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x: on 8/27/11 at 8:46am UTC, wrote + 1 + 1 [equation]

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Anonymous: on 11/27/09 at 7:02am UTC, wrote Hi Ray, Ray@:My model uses Special Unitary groups heavily. I equate the...

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CATEGORY: What's Ultimately Possible in Physics? Essay Contest (2009) [back]
TOPIC: The Intrinsic Structure of the Quantities by Peter van Gaalen [refresh]

Author Peter van Gaalen wrote on Sep. 15, 2009 @ 15:43 GMT
Essay Abstract

By analyzing the dimensions of the quantities I found what I called the main sequence. A column with respectively time, length, mass, momentum and energy. Because of symmetry I concluded that in this main sequence the number of quantities must be extended. And therefore that both the Minkowski metric and the relativistic energy-momentum equation had to be extended. They are combined into the 16-dimensional general metric. From this metric I developed an octonion model of gravity. The elements of the two opposite octonions involved are proportional imaginairy quantities. The physical equations have their origin in and are limited by this intrinsic structure of the quantities.

Author Bio

My name is Peter van Gaalen. Born in the Netherlands, may 16, 1967. I studied biology at Leiden university. Now I am working as a software developer. I always have been interested in different disciplines of science. I am worried about the deterioration of nature and the rapidly vanishing of the indigenous people and their cultures. Blaming the 'western' cultural/social sytem that is out of control. Following the program of E.O. Wilson and trying to study the social system from a biological perspective in order to understand it's emergent behaviour.

Joe Fisher wrote on Sep. 15, 2009 @ 21:16 GMT
An extremely interesting essay.

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Author Peter van Gaalen wrote on Sep. 23, 2009 @ 05:58 GMT

This morning I red: "One of the premises of the CPT theorem is that the background spacetime is flat Minkowski space." (Penrose p818). I realised that in the same line of reasoning about CPT symmetry in my essay, in the octonion model there must be one more symmetry. I call it 'S' from 'substance interchange'. It's the reflexion of marble into wood or visa versa. So the whole symmetry of the gravitomagnetic system is CPTS.

I want to make two corrections in my essay:

page 3: l/c = gmflux must be c l = gmflux. (l = length)

page 8: metric
$f^2 + l_x^2 + l_y^2 + l_z^2 = t + b_x^2 + b_y^2 + b_z^2$

does NOT turn into
$b_x^2 + f^2 + b_z^2 + l_y^2 = l_x^2 + t^2 + l_z^2 + b_y^2$

(in the (latex) preview I didn't see the summation signs between the terms in the metrics, but they ought to be there.)

Jayakar Johnson Joseph wrote on Sep. 26, 2009 @ 09:06 GMT
Dear Peter van Gaalen,

I think, mass is causal for quantity that determines the dimensions of quantities as the point mass by point particles are the points expressed in the geometry of the dynamics of elementary particles in quantum mechanics that are zero-dimensional. The geometric expression originated from a point source that is described by complex and hyper complex number systems is the intrinsic structure of the quantities for their dimensions in quantum mechanics and general relativity of Lambda-CDM cosmology.

But in Cluster-matter universe as the mass of matter has two sets of dimensions by the quantities of cluster-mass and elementary-mass, there are two different geometric expressions from a single point source, where both geometric expressions collate. This implies that the Coherent-cyclic model of Cluster-matter universe does not have any shape and thereby the complex and hyper complex number systems applicable for this model differ from that of the Lambda-CDM model of universe.

By this article I perceive that the descriptions you have provided on fundamental physics is much useful for the formulation of hidden variables in the new physics of BSM and Cosmology that is applicable for both models.

With best wishes,

Jayakar

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Author Peter van Gaalen wrote on Sep. 27, 2009 @ 18:27 GMT
Hello Jayakar,

My system doesn't not say anything about particles wether they are point particles or particles like strings and branes. It only analyses the quantities. So indeed it can be used in different theories.

The concept of 'mass' is a bit confusing in mainstream physics. I often read that "energy is mass" which is a most confusing and wrong statement. Einstein himself was...

view entire post

Jens Koeplinger wrote on Oct. 2, 2009 @ 01:43 GMT
Hi - what I like in your essay is that at the foundation of the forces of nature, you propose two octonions which, when multiplied, produce an equality between a sum of squares. In contrast to classical relativity that requires some directionless magnitudes to remain invariant (mass, proper time), you are requiring a symmetry relation between your two fundamental octonions, and also between the left-hand and right-hand sides of their product equation (the sum of squares). That looks like a beautiful ansatz to me.

Now, regarding the potential relation to physics your suggesting, I've got my reservations ... Let me just point out one conceptual problem. You propose a superficial relation to the field equations from General Relativity. That is not the proper realm for a comparison, IMHO, since the Einstein equations model the dynamic balance between sources of fields and the fields themselves. In your model, in contrast, field self-interaction is absent (not at last since you don't really have a concept of "field" yet). If you were to compare your ansatz with General Relativity, then you may look at the linearized field equations. There still is a concern (though maybe a smaller one), since the linearized field equations from General Relativity are obtained from a weak field and small velocity approximation, whereas your approach could justify the weak field approximation, however, would need to remain valid for any velocity, I think.

