An Exceptionally Technical Discussion of AESToE

[Lawrence B. Crowell]

I thought the problem was with the representation of the embeding.

I think it is best to think physically. If one tries to just quantize basic gravity SO(3,1) you run into a gemish of trouble. The problem is that you can't define a vacuum state, but rather you have a whole set of them which are inequivalent. This is one reason for the euclideanization procedure. Yet that defines an instanton state, or the tunnelling of a cosmology. The transition from SO(4) ---> SO(3,1) is still problematic, and after all the universe is Lorentzian. On SO(4) connection are defined on a finite or compact group, and then under the tunnelling these connections are defined on a noncompact group and the number of solutions becomes "infinite." Physically this means that attempting to define a vacuum is problematic and the physics is not bounded below.

Lawrence B. Crowell

 

[MTd2]

I think it is best to think physically.

Ok, but how does that relate to Distler's Objection?

 

[MTd2]

Maybe you could re interpret Lisi's theory as lying in the whole Total Space, instead of just laying on the fiber.

That is, get the subgroup SU(5)XSU(5) from E(8), on the total space. Now, define SU(5) on the base space and other SU(5) on the fiber.

It might be possible to define a unique connection in both spaces such that the copy on the base space corresponds to the SU(5) with gravity and lorentz signature and the other, on the fiber with SU(5) with euclidean signature. You could use E(8), laying on the total space, to solve general local physical inconsistencies, if they show up.

 

[Lawrence B. Crowell]

Lastly, Berger also classified non-metric holonomy groups of manifolds with merely an affine connection. That list was shown to be incomplete. Non-metric holonomy groups not on Berger's original list are referred to as exotic holonomies and examples have been found by R. Bryant and Chi, Merkulov, and Schwachhofer"

http://en.wikipedia.org/wiki/Holonomy#The_Berger_classification

Here is the paper:

http://arxiv.org/abs/dg-ga/9508014

Maybe Distler is even right, it is just that he wants to be too picky and get one bad interpretation of the problem, instead of the right, and useful one.

This paper is interesting. What is interesting is the statement at the beginning of the paper:

However, it is the subject of the present article to prove that, even up to finitely many
missing terms, Berger’s list is still incomplete. This is done by proving the existence of
an infinite family of irreducible representations which are not on this list, yet do occur as
holonomy of torsion-free connections. These representations are:

Sl(2,C)SO(n,C), acting on R8n ∼= C2 ⊗ Cn, where n ≥ 3,
Sl(2,R)SO(p, q), acting on R2(p+q) ∼= R2 ⊗ Rp+q, where p + q ≥ 3,
Sl(2,R)SO(2,R), acting on R4 ∼= R2 ⊗ R2.
(1)

This infinite family is due to the noncompact nature of these groups. From a mathematical perspective this is one major problem for quantum gravity

If we have a bracket structure in a group G then elements obey

$$\{A,~B\}~=~I_{\omega(dA)}dB~=~-I_{\omega(dB}}dA$$

for $I_{\omega(d**)}$ a pseudocomplex matrix or operator. This is used to define the symplectic structure in classical mechanics for $\omega$ a closed form which maps functions or vectors into a set of symplectic vectors. To do quantum gravity we can't simply define this according to spacetime vector fields, for physically we are talking about states which are functionals over a set of spacetimes. The vector exists in superspace.

I think this bracket structure and the $\omega$ will then have some connection to how gauge fields are compactified. In a post the other day I indicated how SUSY pairs of elementary particles are canceled against "quirky" spacetimes, and I think this somehow plays a role in quantum gravity. To make the matter sucinct quantum fields and elementary particles have the structure they do in order to "regularize" quantum gravity.

Maybe this paper holds a few clues along these lines.

Lawrence B. Crowell

 

[Lawrence B. Crowell]

Maybe you could re interpret Lisi's theory as lying in the whole Total Space, instead of just laying on the fiber.

That is, get the subgroup SU(5)XSU(5) from E(8), on the total space. Now, define SU(5) on the base space and other SU(5) on the fiber.

It might be possible to define a unique connection in both spaces such that the copy on the base space corresponds to the SU(5) with gravity and lorentz signature and the other, on the fiber with SU(5) with euclidean signature. You could use E(8), laying on the total space, to solve general local physical inconsistencies, if they show up.

No that is not how it happens. Just think of SU(5) with a double. The E_8 supports the SO(7,1) + 8 + 8 + 8 and the SU(3) + 3 + bar-3 + 1 + bar-1 which is similar to 11-dimensional supergravity (though the "super" part here is a bit "chopped at the knees") So an lattice in 8-dimensions defines a system of gauge fields in 11-dimensions. E_8(C) will accommodate two SU(5)s very well.

