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

Hi Ed,

You said "Therefore, you may expect my field to introduce new particles, but consider the fact that it may actually replace one or more current fields, leaving us with only the known particles."

You very well could be correct - after all, we haven't yet discovered a true magnetic monopole as Dirac expected (although Gingras' "Spin Ice" has monopole-like quasiparticle behavior [I think the reference is in my and Lawrence's "The Nature of Dimensions" paper], so don't give up on the idea).

In my book, I proposed that the WIMP-Gravity (which may or may not be related to GEM?) coupling has a (mass)^8 dependance (pages 30-33).

We need at least 3 degrees-of-freedom for the W and Z longitudinal polarizations. I'm not opposed to a Higgs-like approach, but suppose GEM provides those dgf's? I'm interested to see if you can derive the CKM and PMNS matrices.

I'm driving to Orlando tomorrow. Its supposed to rain all day, and then I'll be in meetings for two days (joy!). You would think there are good flight options between the state capital, Tallahassee, and the vacation capital, Orlando, but there are no direct flights.

Have Fun!

Dr. Cosmic Ray

Dear Ray,

The other argument against a closely packed lattice is that it would result in light traveling at different velocity dependent upon which way it was going. It would be possible to test for a preferred orientation. I would continue to use the model because it is helpful. We just have to remind ourselves that the model doesn't work for a Lorentz transformation.

Ray, about that monopole---

I have for some time been of the opinion that it may be a good thing that there is no magnetic monopole. If there were, electricity and magnetism would be truly dual and hence, I believe, degenerate. That electric and magnetic fields are dual in source free space is useful-- we get photons. But if there were magnetic monopoles all 'lines of force' would terminate on particles, and there would be, IMHO, no truly distinctive separation of fields. The whole thing would probably collapse. I am being more serious than poetic here. I'm not proposing a theory, and I have no calculations to back up what I'm saying, nevertheless, it's probably valid.

As it is, electric lines of force end on particles and magnetic lines of force are loops. This unique distinction would cease if magnetic field lines terminated on monopoles, and I suspect that the degenerate system would at some point collapse into one state. And it wouldn't look like any state that you're familiar with. So be thankful that there are no monopoles.

Edwin Eugene Klingman

Magnetic monopoles are similar of S-duality. S duality exchanges IIB and I strings where the fields on them are dual. A type of magnetic monopole of this form would be a case of S duality. So if there is a U(1) field on a IIB with an electric charge a magnetic monopole on a type I string would be S dual.

Cheers LC

Dear Ray,

Having already read the ice paper a while ago, I would nonetheless like to support Edwin concerning magnetic monopoles. I should feel a bit like David in front of several Goliaths like you.

I share a lot of your arguments, and I admire your elegant representation. However, I am not sure whether "the interrelationship between Scales and SUSY may provide a mathematical umbrella capable of explaining the unnaturalness of "Infinity"" a "unification of Bosons and Fermions". Do we need an explanation for the unnaturalness of a point? Where may I find an explanation of how you understand the notion Scale? Perhaps did you mean a common theory and not a physical merger between Bosons and Fermions.

Maybe, you will agree in that cosine transform switches a discrete function into a continuous one and vice versa. Engineers like me are convinced that in reality there are neither ideal continuous nor ideal discrete signals.

If A and B do not agree it is certainly opportune to have a balanced opinion: all are half correct. However logic also allows an answer in Gotthold Ephraim Lessing's style too: Maybe both A and B are wrong.

If I am correct in my essay then some mathematical generalizations are at least questionable. I invite you to take issue.

Regards,

Eckard

Dear Eckard,

You said "Do we need an explanation for the unnaturalness of a point?"

I think that a point is physically unnatural, but OK as a model. A physical infinity cannot exist within a finite Observable Universe (13.7 billion light years is finite). Thus, I disagree with the idea of a Black Hole "singularity", and expect the Black Hole core to be similar to a Buckyball of Spacetime (the "Spacetime lattice" equivalent of a Carbon-60 Buckyball) as Lawrence Crowell and I presented in a recent article.

You also said " Where may I find an explanation of how you understand the notion Scale?"

