The Intrinsic Structure of the Quantities by Peter van Gaalen

Hi Peter

Let me restate your argument to see if I got it correctly:

\alpha = \h_electromagnetic / h_gravitomagnetic

Is this correct? After you confirm this, we can continue the discussion; I do not want to start a discussion with a wrong assumption.

Regards,

Florin

Dear Peter,

I agree with Emile. Constants such as h and c must be global. IF hyperspace exists, then there is a broken symmetry between Spacetime and Hyperspace. IF hyperspace has different values of h and c from our Spacetime, then these two types of space cannot connect in a regular manner. I don't understand what sort of topology this implies - perhaps you must travel through a black hole singularity to reach hyperspace.

My model uses Special Unitary groups heavily. I equate the (N-1) rank of the SU(N) algebra with dimensionality (here, I imply mostly unseen space-like dimensions - not 'units' as you use the word). A classic example is the Georgi-Glashow SU(5) GUT. SU(5) has a rank of 4, with four 'charges':color g_3, color g_8, hypercolor, and weak isospin, that relate to the four dimensions of Spacetime. This is all we understand well: the strong, electromagnetic and weak forces, and Spacetime - all remnants of the first four observable dimensions. We do not understand gravity - of course, we have General Relativity but we still haven't confirmed the origin of mass or why mass doesn't seem to be quantized (dimensions 7-10 in my model). We do not understand the origin of generations (dimensions 11 and 12 in my model). Is there a symmetry rule that only 3 (or 4 or 5) generations exist, or can we keep making progressively heavier 'fundamental' particles as we can in nuclear physics? We simply haven't probed high enough energy scales yet. And we don't understand hyperspace (dimensions 5 and up). How can we? We have no direct evidence, but tons of theoretical implications. I have the following branes: Hyperflavor-brane (5th and 6th D), WIMP-Gravity-brane (8th-10th D), and Generation-brane (11th and 12th D), along with 'imaginary time' in the 7th D. Supersymmetry may convert my 12-D model into a 24 or 26-D model similar to Lawrence Crowell's. These branes are new spaces, but note that some are two dimensional, and one is three dimensional. Two dimensional spaces allow anyonic statistics, so the distinction between boson and fermion becomes blurred.

Regarding ratios of 'phases' - this is exactly the origin of Dirac's Large Number ~1040. IMHO, if the WIMP-Gravity-brane has a content of ~1040, then this might 'cause' Dirac's Large Number. The fine-structure constant is an important number, but is it fundamentally any more important the Dirac's Large Number? Should we also expect a Hyperspace brane to have a Planck's constant reduced by Dirac's Large Number as well?

Have Fun!

Ray Munroe

Dear Peter,

I like your ideas because I think they are complementary to mine, not because they are identical to mine. I don't understand hyperspace. I compare it to space-like branes because I don't have a better perspective or comparison. If 'em-length' peoperly describes the fifth dimension, then that is great. It is relevant to talk about Kaluza-Klein 90 years after its conception, although my ideas are 12 dimensional and include the strong nuclear, weak nuclear, and an explanation for three generations of fermions that Kaluza-Klein did not include.

Good luck in your research. It seems to be a work in progress, but I would like to read the final product some day.

Have Fun!

Ray Munroe

Dear Peter,

I see now your argument, but it is wrong. Alpha can be understood as several ratios (http://en.wikipedia.org/wiki/Fine-structure_constant): the square of the ratio of the elementary charge to the Planck charge, or the ration of the velocity of the electron in the Bohr model of the atom to the speed of light. You understand it as a ratio of "another Plank constant" to the usual Plank constant. But let's turn the equation around:

Another Plank constant = Plank constant * alpha

But while alpha is dimensionless, it is not constant: it changes depending on energy and therefore your "Another Plank constant" is not a constant, while the Plank constant it is a true constant.

The reason of the dependence of alpha with energy is in field theory renormalization. Unification of interactions is pursued in part due to the fact that the interaction strength for electromagnetism, weak, and strong force converge at higher energy. Renormalization can be understood using renormalization group approach. The earliest manifestation of this was in fluid dynamics in late 1800s and is related to "effective" parameters. Insert gently a drop of ink in a bathtub. It will take a long time to spread. But stir the water and it will do it right away. In electromagnetism one has virtual photons which create a virtual sea of electron and positrons. This sea of virtual particles shields the bare electron and we observe only the screened mass and charge (or alpha). Change the energy and the shielding yields a different alpha. 1/137 is only the value at zero energy.

To paraphrase you, your another plank constant looks like a duck, but does not quack like a duck, and it is not a duck :)

Regards,

Florin

Hi Florin,

Historically, the first physical interpretation of the fine structure constant was the ratio of the velocity of the electron in the first circulair orbit of the relativistic Bohr atom to the speed of light in vacuum. Equivalently, it was the quotient between the maximum angular momentum allowed by relativity for a closed orbit and the minimum angular momentum allowed for it by quantum mechanics. It appears naturally in Sommerfield's analysis and determines the size of the splitting or fine-structure of the hydrogenic spectral lines.