Good luck, Jens

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Author Peter van Gaalen wrote on Oct. 2, 2009 @ 06:58 GMT
Hello Jens,

"That is not a proper realm for a comparison". You are right with that. I am a total layman with respect to for instance tensor algebra. But I have this vague intuition.

It seems to me that the product of two (different or not) octonions forms a tensor. I do not exactly know what quantities are used in the tensors, but I thought in case of the energy-stress tensor they where energy density and momentum density and stress. those quantities are not in the proportional table with mass and length. But there are more quantity tables with proportional quantities. for instance a table with the proportional quantities mass density, momentum density and energy density. and a table with proportional pressure e.d. All those tables have a general metric.

Maybe the Einstein equation uses quantities from different proportional tables. So therfore I think that there is a link.

And according to Michio Kaku in his book 'hyperspace', the Riemann tensor is about the curvature and torsion of space. I think that the imaginairy units in the tensor have these properties of curvature and torsion.

Greetings,

Peter

Jens Koeplinger wrote on Oct. 2, 2009 @ 13:41 GMT
Ok - I understand you're doing analogy comparisons; highlighting what you feel is similar, and not necessarily equal. Still, you want to compare your formulation with the linearized field equations from GRT, since they do not account for field self-interaction, either. In classical GRT, you can then "bootstrap" up to the covariant form iteratively. If you're curious about the details, I've prepared a summary and reference list about this here ("Spin 2 / GRT: collection of articles"). Yet take that with caution as well: Your approach from the product of two octonions would not result in a spin 2 model (which is good! you don't want that, IMHO spin 2 is a dead end, others may disagree with me), but you're facing something much, much more complicated (which I can't help you with, either, because I'm looking for answers myself).

Thanks, Jens

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Anonymous wrote on Oct. 4, 2009 @ 19:28 GMT
Hi, Jens

I am very curious about what you said about that the approach from the product of two octonions would not result in a spin 2 model. Why do you think that? I hope to hear from your investgations.

Thanks for writting and good luck with your searh.

Peter

The last few days I had some thoughts about the light cone in spacetime. According to Yang-mills theory particles are massless and are traveling with the speed of light. So he particles are on the ligthcone. (without symmetry breaking).

My question: If mass and energy are different manifestations of the same thing, why does yang-mills theory describe only particles with energy and with no mass?

I assumme that yang-mills symmetry is written for particles in spactime.

I we turn time into gmfux then we get gmfluxspace. If paricles are described in this gmfluxspace then these particles are also on a cone. This cone has also the 'speed of light'. But we must not think of 'speed'. These particles will have no energy, but they have mass.

If we have gmfluxspace, and we turn space into burst, then we get burstflux. In this burstflux we have the light cone with the speed of light again. And again the particles will have energy, but no mass.

In this burstflux if we turn gmflux into mass, then we get burstmass. Then our cone is not composed of the speed of light anymore. Instead it is composed of the gravitational constant G.

Peter

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Jens Koeplinger wrote on Oct. 5, 2009 @ 01:23 GMT
Just quickly re "not spin 2": Your octonion product is a sum of scalars, therefore the sources of your fields can be vectors at best, in those cases making your exchange particle spin 1 ... but I can only underwrite this in the distinct cases where you can project your formulation onto a degenerate form (namely, with four-dimensional Minkowskian or Euclidean signature); for all others, I don't know. When you introduce nonassociativity, you can't simply separate out the propagator of your exchange particle (or at least I can't), so you can't examine it easily for its spin. Best wishes, Jens

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Peter wrote on Oct. 14, 2009 @ 06:57 GMT
Hi Peter, my name is also Peter van Gaalen. Born in New Zealand after my parents immigrated from Holland.

You can find me on face book.

De Groeten

Peter

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Author Peter van Gaalen wrote on Oct. 28, 2009 @ 07:08 GMT
Reasons for more dimensions:

If we have complex numbers then {1, i} is not the complete set. {1, i , -1, -i} is the complete set. In the description of spacetime Minkowski used the 'hyperbolic quaternion'. The minkowski metric stops with {1, i, j ,k} but where is the other half? Where are {-1, -i, -j, -k} ? The Minkowski metric is not a closed system, but no one seems to care! This is a fundamental question. In case the Minkowsky metric t^2 - l^2 = S^2 the only thing about the invariant of spacetime S^2 is that it's invariant. It doesn't say how many quantities it's composed of. That's why it's more illuminating to write it like: t^2 - l^2 = f^2 - b^2. ( l = lx, ly, lz and b = bx, by, bz).

In case of the relativistic energy-momentum equation m^2 + p^2 = E^2. Just look at "mass" on wikipedia. What is the difference between "relativistic mass", "restmass" and "invariant mass"? Why three different kinds of mass? And relativistic mass is not even a scalar quantity! Further if we take m^2 + p^2 = E^2 and we translate m^2 + p^2 as the product of the quaternion and conjugate then the energy would be the norm. But that makes no sense. Energy is just another quantity that differs from momentum like momentum differs from mass. m^2 + p^2 = E^2 + s^2 makes more sense. In which m is restmass and s is an vector quantity. Relativistic mass is related to this vector quantity s.

