A Geometrical Approach Towards A Theory of Everything by Ray B Munroe

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Hi Ray,

I've been looking at black hole entropy trying to get some some ideas. I figure that the event horizon can represent the c_1 brane (speed of light for standard space). At the event horizon, the brane has a maximum information content for its surface area. I'd like to hide my c_2 brane, c_3, etc inside of the black hole. A c_2 brane with a speed of light c'=2c, should be able to contain the same information content inside of a smaller surface area, right? Or, at the c_1 surface area, the c_2, c_3... have lots of information content to spare. I'm guessing it might be possible to calculate the surface areas at which these branes becomes black holes. I have to assume that the Boltzman's constant remains unchanged. I expect the charge might scale with the speed of light, but I haven't worked that out yet. For the Planck length, G and h are there. I'd like to scale one of them to see what happens.

I'll let you know if I discover anything really interesting.

Ray Munroe

Dear FQXi Friends,

I am concerned that some of you may think my essay is too complicated. This is a short explaination that I have reposted from James Putnam's blog area.

In my conclusion, I said "One version of Occam's razor says "Plurality ought never be posited without necessity."... Are Beauty and Symmetry necessary reasons to trump Simplicity? If Simplicity always trumps Necessity, then we should be satisfied with the "ugly but practical" Standard Model and a separate General Theory of Relativity, and we need to stop talking about such "foolishness" as Theories of Everything or Not Everything."

I know that my ideas look complicated, but I think it is analogous to finding the least common denominator (LCD) so that we can add fractions. If you wanted to add

[math]1/2 1/3 1/6

[/math]

you would find the LCD = 6, so that

[math]1/2 1/3 1/6=6/6=1

[/math]

and the apparently complicated is simplified. Likewise, if we want to unify the four known forces properly into one algebra, then that one algebra must be at least as large as the sum of its individual components. It looks more complicated because it is bigger and predicts new stuff, but the overall picture is simplified - the fundamental forces are placed on a compatible foundation.

Does a 12-dimensional model seem like "overkill"?Garrett Lisi's 8-dimensional E8 TOE seemed to be a reasonable approach, but Jacques Distler shot holes in it. If E8 isn't large enough, then we need to look for something larger. I have played with 8-, 10-, 12- and 14-dimensional models and the K12' presented in this essay is my favorite model.

Critiques are welcome!

Have Fun!

Ray Munroe

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Are you really using a conceptual LCD approach to unification of the four forces, as in, what do each of these forces have in common?

[deleted]

Its an analogy. They share Lie Algebras of different rank and dimensionality.

Jonathan Dickau

Hello Ray,

I just finished the first read-through of your essay, earlier today. I am impressed by how you seem to link the limits of complexity with the limits of simplicity in geometric construction. I agree that the simplices hold the key to understanding a lot of the underlying order we see. I'll have to give your essay a more thorough read to comment much further, as it does get pretty deep and a bit complicated. I admire the fact that you seem to have paved a road where Lisi ran into a roadblock. That's really very cool.

Despite Occam's razor, I think we must invoke Einstein's quote here "Make things as simple as they are, but no simpler." If you are homing in on how nature uses the available symmetries found in Math, then E8 has to be involved somehow, and your construction shows great promise.

All the Best,

Jonathan

[deleted]

Dear Ray,

Has there been any feedback from the physics community, or anyone participating in this contest, about your book?

James

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News flash: I kept saying these ideas of frequency dependencies, such as from LQG, on the speed of light were wrong. Well read 'em and weep

http://www.nasa.gov/home/hqnews/2009/oct/HQ_09-254_Fermi_anniversary.html

http://arxiv.org/ftp/arxiv/papers/0908/0908.1832.pdf

String theory makes a nice prediction that the quantum foam which produces this effect is valanced or renormalized out from observable physics.

I have been having long hard arm wrestling sessions over this. This makes me absolutely giddy! Bye bye loop quantum gravity breaking of the Lorentz group at small scales -- YIPEEE!!! There are litterally thousands of theory papers now which are worth less than toilet paper. God it feels good. :-)

[deleted]

Dear Lawrence,

I tried both links. The NASA link brought me to the NASA website, no further. Ther arxiv.org link gave me an error. I'd like to know what you're excited about. Are you saying that loop gravity is dead? What exactly killed it?

[deleted]

Dear Jonathan,

My larger paper, "A Case Study" posted on 9-22, shows similarities between K12' and E8xH4 (Lawrence coined "A Quiver of Quaternions" and his Jordan transformation is about twice as big). And of course, E8 is an important subset (the fermion multiplet) of K12'.

Dear James,

My book has received very little attention, and I have been talking about K12' rather than Quantum Statistical Grand Unification (my older, neglected child).

Dear Lawrence,

Congratulations. It is good to stick to your guns and not follow every trend. Jason is having trouble with your links.

Have Fun!

Ray Munroe

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I googled the link. So the speed of light is constant over billions of lightyears over a range of frequencies from gamma rays up to, I guess visible light or something. I think that kills Double Special Relativity. The article I found talked about two neutron stars slamming into each other. In any event, congratulations, Lawrence.