The fine-structure constant plays an important role in QED. \alpha is one of the empirical parameters in the Standard Model of particle physics, whose value is not determined within the Standard Model. (wiki)

Florin, you take the perspective of GUTs and String theories in which there are running coupling constants. This depends on the scale on which we look. If we look at different scale (smaller distance, shorter time, higher energy or bigger momentum) then we get different values for the constants. And this has to do with renormalization (Ray also mentioned that). In quantum theories the charge of for example an electron depends on the cloud of photons, electrons and positrons around that electron. That cloud has different densities (probabilities) on different scales.

wikipedia:"According to the theory of the renormalization group, the value of the fine structure constant (the strength of the electromagnetic interaction) grows logarithmically as the energy scale is increased. The observed value of \alpha is associated with the energy scale of the electron mass; the electron is a lower bound for this energy scale because it (and the positron) is the lightest charged object whose quantum loops can contribute to the running. Therefore 1/137.036 is the value of the fine structure constant at zero energy. Moreover, as the energy scale increases, the strength of the electromagnetic interaction approaches that of the other two fundamental interactions, a fact important for grand unification theories."

I am not trying to defend my baby theory, but I am trying to understand what is going on using different perspectives. I agree that it appears to be that the fine-structure constant is a running coupling constant. From now on lets assume that that is the correct view. But even then it is interesting that the ratio of the fine-structure constant is

[math]\dfrac{e \cdot \dfrac{emflux}{\phi}}{m \cdot \dfrac{m}{\dfrac{gmflux}{\phi}}}[/math]

So for me reason enough to explore the view that h_e is a kind of planck constant. Lets call h_e a running planck constant. In my theory I make a strict difference between energy and mass. They are not the same. So I think it is very confusing to say something like the quote in wiki "The observed value of \alpha is associated with the energy scale of the electron mass". I think they say that the observed value of \alpha is associated with the (relativistic) electron mass". For me it is from a dimensional point of view very interesting to understand the relation between mass and electric charge. What in heavens name is electric charge. I don't know. Dirac had a formula in which he concluded that besides electrons there must be also protons (can anyone explain this to me? is it a formula from wich the root of a square hasnext to the positive mass a positive and a negative charge or something) I think Dirac has a key point. Lorenz thought that the whole electron mass was due to the electric charge of the particle (Feijnman lectures of physics II 28). I also think that it is possible that all mass is a residual of the different kinds of charges. There is no mass other then related to the different charges. (maybe black holes proove the opposite view). Not only (rest-)mass but also energy of the different fields is a residual quantity. Togethes they must obey E = mc2. But overall my purpose is to remove mass and energy (and momentum e.d.) out of my octonion description.

Regards, Peter

Dear Peter,

You said "For me it is from a dimensional point of view very interesting to understand the relation between mass and electric charge. What in heavens name is electric charge. I don't know. Dirac had a formula in which he concluded that besides electrons there must be also protons (can anyone explain this to me? is it a formula from wich the root of a square has next to the positive mass a positive and a negative charge or something) I think Dirac has a key point. Lorenz thought that the whole electron mass was due to the electric charge of the particle (Feynman lectures of physics II 28). I also think that it is possible that all mass is a residual of the different kinds of charges. There is no mass other then related to the different charges. (maybe black holes proove the opposite view). Not only (rest-)mass but also energy of the different fields is a residual quantity. Together they must obey E = mc^2. But overall my purpose is to remove mass and energy (and momentum e.d.) out of my octonion description."

The Dirac equation predicted the existence of positrons (anti-matter electrons with positive electric charge) based on the existence of electrons in 1928, prior to the discoveries of positrons by Carl Anderson (1932) and Chung-Yao Choa (1930). This demonstrates matter-anti-matter symmetries.

In my opinion, you need to separate 'electric charge' from 'mass charge' - they must be two different quantum numbers, and not intimately related. Also, I don't think the octonion is large enough to accomplish a TOE. If the octonion was large enough, we would be able to 'fix' Lisi's E8 TOE. I am playing with the union of an Octonion and a Quaternion, and might need even more dimensions...

You and Florin have sufficiently discussed the fine structure running coupling. It would imply a strange brane if Planck's constant varied with renormalization energy scale.

Have Fun!

Ray Munroe

There must be only one mass in the denominator.