The description of special Relativity was not finished until Minkowski came with his metric about the spacetime-continuum. Relativity is extremely important. A quantum theory without relativity is not complete."What happens inside a black hole?" The einstein equation says that it is a singularity. Because of these infinities general relativity can't be a complete description of the gravito-magnetic system. So why is no one completing classical relativistic mechanics? It's not finished yet! There is no proper understanding of classical relativistic mechanics. Classical mechanics is not finished, but no one seems to care! Most physisists are focused at quantum theories.Without a proper understanding of classical relativistic mechanics, you can't make a quantum theory that also encompasses gravity.

In my model c and G are the same. c and G both displays relativistic effects. So next to light cones we also have cones with G. Physisists even make a difference between special relativity and general relativity, so they didn't understand that the gravitational constant G is the same as the speed of light c. They are not aware of the difference between quantities and proportional quantities. (Minkowski was). They also aren't aware of the concept of periodicity. And they didn't notice that scalar and vector quantities alternate. The "Octonion model of gravity" adresses these issues.

Ray Munroe wrote on Nov. 12, 2009 @ 01:52 GMT
Dear Peter,

I'm sorry I overlooked your essay. This paper uses different arguments from my own to argue for "extra dimensions" in a consistent manner. My twelve dimensions may be an H4 quaternion of Spacetime and an E8 Octonion of Hyperspace (Superspace). But if we apply Supersymmetry, then it may double to a 24 dimensional (E8xH4)x(E8xH4) model. Lawrence Crowell is working with a similar 26 dimensional model. To first approximation, Lawrence's model has three 8-dimensional E8 Octonions and a G2 2-brane. I propose that one of these E8's separates into a pair of H4 Quaternions. E8 has symmetries of 240=8x(2x3x5) and H4 has similar symmetries of 120=4x(2x3x5).

The symmetries of an Octonion break into 1 scalar, 1 pseudoscalar (imaginary), 5 polar vectors, 5 axial vectors, 10 symmetric tensors, and 10 anti-symmetric tensors. The Einstein Field Equations of General Relativity are 10 anti-symmetric tensor equations. This coincidentally echoes the structure of Octonions. Likewise Maxwell's Equations of Electromagnetism can be written as one Quaternion equation. Thus, combining a Quaternion and an Octonion contains sufficient mathematical formalism to contain Maxwell's Equations and Einstein's Equations.

Have Fun!

Ray Munroe

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Ray Munroe wrote on Nov. 12, 2009 @ 15:25 GMT
Dear Peter,

The public vote of the contest is over, and I'm not trying to pick on you, but I think you got it exactly backwards with your first sentence "I wondered why differentiating acceleration gives velocity and why dfferentiating velocity gives distance". Actually, we differentiate distance with respect to time to get velocity, and we differentiate velocity with respect to time to get acceleration. I know it is independent of your extra-dimensional discussion. I just thought you might want to fix your introduction.

What if the "marble" quantities arise from the visible four dimensional Spacetime H4 Quaternion (and you omitted electric quantities such as the Coulomb), and "wooden" quantities arise from the hidden eight dimensional Hyperspace E8 Octonion? Our essays might have more in common than appears on the surface.

Have Fun!

Ray Munroe

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Author Peter van Gaalen wrote on Nov. 12, 2009 @ 21:44 GMT
Hi Ray,

Yes you are right, my mistake. (the third mistake in my essay and there are probably more). Differentiating length gives velocity.

I omitted electric quantites, because I couldn't think of a means in which to include them. In a way electromagnetic flux and electric charge have resemblance with gravitomagnetic flux and mass (That's the reason why I named gmflux 'flux') and just like gmflux = G/c mass, we also have em-flux = K/c electric charge. In my model I did choose gmflux to be the basal proportional quantity, but it is better to take
$m\sqrt{G}$
(I call esu-mass) as the basal proportional quantity because this quantity has the same dimension as
$e\sqrt{K}$
(which I call esu-charge).

We have (from Steven Weinberg article) electric charge Q, electronic hypercharge Y and electronic isospin T. likewise we have respectively the quantities: esu-electric charge e, esu-hypercharge g', and esu-isospin charge g. But I need a metric with electric charge and mass in it. I have some ideas like Dirac: mass can't be negative that's why the root result in (positive mass + positive electric charge) and (positive mass + negative electric charge). But this is premature.

I tried to read your essay (I like the matrix with rotations and reflexions) but it is difficult for me. Can you explain what is the H4 quaternion and what is the E8 quaternion?

Author Peter van Gaalen wrote on Nov. 12, 2009 @ 21:53 GMT
Hi Ray,

It will be great when our model can be unified. But I think that I can't do it because it is difficult for me.

I am trying to develop some algebra's: From the general metric an equation with only scalar quantities:

f2 + E2 = (-t)2 + (-m)2

This metric inspired me to develop an algebra that unifies complex numbers, split complex numbers and hyperbolic complex numbers. Now I am trying to develop an algebra that unifies quaternions, split quaternions and hyperbolic quaternions, but that is a hundred times more difficult then complex numbers.

Greetz, Peter

Ray Munroe wrote on Nov. 12, 2009 @ 22:25 GMT
Dear Peter,

Because electric charge, hypercharge and isospin are all related, you shouldn't need all three quantities. If I understand your ideas, then introducing the Coulomb unit would encompass all three related charges.

Think of H4 as half of an E8. E8 is 8 dimensional. H4 is 4 dimensional and shares the same component symmetries such as Lisi's 3-fold Triality (as well as a 2-fold Duality and a 5-fold Pentality). For more background on H4, check out these references:Coxeter-Dynkin, 120-cell and 600-cell.

