In the September 2007 issue of Physics Worlk, Witten is quoted as having a “… long-standing hope that we can one day derive the fine-structure constant from first principles …”.

It is interesting that he fails to mention any of the following listed works related to calculating the fine-structure constant:

the underlying math ideas of Armand Wyler or the calculation by Gustavo R. Gonzalez-Martin (Univ. Simon Bolivar, Caracas) in physics 0009051 and in his book Physical Geometry, available on-line as pdf at the web site prof.usb.ve slash ggonzalm slash invstg slash order.htm or the work of Carlos Castro on the web at http://www.sciprint.org including his paper castro5.pdf or my physics model

Perhaps Witten may be afraid to investigate mathematical approaches to physics that may have already realized his “long-standing hope”, and so may be more in touch with experimental reality than his own work.

It is indeed a pity that Witten and others do not have time to follow what happens in the periphery outside the spotlights.

The TGD based explanation for the periods accelerated expansion does not require dark energy. At classical level it relies on critical cosmologies allowing almost unique imbeddings as 4-surfaces. The pressure is negative and one obtains the accelerated expansion without dark energy.

Taking seriously the hierarchy of Planck constants one ends up to an interpretation for these accelerating periods of expansion. Space-time sheets do not expand in stationary quantum states of dark matter. Cosmic expansion occurs only in average sense and takes place in quantum quantum phase transitions increasing the gravitational Planck constant and thus the size of space-time sheets involved. Dark energy is replaced with dark matter.

Of course, accepting the spectrum of Planck constants implying quantum coherence in arbitrarily long time and length scales is so dramatic departure from the reductionistic dogmas that it will take more than life time for psychological barriers to fall down. Anthropic principle is much more familiar after all.

Word is getting out that many in physics are unhappy with a cosmic constant, because QFT says it should be either zero or 10^{120} times bigger.

Thank you Tony, for the supportive comments on Quantum Diaries. As usual, the criticsim is without foundation. It is enlightening to hear why some people have sunk so low.

Louise, you are very welcome for my “… supportive comments on Quantum Diaries …”.

Sometimes it is good for someone other than the person atttacked to defend against attacks. For instance, if anyone attacks Witten over on Peter Woit’s blog, Peter Woit immediately comes to Witten’s defense.

One way that the establishment attacks those who they consider to be “crackpots” etc is to isolate them, thus creating the circumstance described by Kea over on Carl’s blog: “… Crackpots are supposed to be fermions, like mathematicians. …”.

If we do as Kea mentioned there: “… creating a crackpot-condensate …”, then people on the internet (including some open-minded physics students) may realize that some of the unconventional ideas out there are held by more than one single individual and therefore worthy of serious consideration and discussion.

A single individual alone can easily be portrayed by the establishment chorus as merely the nail-sticking-up-that-needs-to-be-hammered-down, so united we stand, divided we fall.

In that September 2007 issue of Physics World (sorry for the typo “Physics Worlk” in an earlier comment), David Gross is quoted as saying about superstring theory: “… What we need is some bright young mind playing around and making clever guesses – like Heisenberg, who was messing around with observables and little pieces of the commutation relations until he stumbled across matrices – to complete the string revolution. …”.

However, when Armand Wyler was “… playing around and making clever guesses …” with geometric structures of bounded complex domains and their Shilov boundaries and in doing so “… stumbled across …” a calculation of the fine structure constant, David Gross, in the December 1989 issue of Physics Today, ridiculed Wyler’s work using terms like “numerology”, “speculation”, “semi-serious”, and “vacuity”.

It seems that superstringers like David Gross are only in favor of “bright young mind[s] playing around and making clever guesses” if they are playing within the framework of superstring theory, and that any useful alternative “clever guesses” should be ignored if possible, and, if ignoring doesn’t work, then ridiculed and even blacklisted.

Armand Wyler was a student of Heinz Hopf (e.g. Hopf Algebras, Hopf maps, etc), so one would expect only a high level of mathematical rigor. Bounded complex domains and Shilov boundaries are to this day not part of the standard string theory toolkit, so I’m not sure Wyler’s critics really groped his work.