Dear Peter,

In my models, each new gauge 'charge' corresponds to a new (mostly space-like?) dimension. This is the similarity that I see with your model, where each new 'unit' corresponds to a new dimension. Abbreviations: HF=Hyperflavor (a left-right symmetric extension of the Weak force), WG=WIMP-Gravity (Weakly Interacting Massive Particle Gravity - a short-ranged tensor force similar to Gravity), Gen=Generaton=Generation-brane (a massive boson force responsible for the enforcement of generational structure).

dimension charge

Space_1 Color_g3

Space_2 Color_g8

Space_3 Hypercolor

Time_4 Weak Isospin

HF-brane_5 Isospin_HF3

HF-brane_6 Isospin_HF8

Im_Time_7 Gravity_G

WG-brane_8 WIMP-Grav_F3

WG-brane_9 WIMP-Grav_F8

WG-brane_10 WIMP-Grav_F15

Gen-brane_11 Generaton_Q3

Gen-brane_12 Generaton_Q8

Supersymmetry will at least double the size of this, so I already have at least 24 dimensions. Recent conversations with Lawrence Crowell may be pushing this number up to 28 dimensions. I don't think you can quite accomplish a TOE with an 8-dimensional octonion plus its 8-dimensional Supersymmetric component. Lisi' E8 TOE was close...

Have Fun!

Ray Munroe

Hi Peter,

> In my theory I make a strict difference between energy and mass. They are not the same.

From dimensional analysis this is true, but E = mc^2

> What in heavens name is electric charge.

Electric charge comes out of Noether's theorem: Lagrangian symmetries implies conservation laws (http://en.wikipedia.org/wiki/Charge_(physics)). Charge exists because the field is complex.

> Dirac had a formula in which he concluded that besides electrons there must be also protons (can anyone explain this to me? is it a formula from wich the root of a square hasnext to the positive mass a positive and a negative charge or something)

Dirac's equation contains electron and positron solution, not proton solutions. But at that time, the positron was not yet discovered and Dirac was too afraid to speculate about its existence based on his equation. Instead he thought 2 of the 4 solutions corresponds to two proton particles (with opposite spin helicity). The mass between electrons and protons is different, but his equation shows the same mass. To explain this away, he introduced a roundabout theory of vacuum holes. After the discovery of the positrons, things were properly explained.

Regards,

Florin

Dear Peter,

I knew that you had two octonions. I interpreted the 2nd octonion as supersymmetry. If it is supersymmetry, then your model is effectively the same size as a supersymmetric Lisi E8 model - and I don't think this is quite large enough. If your second octonion isn't supersymmetry, then you still need to double this model and you will have 32 dimensions (I'm not proposing 32 dimensions - just talking about theoretical consistency with supersymmetry).

If you introduce magnetic charge, magnetic flux and their supersymmetric equivalent terms, you might get a model closer to mine.

Have you read Rick Lockyer's web site about octonions? He has a left-handed octonion and a right-handed octonion.

Have Fun!

Ray Munroe

Hi Peter,

The ict idea is profoundly wrong. There is no "imaginary" display at my watch. If x is real and t is imaginary, then they cannot be transformed one into the other, and we are back to Newton. The correct idea is the metric tensor, but the explanation is rather complicated. Here is a 10,000 feet sketch.

Imagine a soccer ball. At a (each) point on its surface put a straight sheet of paper. This represents the "tangent plane" at that point. Arrows drawn on this paper with the origin at the touching point are called vectors. The sheet of paper is a vector space. Each linear vector space has a dual. (And the dual of a dual is the original space). The elements of the dual space are called 1-forms. If a vector is represented by an arrow, a 1-form is represented by an infinite collection of equidistant planes. The distance between planes is inverse proportional to the magnitude.

A metric tensor is a mathematical object mapping a vector with a 1-form. A scalar product is the number of piercing a vector arrow punches the infinite number of equidistant planes.

1-forms can be also visualized as vectors (the vector perpendicular to the equidistant planes). Let's denote a vector as v_1 (lower index) and a one-form as v^2 (upper index). A metric tensor G switches the lower to upper (vectors into 1-forms) and upper to lower (1-forms into vectors) indexes.

The dot product of 2 vectors is v_1*v_2 = v_1Gv_2= v_1 v^2 = the number of piercing done by v_1 arrow onto v_2's family of planes.

In Euclidean spaces, the metric tensor is the identity matrix (diagonal 1's) and there is practically no difference between vectors and 1-forms. But in relativity, one of the 4 diagonal 1's is -1. So if vector v_1 = (2,4,3,1) (time = 2, x=4,y=3, z=1), then v^1 = (-2, 4,3,1) and v_1*v_1 = v_1 v^1 = -4+16+9+1 = 22. Changes of coordinates change the components in that representation, but not the vector. The 22 value is the same in any reference frame.

There is basically no "i" in relativity. And in the naïve ict, the i belongs to t not c. there is no ic and no (ic)^2. The "i" is poor's man reminder of the -1 factor in G for the vector dot product.

Regards,

Florin