In Clifford algebra, the Quaternion has a 4 dimensional (1,4,6,4,1) (scalar, axial vector, tensor, polar vector, pseudoscalar) component symmetry whereas the Octonion is comparable to a complex (real plus imaginary) Quaternion with an 8 dimensional (1,5,10,10,5,1) (scalar, axial vector, anti-symmetric tensor, symmetric tensor, polar vector, pseudoscalar) component symmetry.

I don't know about negative mass. In some regards, anti-matter could almost be treated like a negative mass, but then gravity seems to always be attractive. Consider pair production from gamma + gamma -> electron + positron. If we treat the positron like a positive mass, then our mass terms don't equate on both sides of the equation. If we treat our positron like a negative mass, then mass could equal (zero) on both sides of the equation.

My model also implies imaginary mass ("scalar fermions" or tachyons mentioned in the essay) and imaginary time (not mentioned in the essay - I'm still trying to understand my 7th dimension - It doesn't fit into M-theory, but everything else does).

Have Fun!

Ray Munroe

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Author Peter van Gaalen wrote on Nov. 13, 2009 @ 07:24 GMT
Hi Ray,

What I am doing is classical relativistic mechanics, it is not quantum mechanics. But it is interesting that when using 'proportional imaginairy units' we get imaginary units used in quantum mechanics for free. The planck constant in quantum mechanics is written ih (h-bar). My model automatically generates the 'i'. In my model planck constant is -Lh (L = imaginairy unit) it is derived from the product of the proportional imaginary quantities: (-t/phi * LE; ix/phi * iLpx; f/phi * -Lm) phi = phase.

Maybe classical relativistic mechanics and quantum mechanics aren't that different afterall.

What I do not understand is that quantum mechanics is only using one planck constant. According to my model there has to be 8 different planck constants (of which 4 vector quantities so a total of 16). They are combinations of the planck constant, the light constant and the gravitational constant. But they are different quantities!

I don't know if it is possible to incorporate electric charge. Maybe there is an essential difference between the classical relativistic gravitomagnetic quantities and the other quantities. If it is possible, then I don't know how to start. Do I need the sedenion? or do I need complexified octonions? But the most important is to find a classical relationship between electric charge and mass. I tried the Kerr-Newman metric (electric charged rotating black hole). Maybe I should take a look again at that metric.

I think that it is fundamental to ask what is a particle? I think that they are droplets or bubbles of 'generalized spacetime'. A package of quantities.

And what are the waves that come with particles? A wave packet has an imaginary component. what quantitie(s) is this imaginary component composed of?

What is a wave related to an octonion? or what is a wave related to a complex number?

Regarding electric charge, hypercharge and isospin. I don't think that introducing the Coulomb unit would encompass all three related charges. They are different quantities. I think there must be a metric with all three quantities in it.

I don't think the Coulomb unit would encompass the three related charges.

Coxeter-Dynkin is interesting. I have seen those graphs before, but I didn't understand them. I have to take a closer look at them.

You say that your model implies imaginary mass. This is related to another problem of me: on the one hand there is the difference between the (imaginary) signature of the quantities and on the other hand there is the value of the quantities. In my model proportional length is 'ix'. but we can have a positive length and a negative length.

So is the value of mass imaginary? or is the quantity 'imaginary mass'?

Greetz, Peter

Ray Munroe wrote on Nov. 13, 2009 @ 14:12 GMT
Dear Peter,

In the Clifford divisor algebras, we progress from real to imaginary to Pauli matrices to Quaternions (Dirac matrices) to Octonions. Imaginary numbers are rooted in all of the more complex algebras. I think it is appropriate that these factors of 'i' keep appearing. It is a phase factor.

Regarding electric charge, hypercharge and isospin, they are related via

Q=T3 plus Y/2.

I don't think you need to include all three charges, but you probably do need an electric charge, an electric flux, a magnetic charge, and a magnetic flux. Do you need to include color charges for the strong nuclear force?

If we supersymmeterize Garrett Lisi's E8 TOE, then we would have 16 dimensions. You discussed 16 dimensions in your essay. If we supersymmeterize my K12' TOE, then we would have at least 24 dimensions. Do the electric quantities make up these extra dimensions?

I am curious about the 8 components of your Planck constant. Theodor Kaluza unified Gravity and Electromagnetism in 5 dimensions. My model has 12 dimensions, but 8 are part of an unseen Hyperspace. Perhaps these 8 unseen dimensions can be effectively represented by one (Kaluza's fifth dimension). Likewise, your 8 components of the Planck constant can be effectively represented by one (the Planck constant that we measure in the laboratory). I need to read your essay more closely to better understand this idea.

Have Fun!

Ray Munroe

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Author Peter van Gaalen wrote on Nov. 13, 2009 @ 17:13 GMT
Hi Ray,

According to the tables I found there is no table with magnetic charge in it.

Dirac hypothised magnetic charge in the Maxwell equations, but when we take a closer look at what he called magnetic charge, we see that the quantity he had is in fact electromagnetic flux. Below e = 'electric' em = 'electromagnetic'.

