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

Dear Steve,

Let me read and think about this more before I give a complete response. I agree that within our scale, and to the best of our current experimental data, the photon seems to have the maximum speed and the photon seems to have the maximum spin of a fundamental particle (although that spin is the same as gluons, W's and Z's).

Theoretically, the graviton should have a spin-2 (which would be maximal spin), but we haven't yet observed a graviton within our scale. Likewise, tachyons are mathematically possible within the framework of our theories. Tachyons should travel faster than the speed of light, but we also haven't yet observed them within our scale.

Have Fun!

Dr. Cosmic Ray

Hi Ray, thanks it's cool.

It's intriguing and fascinating this maximum E in all things.

About particules which can go faster than light,I think it's in an other logic than with our light perception.In all case if a technology is invented, it's sure that it's the rotations of these spheres the secret.If we take a gauge of perception,and a specific system of rotations, thus...perhaps it's possible to accelerate these stabilities,but the problem is what we can't see them in logic.An extrapolation , topological thus becomes essential, and a center also, here the sphere and its center , cosmological and quantic.

Best Regards

Steve

Dear Steve,

If you insert real masses (tardyons) into Einstein's Special Theory of Relativity, you find that it takes an infinite amount of energy for a real mass to asymptotically approach a speed as fast as c - the speed of light.

However, if you insert imaginary masses (tachyons) into Einstein's Special Theory of Relativity, you find that they naturally travel faster than the speed of light, and that you must put an infinite amount of energy into them for them to asymptotically approach a speed as slow as c.

Our experimental methods are limited by the speed of light (speed of observation), and the (slower) speed of electrons (speed of electronic response). A tachyon travelling through free space will outpace all of these techniques and appear to be an unidentifyable accident, or electronic feedback. Our best chance of identifying a tachyon is at a supercollider where we can reconstruct all of the event jets and imply the existance of a tachyon.

I think that this question is related to Scales. Perhaps an observation speed greater than c exists at a scale of greater complexergy than ours. This scale limitation might then explain our speed limitation, c. If tachyons and/or greater speeds than c exist, then this might allow us to explain the so-called action-at-a-distance behavior of gravitation in terms of Spacetime curvature and intermediating quantum gravitons - both simultaineously, not just one or the other. It would also be interesting if tachyons are somehow involved in entangled states. Likewise, I expect gravitons (of spin-2 which is greater than the spin-1 photon) to exist at Black Hole cores and/or a scale of greater complexergy.

Have Fun!

Dr. Cosmic Ray

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

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

Hi Peter,

What we naively refer to as the "Quantum Scale" is actually two self-similar scales: a Quantum and a Sub-Quantum. The implication of "sub-quantum" (which I compare with the Dirac Sea, and I think is the origin of mass) is that some of these "fundamental particles" that we observe at the Quantum Scale may actually be composite particles. I know that Technicolour is out of fashion because it hasn't been supported by experimental data (yet), but my paper in Prespacetime Journal, volume 1, issue 9, implies that gluons may behave like Cooper pairs of something more fundamental.

I know that Edwin Eugene Klingman has serious problems with QCD and its 5% (at best - after radiative corrections) accuracy. Perhaps we are incorrectly treating a Cooper pair quasiparticle like a fundamental particle (gluons). This could have significant implications regarding the use of the Partition Function and radiative corrections.

Your General Metric implies at least 16 dimensions. I am proposing that these dimensions are scattered over different scales, but that these different scaled dimensions twist together (like twistors, and perhaps because of the properties of Lucas numbers?) into effective quasi-dimensions that have this oddball nature of wave-particle duality (and the corresponding continuous-discrete duality) because our "dimensions" are actually composite. This allows a fractal reality (self-similar scales implies fractal) to appear discrete (we observe 3 spatial plus one temporal dimensions - not fractions of dimensions)because of Lucas Numbers: 1.618-0.618=1.000 TIME!, 2.618+0.388=3.000 SPACE!, etc.

Any particular measurement can only obtain - at most - half of the dynamic variables present (say momentum OR position), so pairs of twisted reciprocally-scaled dimensions (sounds a lot like Cooper pairs, but these Lucas numbers can have identical, even or odd symmetries) can behave like single quasi-dimensions.

Your analysis of the Planck units opens more questions than it answers. Suppose that each Scale has its own Planck Constant?

You said "Particles have discrete character and spacetime (= relativity) has a continuous character." I agree, and I am saying that this is caused by interacting Scales and twisted quasi-dimensions.

You asked "Do you think that the difference between the Probability Wave description (= continuous) and the description of particles (= discrete) is only a mathematical problem?" I think it is due to wave-particle duality, which is due to these twistor-like reciprocally-scaled dimensions.

I hope I answered your questions thoroughly enough. I look forward to seeing if your ideas reinspire mine, and/or vice versa.

Have Fun!

Dr. Cosmic Ray

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....