Lawrence B. Crowell

 

[MTd2]

No that is not how it happens.

I understand what you say, and I agree with that. I thought that you could interpret this problem in terms of fibre buddle. The total space containing E(8), while the fibre and the base, each one, containing a kind of SU(5), although with different signatures. It would also make a map betten gravity and the other fields, without coupling them. The coupling would be done at the total space.

To see in other way. Let's say that E(8) is the bulk, like the containing parts of an aquarium. If you see from one side, you see everything from the point of view of gravity, or aproximately, General Relativy. You face the fish. If you look from the other side, you see see everything from the point of view of the other fields, or aproximately, the Standard Model. You can project all the E(8) fields on each side, but this symmetry will be broken. But the overall it is the same thing.

So, that's why I am asking about this scheme. I would like a one-to-one mapping between parts of the same problem, while trying to make some sense of what would be the relation, in this case between the tangent space and the bundle. That is they don't interact at all. Also, it would be nice to not let them interact at all, making them just different descriptions of what is happening on the bulk, total space.

PS.: This is just crackpotery at best, I'm afraid. But... I'm trying!

 

[Lawrence B. Crowell]

I understand what you say, and I agree with that. I thought that you could interpret this problem in terms of fibre buddle. The total space containing E(8), while the fibre and the base, each one, containing a kind of SU(5), although with different signatures. It would also make a map betten gravity and the other fields, without coupling them. The coupling would be done at the total space.

E_8 is a lattice of roots, which exists in 8 dimensions. The lattice is defined by the set of Weyl chamber reflections

$$x~\rightarrow~x~-~2r\frac{r\cdot x}{|r|^2}$$

on any vector x by the root vector r. These reflections define a set of angles, which for complex groups include dihedral angles and angles between higher dimensional sublattice structures. For E_8 the set of roots, 240 in all, defines the Grosset polytope which exists in 8 dimensions.

The roots may correspond to roots for some subgroups, and this can be broken out in a number of ways. As you said Baez indicated that a representation of a group does not give automatically a representation of all its subgroups. .

What you indicate with respect to the "bulk" is not far off the mark from what people want to do. We have groups of interior symmetries $[A_i,~A_j]~=~C^k_{ij}A_k$, such as found in gauge fields, and there are then exterior symmetries given by the Lorentz-Poincare generators $P_a$ and $M_{ab}$ (and the Pauli-Ljubanski vector), with possible symmetries on the (0, 1/2)-(1/2, 0) spinor representations of the theory (supersymmetry) and finally the discrete symmetries on C-P-T. One central distinction between the internal symmetries and exterior symmetries (spacetime) is that internal symmetries are compact such as SO(n) while exterior symmetries are noncompact such as SO(3,1). Now in the E_8 root paper by Garrett there is the group SO(7,1) = SO(3,1)xSO(4) (plus on the algebra level) and of course the three "8's" framed on this. In this way a noncompact group can have a compact subgroup.

A simple example is the the Lorentz group which consists of three ordinary rotation in space plus three boosts, which are hyperbolic. This is SL(2,C) ~ SU(2)xSU(1,1), and so we might think of the embedding of gauge groups with compact group structure with general relativity as analogous to this.

If we think of gravity as a gauge-like theory with $F~=~dA~+~A\wedge A$ for nonabelian gauge fields the DE's for these on the classical level are nonlinear. Yet we can quantize these, but renormalization is a bit complicated. We can well enough quantize a SO(4) theory obtained in euclideanization. But gravity is a strangely different. Why? The gauge group SU(1,1) is hyperbolic. In the Pauli matrix representation we have that $\tau_z~=~i\sigma_z$. So we cha form a gauge connection

$$A~=~A^{\pm}\sigma_{\pm}~+~iA^3 \sigma_3$$

and for the group element $g~=~e^{ix\tau_3}~=~e^{-x\sigma_3}$ the connection term transforms as

$$A'~=~g^{-1}Ag~+~g^{-1}dg~=~e^{-2x}A^{\pm}\sigma_{\pm}~+~iA^3\sigma_3$$

and for $x~\rightarrow~\infty$ this gives $A~\rightarrow~iA^3\sigma_3$. Now $A^{\pm}\sigma_{\pm}$ and $A^3\sigma_3$ have distinct holonomy groups and are thus distinct points (moduli) in the moduli space. But this limit has a curious implication that the field $F~=~dA~+~A\wedge A$ for these two are the same and the moduli are not separable. In other words the moduli space for gravity is not Hausdorff. This is the most serious problem for quantum gravity.

