambda should be replaced by inverse cube-roots (~10^41 - Dirac's Large Number) or by new modeling.

By the way, this variance in Niobium Cooper-pairs is fairly small. A change in the application of Statistical Mechanics may make-up this difference. Please contrast my Prespacetime Journal volume 1 issue 9 paper with Chapter 4 of my book.

You said that the "curvature of space is limited". I agree. At some energy level, we will promote matter-anti-matter pairs out of the Dirac Sea, and this may have a lattice-like "pinching off of Spacetime" effect. I propose that the core of a static black hole may be surrounded by a Buckyball (a nearly spherical lattice that has lattice bonds to resist it from being deflated by the gravitational near-singularity) consisting of the very fabric of Spacetime. The curvature of the Buckyball initiates Spacetime curvature. There is a smooth homotopy between a pair of nested Buckyballs and a lattice-like torus (donut), and this application may be appropriate for rotating Black Holes. In fact, normal Carbon fullerenes (such as the Buckyball) may have superconductor characteristics. Is the Black Hole core a Superconductor? If so, then a rotating superconducting GEM torus would produce a powerful dynamo. That would tie your ideas, my ideas, and Tajmar's, Chiao's and Podkletnov's ideas together...

I still disagree about 4 fundamental particles, but your field approach is interesting...

Have Fun!

Dr. Cosmic Ray

Dear Ray,

Maybe this is just a bad luck. I chose some essays at random. You know, there is probably more than 100. The first one was quite easy to get (with some help from the Internet). The next impossible. Yours is the fourth and it is also too hard to understand and evaluate. Too much equations and professional jargon. For example:

"In covariant notation, the Dirac Equation [4] is:

-ih ¶my + y = 0" (I is not pasted correctly!)

I am not a professional physicist. I am only Scientific American reader. According to FXQi: the essays shall be accessible to a diverse, well-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature.

Anyway I wish you good luck!

Walter John

Dear Walter,

I understand that we have an interesting mixture of backgrounds here - some professional scientists, some "former scientists" (if such a thing actually exists - I can't get science out of my head even though I left the field as a full-time professional 12 years ago), and a lot of science enthusiasts.

This paper was less mathematical than my last FQXi essay, and less mathematical than most of my publications. I appealed to Dirac's Equation as a basis for my modeling, but spared the audience the full mathematical details. Many of the numbers were inserted to show the properties of powers of the Golden Ratio and Lucas numbers.

I have been blogging on FQXi for nearly three years, and we have built-up many friendships on this blog site. A couple of my FQXi friends, Thomas H. Ray @ topic #871 and Georgina Parry @ topic #860 wrote non-mathematical essays (Tom is well-versed in mathematics, but Georgina seems to have an aversion to mathematics). Some of my FQXi friends were at least as mathematical as I was (such as Jason Wolfe @ topic #828 and the Edwin Eugene Klingman essay that you have read). Lawrence Crowell's essay @ topic #810 (and similarly, vixra's Philip Gibbs @ topic #798) is very mathematical, very deep from a philosophical perspective, and very relevant to the primary essay question, but it is the kind of paper that needs to be read several times over (even by professionals) before it can be fully appreciated.

Good Luck in your reading!

Have Fun!

Dr. Cosmic Ray

p.s. - If anyone has specific questions about my essay, please ask, and I will try to answer them. As a former teacher, I may have alternate analogies to these concepts.

Have Fun!

Dr. Cosmic Ray

Dear Ray,

I try to understand what you wrote, correct me if I am wrong. You say that there is more then one scale. At least four scales in an hierarchical order. Some scales are smaller then the quantum scale (Dirac Sea scale?) and other scales are bigger then the classical scale (Multiverse scale). SUSY unites classical and quantum scales.

Next to the Classical scale we have the Quantum Scale. I think that we can divide Quantum Scale into two different dual descriptions: First a Probability Wave description which has a continuous character. Second a Physical Objects description. This Physical Objects description has both a discrete and a continuous character: Particles have discrete character and spacetime (= relativity) has a continuous character.

Do you think that the difference between the Probability Wave description (= continuous) and the description of particles (= discrete) is only a mathematical problem?

Friendly regards

Peter

Ray How can I calculate this o² and s² and how can I calculate the numbers of cosmological spheres.If I have that, It will be easier.Perhaps it's the same than c , but I doubt , if the volumes of entangled spheres are inserted...we can class all dear Dr Cosmic Ray.

Now must I consider only one sphere for this entanglement with its intrinsic spheres or each spheres of this entanglement must be analyzed??? I become crazzy with this serie, I must find this number, it exists a pure number of cosmological spheres and I am persuaded that the ultim entanglerment is the same. An approximation is difficult.

It's as the ultim main cetral sphere as our center of our Unievsral sphere, what is its volume??? and where is this central main sphere where all turns around. The BB in logic , as a spherical expansion contraction towards the perfect equilibrium between mass systems.

Best Regards

Steve

Hi Steve,

I really don't follow your idea. At first order approximation, o^2*s^2=1. Higher-order terms must include powers of (v/c)^2.

How many cosmological spheres are there? What if that number is 10^41 or 10^500 or "infinity"? I think it is appropriate to build the most complete model with the smallest number of "cosmological sphere" degrees-of-freedom. Your fundamental symmetry seems tetrahedral (and identical to the Face-Centered Cubic symmetry presented in Figure 1 of my essay), so the minimum basis would contain 4 spheres. You might reread the Hyperflavor section of my book (Section 7.2). That contains a tetrahedral symmetry, but you (like Ed Klingman) probably want to explain as much as possible with as few assumed degrees-of-freedom as possible, so replace Hyperflavor-Electro-Weak with Gravi-Electro-Weak if you can. I have told Ed that his 4 fields (G,C,E,B) do not contain enough degrees-of-freedom to represent reality as we know it. Likewise, I don't think that 4 spinning spheres can do the job either.