It’s only this year that string theorists are looking at Hermitian symmetric tube domains and their relation to black hole degeneracies and topological strings (arxiv: 0707.1669). So it very well may be that Wyler’s work was ahead of its time.

kneemo said “… it very well may be that Wyler’s work was ahead of its time …”.

In case anyone might be interested (maybe kneemo has already seen it), Wyler wrote two papers at the Princeton IAS, neither of which were ever (AFAIK) published. They were “Operations of the Symplectic and Spinor Groups” (17 pages) and “The Complex Light Cone, Symmetric Space of the Conformal Group” (40 pages). I have put then on the web as a pdf file on my web site at http://www.valdostamuseum.org/hamsmith/WylerIAS.pdf The Operations paper is at pages 1-17 and the Light Cone paper is at pages 18-57.

In case anyone might be interested (maybe kneemo has already seen it), Wyler wrote two papers at the Princeton IAS, neither of which were ever (AFAIK) published.

I haven’t seen these, but they are wonderfully self-contained papers. I especially enjoy the discussion of the Hopf fibration S^15 -> S^8. Can’t we also accomplish this fibration by mapping normalized elements of O^2 to OP^1, using the Penrose outer product trick?

kneemo, thanks for looking at the Wyler papers. Aside from my friends Robert Gilmore, Carlos Castro and Ark Jadczyk, and me, you may be the only person who has seriously read them. That is unfortunate, because at the end of the last paper (pages 55-56 of the pdf file) Wyler comes the closest he ever did to giving a good physical interpretation for his alpha calculation. My rough paraphrase of that is:

“We now construct the elementary solution Sn of the Dirac equation … we obtain Sn tothe 2 = Pn … the elementary solution Pn of the Laplace operators on Dn …is… Pn = (V(Dn)) tothe(1/2) …etc… and therefore the coefficient of … Sn is ((V(Dn) tothe ](1/2)) tothe (1/2) …etc… The structure constant alpha, which measures the elementary charge, is interpreted as coefficient of the Green function of the Dirac equation in momentum space … the coefficient of the Fourier transform of the elementary solution is … (V(D5) tothe (1/4) …etc… “.

What happened at the IAS is tragic. Here is my understanding: After Wyler had published his calculation of alpha (albeit not with as much physical justification as set out above), Dyson as IAS director invited Wyler to spend the 1971-72 year at IAS to get more details worked out. Wyler’s personality was such that he did not interact with anyone (not even Dyson), but just stayed in his cubicle (then called a cubby-hole) and worked alone, not even giving any talks. Near the end of the year, Dyson was unhappy at not seeing anything done, and told Wyler to write up whatever he had done. So, Wyler wrote those two papers and gave them to Dyson with the handwritten dedication you see on page 1. However, Wyler did not sit down and explain stuff to Dyson, and Dyson did not understand them.

When Robert Gilmore (author of the 1974 book “Lie Groups, Lie Algebras, and Some of Their Applications”) was trying to understand Wyler’s work, he went to the IAS to ask Dyson about it. Dyson said that he did not understand what Wyler was doing, and was disappointed in Wyler’s year at IAS, and gave the papers to Gilmore. As you can see, they were Dyson’s only copy.

When I was trying to understand Wyler’s work, I saw a reference to it in Gilmore’s book, so I asked Gilmore about Wyler’s work, and Gilmore gave the papers to me. I scanned them into pdf format and put them on the web, so that maybe they might be preserved for posterity (even though people like David Gross went to great lengths to ridicule Wyler’s work, thus discouraging any physicist who cared about career advancement from working on Wyler’s approach).

A very sad aspect of all this was found by my friend Ark Jadczyk who “… learned … directly from a fellow Swiss physicist who was in Geneve at the time .. that Wyler was locked away in an instituion for the insane … and … that Wyler had “lost it” while AT Princeton, and was sent home and institutionalized …”. My guess is that the trigger event whereby Wyler “lost it” was Dyson’s inabiilty to understand, and Wyler’s inability to explain in a way that Dyson could understand, the papers written in June 1972 that are in the pdf file.

In my mind, that tragedy ranks with the house arrest of Galileo and the burning of Bruno as exemplifying human tragedy and delay in advance of science due to ruthless demand for conformity by authoritarian establishments.

Tony Smith

PS – You may be right on ways to see the Hopf fibration S7 to S15 to S8.