I have written some on this, and later I might illustrate how this requires some interplay between Golay codes and Goppa codes. Goppa codes are a very different domain, where here the Hamming distance is computed from algebraic varieties, such as projective varieties or elliptic curves. The point set topolology is non-Hausdorff or Zariski in this system. This is a crucial element to quantum gravity, unless you want to work completely in an elliptical domain, but this physically would mean the universe has not tunnelled out of the vacuum with imaginary time into a real state with real time. So there is a lot more to this physics than finding representations of groups --- though that is an important part.

Lawrence B. Crowell

 

[Lawrence B. Crowell]

rntsai said ".. garett only claims that it [ E8 physics ] works for 1 generation (Distiler
says it works for none). ...".

Jacques Distler said ... .

As he went on to say
"... Note that we are not replacing commutators by anti-commutators for the “fermions.” ... that would ... correspond to an “e 8 Lie superalgebra.” Victor Kač classified simple Lie superalgebras, and this isn’t one of them. ...
the “fermions” will have commutators, just like the “bosons.” ...".
That is one reason that conventional supersymmetry is not used in the construction I outlined above.

So, just as Distler pointed Garrett in the direction of using Spin(16) (and so two copies of D4) in E8 instead of F4 in E8,
Distler has indicated that E8 physics should have 1 generation of fundamental fermions, with generations 2 and 3 being more composite than fundamental,
and
Jacques Distler's arguments, far from disrediting E8 physics, show the robustness of E8 physics modelling.

Tony Smith

If you have a bosonic field B and it is framed with a fermionic field F with the Grassmannian @ the $B~+~\theta F$ then the commutators of the bosonic field are extended to anticommutators of F. In supersymmetric theory the Grassmannians are parameters with the supergenerators give the SUSY commutator

$$[\theta Q,~{\bar\theta}{\bar Q}]~=~2\theta\sigma^\mu{\bar\theta}P_\mu$$

which is where Distler's comment about E_8 superalgebra comes from. If we use the Berezin integral

$$\int d(\theta)f(\theta)~=~f_1$$

then $f(\theta)~=~f_0~+~\theta f_1$ in a Taylor series using $\int d\theta\theta~=~1$. We might then generalize the Cl(7,1) Clifford basis as

$$\Gamma_\mu~=~\Gamma^0_\mu~+~\theta_\alpha f^\alpha_\mu$$,

where $f^\alpha_\mu$ acts on the connection term to give a spinor connection in the superalgebra. In this way the theory is extended to E_8(C) ~ E_8xE_8.

Lawrence B. Crowell

 

[MTd2]

Someone pointed this at cosmic variance:

"Should E8 SUSY Yang-Mills be Reconsidered as a Family Unification Model?" http://arxiv.org/PS_cache/hep-ph/pdf/0201/0201009v3.pdf

 

[Lawrence B. Crowell]

gauge theory in v*f contraction

The duality of a differential form and a vector $\vec v$, $\underline f$ is seen in the product

$$\vec{v} \underline{f}~=~v^i\vec{\partial_i}\underline{dx}^j f_j~=~v^if_i$$

Let us write the vector as ${\vec v}~=~e^{-2V}D_\alpha$ and the differential form as ${\underline f}~=~e^{2V}{\underline dx}^\alpha$. The differential $D_\alpha$ in general may be gauged. For V constant the duality is clearly ${\vec v}{\underline f}~=~1$ and in more general

$${\vec v}{\underline f}~=~1~+~(2D_\alpha V){\underline dx}^\alpha.$$

We now consider this system under the gauge transformation

$$e^{2V}~\rightarrow~e^{-i\Lambda^\dagger}e^{2V}e^{i\Lambda}$$

which for $\Lambda$ "small" gives a variation

$$\delta V~=~e^{2V}~+~i(e^{-2V}\Lambda~-~\Lambda^\dagger e^{-2V}~\simeq e^{-i\Lambda^\dagger}e^{2V}e^{i\Lambda} ~i(\Lambda~-~\lambda^\dagger)~+~\frac{i}{2}[V,~\Lambda~+~\Lambda^\dagger]$$

and the contraction transforms as

$${\vec v}{\underline f}~\rightarrow~v_if^i~+~e^{-i\Lambda^\dagger}\big(D_\alpha V~+~i(D_\alpha\Lambda~-~D_\alpha\Lambda^\dagger)\big)e^{i\Lambda}$$

For $F_\alpha~=~D_\alpha V$ a gauge potential this transformation of the contraction then defines the transformation of the gauge potential by

$$F_\alpha~=~F_\alpha~+~i(D_\alpha\Lambda~-~D_\alpha\Lambda^\dagger)$$

Lawrence B. Crowell

 

[MTd2]

Sorry... But I don't get where you are trying to go.