I didn't really define scales thoroughly - Laurent Nottale has done that over the last two decades, and he has a book coming out this year (I've read part of it, but - as I recall - it is 600 pages long). Nottale defines scales in terms of complexity and energy content. By Scales, I mean that some numbers are large, some are small, and some are inverses. Consider the differences of conjugate (essentially inverse) scales of position and momentum (or energy and time as Lawrence Crowell developed in his paper).

You also said "Perhaps did you mean a common theory and not a physical merger between Bosons and Fermions."

IMHO, a TOE must include both Bosons and Fermions, and both Spacetime and Hyperspace, but all of these concepts might not fall into the same Lie algebra (unless it is something like SO(32)~E8xE8?) because bosons and fermions need to be inverse/reciprocal/conjugate-like variables with respect to each other.

You also said "Maybe, you will agree in that cosine transform switches a discrete function into a continuous one and vice versa."

Equation 4 in my essay is the general form of a cosine transform (using e^(ix) = cos(x) i sin(x)) in multiple dimensions, and Equation 2 is distantly related (the matrix inversion is related to a Fourier transform) to these transforms.

You also said "Engineers like me are convinced that in reality there are neither ideal continuous nor ideal discrete signals."

I agree. That was the first sentence of my Abstract, and the last sentence of my Conclusion. It all goes back to Wave-Particle Duality.

Have Fun!

Dr. Cosmic Ray

Hi, Dr. Ray:

It is my position that reality has both the continuous and the discrete.

The big questions are basically what fundamentals get quantized and how these fundamentals get quantized. I think my essay points to the answers.

Because we obviously have hierarchical discrete/quantized phenomena, it is plausible that overall the cause is also a hierarchical process. Perhaps this is why you have your scales.

You might also consider a full-tensor (3-D) factor in the relativistic mass equation, instead of just the Lorentz half-tensor (2-D) factor -- after all mc2 (final E) is not m0c2 (initial E0).

Castel

Dear Ray,

Thank you for confirming that we agree in almost all questions. However, I am not sure. How may I interpret your refusal to rebut my main argument? I found overwhelming indications for a suspicion of mine: Ideal symmetries tend to be artifacts. You are quite right the matrix inversion is related to a Fourier transform. The question is, does our possibility to describe nature allow and possibly even require matrices that do not exhibit Hermitian symmetry?

If it is possible, reasonable, and as I am arguing natural to restrict scales to merely positive values by appropriately shifting them, then only half-matrices are required. Please feel challenged to object here. Edward Klingman so far confessed being unable to object. I pointed to consequences.

Regards,

Eckard

Dear Ray,

I was actually impressed by your view's bit of focus on the wave-particle duality. Basically, my bit of focus is on the fundamental idea of motion.

The electromagnetic theory describes transverse wave motion. So, to me, light, the phenomena in nature, is of the fundamental essence of motion - and the electric and magnetic are of the same fundamental essence.

My idea regarding particles is that the waves/motions get wrapped or folded into the particulate essence - perhaps in somewhat the same manner as that of the loops of space of Astekhar, Smolin and Rovelli, only that I see loops of motion instead of space.

I have been thinking about the idea of a hierarchical cosmos wherein the cosmic subsystems have alternating periods of densification and attenuation that establish the upper and lower limits for the quantization of the particulate cosmos. My idea is that gravity gathers and densifies the cosmic subsystems, and eventually, with their increased mass-energy, each cosmic subsystem is taken by its own increased orbital momenta towards an orbital apex that initiates a period of attenuation with the cosmic subsystem getting fragmented. This renders a picture of an expanding and spiralling cosmos but with cosmic mass-density accordingly maintained and the particles multiplied.

The above is a difficult picture. But, is this possible in your view?

It would be a beauty if you can describe a picture of how your scales look like - especially if you go 'vectorial' just a little bit in your explanations.

(What I've described above is still a rather simplistic picture. What I really envision is a process that involves relative motions from all directions for each cosmic subsystem in the hierarchical cosmos. This suggests to me the reason for the occurrence of gravity and why the observable phenomena are 'waves' of radiant motion or 'particles' of concentric motion wrapped around their centers. This is somewhat like the cyclical chicken-or-egg reasoning; and I am therefore a bit abashed to present the idea in full.)

Anyway, I just wanted to express my opinion - hoping that I might get some positive ideas from you.