In this respect it is interesting that the hall effect...

view entire post

Ray Munroe wrote on Nov. 13, 2009 @ 17:59 GMT
Dear Peter,

I see you have put a lot of thought into this. I agree with your comparison "If we want an analogy of this in spacetime, then the electric and magnetic fields are just like a 'length field' and a 'time field' alternating." I'm not certain of proposing magnetic charge with electric charge and electric flux with magnetic flux - it was just an idea. Certainly phi and J are also relevant.

As I recall Dirac's argument, the fine structure constant (a multiple of e2) is 1/137, whereas the magnetic charge strength is related to the inverse: 137/4. So perhaps one is wooden and the other is marble, but we haven't yet discovered the magnetic monopole and don't yet know all of its properties. This also ties into S-duality in String Theory. Does the classification of marble versus wooden tie into S and T duality symmetries? Lawrence Crowell sent me the attached paper on the magnetic monopole.

Have Fun!

Ray Munroe

attachments: 1_1_375.pdf

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Anonymous wrote on Nov. 13, 2009 @ 19:09 GMT
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, Peter

attachments: new_twist_for_magnetic_monopoles.pdf

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Ray Munroe wrote on Nov. 13, 2009 @ 19:51 GMT
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

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Peter van Gaalen wrote on Nov. 13, 2009 @ 22:43 GMT
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)

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Ray Munroe wrote on Nov. 14, 2009 @ 02:29 GMT
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

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Peter van Gaalen wrote on Nov. 15, 2009 @ 07:59 GMT
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?

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Ray Munroe wrote on Nov. 15, 2009 @ 14:34 GMT
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).

Have Fun!

Ray Munroe

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Author Peter van Gaalen wrote on Nov. 16, 2009 @ 07:09 GMT
Hi Ray,

Length is a quantity with unit 'meter'. Length has dimension. Phase is a quantity with unit 'cycle', but what word indicates phase? I can't use 'dimension', but how should I call it? Isn't there a generic word I can use to point out both the dimension of length and the 'dimension' of phase? To call phase unitless is misleading. I like to distinguish between for example time and period, between arc length and circle circumference, between orbital velocity and rotational frequency. lets call it 'phasiality'. So now we can ask for both the dimension and for the phasiality of a quantity. The product of a quantity and phase has a certain 'phasiality', but also the ratio quantity/phase has a certain 'phasiality'.

The dimension of Dirac's large number has very much in common with the fine structure constant. Dirac's large number:

$\dfrac{4 \pi \epsilon_0 G m_p m_e}{e^2}$

Fine structure constant:

$\dfrac{e^2}{h c 4 \pi \epsilon_0}$

Ray:"My Quantum Statistical Grand Unified Theory couldn't fit those numbers if they had different units from each other "

I think this is the hole point. The interesting thing is that they don't have the same phasiality. My surprise with regard to the fine structure constant is that I suggest that the reciprocal of dirac's large number has indeed the same dimension as the fine structure constant. But now I have already told you to much.

Ray thanks for being interested in this subject.

Greetz, Peter

Ray Munroe wrote on Nov. 16, 2009 @ 13:26 GMT
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

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Author Peter van Gaalen wrote on Nov. 16, 2009 @ 20:44 GMT
fine structure constant:
$\dfrac{e^2}{\hbar c 4 \pi \epsilon_0} = \dfrac{\dfrac{e^2}{4 \pi c \epsilon_0}}{\dfrac{h}{2 \pi}}$

Author Peter van Gaalen wrote on Nov. 16, 2009 @ 21:29 GMT
Hi Ray,

I was testing the h-bar in Latex but it doesn't work out well.

fine structur constant:
$\dfrac{\dfrac{e^2}{4 \pi c \epsilon_0}}{\dfrac{h}{2 \pi}}$

And because
$c \cdot \epsilon_0 = \dfrac{e}{emflux}$

and
$h = mass \cdot \dfrac{gmflux}{\phi}$

therefore the dimension of the fine structure constant:
$\alpha = \dfrac{ e \cdot emflux}{mass \cdot \dfrac{gmflux}{\phi}}$

Now my suggestion is that there is also a phase in the numerator:

$\alpha = \dfrac{ e \cdot \dfrac{emflux}{\phi}}{mass \cdot \dfrac{gmflux}{\phi}}$

The meaning of this is that there is not one, but there are two different planck constants!!!! And the fine structure constant is the ratio of these two different planck constants:

$\alpha = \dfrac{h_e}{h_g}$

This also illuminates the Aharonov-Bohm effect in which a charged particle acquires an additional phase.

According to GUTs there are running coupling constants. It predicts that the value of [equation]h_e[\equation] will change at higher energies.

(correct me if I am wrong)

Greetz, Peter

Ray Munroe wrote on Nov. 16, 2009 @ 21:53 GMT
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

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Florin Moldoveanu wrote on Nov. 19, 2009 @ 17:08 GMT
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.

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Ray Munroe wrote on Nov. 19, 2009 @ 19:12 GMT
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

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Anonymous wrote on Nov. 19, 2009 @ 19:55 GMT
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?

$q_p = \sqrt{4 \pi \epsilon_0 \hbar \ c}$

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

$q_p^2 = \alpha 4 \pi \epsilon_0 \hbar c$

And because
$\alpha = \dfrac{h_e}{h} \ \ \ \hbar = \dfrac{h}{2 \pi}$

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

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?

