Emergent Gravity or Potpourri of Nonsense

[Newton]

Tony (Smith) once got John Baez to agree that E6/F4 would be great for quantization of everything not just gravity.

This forum is quite interesting. I agree with the above. I noticed that the product of two symplectic variables (bivectors in polar coordinates) is an E6 octonion and a scalar (zero order PDE - translational group) that produces constant acceleration thru the exp map. In other words - gravity.

And E6 has torsion and is a polygon (for simple one dimensional interaction between two Bosons) when the Boson's orbit in SP(4) is quantized.

What makes this a bit tricky is that Bosons require an infinite dimensional manifold - they have a Kac-Moody algebra. So the solution is a superposition of polygons analogous to the superpostion of harmonic functions with complex vars.

So as a gross overstatement - I'm suggesting that Fermions are comprised of two extremely high energy Bosons.

(And you thought Tony was the crazy one)

Newton

 

[Newton]

Regarding Rodrigues' arguments... (the original topic of this thread)

The key is that Rodrigues doesn't know that phase-space manifolds only exist in 1, 2, 4 and 8 dimensions. Riemannian manifolds in 3-dim have a zero divisor. He needs to unlearn his differential geometry!

 

[ark]

The key is that Rodrigues doesn't know that phase-space manifolds only exist in 1, 2, 4 and 8 dimensions.

You see, it is like with Laplace-Beltrami operator. You have one definition, and other mathematicians - who are experts and authors of monographs, have different definitions. So what you wrote above does not mean anything unless you provide your complete and precise definition of a "phase-space manifold". Can you do it for me, here, so that we can discuss your point in a precise way?

 

[Ruth]

I'm back from about 40 days and 40 nights of self-imposed computer exile... I like Jack too but for me Jack is kind of like Carl Jung, it's best not to read him in his own words.

I don't understand, why is it best not to read him in his own words, doesn't he own them? What could be a better way to understand a person if not "straight from the horse's mouth".

 

[ark]

Jack's own words:

Look Dan, you don't get the Enemy Within is quickly destroying America. Look at the Mexican Illegal insurgency in the streets now led by Iran, Castro, Chavez with American Liberals with Mental Disorders. We have been invaded and the Iraqi insurgency is already in the streets of America. It's outside my door in San Francisco. It's time for COUNTER-REVOLUTION!

tell all about him, indeed. At least he is not trying to disguise himself. It is clear whom is working for. And this is what I like about him. Of course there is a method in his madness, but seing through this method is very informative and serves well as an educational exercise.

 

[John G]

I'm back from about 40 days and 40 nights of self-imposed computer exile... I like Jack too but for me Jack is kind of like Carl Jung, it's best not to read him in his own words.

I don't understand, why is it best not to read him in his own words, doesn't he own them? What could be a better way to understand a person if not "straight from the horse's mouth".

Jack mixes in a lot of math and terminology that I'm not familiar with so for me I need the opinion of someone who uses words and math ideas I'm more familiar with. With Jung I was told it's best to start out reading the words of one of Jung's followers like June Singer. For Jung I think the problem is Jung being from both a different country and a different time period than me plus he wasn't writing for the general public. I do read Jack's words and have read Jung, certainly nothing wrong with doing that also.

 

[John G]

Tony (Smith) once got John Baez to agree that E6/F4 would be great for quantization of everything not just gravity.

This forum is quite interesting. I agree with the above. I noticed that the product of two symplectic variables (bivectors in polar coordinates) is an E6 octonion and a scalar (zero order PDE - translational group) that produces constant acceleration thru the exp map. In other words - gravity.

Like Ark, I may need you to explain your use of terminology as compared to others (like Tony). E6/F4 is a 26-dim bosonic string type of gravity for Tony. This can be thought of as a Triality of octonion spaces (for spacetime, matter, antimatter). The octonion for Tony comes from the vector part of Cl(8) and the zero-vector would be the Higgs scalar. The gravity translations would be part of the bivectors of Cl(8).

And E6 has torsion and is a polygon (for simple one dimensional interaction between two Bosons) when the Boson's orbit in SP(4) is quantized.

There is torsion for Tony which I find easier to think about using the Cl(8) bivectors rather than the 26-dim gravity. Tony likes a lattice for boson interaction but it's an E8 polytope lattice (4-dim hyperdiamond lattice after dimensional reduction).

What makes this a bit tricky is that Bosons require an infinite dimensional manifold - they have a Kac-Moody algebra. So the solution is a superposition of polygons analogous to the superpostion of harmonic functions with complex vars.

A superposition of lattices and the complex octonionic spacetime are both useful structures for Tony though most fundamentally Tony does not have to go to infinite dimensions/information (perhaps related to the sporadic simple group exceptions to the need for infinite families?)

So as a gross overstatement - I'm suggesting that Fermions are comprised of two extremely high energy Bosons.

(And you thought Tony was the crazy one)

You're not too crazy, modeling a boson as a fermion pair or a fermion as a boson pair is Tony-like and with Planck distance lattice spacing it would be high energy.

 

[ark]

And E6 has torsion and is a polygon

How E6 is a polygon? What is your definition of a polygon?