 

[Lawrence B. Crowell]

Sorry... But I don't get where you are trying to go.

I have this idea cooking in my head, so I am bouncing it off here. It concerns a general approach to framing fields. This is just the preliminary parts here, and I am slamming out some of the notation --- I hope I get the indices etc more or less right.

A differential form and its dual vector $\vec v$, $\underline f$ is seen in the product

$$\vec{v} \underline{f}~=~v^i\vec{\partial_i}\underline{dx}^j f_j~=~v^if_i$$

What I did was to assume that the differential form had the form ${\underline f}~=~e^{V}{\underline dx}$. The contraction is then

$$v^i\vec{\partial_i}\underline{dx}^je^{V_j}~=~v^ie^{2V_j}{\partial_i}\underline{dx}^j~+~v_i(\partial_iV_j){\underline dx}^j.$$

Then consider a transformation $e^{V}~\rightarrow~e^{-i\chi^\dagger}e^{V}e^{i\chi}$ which gives a variation in V as

$$\delta V~=~i(\chi~-~\chi^\dagger)~-~{i\over 4}[(\chi~+~\chi^\dagger),~V]$$

and the deviation in the contraction is

$$\langle v,~F\rangle~\rightarrow~v_ie^{V_i}~+~e^{-i\chi^\dagger}\big(\partial_iV~+~i\partial_i(\chi~-~\chi^\dagger)\big)e^{i\chi}$$

We might now want a form of this contraction which is gauge covariant. So to do this we back track and consider $y^i~=~x^i~+~\lambda^\alpha\sigma^i_{\alpha{\dot\beta}}\lambda^{\dot\beta}$. We then have that

$$dy^i~=~dx^i~+~ d\lambda^\alpha\sigma^i_{\alpha{\dot\beta}}\lambda^{\dot\beta}~+~\lambda^\alpha\sigma^i_{\alpha{\dot\beta}}d\lambda^{\dot\beta}$$

The differential operators dual to this system are

$$\partial_i,~D_\alpha~=~\partial_\alpha~+~i\sigma^i_{\alpha{\dot\beta}}{\bar\lambda}^{\dot\beta}\partial_i$$

Then for the vector ${\underline f}~=~e^{V}{\underline dy}$ there exists a differential form contraction will result in

$$\omega_A~=~\sigma^i_{\alpha{\dot\beta}}\partial_i V d\lambda^{\dot\beta}~+~d\lambda^\alpha\sigma^i_{\alpha{\dot\beta}}\lambda^{\dot\beta}~+~\lambda^\alpha\sigma^i_{\alpha{\dot\beta}}d\lambda^{\dot\beta},$$

where the left index A runs over i and $\alpha$. This is analogous to the differential forms $\omega^0~=~\gamma(dx^0~-~u^0 dx)$ and $\omega^i~=~\gamma(dx^i~-~u^idt)$ corresponding to special relativity. This is a Finsler bundle, and from this a generalized lifting condition (an Euler-Lagrange equation constraint) will be derived for the framing of fields.

An invariant vector for the contraction $v^\alpha (D_\alpha\Phi) {\underline d\lambda})$ for $\Phi~=~(1/4) {\bar D}{\bar D}V$ will define under the contraction

$$\Phi_\alpha~=~D_\alpha\Phi~=~\frac{1}{4}{\bar D}{\bar D}D_\alpha V$$

which if we impose the holomorphic condition $D_\alpha\chi^\dagger~=~0$ then this is gauge invariant for $V~\rightarrow~V~+~\chi~+~\chi^\dagger$. In general

$$\Phi_\alpha~=~\frac{1}{4}{\bar D}{\bar D}e^{-V}D_\alpha e^V$$

which is also gauge covariant as $\Phi_\alpha~\rightarrow~e^{-i\chi}\Phi_\alpha e^{i\chi}$

 

[MTd2]

How does it relate to this thread?

 

[Lawrence B. Crowell]

How does it relate to this thread?

I think that the whole framing of fields should be generalized. I think that Garrett's work is in some ways just the beginning.

Lawrence B. Crowell

 

[MTd2]

Ok, but I would you mind giving an intuitive reason to understand your choice for this generalization?

