The Intrinsic Structure of the Quantities by Peter van Gaalen

Hi Ray,

I have a surprise with regard to the fine structure constant, but I can't tell it to you right now. Maybe another contest.

You asked: "Does the classification of marble versus wooden tie into S and T duality symmetries?" Proportional burst2, proportional length2 and proportional mass2 are all three dual. both burst and length are marble quantities and mass is a wooden quantity. So duality has nothing to do with marble or wood I think.

But I think indeed that the duality in string theory has it's relationship with the dualities in the octonion model of gravity. I think stringtheory is wrong in that it uses to many spatial dimensions. There are only three spatial dimensions but there are other dimensions.

Here the different proportional planck constant's (i,j,k and L imaginary units):

iLhc-3 (quantizes (string time)/phase) (vector)

Lhc-2 (quantized (mass time)/phase) (scalar)

-iLhc-1 ((quantized (mass centre motion)/phase) (vector)

-Lh (quantized angular momentum) (scalar)

hGc-5 (quantized time2/phase) (scalar)

ihGc-4 (quantized (length time)/phase)(vector)(used in string theory I think)

-hGc-3 (quantized area/phase) (scalar)

-ihGc-2 (quantized (burst time)/phase)(vector)

hGc-1 (quantized flux2) (scalar)

Greetz, PeterAttachment #1: new_twist_for_magnetic_monopoles.pdf

Dear Peter,

You have a surprise with regard to the fine structure constant? I attacked that problem before I attacked a TOE - please see Section 4.2 ofmy book. Last year, I corresponded with Mohamed El Naschie about alpha bar theory. He has a fractal approach that updates Sir Arthur Eddington's ideas.

Your attached paper on the magnetic monopole is interesting, but the other one is more current, and I like the fact that they are using tetrahedra (my K12' also uses tetrahedra and related simplices).

My model may be compatible with String/ M-Theory or CDT, but it is not identical. In my model, the H4 Quaternion inflated to produce the visible 4-dimensional Spacetime, whereas the E8 Octonion remained small to produce the unseen 8-dimensional Hyperspace.

I need to think on this marble versus wooden problem. Does it relate to Dirac's Large Number Hypothesis? I don't have any new insight at this moment.

Have Fun!

Ray Munroe

Two questions:

1. what is the dimension of pi.

2. what is the dimension of the fine structure constant?

(two independend questions, they are not related)

Dear Peter,

OK - I'll give your riddle a guess.

Powers of pi enter into the surface area of every hypersphere with dimension greater than or equal to two. Pi itself can be represented by an infinite series, but the concept itself has origins in the second dimension.

According to my model, the first and second dimensions are related to the Strong Nuclear colors, the third dimension is related to hypercharge, and the fourth dimension is related to weak isospin. Because electric charge (the square root of the fine structure constant) depends on both hypercharge and isospin, I would say that a proper representation of the fine structure constant is 4 dimensional.

Because the field strength of magnetic charge is greater than 1, it does not renormalize at small scales (perturbation theory does not asymptotically approach a finite value when the perturbations are too large). Thus magnetic charge is marble. Because photons have energy, they have effective mass (regardless of how small from E=mc^2) and thus cannot have a truly infinite range (range falls off as an exponential dependence on mass). Thus electric charge is wooden.

Have Fun!

Ray Munroe

The riddle of pi:

a = angle; b = arc length; ph = phase; r = radius

a = b/r; a = 2pi ph; 2pi ph = b/r

=> 2pi = b/(r ph)

pi has dimension: 1/phase

Some people say that pi is dimensionless, but I don't think that is true. At least pi has dimension 1/phase. (I think that it is also important to distinguish between arc length and radius, but they have the same dimension)

More riddles:

People say that the fine sructure constant is dimensionless. An interesting statement, but can they show it? and what if they do?

Dear Peter,

I took you literally at "dimensions", when you were referring to "units".

Yes Pi is a phase defined in "unitless" radians.

Likewise, the fine structure constant was defined to be unitless. Ultimately, this number tells the Feynman diagram vertex what the strength of electromagnetic interactions is. Dirac's Large Number is also unitless - it's what makes those combinations of numbers interesting. My Quantum Statistical Grand Unified Theory couldn't fit those numbers if they had different units from each other (although it would still work if they all had units of radians).