If you go to:

http://mathworld.wolfram.com/Polygon.html

you find that: Polygon is "A closed plane figure with n sides. " I don't think E6 satisfies this definition ;) Unless you have your own definition of E6. If so, what is it?

 

[Newton]

I did this a while ago, but as I remember, one can take an orbit on a SP(4) manifold described by a quaternion (fixed radii, proportional angular velocities, and add another radius and orthogonal angular velocity (to the other two) to get an orbit in E(6). If the last radius and angular velocity is set to the right ratio of the other two (so that the 'knots' are removed) the trajectory is flat (the donut shaped SP(4) orbit is flattened), you get a polygon.

So for at least the special case when the 'knots' were unwound , I got polygons on this only possible (I believe) mapping to Euclidean space.

If you recall differential geometry, one flattens the OU manifold (strong solution of Langevin with torsion) to get the Navier-Stokes PDE, but here I added a radius and rotation to flatten the geometry.

 

[ark]

Well you did not answer my question. Can you answer it? Please ....

 

[ark]

Well you did not answer my question. Can you answer it? Please ....

How E6 is a polygon? Do you know what E6 is at all?

E6 is a Lie group - see

http://en.wikipedia.org/wiki/E6_%28mathematics%29

How A Lie group can be a polygon????

Perhaps you mean:

The E6 polytope is the convex hull of the roots of E6. It therefore exists in 6 dimensions; its symmetry group contains the Coxeter group for E6 as an index 2 subgroup.

But the polytope is not the same as polygone, and the convex hull of the roots of E6 is not the same as E6!!!

 

[Newton]

Well you did not answer my question. Can you answer it? Please ....

How E6 is a polygon? Do you know what E6 is at all?

E6 is a Lie group - see

http://en.wikipedia.org/wiki/E6_%28mathematics%29

How A Lie group can be a polygon????

Perhaps you mean:

The E6 polytope is the convex hull of the roots of E6. It therefore exists in 6 dimensions; its symmetry group contains the Coxeter group for E6 as an index 2 subgroup.

But the polytope is not the same as polygone, and the convex hull of the roots of E6 is not the same as E6!!!

How can an Octonionian manifold not be a polygon or polyhedron?

Lie groups are manifold(s) and operation(s). There are four types for Hamiltonian flows.

Translational - inifinite abelian, scalar (the old Galilean group from classical mechanics)
Rotational - finite abelian, vector in polar coordinates
Symplectic - finite non-abelian (non-communative algebra from Euclidean space) and torsion-free, Bi-vector (quaternion)
Octonionian - fixed non-abelian, Bi-vector x Bi-vector, only has identity operation.

Everytime a manifold becomes more robust (actually constrained) an operation is lost from it's algebra. The only operation left for the Octonions is the identity, which means E(6) can only do a fixed 'shift' in one of the allowable directions. For a E(6) flattened to 2-D, I see a polygon if mapped from a quantized symplectic orbit. What other object has that symmetry?

A E(6) manifold will map to a polyhedron in 3-D.

Remember, the octonions are extremely constrained Lie groups!

 

[ark]

Interesting development in Jack's Sarfatti saga:

I wrote to Jack:

On 20 Nov 2006 at 20:53, Jack Sarfatti wrote:

> The problem is that Waldyr is a strict formalist and does not think
> physically. Waldyr, like all mathematicians, gives to much weight to
> rigorous proofs.

Jack,

Sorry, but I must say this: sometimes you talk nonsense. If you use certain mathematical terms and concepts, you are supposed to know their precise meaning and obey the rules of mathematics.

Or, if you wish, state explicitly at the very beginning:

"I, Jack Sarfatti, am going to use mathematics in my own creative way, and I am not going to obey neither the logic nor the precision required. The fact is that I have neither wish nor time to study the required mathematics, and I do not claim that my papers have ANY mathematical meaning at all. They may even contain serious mathematical errors. They may lead other people astray - I do not care, as I have other priorities."

If you start your papers with such an preamble - no one will ever criticize the lack of consistency or misleading/erroneous statements or formulas, you will be happy, and Waldyr will be able to use his time more creatively.

When you write something like 2+2=5, then thinking physically may indeed lead you or other people to new discoveries. Either about numbers or about you :)

Best wishes,

ark

and Waldyr Rodrigues wrote today:

Dear Jack,

1) Jack said: "Meantime mediorcre hack-minds like Hillman and Singer et-al use Waldyr's "potpourri of mathematical nonsense" to smear me on Wikipedia!"

Well, I regret to say again:

As wrote in my paper (gr-qc/0602111)) your gr-qc/0602022 paper (all versions) is indeed (and unfortunately) a potpourri of mathematical nonsense. And indeed, let me propose the following challenge:

If you find a mathematician (with more than 15 papers reviewed in Mat. Rev.) that says that to your arXiv paper (gr-qc/0602022) is not a potpourri of mathematical nonsense and publish his notes in the arXiv, I will send US$ 1000.00 to him and equal amount to you. If he found errors in my arXiv paper (gr-qc/0602111) with criticisms to your paper I will send to him additional US$ 1000.00.