 

[Lawrence B. Crowell]

Ok, but I would you mind giving an intuitive reason to understand your choice for this generalization?

I think that what is required is a general framing system for fields, which remove the sharp distinctions between inertial and noninertial frames. The radiation reaction of an accelerated charge is derived from the Lamour radiation formula for an oscillating charge. This is an important key: The radiation reaction is due to a changing acceleration, such as due to the orbit of a charged particle in a bound state. Another example of a quantum physics on an accelerated from is Unruh radiation, which is calculated for a constant acceleration.

The radiation reaction of an accelerated charge is due to the interaction of a charge with its own field. This of course leads to some conundrums. The Coulomb attraction between two charges diverges as the distance between the charges goes to zero. Hence the self-energy due to the charge of an electron will be infinite. It might be simply declared that an electron does not interact with its own field, but this leads to open questions, in particular a charged particle will resist changes in its momentum more than an uncharged particle --- the field contributes to inertia. So we might then say that even if the electron interacts with its field it does so in a spherically symmetric manner and the region "at infinity" pushes back in a way as to cancel out this self-repulsion. But a naive interpretation of this will mean that a charged particle under a small perturbation will have its "self-force" canceled in one direction more than another, so the electron can accelerate to v ---> c by riding on its own field. Clearly that does not happen, and one way out of this was the Wheeler-Feynman absorber theory with positied advanced potentials coming in from the future that in a Lorentz invariant manner prevented these spurious solutions.

The Unruh radiation is due to the interaction of a body with the vacuum state. The motion of a uniformly accelerating object is defined within a Rindler wedge which partitions off a corner of spacetime as what the body on the accelerated from can have complete causal contact with. An instanteous surface of simultaneity on the accelerated frame will have field amplitudes on it which are unique within the Rindler wedge, but across the split horizon beyond the wedge spatial surfaces intersect, which means that Cauchy data is not uniquely specified there. So fields or quanta within the Rindler wedge which are nonlocally correlated on any spatial surface of simultaneity will be entangled with quanta across the horizon and in a way which breaks up the time ordering of fields. This ambiguity or "scrambling" means that fields accelerated on the frame will exhibit a thermal distribution of quanta. A body on an accelerated frame will then come to a thermal equilibrium with a temperature corresponding to this "Unruh radiation."

Are these two related? Probably, but in ways not currently well understood. This may point to a central problem with the foundations of physics. Theories are formulated on a frame bundle --- something which has persisted since the days of Newton. Newton's first law dictates that physics is to be observed from inertial frames. The Einstein equivalence principle operates to give a sharp distinction between inertial frames and accelerated frames. Yet recent developments at least suggests that a comprehensive theory of quantum gravity, and one which can account for the behavior of gauge fields in accelerated frames, may well require a more general formulation of physics on a more general frame construction which places inertial and noninertial frames on a commensurate basis.

Lawrence B. Crowell

 

[MTd2]

Larence, have you seen STVG? You might look at its equations and think very seriously about it. The preditive power is superior to any dark matter model, and can also finely describe the Train Wreck Cluster (Abel 520), which isn´t very well modeled by dark matter, and the Bullet Cluster.

http://arxiv.org/PS_cache/gr-qc/pdf/0506/0506021v7.pdf

And its predictive tests:

http://arxiv.org/PS_cache/arxiv/pdf/0710/0710.0364v4.pdf

http://arxiv.org/PS_cache/arxiv/pdf/0708/0708.1264v3.pdf

http://arxiv.org/PS_cache/astro-ph/pdf/0702/0702146v3.pdf

I think it has some relation to your ideas. Check this one for a sanity test: http://arxiv.org/PS_cache/arxiv/pdf/0710/0710.3415v2.pdf

 

[Lawrence B. Crowell]

Thanks for the references. I have heard of these theories by Moffat. It is similar to my idea that gravitation involves a hierarchy of spins.

Unfortunately I have become a bit tied up with some things so I have not been able to continue here much. I hope to break out more on my idea about the bundle structure of framing this weekend.

Lawrence B. Crowell

 

[John G]

rntsai: "Now a3 also has a d2 subalgebra, under that the 15 breaks down as 3+3+4+4+1; the 3+3 is d2 itself (rotations/boosts), the 4 is translation, the other 4 works out to special conformal operations; the 1 is scaling or dilation."

Tony Smith: "one d4 includes a conformal d3 = a3 = SU(2,2) = Spin(2,4) Conformal MacDowell-Mansouri gravity that acts on the 4-dim physical spacetime part of the 8-dim Kaluza-Klein"

Lawrence B. Crowell: "Spin(8) embeds spin(6) as well. So it appears possible to define a conformal theory of gravity. Conformal gravity is a "good thing."