[deleted]

I didn't really accomplish anything, other than to work and argue from a stance in opposition to these ideas.

This pretty much does rule out some quantum gravity theories. Various models of quantum gravity, except string/M theory , have spacetime broken into struts and links near the Planck scale. This results in the breaking of Lorentz symmetry (spacetime symmetry of relativity) at very short scales. These models include LQG and Dynamical Triangulated Causal Nets and so forth, have these features. The one alternative to string theory which fly through this problem is twistor theory, which in what I am working on with string/M-theory does emerge. These various models are going to have to be either seriously revised or scrapped.

Loop Quantum Gravity is not dead though. In fact I have been working, rather unsuccessfully to be honest, on how LQG could be a system of constraints which exist in a map from the string/M-theory AdS_5 spacetime to the physical (the real universe) de Sitter spacetime. String theory works on the anti-de Sitter spacetime, but that is not the universe. It maps to the de Sitter spacetime under a Wick rotation. A BTZ black hole on AdS spacetime makes this rotation-map difficult, but I think the BPS charge of that black hole maps to the LQG constraints on physical spacetime. This problem has proven to be abominably difficult though. But I think something like this has to happen. String/M-theory stuck forever in the AdS domain does not do as much good for understanding this universe.

Lawrence B. Crowell

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Lawrence,

A Wick rotation refers to imaginary time. Are you considering the idea of imaginary time inside of the black hole?

Lawrence Crowell

Well one can think of the radius becoming a time direction and the time direction becoming a spatial direction beyond the event horizons. There are some funny problems with thinking this way though. However, there is no Wick rotation of one coordinate alone.

Cheers LB

Ray Munroe

Dear Lawrence and Jason,

Regardless of whether we change the metric signs on time or space, we still have at least one imaginary dimension. I'm not sure what the 7th dimension is. What if the 7th dimension is imaginary time and we need to consider the possibility of complex time? The other 11 dimensions in my model seem consistent with M-Theory configurations.

I think Causal Dynamical Triangulation has some structural similarities with my simplices. Is it dead? Or does the symmetry-breaking mechanism need to be revised?

Have Fun!

Ray Munroe

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It is refreshing that progrss is being made in experimental physics. The LHC is supposed to be fully operational in November. Maybe we'll get a Higgs particle for Christmas!

http://dvice.com/archives/2009/10/large-hadron-co-6.php

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Tessellations of 10 or 11 dimensional superspace is somewhat different than what Fermi has found. For one thing the tessellation is a system which defins a quantum error correction code. It is not something which is hard and physical. In fact it can't be, because a tessellation is only valid in a certain frame bumdle or gauge choice. What has happened is that loops or struts in spacetime time which violate Lorentz symmetry, common in LQG and with some CDT ideas, has been falisified.

Lawrence B. Crowell

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Ray,

I have been doing some back reading on issues of journals I have let stack up. This is a "Perspectives" write up of two articles in AAAS "Science" October 16. You might find this interesting. It involves the formation of a Dirac monopole in certain condensed matter systems. If you want I can send the main articles.

Cheers LCAttachment #1: 375.pdf

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Dear Lawrence,

Thank you for the paper. They were also using tetrahedra!

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I attach an image from a part of one of these articles. The spin vertices of the tetrahedra have two pointing in and two pointing out. This gives the Pauling model for the entropy of "cies." Yet a defect on one tetrahedra and the opposite defect on the other tetrahedra results in a Dirac sting. I suspect this can apply to octahedral sphere packing as well. The B_4 representation of the 24-cell is an 8-tetrahedral and 16-cell structure. This is in a way similar to how the Skyrme fermionic field in what I am working with generates flux tubes which are what we call strings, as well as higher structures.

Cheers LCAttachment #1: Bfield_on_tetrahedra.JPG

[deleted]

Dear Ray,

it is a pity that your Physics training finally comes to managing your family retail business. There is so much potential in the geometrical approach in evolving Physics, as nature has symmetries and basic simplicity in its structures. However, just like crystal defects we have breakdown of symmetries that are also significant, as these provide the variety in Nature that we observe too. Somehow, we are not bale to solve several mysteries of the universe, specially the ones that arose since early universe, like dark matter/energy and somewhat later the black holes of both large and small size. The anamoly of Big Bang birth results in such anamolies as we are unable to obtain experimental data about that period through cosmological measurements. t is my feeling that if we are able to discern these secrets we shall resolve many of the problems in Physics. There is also a hiddden secret behind the emergence of four force fields in a sequential manner, gravity being oldest. The other three evolved as strong nuclear, electromagnetic and weak nuclear in accordance witht the logic of evolution. There is thus an undercurrent of gravity in all the other force fields that we have not been able to isolate. That may helpm unify the overall picture.

Lot of postings on your essay makes me feel, you have a good task ahead in Physics for which you may sacrifce some of your commercial activities! If time is available, i will value your comments on my essay on this forum.

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