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Florin Moldoveanu wrote on Nov. 20, 2009 @ 06:06 GMT
@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.

Wh
at 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/)

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Author Peter van Gaalen wrote on Nov. 20, 2009 @ 07:59 GMT
Hi Florin,

Planck's constant. (I am also working with 'gmflux' therefore I show the relationship between those products). length, time, mass and energy are all gravitomagnetic quantities. Planck's constant is inherently gravitomagnetic:

$h = E \ \cdot \ \dfrac{t}{\phi} \\ h = p \ \cdot \ \dfrac{x}{\phi} \\ h = mass \ \cdot \ \dfrac{gmflux}{\phi}$

electric charge and electromagnetic flux are inherently electromagnetic.

It would be foolish of me to argue against some math that I don't understand. So I think the article of Grgin is correct. But I am not convinced that Grgin is talking about the electromagnetic system.

And suppose the article indeed applies also to the quantities of the electro-magnetic system. Then what is the fine structure constant? The dimensions I am talking about are correct. The only thing I did is adding a phase to the fine structure constant, therefore it becomes completely 'dimensionless'. If we don't add the phase then the fine structure constant has 'dimension' 1/phase. Florin, I am really interested in your opinion about the 'dimension' of the fine structure constant.

Is Grgin the same as Emile Grgin that posted an essay to the contest? If so then we can ask him for his opinion. We can ask if his article also applies to the electromagnetic system.

Greetz, Peter

Florin Moldoveanu wrote on Nov. 21, 2009 @ 05:45 GMT
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

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Ray Munroe wrote on Nov. 21, 2009 @ 16:03 GMT
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

$A=\pi r^2$

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.

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

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Author Peter van Gaalen wrote on Nov. 22, 2009 @ 12:42 GMT
Hi Ray,

I think you are right, I also had troubles in finding the exact dimension and the exact 'phasiality'. It cost me a lot of trouble to find out. And I think it's not sufficient to call them all 'dimensionless'. It's appropriate to also define the 'phasiality' of quantities (phasiality: if there are one or more phases involved in the numerator or in the denominator).

quantity phase \phi is measured in unit 'cycles'. Cyclical processes can be rotations, oscilations, waves e.d.

Also there are quantities radius r and arc length L.

angular frequency (or angular speed) is the magnitude of angular velocity.

[equation]angle \ \ \theta = \dfrac{L}{r} = 2 \pi \phi \\

circle \ circumpherence = \dfrac{L}{\phi} = 2 \pi r \\

quantity \ pi = \dfrac{L}{r \phi} = \dfrac{\theta}{\phi} = 2 \pi \\

period \ T = \dfrac{t}{\phi} \\

angular \ freq. = \omega_{rad} = \dfrac{2\pi \phi}{t} \ in \ units \ \dfrac{rad}{sec} \\

cyclic \ freq. = \omega_{cyc} = \dfrac{\phi}{t} \ in \ units\ \dfrac{cyc}{sec}[/equation]

The planck constant uses cyclic frequency. The reduced planck constant uses angular frequency.

[equation]Action = E \ \cdot \ t \\

Cyclic \ momentum = E \ \cdot \ \dfrac{t}{\phi} \ \rightarrow \ planck \ constant \ h \\

Angular \ momentum = E \ \cdot \ \dfrac{t}{2 \pi \phi} \ \rightarrow \ reduced \ planck \ constant \ \hbar\\[/equation]

The surface area of a circle and the surface area of a sphere have the same dimensionality, but they have different phasiality.

And I am not particulary happy with 2pi, because this only accounts for a two dimensional flat plane. if we have a rotating disc then the circumpherence will be smaller. So 2pi must be adjusted by means of the lorenzfactor. (so we can use the numerical value of 2pi anyway). Angular frequencey is more correct to write it like:

$\omega_{rad} = \dfrac{\dfrac{L}{r}}{t}$

Cheers, Peter

Author Peter van Gaalen wrote on Nov. 22, 2009 @ 14:11 GMT
Hi Ray,

Ray@: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.

No, I am sorry for being not clear. With gravitomagnetic I mean all quantities like time,length, gmflux, mass, momentum, energy e.d. and...

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Author Peter van Gaalen wrote on Nov. 22, 2009 @ 14:31 GMT
Hi Florin,

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

I hope I did explain in the post above.

Florin@: The fine structure constant is dimensionless.

So if in the denominator of the fine structure constant there is the classical planck constant, what constant is in the numerator? It has the same dimension as the planck constant and it also is a constant "If it looks like a duck, walks like a duck, and talks like a duck, then it's probably a duck." :)

>\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.

Yes, I agree. Quantum mechanics is a mechanics about quantized particles with mass, momentum or energy. All particles have gravitomagnetic-based spin. chirality, left-handed right-handed are all properties of the gravitomagnetic system. Isn't that interesting? The electric and electromagnetic properties can't be described by gravitomagnetic quantities. A particle like an electron is a hybrid of the two different systems. a particle has mass and spin, but it also has electric charge (hybrid). The (gravitomagnetic) spin accounts for the quantum effects. the electromagnetic charge is doing nothing. The only thing it does is producing a specific kind of particles: (virtual) photons. but the photons are also hybrid particles and the quantum effects (interactions) of photons are also based on the (gravitomagnetic) spin.