Congratulations! Our discussions have brought your paper to the home page.

Have Fun!

Ray Munroe

Dear Peter,

Just call your phases 'radians'. I think that is as clear as you can be about the concept.

You said "the reciprocal of Dirac's large number has indeed the same dimension as the fine structure constant". If so, then my theory still works because that is the relationship with which I have also been working. If I have to call it 'radians' or 'inverse radians', then that is a minor correction. I have posted a free partial preview of my book on other links. The first half of the book introduces Quantum Statistical Grand Unification, and the second half of the book introduces Hyperflavor, WIMP-Gravity and K12' (E12 in my book).

I am interested in Physics and in talking to other intelligent and interesting people. We coincidentally have some overlapping interests.

Have Fun!

Ray Munroe

Dear Peter,

Cool idea! Bringing in my multi-dimensional (and I mean dimensions, not units) ideas, this means that h_e is the Planck constant for the space-brane and real time (dimensions 1-4) and h_g is the "Planck constant" for the WIMP-Gravity-brane and imaginary time (dimensions 7-10). I just don't know how to measure that! Dimensions 5 and 6 are the AdS M2-brane that Lawrence Crowell and I have discussed. In prior discussions, Jason Wolfe and I talked about Planck's constant representing our "resolution" scale for a given brane's reality.

Running couplings tie into renormalization. In my book, I combined Quantum Statistical Grand Unified Theory with the Renormalization Group Equations to "create" Variable Coupling Theory.

Our ideas seem to intersect at several points...

Have Fun!

Ray Munroe

Peter,

There is only one Planck constant and the root cause for it is the existence of the tensor product in QM. In physical terms it corresponds to the ability to compose 2 QM systems and the combined system is still a QM sytem.

See: http://arxiv.org/abs/quant-ph/0301044

Besides this mathematical proof, there is experimental evidence for the uniqueness of Plank's constant.

Dear Peter,

Florin is very knowledgable - you should check out his objections.

I am "open-minded" to the idea because I had a similar type of contribution to intrinsic spin arising in higher dimensions in my K12' model. Quite frankly, my multi-dimensional intrinsic spin analysis was the only way to make sense out of "scalar fermions". Within this context, I would not be too surprised if there is a higher-dimensional contribution (and correspondingly larger matrix products) to Planck's constant. Of course, we know the value of Planck's constant in the 4 dimensions of Spacetime.

Georgina recently posted "The trouble with having an open mind, of course, is that people will insist on coming along and trying to put things in it." Terry Pratchett. I agree with her, and we need to be careful about our speculations.

Have Fun!

Ray Munroe

Hi Florin,

Nice try. But the article is refering to a mixed quantum-classical system in which the classical system has a planck constant with value zero. "Inherent in a quantum system is a Planck's constant (PC) governing its behaviour whereas a classical system can be thought of as a system with zero PC." And also the article analyzes different quantum systems with different planck constants.

But all those different quantum systems are gravitomagnetic systems! i.e. the quantities in the gravitomagentic system are products or ratios of length, speed and gravicity (the gravitational constant is maximal gravicity).

In other words: all planck units of the quantities of the gravitomagnetic system can be derived from the speed of light, the gravitational constant and the planck constant. But not the planck units of the quantities of the electromagnetic system.

The electromagnetic system is completely separated from the gravitomagnetic system. you can't derive quantities like electric charge and electromagnetic flux from quantities in the gravitomagnetic system.

For example what is the planck unit of electric charge?

[math]q_p = \sqrt{4 \pi \epsilon_0 \hbar \ c}[/math]

I think its more correct to use the fine structure constant:

[math]q_p^2 = \alpha 4 \pi \epsilon_0 \hbar c[/math]

And because [math]\alpha = \dfrac{h_e}{h} \ \ \ \hbar = \dfrac{h}{2 \pi}[/math]

And this would result in the planck unit of electric charge [math]q_p = \sqrt{2 h_e c \epsilon_0}[/math]

No quantities from the gravitomagnetic system are used for the planck unit of electric charge.

What is the experimental evidence for the uniqueness of Planck's constant?

@Ray,

Thanks Ray, but I am not that knowledgeable.