You may be right on ways to see the Hopf fibration S7 to S15 to S8.

The Hopf fibration S^7 -> S^15 -> S^8 arises in string theory as the tachyon configuration for a Type I D1-brane ending on a D9-brane. Polchinski gave this construction in 2005 on page 7 of hep-th/0510033. The other three Hopf maps:

describe the D8-brane, D7-brane and D5-brane ending on a D9-brane. These are the only possible types of D-branes that may end on a D9-brane in Type I string theory (see page 4 of hep-th/0606216).

While searching for papers on superconformal algebra, I came across a paper by Lars Brink, Martin Cederwall, and Christian Preitschopf entitled N = 8 Superconformal Algebra and the Superstring. In it they explore the connection between the division algebras and SUSY in D = 3, 4, 6 and 10. The paper is similar to that by J. M. Evans: Auxiliary Fields for Super Yang-Mills from Division Algebras. If you haven’t read the Evans paper already, make sure to see page 5 where he states that in order to find a solution to a certain D=10 SUSY equation (eq. 3), one must restrict both spinor components to lie in a complex subalgebra of the octonions, recovering an SO(3,1)xU(1)xSU(3) residual invariance.

Kea and I were thinking about how to see the division algebra/SUSY relationship using operads, earlier this year. We speculated that there should be an octonionic twistor theory, and interestingly enough Brink came to this same conclusion in his N=8 paper, by introducing octonionic twistors to close his N=8 current algebra.

## Anonymous said,

September 5, 2007 @ 4:50 am

In the September 2007 issue of Physics Worlk, Witten is quoted as having a “… long-standing hope that we can one day derive the fine-structure constant from first principles …”.

It is interesting that he fails to mention any of the following listed works related to calculating the fine-structure constant:

the underlying math ideas of Armand Wyler

or

the calculation by Gustavo R. Gonzalez-Martin (Univ. Simon Bolivar, Caracas) in physics 0009051 and in his book Physical Geometry, available on-line as pdf at the web site prof.usb.ve slash ggonzalm slash invstg slash order.htm

or

the work of Carlos Castro on the web at http://www.sciprint.org including his paper castro5.pdf

or

my physics model

Perhaps Witten may be afraid to investigate mathematical approaches to physics that may have already realized his “long-standing hope”,

and so may be more in touch with experimental reality than his own work.

Tony Smith

## Matti Pitkanen said,

September 5, 2007 @ 5:58 am

It is indeed a pity that Witten and others do not have time to follow what happens in the periphery outside the spotlights.

The TGD based explanation for the periods accelerated expansion does not require dark energy. At classical level it relies on critical cosmologies allowing almost unique imbeddings as 4-surfaces. The pressure is negative and one obtains the accelerated expansion without dark energy.

Taking seriously the hierarchy of Planck constants one ends up to an interpretation for these accelerating periods of expansion. Space-time sheets do not expand in stationary quantum states of dark matter. Cosmic expansion occurs only in average sense and takes place in quantum quantum phase transitions increasing the gravitational Planck constant and thus the size of space-time sheets involved. Dark energy is replaced with dark matter.

Of course, accepting the spectrum of Planck constants implying quantum coherence in arbitrarily long time and length scales is so dramatic departure from the reductionistic dogmas that it will take more than life time for psychological barriers to fall down. Anthropic principle is much more familiar after all.

## L. Riofrio said,

September 5, 2007 @ 6:18 am

Word is getting out that many in physics are unhappy with a cosmic constant, because QFT says it should be either zero or 10^{120} times bigger.

Thank you Tony, for the supportive comments on Quantum Diaries. As usual, the criticsim is without foundation. It is enlightening to hear why some people have sunk so low.

## Anonymous said,

September 5, 2007 @ 10:53 am

Louise, you are very welcome for my “… supportive comments on Quantum Diaries …”.

Sometimes it is good for someone other than the person atttacked to defend against attacks.

For instance,

if anyone attacks Witten over on Peter Woit’s blog, Peter Woit immediately comes to Witten’s defense.

One way that the establishment attacks those who they consider to be “crackpots” etc is to isolate them, thus creating the circumstance described by Kea over on Carl’s blog: “… Crackpots are supposed to be fermions, like mathematicians. …”.