Garrett: "Regarding conformal gravity: in this E8 theory the frame and Higgs are literally multiplied in the frame-Higgs part of the connection. Because of this, the scale of the Higgs and the scale of the frame are a shared degree of freedom -- the conformal degree of freedom is described redundantly by the frame and Higgs scale."

http://www.space.com/scienceastronomy/080229- spacecraft -anomaly.html

Seems like a job for conformal gravity or as I said it in another forum, "conformal dark energy unimodular relativity". Are you listening, David Finkelstein? Grumble, grumble.

 

[MTd2]

This anomaly was first noticed in 1990, in a Galileo flyby, his is anomaly is said to be descbided http://en.wikipedia.org/wiki/Flyby_anomaly . It's not something really new, so there should be something more to that article. Besides, near Earth asteroids also suffer this effect.

 

[CarlB]

I've typed up a new preon model that should be natural to get E8 style quantum numbers here:
http://carlbrannen.wordpress.com/2008/03/03/pascals

 

[Lawrence B. Crowell]

I am not sure if this is evidence of conformal gravity. These anomalous flyby trajectories may be due to unknown aspects of the mass distribution in the Earth. At least that has to be ruled out first. Also I don't consider the Pioneer anomaly as anything worth considering. If this were evidence of new physics it should be impacting the Voyager crafts as well. This sounds like an "instrument error," since it depends on two identical systems. A recent pop-science report on these is at

http://www.space.com/scienceastronomy/080229- spacecraft -anomaly.html

The SU(2,2) or spin(2, 4) has 15 elements (3+3) + (4+4)+ 1 where the 3+3 are boosts and rotations and the other elements are the dilaton fields. The system exists in the space $R^{4,2}$ with the metric

$$ds^2~=~-du^2~-~dt^2~+~dx^2~+~dy^2~+~dz^2~+~dv^2,$$

where this "light cone" is $PR^{4,2}$ of five dimensions. Then if we consider the plane $v~-~u~=~F$, then for fixed F this defines a hyperboloid which is the spacetime with the standard metric. This spacetime is determined by the intersection of the lightcone and the plane ${\cal P}\cap PR^{4,2}$Now we can "fiddle" F as we see fit, and define a different hyperboloid which are all identical under a rescaling, so long as the plane does not go through the origin of the 5 dimensional lightcone. The plane which goes through the origin defines conformal "infinity."

In four dimensions the action for such a theory with a dilaton field $\phi$is

$$S~\simeq~\int d^4x\Big(\sqrt{-g}\kappa\phi^2R~+~\frac{1}{2}|\nabla\phi|^2~-~V(\phi)\Big),$$

is reduced the problem to a scalar field on a four-manifold. The fifth dimension defines $\phi$ as a dilaton field that acts on the embedded four dimensional spacetime or D4-brane. For the scalar potential $V(\phi)~=~-(1/2)m^2\phi^2~+~(\sigma^2/4)\phi^4 F_{ab}F^{ab}$ defines a Klein-Gordon wave equation for $\phi$

$$\partial_a\partial^a\phi~=~-m^2\phi~+~\sigma^2\phi^3 F_{ab}F^{ab},$$

where $F_{ab}$ is a Kaluza-Klien U(1) field tensor.

Now the dilaton field presumably after inflation "settles" down to a configuration so that $\nabla^2\phi~=~0$. But this field is multicomponent and maybe a "Goldstone" part is removed and a component remains with a small field amplitude. So for 9 components, eight of which might be identified as the Higgs fields, the remaining field might have a residual component with some small amplitude.

So this sort of physics certainly can be tested. Maybe this residual scalar field amplitude gives a Brans-Dicke type of gravity on the classical level. But of course we have to eliminate mass distribution effects first.

Lawrence B. Crowell

 

[Tony Smith]

Lawrence B. Crowell said that he does not "... consider the Pioneer anomaly as anything worth considering. If this were evidence of new physics it should be impacting the Voyager crafts as well. ...".

No. That is not true.
According to a google cache of an Independent UK 23 September 2002 article by Marcus Chown:
"... The Pioneers are "spin-stabilised", making them a particularly simple platform to understand. Later probes ... such as the Voyagers and the Cassini probe ... were stabilised about three axes by intermittent rocket boosts. The unpredictable accelerations caused by these are at least 10 times bigger than a small effect like the Pioneer acceleration, so they completely cloak it. ...".