2) Also, please, substitute one of my previous observations (with misprints and grammatical errors), namely: "It is true that your suggestion for the introducing the tetrad fields is based on physical ideas and they are intuitively correct, but this does not means that you have a correct theory'' by the following one: ''It is true that your suggestion for introducing the tetrad fields is based on physical ideas and even if they are intuitively correct to you, this does not mean that you have a correct theory''.

3) Also, if one day you or someone else find a way to travel in time, and construct a time machine, please, do not forgot to send to me a copy of this e-mail which must arrive one day before the one when I posted my paper (gr-qc/0602111). In that case I will not post it, and so you will not have any problems with Hilmann, Singer, Nick and so on. A better idea is: please, send a copy of this e-mail to me one week before the day I posted it, for in this case I will not loose my time writing it.

Best regards,
Waldyr

to which Jack replied (I am quoting only the interesting part)

[...] The laymen who read Wikipedia are not able to understand what you write in your archive paper - all they see is the smear of me gleefully cited by my political and personal enemies. That's the point here. The real issue is UFO Disclosure and the reality of signal nonlocality as shown by Puthoff and Targ in the CIA-funded experiments as an explanation of the paranormal including the use as time travel weapons.

[...]

"If we knew what it was we were doing, it would not be called research, would it?" - Albert Einstein

to which I replied

Jack, this is the most idiotic quotation to support your math. The monkey certainly does not know what he is doing. Do you call it - having Einstein as your support - "research?"

Please, Jack, be serious, and think before writing such things.

If you want to be treated seriously, you need to behave seriously. You need to use logic.

Best wishes,

ark

 

[Newton]

I had some time so I read Jack Sarfatti paper on gravity as well as the Waldyr A. Rodrigues' review. I tend to support Sarfatti's ideas and think he's on the right track.

Sarfatti's math and approach was unclear at best, but Rodrigues presented only 'junk' math in rebuttal. I frankly don't understand why Rodrigues, with an obviously limited math background, would comment on something out of his league...

 

[shijing]

I'll admit right off that I'm way out of my league on this topic, but I noticed an article in New Scientist about it today, so I thought I would post it in case it might be of interest to anyone out there. This seemed to be the best thread on which to continue the topic. The information below is about a particular theory of gravity by Erik Verlinde, in which he postulates that it is an emergent property, and part of his theory apparently deals well with dark energy, which came up in the recent 1/29/10 session. The following is an abstract from his recent paper:

http://arxiv.org/abs/1001.0785

Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.

Below is a bit more about Verlinde and his theory:

http://en.wikipedia.org/wiki/Gravity_as_an_entropic_force

Gravity as an entropic force

The hypothesis of gravity being an entropic force has a history that goes back to the studies on black hole thermodynamics by Bekenstein and Hawking in the mid-70s of the twentieth century. These studies suggest a deep connection between gravity and thermodynamics. In 1995 Jacobson demonstrated that the Einstein equations describing relativistic gravitation can be derived by combining general thermodynamic considerations with the equivalence principle. Subsequently, other physicists have further explored the link between gravity and entropy.

Verlinde's statistical description of gravity as an entropic force leads to the correct inverse square distance law of attraction between classical bodies.

End 2009, Verlinde disclosed a conceptual theory that describes gravity as an entropic force. This theory combines the thermodynamic approach to gravity with 't Hooft's holographic principle. If proven correct, gravity is not a fundamental force, but an emergent phenomenon which arises from the statistical behaviour of microscopic degrees of freedom encoded on a holographic screen.

Verlinde's suggestion of gravity being an entropic phenomenon attracted considerable media and weblog exposure, and led to immediate follow-up work in cosmology, the dark energy hypothesis, cosmological inflation and loop quantum gravity. Also, a specific microscopic model has been proposed that indeed leads to entropic gravity emerging at large scales.

http://en.wikipedia.org/wiki/Erik_Verlinde

Erik Peter Verlinde (born 21 January 1962, Woudenberg) is a Dutch theoretical physicist and string theorist. He is the identical twin brother of physicist Herman Verlinde. The Verlinde formula, which is important in conformal field theory and topological field theory, is named after him. His research deals with string theory, gravity, black holes and cosmology. Currently he works at the Institute for Theoretical Physics at the University of Amsterdam.

At a symposium at the Dutch Spinoza-instituut on 8 December 2009 he introduced a theory that derives Newton's classical mechanics. This was followed by the publication of 'On the Origin of Gravity and the Laws of Newton' on 6 January 2010. In his theory gravity exists because of a difference in concentration of information in the empty space between two masses and its surroundings. He does not consider gravity as fundamental, but as an emergent phenomenon that arises from a deeper microscopic reality. He said in an interview with the newspaper de Volkskrant, "On the smallest level Newton's laws don't apply, but they do for apples and planets. You can compare this to pressure of gas. Molecules themselves don't have any pressure, but a barrel of gas has."

Verlinde's approach to explaining gravity apparently leads naturally to the correct observed strength of dark energy. Previous failures to explain its incredibly small magnitude have been called "the greatest embarrassment in the history of theoretical physics".