*Tony Smith [Frank D. (Tony) Smith, Jr.] is suppressed by other ignorant Theorists*

On the Amazon.com discussion board for Woit's book

*Not Even Wrong,*Tony Smith has placed some intriguing comments relating to Dr Woit's

*Not Even Wrong*and also to Dr Smolin's forthcoming

*The Trouble with Physics: The Rise of String Theory, The Fall of a*

*Science, and What Comes Next,*which I can't respond to there because I'm an Amazon.co.uk customer and you have to have bought a book from Amazon.com (not Amazon.co.uk) in order to participate.

Dr Smith comments:

"The Standard Model, which is at present completely consistent with experimental results, but which by itself is not unified with Gravity, is well described in Woit's book. ...

"The

*Rise of String Theory*as an attempt over the past 20 years or so to unify the Standard Model with Gravity is described by both Smolin and Woit. The

*Fall of a Science,*due to the failure of superstring theory to deliver on its early promise of unification of the Standard Model and Gravity, is also described by both Smolin and Woit. Smolin's

*Book Description*says that superstring theory: '... has been a colossal failure. And because it has soaked up the lion's share of funding, attracted some of the best minds, and penalized young physicists for pursuing other avenues, it is dragging the rest of physics down with it. ...'.

"As Feynman said in the book

*Superstrings,*by Davies and Brown (Cambridge 1988, pp. 194-195): '... I do feel strongly that this is nonsense! ... I think all this superstring stuff is crazy and is in the wrong direction. ... I don't like it that they're not calculating anything. ... why are the masses of the various particles such as quarks what they are? All these numbers ... have no explanations in these string theories - absolutely none! ... '

"

*What Comes Next*is not dealt with by Woit (which is why I gave his book only 4 and not 5 stars), but Smolin advocates his personal approach to physics, known as Loop Quantum Gravity, which is an alternative to superstring theory that has some establishment support, but not nearly as much as superstring theory (maybe Loop Quantum Gravity gets 10% of the high energy theoretical physics funding and jobs, with superstring theory getting 90%, and other approaches getting relatively insignificant amounts. Smolin's failure to advocate exploration of such 'other approaches', while trumpeting his own Loop Quantum Gravity as his anointed successor to superstring theory, is why I gave his book only 4 stars. For the context of a concrete example of Smolin's indifference to 'other approaches', consider a June 2006 talk by John Baez at the University of Western Ontario (nearby Smolin's Perimeter Institute in Waterloo, Ontario). Baez's talk was entitled

*Fundamental Physics: Where We Stand Today,*and discussed Six Mysteries whose solution would advance Fundamental Physics. Baez's Six Mysteries are:

'... Mystery 1. What is making the expansion of the universe accelerate? Does the vacuum have negative pressure?... Mystery 2. Does the Higgs really exist? What is the origin of mass?Mystery 3. Why do these 18 numbers [that]... describe the strengths of all these interactions ...[of]... the Standard Model ... have the values they do?Does this question even have an answer?... Mystery 4. Do neutrino oscillations fit into a slightly modified Standard Model- now requiring 25 dimensionless numbers - or must the theory be changed more drastically?... Mystery 5. What happens to things when they fall into a black hole?... Mystery 6. What is cold dark matter- or what else explains what this hypothesis tries to explain...[such as]...that the energy of our universe ... is made of: 4% normal matter 23% cold dark matter 73% vacuum energy ...'.

**"My concrete example is that, shortly after Baez described his Six Mysteries in Ontario, I sent an e-mail message to Smolin**

**saying**:

'... I would like to present, at Perimenter, answers to those questions, as follows:Mysteries 2 and 3: The Higgs probably does exist, and is related to a Tquark-Tantiquark condensate,and mass comes from the Standard Model Higgs mechanism, producing force strengths and particle masses consistent with experiment, as described in http://www.valdostamuseum.org/hamsmith/YamawakiNJL.pdfandhttp://www.valdostamuseum.org/hamsmith/TQ3mHFII1vNFadd97.pdf

'Mystery 4: Neutrino masses and mixing angles consistent with experimentare described in the first part of this pdf file http://www.valdostamuseum.org/hamsmith/NeutrinosEVOs.pdf