If we do as Kea mentioned there: “… creating a crackpot-condensate …”, then people on the internet (including some open-minded physics students) may realize that some of the unconventional ideas out there are held by more than one single individual and therefore worthy of serious consideration and discussion.

A single individual alone can easily be portrayed by the establishment chorus as merely the nail-sticking-up-that-needs-to-be-hammered-down, so

united we stand, divided we fall.

Tony Smith

## Anonymous said,

September 5, 2007 @ 11:27 am

In that September 2007 issue of Physics World (sorry for the typo “Physics Worlk” in an earlier comment),

David Gross is quoted as saying about superstring theory:

“… What we need is some bright young mind playing around and making clever guesses – like Heisenberg, who was messing around with observables and little pieces of the commutation relations until he stumbled across matrices – to complete the string revolution. …”.

However, when Armand Wyler was “… playing around and making clever guesses …” with geometric structures of bounded complex domains and their Shilov boundaries and in doing so “… stumbled across …” a calculation of the fine structure constant,

David Gross, in the December 1989 issue of Physics Today, ridiculed Wyler’s work using terms like “numerology”, “speculation”, “semi-serious”, and “vacuity”.

It seems that superstringers like David Gross are only in favor of “bright young mind[s] playing around and making clever guesses” if they are playing within the framework of superstring theory,

and

that any useful alternative “clever guesses” should be ignored if possible, and, if ignoring doesn’t work, then ridiculed and even blacklisted.

Tony Smith

## kneemo said,

September 5, 2007 @ 7:09 pm

Armand Wyler was a student of Heinz Hopf (e.g. Hopf Algebras, Hopf maps, etc), so one would expect only a high level of mathematical rigor. Bounded complex domains and Shilov boundaries are to this day not part of the standard string theory toolkit, so I’m not sure Wyler’s critics really groped his work.

It’s only this year that string theorists are looking at Hermitian symmetric tube domains and their relation to black hole degeneracies and topological strings (arxiv: 0707.1669). So it very well may be that Wyler’s work was ahead of its time.

## Anonymous said,

September 5, 2007 @ 8:03 pm

kneemo said “… it very well may be that Wyler’s work was ahead of its time …”.

In case anyone might be interested (maybe kneemo has already seen it), Wyler wrote two papers at the Princeton IAS, neither of which were ever (AFAIK) published. They were

“Operations of the Symplectic and Spinor Groups” (17 pages) and

“The Complex Light Cone, Symmetric Space of the Conformal Group” (40 pages).

I have put then on the web as a pdf file on my web site at

http://www.valdostamuseum.org/hamsmith/WylerIAS.pdf

The Operations paper is at pages 1-17 and the Light Cone paper is at pages 18-57.

Tony Smith

## Kea said,

September 5, 2007 @ 10:21 pm

Let’s properly linkify Wyler’s work. Thanks, Tony, I must read it. Here was my own very modest estimate for alpha based on knot invariants.

## kneemo said,

September 6, 2007 @ 1:08 am

In case anyone might be interested (maybe kneemo has already seen it), Wyler wrote two papers at the Princeton IAS, neither of which were ever (AFAIK) published.I haven’t seen these, but they are wonderfully self-contained papers. I especially enjoy the discussion of the Hopf fibration S^15 -> S^8. Can’t we also accomplish this fibration by mapping normalized elements of O^2 to OP^1, using the Penrose outer product trick?

## Anonymous said,

September 6, 2007 @ 4:23 am

kneemo, thanks for looking at the Wyler papers.

Aside from my friends Robert Gilmore, Carlos Castro and Ark Jadczyk, and me, you may be the only person who has seriously read them.

That is unfortunate, because at the end of the last paper (pages 55-56 of the pdf file) Wyler comes the closest he ever did to giving a good physical interpretation for his alpha calculation.

My rough paraphrase of that is:

“We now construct the elementary solution Sn of the Dirac equation … we obtain Sn tothe 2 = Pn … the elementary solution Pn of the Laplace operators on Dn …is…

Pn = (V(Dn)) tothe(1/2) …etc…

and therefore the coefficient of … Sn is

((V(Dn) tothe ](1/2)) tothe (1/2) …etc…

The structure constant alpha, which measures the elementary charge, is interpreted as coefficient of the Green function of the Dirac equation in momentum space … the coefficient of the Fourier transform of the elementary solution is …

(V(D5) tothe (1/4) …etc… “.