In any case, many thanks to you.

Rafael

Dear Eckard,

I like Hermitian matrices, but I don't limit myself exclusively to Hermitian matrices in my search for a TOE. I'm still searching and don't have an answer...

Hopefully I can read your essay next week. I enjoy your applications and insights.

Have Fun!

Dr. Cosmic Ray

Dear Rafael,

I was hesitant to present all of the details of my ideas, because some are a bit maverick, and probably too detailed for this type of essay. I competed in the second FQXi essay contest, was in the top five after the public and community votes, but didn't finish in the top 18 - I attributed this to the fact that that essay was very mathematical.

In my "The Interrelationship of Spin and Scales" paper, I suggested that the Multiverse (or super-Cosmic) scale is the largest scale from which we can feel effects. If a larger scale exists, we may never know. The Multiverse scale is related to the Graviton (and the origin of gravity), and is a continuous (boson-like) space. Complexity of this scale may be infinite, although this also implies an infinite Multiverse.

Below the Multiverse scale is a Cosmic Scale. This Cosmic Scale is related to the Gravitino, and is a discrete(?) (fermion-like) space. This discrete structure may exhibit itself as cosmic strings and their effects. Perhaps the discrete Holographic Principle occurs at this scale. The mass distribution of our Universe is not isotropic and homogeneous, but is coursely grained. Complexity of this scale may be based on the number of possible string vacua of ~10^500.

You said "I have been thinking about the idea of a hierarchical cosmos wherein the cosmic subsystems have alternating periods of densification and attenuation that establish the upper and lower limits for the quantization of the particulate cosmos. My idea is that gravity gathers and densifies the cosmic subsystems, and eventually, with their increased mass-energy, each cosmic subsystem is taken by its own increased orbital momenta towards an orbital apex that initiates a period of attenuation with the cosmic subsystem getting fragmented. This renders a picture of an expanding and spiralling cosmos but with cosmic mass-density accordingly maintained and the particles multiplied."

I think that our ideas are complementary, and perhaps even identical.

Below the Cosmic Scale is the very familiar Classical Scale. The Classical Scale is related to Vector Bosons, and is a continuous (boson-like) space. Complexity of this scale is based on Dirac's Large Number of ~10^41.

Below the Classical Scale is the Quantum Scale. The Quantum Scale is related to normal matter Fermions, and is a discrete (fermion-like) space. Complexity of this scale may be of order 496 ~ SO(32) ~ E8xE8*.

Below the Quantum Scale is the sub-Quantum or Dirac Sea Scale. This Dirac Sea Scale is related to Scalar Bosons, the so-called Higgs Mechanism and the origin of mass, and is a continuous (boson-like) space. Complexity of this scale may be of order 32.

You said "My idea regarding particles is that the waves/motions get wrapped or folded into the particulate essence - perhaps in somewhat the same manner as that of the loops of space of Astekhar, Smolin and Rovelli, only that I see loops of motion instead of space."

Of course position and momentum space are reciprocal lattices, and conjugate variables. We may have quantization of position such as Kissing Spheres or Causal Dyanamical Triangulation that provides lattices and their reciprocal scaled lattices (that appear continuous because of the large number of states). OR we may have quantization of momentum such as String Loops or String Winding modes that provides lattices and their reciprocal scaled lattices (that appear continuous because of the large number of states).

I agree that it is a Chicken-Egg type of question, that both continuous waves and discrete particles are fundamental, and the existance of either probably necessitates the existance of the other.

Along the lines of this wave-particle duality, I think that fields require mediating bosons and vice versa. The Electric Field required the Photon with fine-structure constant of 1/137, whereas the magnetic field requires the magnetic monopole with coupling of 137/4 (with an apparant S-Duality). My Quantum Statistical Grand Unified Theory does not predict a force of strength 137/4, nor have we observed the magnetic monopole. Thus the question should be 1) Does the magnetic monopole exist at a scale we haven't yet observed? or 2) Did the magnetic monopole degrees-of-freedom get absorbed into another physical effect (such as my interpretation of Edwin Klingman's ideas whereby the gravitational magnetic monopole degrees of freedom may explain the CKM and/or PMNS matrices).