**http://www.valdostamuseum.org/hamsmith/sGmTqqbarPion.pdf Mysteries 6 and 1:The Dark Energy : Dark Matter : Ordinary Matter ratioof about 73 : 23 : 4 is described in http://www.valdostamuseum.org/hamsmith/WMAPpaper.pdf**

*Mystery 5: A partial answer: If quarks are regarded as Kerr-Newman black holes, merger of a quark-antiquark pair to form a charged pion produce a toroidal event horizon carrying sine-Gordon structure, so that, given up and down quark constituent masses of about 312 MeV,the charged pion gets a mass of about 139 MeV, as described in*'Please let me know if you would be interested in me making such a presentation at Perimeter.

Tony Smith

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

'PS - I expect that I could pay my own expenses, including traveland lodging, and that I would not require any funding by Perimeter. ...'.

"I have yet to receive even the courtesy of a reply from Smolin, much less any interest in a presentation of my approach, which is different from both superstring theory and Smolin's Loop Quantum Gravity. Maybe my approach has some flaws of which I am unaware (one reason to make such a presentation is to find out if others can spot such flaws, so that they can either be corrected or the flawed stuff discarded) or maybe my approach is substantially sound and would be a significant contribution to

*What Comes Next,*but if physicists in leadership positions, such as Smolin, are unwilling to consider such possible alternatives to their own pet theories around which their jobs/funding empires are built, the Future of Theoretical High Energy Physics is indeed Dark (at least in North America).

"Frank D. (Tony) Smith, Jr. http://www.valdostamuseum.org/hamsmith/"

I think Tony Smith is a free thinking orthodoxy-inclined mathematical physicist. What is weird is that he is a string theorist, and yet has been banned from string theory arXiv.org as I was, for no good scientific reason whatsoever (i.e., because Tony Smith sticks to 26-dimensional string theory instead of the celebrated 10/11 dimensional M-theory version of Edward Witten; Tony Smiths version is the only one to offer any sort of predictions and thus to offer the scientific criterion of falsifiability), and provably for reasons of prejudice unrelated to content:

The people who run arXiv.org deleted Tony Smith's seminal 340 book after just4 minutes and 7 seconds, and since nobody has claimed to be able to read 340 pages of mathematical physics in 4 minutes 7 seconds, they not honest if they claim to have any science behind suppressing it. They are

**all**a load of ------- and -------. I've commented on this blog before that Danny Ross Lunsford was censored off arXiv.org.

As for Dr Lee Smolin and Dr Peter Woit, they are doing their best although both are clearly inexperienced in formulating physical theories which can be easily checked and tested (they are however more competent than the likes of Hawking and . Although arXiv.org's Dr Jacques Distler has banned arXiv.org trackbacks to Woit's blog

*Not Even Wrong,*it is clear from the stance of string theorists that they will complain about THEIR freedom being threatened by insistence that some money goes to alternatives, while ganging together to PREVENT freedom of people to publish alternatives.

Notice above, in quoting Tony Smith, I put one section in red. Tony Smith's talk about explaining dark energy is wrong (see HERE for details, which is in the fast comment section of Dr Motl's blog), but his description of quark as spinning black hole is a vital insight.

What always happens in the world is a seesaw from one extreme mainstream viewpoint to another extreme mainstream viewpoint. There can be no wide diversity of officially published and acknowledged ideas waiting to be checked in a professional science culture. Such a wide diversity would make the subject look too 'amateurish' (why sneer at amateurs, what is wrong with amateurs, why are people so sneering at science when they would never do that of amateur sportsmen or amateurs in other subjects, what is wrong with society when it comes to science, it is totally screwed up by the ignorance due to Hollywood) destroying the pseudo-credibility which is current upheld by falsehood and propaganda in favour of officialdom speculations.

It is not down to Smolin or Woit, or Baez or even President Bush to decide what facts get money for publicity, publication and further investigation. It is a free market of ideas and we have to get dirty and improve and clarify and popularise the facts we have found out without waiting for the helpful intervention of any particular big name. Those guys and girls will only jump on a successful bandwaggon, they aren't - in this day and age - interested in non-mainstream ideas which are obscure, and which are quietly defended; at he same time they are even less sympathetic to loudly presented ideas which are inadequately checked and presented. So the ideas need to have not only marketing, but more important, scientific development as far as possible.