@Peter

Hi Peter,

Nice try for the nice try, but the paper does contain the proof of the uniqueness in section 5, independent of the mixing of classical and quantum systems.

The story goes like this. In 1974 Grgin and Petersen wrote a seminal paper: "Duality of observables and generators in classical and quantum mechanics" J.Math.Phys. 15, 764.

The following year they wrote another major paper about composability (E. Grgin and A. Petersen, Commun. Math. Phys. 50, 177 (1976)), clarifying the earlier ideas, but this one is not well known. Sahoo was colleague at that time with Grgin and Petersen at Yeshiva University, and he wrote 2 papers in this area, one being this http://arxiv.org/PS_cache/quant-ph/pdf/0301/0301044v3.pdf.

What Grgin and Petersen observed is that QM and classical mechanics have 2 products: a symmetric product \sigma: (anticommutator for CM, and regular function multiplication for CM) and an antisymmetric product \alpha: (commutator for QM, Poisson bracket for CM).

The 2 products obey 3 identities: Jordan identity for \alpha (because it is a Lie algebra), Leibniz (or derivation identity) for \alpha and \sigma (making the 2 products compatible), and an associator identity where LHS is in \sigma, and RHS is in \alpha and the proportionality constant in the RHS could be -1, 0, or 1.

The origin of those identities is the so-called composability principle: take any 2 physical system described by CM (or QM), put them in contact, and the total composed system should be described by the same formalism (CM or QM). -1, 0, and 1 correspond to 3 independent composability classes: (1 = QM, 0 = CM, -1 = hyperbolic QM). What Sahoo is doing is working the composability paper: E. Grgin and A. Petersen, Commun. Math. Phys. 50, 177 (1976). in reverse, but because there are 3 independent composability classes, his main result of proving the impossibility of combining QM with CM is rather trivial. (Enrico Prati proved the same thing in the essay contest from the C* algebra point of view.)

The argument for the uniqueness of PC is rather trivial as well: the +1 dimensionless parameter is proportional with (1/4) \hbar^2, and stability under composability demands (1/4)\hbar^2 to be the same always (this is exactly how Sahoo is doing it).

I told you earlier that today Grgin's 1974 paper is well known. This paper started the study of the so-called Jordan-Lie algebras. Augmented with the norm property, they gave rise to the study of the modern JB (Jordan Banach) operator algebras for QM.

About the experimental evidence, I do not recall it now exactly, but I think there were comparisons between different elementary particles and comparing experimental measurements between them. (See the references in Sahoo and also: http://www.springerlink.com/content/67238242437h73g4/)

Hi Peter,

>I am confused, what is your phase? Is it measured in radians? If so, it is dimensionless.

>Yes, it is the same Grgin.

>The fine structure constant is dimensionless.

>\hbar is QM-based, not electromagnetic-based (or other kind of interaction). Think of deBroglie original theory. \hbar there is universal for all matter. Suppose 2 physical systems have 2 different \hbar. Put them together and ask what the composite system \hbar is? (Sahoo does this computation explicitly) Unless the composite system has the same \hbar, then by arbitrary composing systems one can obtain whatever value one wants, rendering quantification meaningless.

Regards,

Florin

Dear Peter,

I think I understand both your perspective and Florin's.

To Florin's point, we are taught from an early age that pi has "dimensionless" units of 'radians'. Equations such as

[math]A=\pi r^2[/math]

make us callous to the idea that pi is a phase.

By "gravomagnetic", I assume you are saying that Planck's constant relates gravitational and electromagnetic quantities. In the absence of a unified theory of gravity and electromagnetism, we do not understand the significance of that.

Your ratios of phases should lead you to Dirac's Large Number.

I agree with Florin and Emile that there is one Planck's constant for the Spacetime Universe that we live in. Planck's constant is our "resolution scale". Suppose that Hyperspace also exists, did not inflate as much as Spacetime, and is hidden from us by our resolution scale (h-bar). From my essay, this Hyperspace might be composed of multiple branes with crystalline-like properties. These branes may each have different resolution scales (h'-bar). Unfortunately, this is pure speculation until we can travel to Hyperspace and perform our own quantum experiments.

Have Fun!

Ray Munroe