What happened at the IAS is tragic. Here is my understanding:

After Wyler had published his calculation of alpha (albeit not with as much physical justification as set out above),

Dyson as IAS director invited Wyler to spend the 1971-72 year at IAS to get more details worked out.

Wyler’s personality was such that he did not interact with anyone (not even Dyson), but just stayed in his cubicle (then called a cubby-hole) and worked alone, not even giving any talks.

Near the end of the year, Dyson was unhappy at not seeing anything done, and told Wyler to write up whatever he had done. So, Wyler wrote those two papers and gave them to Dyson with the handwritten dedication you see on page 1.

However, Wyler did not sit down and explain stuff to Dyson, and Dyson did not understand them.

When Robert Gilmore (author of the 1974 book “Lie Groups, Lie Algebras, and Some of Their Applications”) was trying to understand Wyler’s work, he went to the IAS to ask Dyson about it. Dyson said that he did not understand what Wyler was doing, and was disappointed in Wyler’s year at IAS, and gave the papers to Gilmore. As you can see, they were Dyson’s only copy.

When I was trying to understand Wyler’s work, I saw a reference to it in Gilmore’s book, so I asked Gilmore about Wyler’s work, and Gilmore gave the papers to me. I scanned them into pdf format and put them on the web, so that maybe they might be preserved for posterity (even though people like David Gross went to great lengths to ridicule Wyler’s work, thus discouraging any physicist who cared about career advancement from working on Wyler’s approach).

A very sad aspect of all this was found by my friend Ark Jadczyk who “… learned … directly from a fellow Swiss physicist who was in Geneve at the time .. that Wyler was locked away in an instituion for the insane … and … that Wyler had “lost it” while AT Princeton, and was sent home and institutionalized …”.

My guess is that the trigger event whereby Wyler “lost it” was Dyson’s inabiilty to understand, and Wyler’s inability to explain in a way that Dyson could understand, the papers written in June 1972 that are in the pdf file.

In my mind, that tragedy ranks with the house arrest of Galileo and the burning of Bruno as exemplifying human tragedy and delay in advance of science due to ruthless demand for conformity by authoritarian establishments.

Tony Smith

PS – You may be right on ways to see the Hopf fibration S7 to S15 to S8.

## kneemo said,

September 6, 2007 @ 9:41 pm

You may be right on ways to see the Hopf fibration S7 to S15 to S8.The Hopf fibration S^7 -> S^15 -> S^8 arises in string theory as the tachyon configuration for a Type I D1-brane ending on a D9-brane. Polchinski gave this construction in 2005 on page 7 of hep-th/0510033. The other three Hopf maps:

1) S^0 -> S^1 -> S^1

2) S^1 -> S^3 -> S^2

3) S^3 -> S^7 -> S^4

describe the D8-brane, D7-brane and D5-brane ending on a D9-brane. These are the only possible types of D-branes that may end on a D9-brane in Type I string theory (see page 4 of hep-th/0606216).

http://arxiv.org/abs/hep-th/0606216

## kneemo said,

September 11, 2007 @ 5:21 am

Tony

While searching for papers on superconformal algebra, I came across a paper by Lars Brink, Martin Cederwall, and Christian Preitschopf entitled N = 8 Superconformal Algebra and the Superstring. In it they explore the connection between the division algebras and SUSY in D = 3, 4, 6 and 10. The paper is similar to that by J. M. Evans: Auxiliary Fields for Super Yang-Mills from Division Algebras. If you haven’t read the Evans paper already, make sure to see page 5 where he states that in order to find a solution to a certain D=10 SUSY equation (eq. 3), one must restrict both spinor components to lie in a complex subalgebra of the octonions, recovering an SO(3,1)xU(1)xSU(3) residual invariance.

Kea and I were thinking about how to see the division algebra/SUSY relationship using operads, earlier this year. We speculated that there should be an octonionic twistor theory, and interestingly enough Brink came to this same conclusion in his N=8 paper, by introducing octonionic twistors to close his N=8 current algebra.