Tony Smith

 

[Kea]

These anomalous flyby trajectories may be due to unknown aspects of the mass distribution in the Earth.

Yes, Louise Riofrio has suggested that the black hole at the centre of the Earth explains the anomalies.

 

[Lawrence B. Crowell]

"... The Pioneers are "spin-stabilised", making them a particularly simple platform to understand. Later probes ... such as the Voyagers and the Cassini probe ... were stabilised about three axes by intermittent rocket boosts. The unpredictable accelerations caused by these are at least 10 times bigger than a small effect like the Pioneer acceleration, so they completely cloak it. ...".

Tony Smith

There might possibly be something with new physics going on, but this acceleration is not measured by a controlled experiment. We have two old spaceprobes heading out of the Oort region which have a small anomalous acceleration. Two other spacecraft of a different design do not exhibit this. So there could be a range of plausible explanations for this which can't be eliminated easily. It also again appears to be device dependent. There might be a range of possible reasons for this: a tiny leaks from a tank, asymmetry in how optical or IR radiation is effecting off and heating surfaces, and ... . In an experiment you have to isolate variables to remove competing influences. We are not able to do this with the Pioneer craft, which means we simply can't determine much of anything about the source of this anomalous acceleration.

Lawrence B. Crowell

 

[Lawrence B. Crowell]

Yes, Louise Riofrio has suggested that the black hole at the centre of the Earth explains the anomalies.

I hope not. A mini black hole eating away the core of the Earth is not comforting. If the thing were at the center of the Earth I would suspect its gravitational influence would be radial. Then again the thing might be weaving a path through the Earth's interior eating it out like a worm in an apple. In that case there might be a time dependent gravitational anomaly.

Black holes are thermodynamically unstable. Consider a black hole has a mass $M$ that determines a temperature $T~\sim~A/4$, for the area $A~=~2\pi r^2$ and $r~=~2M$. Further consider the black hole as having the same temperature as its environment, which is easily modeled as the CMB. Then if the black hole absorbs a quanta with a mass $\delta m$ or emits by Hawking radiation a quanta of the same mass the black hole temperature deviates from that of its environment. Black hole thermodynamics does not permit equilibrium in the standard sense. The effective heat capacity of spacetime is negative.

This means a black hole in the Earth's interior would either emit radiation and explode, or it would eat away at the planet and turn it into a black hole the size of a ball bearing, or in the case of a Jovian giant about the size of a basketball. I don't remember what the Earth's interior temperature is, I think it is around 5000deg C, so the black hole would probably either quantum decay quickly or devour the planet. That temperature zone has a narrow range where a black hole could be quasi-stable. I suppose we will have to wait and see if any of these extrasolar planets identified by Doppler wobbling turn out to be little black holes.

Lawrence B. Crowell

 

[MTd2]

Two other spacecraft of a different design do not exhibit this.

You can´t just cut voyager's propellers for this experiment. They are still functioning and returning useful scientific results where they are, the heliopause. There are much better ways to make this experiment, such as attaching probes to comets and studying their trajectory with high precision telemetry.

 

[Lawrence B. Crowell]

I've typed up a new preon model that should be natural to get E8 style quantum numbers here:
http://carlbrannen.wordpress.com/2008/03/03/pascals

I suspect that systems of inequivalent Hadamard matrices will give a triality on the Jordan algebras $J^3(V)$ of 27 dimensions. There is then a fundamental representation of 27-dimensions, where three copies of these modulo three dimension for the $Z_3$ gives the 78 dimensions of $E_6$. Might the MUB's be a way of constructing a triality condition on the Jordan algebra to define the 3-cyclicity on the E_6?

From there this might be extended to $E_8$ lattices and sporadic groups. The Hamming code $H_8$ can be used to construct $E_8$, with the Weyl group matrix $W(E_8)$. This construction involves the Kissing number (minimal sphere packing condition in 8-dim) with the icosian pairing of quaterions $diag[Q_4,~Q_4]$. This gives [itex]2^4\times 14~=~224[/tex] minimal vectors $((\pm 1/2)^4,~0^4)$, and just as in the Grossett polytope these give the 240 lattice with the 8 additional weights for 248. A triality structure on the Hadamard matrices might be one natural way to construct a $\Lambda_{24}$.

I am not sure what bearing this has on the preon models you are working up here. The Pascal triangle construction you are arguing for look like some polynomial system you are constructing form the MUB system. I will have to look at this more closely. I am still doing a bit to get a working knowledge of Bengtsson papers.

Lawrence B. Crowell

 

[Kea]

Black holes are thermodynamically unstable.