Regards, Peter

Florin Moldoveanu wrote on Nov. 22, 2009 @ 21:09 GMT
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

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Ray Munroe wrote on Nov. 22, 2009 @ 22:03 GMT
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

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Author Peter van Gaalen wrote on Nov. 23, 2009 @ 06:41 GMT
Dear Florin,

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

\alpha = \h_electromagnetic / h_gravitomagnetic

Is this correct?

Peter: Yes, that is correct.

And h_gravitomagnetic is the classical planck constant. h_electromagnetic is the 'new' one.

Regards, Peter

Author Peter van Gaalen wrote on Nov. 23, 2009 @ 07:09 GMT
Hi Ray,

You mentioned hyperspace. And I think you believe that those extra dimensions of hyperspace are spatial dimensions.

Lee Smolin about Kaluza-klein theory in "The Trouble with Physics":

"To get electromagnetism out of the theory, the radius of the circle must be frozen,changing in neither space nor time.

This is the Achilles' heel of the whole enterprise and led directly to it's failure. The reason is that freezing the radius of the extra dimension undermines the very essence of Einstein's theory of general relativity, which is that geometry is dynamical. If we add an other dimension to spacetime as described by general relativity, the geometry of that extra dimension should also be dynamical. And indeed, it would be, were the radius of the little circle allowed to move freely. The theory of Kaluza and Klein would then have infinitely many solutions in which the radius of the circle varies over space and changes in time. This would have wonderfull implications, because it would lead to processes in which gravitational and electrical efects convert into each other. It would also lead to processes in which electrical charges vary over time.

But if the Kaluza-Klein theory is a true unification, the fifth dimension cannot be treated diferently from the others: The little circle must be allowed to change. The resulting processes are hence the necessary consequences of unifying electricity and geometry. If they were ever observed, they would confirm directly that geometry, gravity, electricity, and magnetism are all aspects of one phenomenon. Unfortunately, such efects have never been observed."(Smolin p47)

I think that the extra dimension in Kaluza-Klein theory can't be a normal spatial dimension. I think that it could be what I call "em-length". And the definition of em-length: em-lengt c = electromagnetic-flux.

If we take em-length then the problem is solved. gravity has no influence on em-length, but electric charge has. But in this modified Kaluza-klein equation we use quantities of two completely separated physical systems.

Regards, Peter

Ray Munroe wrote on Nov. 23, 2009 @ 13:08 GMT
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

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Florin Moldoveanu wrote on Nov. 24, 2009 @ 05:40 GMT
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

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Peter van Gaalen wrote on Nov. 24, 2009 @ 07:06 GMT
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...

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Ray Munroe wrote on Nov. 24, 2009 @ 13:49 GMT
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

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Correction wrote on Nov. 24, 2009 @ 18:12 GMT
There must be only one mass in the denominator.

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Author Peter van Gaalen wrote on Nov. 24, 2009 @ 19:07 GMT
Hi Ray,

Do you think that your branes are different physical systems, for example a spacetime brane and an electromagnetic brane and a colour brane e.d.?

What relation have your branes with the physical quantities?

What relation have unitairy dimensions (dimensions of gauge groups) with real physical dimensions?

Friendly regards, Peter

Ray Munroe wrote on Nov. 24, 2009 @ 21:24 GMT
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

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Florin Moldoveanu wrote on Nov. 25, 2009 @ 05:51 GMT
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

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Author Peter van Gaalen wrote on Nov. 25, 2009 @ 07:05 GMT
Hi Florin,

At the speed of light:

ict = length

The same for mass and energy:

E = m(ic)2 = -mc2

:)

Thanks for the link to wikipedia. It is very interesting.

The last Part: I wanted to write 'positron' but I wrote 'proton'. My mistake.

Hi Ray,

I have to think about what you wrote.

Cheers, Peter

Author Peter van Gaalen wrote on Nov. 25, 2009 @ 07:17 GMT
Hi Ray,

My octonionic model of gravity uses two octonions. A positive octonion and a negative octonion. So I have a total of 16 dimensions. In the general metric on the left side of the equation there is the product of the positive octonion and conjugate. On the right side of the equation there is the product of the negative octonion and conjugate.

Cheers, Peter

Author Peter van Gaalen wrote on Nov. 25, 2009 @ 07:23 GMT
Hi Florin,

>Thanks for the link to wikipedia. It is very interesting.

Well, uhh is it the correct link??

Cheers, Peter

Ray Munroe wrote on Nov. 25, 2009 @ 14:10 GMT
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

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Florin Moldoveanu wrote on Nov. 26, 2009 @ 17:14 GMT
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

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Author Peter van Gaalen wrote on Nov. 26, 2009 @ 19:40 GMT
Hi Florin,

In his book 'Relativity' Einstein mentions that "The discovery Minkowski did, was important for the formal development of the theory of relativity" "The importance lays down in the fact that he saw that the 4 dimensional spacetime continuum of the special theory of relativity in his most essential formal property had a very pronounced relationship with the 3 dimensional continuum of euclidian geometry. To make this relationship more clear we have to replace the usual time coordinate t with the proportional imaginary quantity ict. Then the laws of physics, (that satisfy the demands of special relativity) take the mathematical form in which the time coordinate exactly plays the same rol as the three space coordinates." (Translation could be messy)