I know that my ideas are maverick, but I also think that we are a long way from a TOE without some radical thinking.

Have Fun!

Dr. Cosmic Ray

Thus far, from you posts, I see the following:

- the Super-Cosmic scale (Multiverse scale), with the [Vector] Gravitons, and this scale is associated with a Graviton space or field (continuous)

- the Cosmic scale (Universe scale), with the [Vector] Gravitinos, a Gravitino space (discrete)

- the Classical scale, with the Vector Bosons, a Vector Boson space (continuous)

- the Quantum scale, with the matter Fermions, a Fermion space (discrete)

- the sub-Quantum scale (Dirac scale), with the Scalar Bosons, a Scalar Boson space (continuous)

you indicated "the Higgs Mechanism and the origin of mass" in the Dirac scale

You described scale 'boundaries' - the Cosmic scale (I presume the scale of the observable universe, the Universe scale) and the Multiverse (super-Cosmic) scale. You also say that "the Multiverse...is the largest scale from which we can feel effects." And you mention the implication of "an infinite Multiverse". You say "The mass distribution of our Universe is not isotropic and homogeneous, but is coursely grained." And you also mentioned elsewhere that a black hole singularity (infinitely dense) cannot exist in a finite universe.

By 'finite' I am of course assuming you mean the 'scale', not the 'amount' of the components that meet the measures of the scale... By "coursely grained", I will presume that you mean "coarsely grained" as to discrete texture and not "coursely grained" as to mean grained by coursed flow or routed with direction. (Although this is also a beauty.)

I will not question the categorization of the scales to continuous and discrete. I'll wait until I can have a clearer image of the possible lattices and how they stretch or curve.

According to your suggestion of possible effects of the Multiverse scale on the Cosmic scale, which I assume would mainly be a gravitational condensation effect because of the Graviton space or field, I now ask:

What sort of process would produce such effects? Gravitational-mass-induced mass-energy condensation? Incident gravitational-vacuum-induced radiative expansion? Could it be both? And if both, could it be alternating? simultaneous? Gravitational momentum? Perhaps, something else?

I am thinking of the scales for the range of kinematic densities exemplified by the voids at the vacuum end, by everything in the middle, and by the black holes at the superdense end. I am interested in where you place the supervoids and the superdense in your scales (or what supervoids and what superdense you put in what scales) and what processes govern their states. So, I can't help but ask:

What particular types of constructs are coarse in what scales? How are the voids made vacuous in your scales? How are the black holes made dense in your scales?

You have of course given complexity numbers - but how do the processes look like in terms of incident equilibrium states between condensation and radiation in the appropriate scales?

I am interested in how the processes look like so that I can properly fit them in my idea of motion transformations. I'd like to see the processes within volumetric space. It appears to me that whatever your answers, they could fit in my ideas of "motion constructs" and "motion transformations".

Ray, I've been rather alone regarding my idea of the "transformations of motion"; everyone else seems to be talking "spacetime transformations". My googling and yahooing found hardly anything consoling...

I sincerely would like to learn of your opinions regarding the above - even just the little that you can allow yourself to dislose.

I know I am being a bit devious here, since I am hoping somebody else could work out the mathematical (numbers) and logical (words) answers to my own questions. (hehe!) I carry a lot of question marks for my queries, but few exclamation marks for my own eurekas. I hope you won't mind so much.

Rafael

Ray,

I am taking our discussion to my own FQXi forum link. I think this will inspire me a bit more and make our discussion more interesting. I hope you will grant me the courtesy of following our discussion at my turf. HeHe!

Rafael

Ray

Excellent read (between all those numbers!) and I found myself more convinced than I'd expected with your notions.

I've already raised this with Edwin, but have you considered the toroid form of tokamaks as a complete unit scalable both up and down, my current paper identifying them as not only the galactic black hole and quasar configuration, but also as a candidate for recycling the universe in the Big Blazar! How's that for a crazy notion.

The point of it is it has intrinsic spin, and dual axis / helical spin, producing... anyway I'm sure you understand them much better than me.

I feel a good score coming in your diretion. I particularly agree with the equivalent of your conclusion, most current physics is at least half wrong!

I'd be interested in any views on my own paper, if you can think without numbers!?

Best wishes

Peter