Given that the justification for black holes in the Earth is a quantum gravitational cosmology, in which cosmic time is directly linked to the emergent classical thermodynamics of black holes, these semiclassical arguments do not necessarily hold. Admittedly, much has yet to be done.

P.S. Hadamard matrices are cool.

 

[Lawrence B. Crowell]

You can´t just cut voyager's propellers for this experiment. They are still functioning and returning useful scientific results where they are, the heliopause. There are much better ways to make this experiment, such as attaching probes to comets and studying their trajectory with high precision telemetry.

Voyager's PGU (propulsion guidance unity) does not run continuously and was only used to tweak the trajectory of the craft for insertions through orbital windows. I am not sure if the system is even usable any more.

The problem with the whole Pioneer anomaly is that this is an unintended unconcontrolled experiment that measures some sort of accelerating force. The problem is that I see no way to conclusively eliminate device dependencies in order to conclude that there is some sort of real physics here.

Lawrence B. Crowell

 

[MTd2]

Voyager's PGU (propulsion guidance unity) does not run continuously and was only used to tweak the trajectory of the craft for insertions through orbital windows.

"The identical Voyager spacecraft are three-axis stabilized systems that use celestial or gyro referenced attitude control to maintain pointing of the high-gain antennas toward Earth."

http://voyager.jpl.nasa.gov/ spacecraft /index.html

It is still working too keep the antenna aimed at earth. That small accelaration always change the orbit enough so much that it invalidates any possible attempt to measure the anomaly.

 

[Lawrence B. Crowell]

Given that the justification for black holes in the Earth is a quantum gravitational cosmology, in which cosmic time is directly linked to the emergent classical thermodynamics of black holes, these semiclassical arguments do not necessarily hold. Admittedly, much has yet to be done.

P.S. Hadamard matrices are cool.

The Hawking result with black hole radiation requires a classical or semi-classical metric back reaction. So the theory is approximate. Yet I imagine that it is a pretty good theory for the quantum radiance of black holes with a mass $M~>>~M_p$.

Entries in Hadamard matrices can be defined according to sets of group homomorphisms. You can then define a "tower" or succession of such matrices in a recursive system of these homomorphisms. For the $n^{th}$ map matrix elements $M_n$ define the Hadamard matrix as

[tex]

F_{2^n}~=~M^\dagger_n M_n.

[/itex]

So Hadamard matrices can be constructed in a manner similar to partial isometries used in some scattering theory. This also defines the Hadamard matrix as an error correction code of rank n.

Hadamard matrices are also used to describe the non-unitary equivalency of vacua in black hole radiation and the Unruh effect. So error correction codes, Hadamard matrices, etc are I think required tools in one's tool kit to look at quantum gravity. I started a thread here on frame bundles, which is centered to a degree around these issues. Life suddenly got a bit busy with other things.

Lawrence B. Crowell

 

[Lawrence B. Crowell]

"The identical Voyager spacecraft are three-axis stabilized systems that use celestial or gyro referenced attitude control to maintain pointing of the high-gain antennas toward Earth."

http://voyager.jpl.nasa.gov/ spacecraft /index.html

It is still working too keep the antenna aimed at earth. That small accelaration always change the orbit enough so much that it invalidates any possible attempt to measure the anomaly.

The use of gyroscopic aiming is an internal force or torque on the craft. Assuming that Newton holds then this should not provide an external force on the craft. I might have to look this up, but the PGU on the Voyagers must be either used up or nearly so. They are not used to maintain any constant thrusting or used to aim the craft. The fuel and oxidant tanks on these things are like the pressurized cans of products we buy in the store --- use them enough and they eventually run out.

Lawrence B. Crowell

 

[MTd2]

I might have to look this up, but the PGU on the Voyagers must be either used up or nearly so.

According to the article on that page it ends between 2010-2012, if I am not mistaken.

Changing the subjet, really, between dark matter, superstrings, black holes everywhere, I think that Mosfat theory is nice, mathematicaly conservative, and fits nicely just too many different phenomena. Myabe that´s a better starting point, in the macrocosmic sense, to quantum gravity than GR. At least, I will try to persuit that path.

 

[Lawrence B. Crowell]

According to the article on that page it ends between 2010-2012, if I am not mistaken.

I think that Mosfat theory is nice,

So the craft is still alive in a sense. I suppose they must have some method for maintaining a telemetered connection with Pioneer as well.

As for Mosfat, what came to mind was MOSFET which is a transister. I tried looking this up but didn't find anything. In fact in a general search it appears there is some version of electronics called a Mosfat.

Lawrence B. Crowell