Length and time differ by dimension 'velocity'. gmflux and length also differ by dimension 'velocity'. and suppose we have another dimension 'burst'. burst and gmflux differ by dimension velocity. if we apply special relativity to al those dimensions, then we have to replace the usual time coordinate t with the proportional imaginairy quantity ict. length stays just 'length'. if we want to describe gmflux in the same relativistic picture, then we have to replace gmflux with proportional imaginairy quantity -i(gmflux/c). and that is the same as gmflux/(ic). If we also want to describe burst in a similar manner then we have to replace burst with proportional quantity -burst/c2 which can be written as burst/(ic)2. So it appears to be that the imaginary unit i is linked to the light constant c. And suppose we have a quantity 'valention'. Valention differs from burst also with velocity. Then in the relativistic picture we have to replace valention with the proportional imaginary quantity: i valention/c3 we can also write this as val/(ic)3.

You don't have to bring in general relativity, because the relation between energy and mass is a special relativistic one and not a general relativistic one. the relativistic relation between time and gmflux is the same as the relativistic relation between energy and mass.

Interesting is that proportional time and proportional valention have the same imaginary unit. I think the physical interpretation of this is that in a relativistic equation we can exchange proportional time with proportional valention. The equation stays correct. Thus we have a kind of duality in classical relativistic mechanics.

Friendly regards,

Peter

Anonymous wrote on Nov. 27, 2009 @ 07:02 GMT
Hi Ray,

Ray@: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...

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Ray Munroe wrote on Nov. 27, 2009 @ 14:35 GMT
Dear Peter,

You said "Yes, and some combination of the (internal dimensional) running planck charges will equal the classical planck constant at a specific temperature. I don't know what it means that at a certain temperature all forces become the same strength. The many different charges don't disappear to become one charge, but the stay different charges, but they have the same strength."

In my book, I proposed the idea of a Grand Unified Mediating (GUM) Boson with different quantum states: n=1 -> Strong Nuclear (gluons), n=2 -> Electromagnetic (photons), n=3 -> Weak Nuclear (Intermediate Vector Bosons), n=4 -> Gravitational (gravitons), n=5 -> WIMP-Gravitational (WIMP-gravitons), etc...

At the original GUT, the temperature was approximately 'infinity' and the occupation probabilities (equivalent to relative coupling strengths) of these various quantum states were simple ratios of each other (not necessarily equal).

If we tie in your ideas of various Planck scales, then that implies that the Planck scales were all comparable at the GUT/ TOE. However, spontaneous symmetry breaking of the GUT and Inflation would have allowed those Planck scales to separate into a variety of Planck scales. This is speculation. It is awkward that everything varies with temperature/ energy scale and thus nothing seems to be a true constant (not even h?) if we consider this possibility.

Have Fun!

Ray Munroe

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Author Peter van Gaalen wrote on Nov. 30, 2009 @ 06:46 GMT
Hi Ray,

Ray@: 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).

Supersymmetry is derived from the super-poincaré group. That group also contains Lorenz symmetry. Lorenz symmetry generates gravity. I think supergravity is wrong in that it uses the super-poincaregroup as a local symmetry like a Yang-Mills symmetry. The internal dimensions can't be ordinary spacetime dimensions. The planck constant is part of the spacetime dimensions. The internal dimensions maybe have their own planck constants and in that case according to Grgin that would be another reason that the internal dimensions are totally different physical systems. So indeed the two different octonions maybe already contain supersymmetry. And according to Jens Koeplinger at first sight it looks like that the general metric doesn't account for particles with spin 2, in that case there are no gravitons. That suggest spacetime is not quantized. And the gravitational force is inherently different from the other forces. Spinorial space is also part of the base manifold and not a part of the internal dimensions.

But if the second octonion is supersymmetry, then how is Grassmann algebra involved? Has it something to do with anticommuting spinor generators? Do you have any idea's?

Friendly regards,

Peter

Ray Munroe wrote on Nov. 30, 2009 @ 16:15 GMT
Dear Peter,

I have seen Maxwell's four equations of Electromagnetism written as one Quaternion equation, so I know that tensors, cross (Grassman/ exterior) products and dot products are contained in the algebra. Also, my approach is very geometrical and should be quite consistent with differential geometry and algebraic geometry.

Similarly, an Octonion contains 10 symmetric tensor, and 10 anti-symmetric tensor components. I think sufficient structure exists for multiple particles of spin-2 (tensors), thus my Graviton and WIMP-Gravitons.

Certainly, details need to be fleshed out. Lawrence Crowell and I are still considering different foundational models. I think that having a universal foundation is most important, and the details will naturally fall out - its just a lot of algebra at that point.

After many conversations with Lawrence, I think that the Octonion is closely related to E8. In my models, bosonic and fermionic structures seem to be reciprocal lattices of each other. The reciprocal lattice of E8 is another E8, and I think this second E8 may be related to Supersymmetry.

Likewise, I think that the Quaternion may be related to H4. H4 represents the two reciprocal lattices: the 120-cell and 600-cell, so Supersymmetry gets more complicated (and looks less universal) at this stage of my model.

What 'units' have you ommitted thus far? I think you should separate electric and gravitational charges. This will give you more 'dimensions'.

Have Fun!

Ray Munroe

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x wrote on Aug. 27, 2011 @ 08:46 GMT
+ 1 + 1

$+ 1 + 1$

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