Good Luck and Have Fun!

Dr. Cosmic Ray

p.s. - Steve,

If a tetrahedron with 4 vertices is too simplistic a framework for a TOE, then we should look at the most natural extensions of the tetrahedron. The smallest natural extention of the tetrahedron is to nest two tetrahedra into an octahedron with 8 vertices (8 spheres) and an octahedral symmetry. The next smallest extension of the tetrahedron is to include the tetrahedron's nearest-neighbors with (4+24) vertices (see Table 7 of my book) (28 spheres).

Coincidentally, this is the number of dimensions (28) of the F-theoretic model that I proposed in "The Nature of Dimensions" with Lawrence Crowell in PSTJ 1,7.

At some point, Occam's razor demands that we justify the additional complexity of our model. I'm working on it...

Have Fun!

Dr. Cosmic Ray

p.s. - Steve - I read Vladimir Tamari's essay @ topic #836 this afternoon, and realized that his ideas sound a lot like the tetrahedral/FCC symmetries of my Hyperflavor-Electro-Weak theory (one component of my TOE), your spinning spheres, and Gingras' magnetic spin ice. You should read his essay...

Have Fun!

Dr. Cosmic Ray

Ray ,

I have read all essays, and several are rationals,Dr Layzer, Hector, Dr Klingman ...them they are rational.

I see never you shall change Dr Cosmic Ray.You are incredible, surprising even

Dr Cosmic Ray,I speak about the ultim fractal of the main central sphere and its volume and you insert still your confusions you make me crazzy Dr Cosmic Ray......Ray you need to focus on foundamentals .You think what you are going to have prizes with Ex toe or what???It is not possible.With your creativity and your potential of superimposings, it is sad you forget the generality of our rationalities.If you were general and foundamental, you shall be very very relevant and not a little as Lawrence in Fact and Florin.I am irritated by so many skillings and it lacks the essential, this uniqueness.Sad and so real in the sciences community.It is that Dr Cosmic Ray an Ocham Razo, the uniqueness, and even for a turing machine, the sortings are so essential when we want explain our pure realism and its constants, irreversibilities....

In fact as many you do not really understand my Theory of Spherization.How can you insert the correct number if you begin with infinities for the ultim entanglement.

PS WHEN i CONSIDER 1 SPHERE IT IS FOR A KIND OF SPHERE WITH ITS SPHERES? THUS JUST FOR A GENERALITY OF MY EQUATION and for facilitating the calculations.Thus the light has an entanglement and momemtum we can fractalizes also this serie with its properties.

Best Regards

Steve

what do you think about a quark gluon plasma with a partition function....

Hi Steve,

I was at the beach for the last couple of days. It was relaxing to get away. What if the "sphere" is a Buckyball that surrounds the Black Hole "near singularity", and "spinning" tetrahedra (Vladimir Tamari's basic idea - perhaps of red-green-blue-white "color"?) are situated at each of the 60 vertices (of the Carbon-60 Buckyball). This would yield 240 degrees-of-freedom similar to Garrett Lisi's E8 roots, but we would only have 3 dimensions at each of two different scales (the 3-D buckyball scale, and the 3-D tetrahedra scale). I've always liked Buckyballs, and one of the discoverers of Carbon-60, Sir Harry Kroto, lives im my neighborhood.

In case of a rotating Black Hole, the Buckyball symmetry may not be stable enough, and two nested Buckyballs may transform into their homotopic cousin, a lattice-like near-torus (similar to a lattice-like Tokamak) with spinning tetrahedra at each of 120 vertices. This would yield the 480 degrees-of-freedom of a Supersymmetric model similar to Lisi's.

I need to reread Vladimir's essay, and think more on these ideas.

Have Fun!

Dr. Cosmic Ray

Hi Ray,

Your application of Lucas Numbers is verry interesting. Also what you say about the different dimensions that it is possible to see them as different scaled dimensions.

In my model I treat dimensions like time and length in the same way as the dimensions of mass, momentum and energy. But I don't have any justification for that. Maybe only because I say that the speed of light and the gravitational constant are the same kind of constant. Both expressing relativistic properties. But there are some nagging things with this view.

For example. we can have different velocities below the limit of the speed of light, but are there also different gravicities below (or above) the gravitational constant? (gravicity is the variable quantity of which the gravitational constant is the limit.)

And the problem with the planck values: 'wooden' quantities like Mass, momentum and energy have upperlimits and 'marble' quantities like time, length and gm-flux have lower limits. Why? what is the meaning of this?

Mostly the planck constant is the product of a marble quantity together with a wooden quantity. (but in my model it is also possible to have purely marble or purely woorden 'planck constants', but that is only theoretical.)

Friendly regards

Peter

you make me more crazzy than I am .At the beach, if I could, I will rest me and hop a little of surf.hihih you know I have always dreamed to learn the surf.But in belgium of course you shall understand it is difficult.

Ray do you know how I must do for having a kind of bourse at harvard, I d like learn the computing and enginiering.I have more than 200 inventions you know, and I don't speak of ideas, in all humility.My lacks of knowledges is in the computer language and the programmation for computing.I need to learn more about semiconductors.and linux and this and that ....and more about programmation.I have always dreamed to be in an university in fact in USA. I need to learn more Ray, there I need to learn still and always more.I am frustrated to rest at home.I become really crazzy.

ps Vladimir essay is relevant indeed if we consider the first division, this ultim mitosis meiosis of the main central sphere, the biggest volume in logic.The polyhedrization and the spherization are so the same.

Regards

Steve