Should I submit a paper to Dr Anthony Garrett who is an expert editor offering presentation-editing help for reasonable remuneration? Although I'm already author of a number of Electronics World articles and letters. I'm not arrogant or proud enough to believe that I'm the best writer; my writing less inhibited than my speech since I don't value writing so much. I certainly always find plenty of inadvertent errors in what I write when I read my own writings at a later date. So I may try that. The efforts I will have to make to draft a reasonable manuscript for him to consider would probably be immensely valuable, as much progress in minutiae has been made this year which has not been published.

*****

Update:

One very interesting paper by Frank D. (Tony) Smith, Jr., that I recommend (compare it to my Electronics World articles of August 2002 and April 2003), is "Sine-Gordon Quarks and Pion", PDF here. See http://www.valdostamuseum.org/hamsmith/Jun2006Update.html (extracted text below excludes illustrations):

*Sine-Gordon Quarks and Pion*

Frank D. (Tony) Smith, Jr.

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

June 2006

Frank D. (Tony) Smith, Jr.

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

June 2006

Abstract: The charged pion, made up of Up plus antiDown or Down plus antiUp quarks, is described in terms of the sine-Gordon and massive Thirring models. When the quark and antiquark are seen as Kerr-Newman black holes each having constituent mass about 312 MeV, the pion is seen as resulting from their merger, whch produces a black hole with toroidal event horizon representing a sine-Gordon meson whose mass can be calculated. The charged pion mass calculation gives a charged pion mass of about 139 MeV, which is substantially consistent with experimental results.

The quark content of a charged pion is a quark - antiquark pair: either Up plus antiDown or Down plus antiUp. Experimentally, its mass is about 139.57 MeV.

The quark is a Naked Singularity Kerr-Newman Black Hole, with electromagnetic charge e and spin angular momentum J and constituent mass M 312 MeV, such that e^2 + a^2 is greater than M^2 (where a = J / M).

The antiquark is a also Naked Singularity Kerr-Newman Black Hole, with electromagnetic charge e and spin angular momentum J and constituent mass M 312 MeV, such that e^2 + a^2 is greater than M^2 (where a = J / M).

According to General Relativity, by Robert M. Wald (Chicago 1984) page 338 [Problems] ... 4. ...:

"... Suppose two widely separated Kerr black holes with parameters ( M1 , J1 ) and ( M2 , J2 ) initially are at rest in an axisymmetric configuration, i.e., their rotation axes are aligned along the direction of their separation.

Assume that these black holes fall together and coalesce into a single black hole.

Since angular momentum cannot be radiated away in an axisymmetric spacetime, the final black hole will have momentum J = J1 + J2. ...".

The neutral pion produced by the quark - antiquark pair would have zero angular momentum, thus reducing the value of e^2 + a^2 to e^2 .

For fermion electrons with spin 1/2, 1 / 2 = e / M (see for example Misner, Thorne, and Wheeler, Gravitation (Freeman 1972), page 883) so that M^2 = 4 e^2 is greater than e^2 for the electron. In other words, the angular momentum term a^2 is necessary to make e^2 + a^2 greater than M^2 so that the electron can be seen as a Kerr-Newman naked singularity.

Since the magnitude of electromagnetic charge of each quarks or antiquarks less than that of an electron, and since the mass of each quark or antiquark (as well as the pion mass) is greater than that of an electron, and since the quark - antiquark pair (as well as the pion) has angular momentum zero, the quark - antiquark pion has M^2 greater than e^2 + a^2 = e^2.

( Note that color charge, which is nonzero for the quark and the antiquark and is involved in the relation M^2 less than sum of spin-squared and charges-squared by which quarks and antiquarks can be see as Kerr-Newman naked singularities, is not relevant for the color-neutral pion. )

Therefore, the pion itself is a normal Kerr-Newman Black Hole with Outer Event Horizon = Ergosphere at r = 2M ( the Inner Event Horizon is only the origin at r = 0 ) as shown in this image http://www.valdostamuseum.org/hamsmith/sGmTqqbarPion.pdf

from Black Holes - A Traveller's Guide, by Clifford Pickover (Wiley 1996) in which the Ergosphere is white, the Outer Event Horizon is red, the Inner Event Horizon is green, and the Ring Singularity is purple. In the case of the pion, the white and red surfaces coincide, and the green surface is only a point at the origin.

According to section 3.6 of Jeffrey Winicour's 2001 Living Review of the Development of Numerical Evolution Codes for General Relativity (see also a 2005 update):

"... The black hole event horizon associated with ... slightly broken ... degeneracy [ of the axisymmetric configuration ]... reveals new features not seen in the degenerate case of the head-on collision ... If the degeneracy is slightly broken, the individual black holes form with spherical topology but as they approach, tidal distortion produces two sharp pincers on each black hole just prior to merger. ... Tidal distortion of approaching black holes ...

... Formation of sharp pincers just prior to merger ..

... toroidal stage just after merger ...

At merger, the two pincers join to form a single ... toroidal black hole.

The inner hole of the torus subsequently [ begins to] close... up (superluminally) ... [ If the closing proceeds to completion, it ]... produce[s] first a peanut shaped black hole and finally a spherical black hole. ...".

In the physical case of quark and antiquark forming a pion, the toroidal black hole remains a torus. The torus is an event horizon and therefore is not a 2-spacelike dimensional torus, but is a (1+1)-dimensional torus with a timelike dimension.

The effect is described in detail in Robert Wald's book General Relativity (Chicago 1984). It can be said to be due to extreme frame dragging, or to timelike translations becoming spacelike as though they had been Wick rotated in Complex SpaceTime.

As Hawking and Ellis say in The LargeScale Structure of Space-Time (Cambridge 1973):

"... The surface r = r+ is ... the event horizon ... and is a null surface ...

... On the surface r = r+ .... the wavefront corresponding to a point on this surface lies entirely within the surface. ...".

A (1+1)-dimensional torus with a timelike dimension can carry a Sine-Gordon Breather, and the soliton and antisoliton of a Sine-Gordon Breather correspond to the quark and antiquark that make up the pion.

Sine-Gordon Breathers are described by Sidney Coleman in his Erica lecture paper Classical Lumps and their Quantum Descendants (1975), reprinted in his book Aspects of Symmetry (Cambridge 1985), where Coleman writes the Lagrangian for the Sine-Gordon equation as ( Coleman's eq. 4.3 ):

L = (1 / B^2 ) ( (1/2) (df)^2 + A ( cos( f ) - 1 ) )

file:///Users/Shared/Pion%20PDF/sGmTpion.html (4 of 11)5/25/06 10:35 AM

June 2006 update

and Coleman says:

"... We see that, in classical physics, B is an irrelevant parameter: if we can solve the sine-Gordon equation for any non-zero B, we can solve it for any other B. The only effect of changing B is the trivial one of changing the energy and momentum assigned to a given soluition of the equation. This is not true in quantum physics, becasue the relevant object for quantum physics is not L but [ eq. 4.4 ]

L / hbar = (1 / ( B^2 hbar ) ) ( (1/2) (df)^2 + A ( cos( f ) - 1 ) )

An other way of saying the same thing is to say that in quantum physics we have one more dimensional constant of nature, Planck's constant, than in classical physics. ... the classical limit, vanishingf hbar, is exactly the same as the small-coupling limit, vanishing B ... from now on I will ... set hbar equal to one. ...

... the sine-Gordon equation ...[ has ]... an exact periodic solution ...[ eq. 4.59 ]...

f( x, t ) = ( 4 / B ) arctan( ( n sin( w t ) / cosh( n w x ))

where [ eq. 4.60 ] n = sqrt( A - w^2 ) / w and w ranges from 0 to A. This solution has a simple physical interpretation ... a soliton far to the left ...[ and ]... an antisoliton far to the right. As sin ( w t ) increases, the soliton and antisoliton mover farther apart from each other. When sin( w t ) passes thrpough one, they turn around and begin to approach one another. As sin( w t ) comes down to zero ... the soliton and antisoliton are on top of each other ... when sin( w t ) becomes negative .. the soliton and antisoliton have passed each other. ...[

This stereo image of a Sine-Gordon Breather was generated by the program 3D-Filmstrip for Macintosh by Richard Palais. You can see the stereo with red-green or red-cyan 3D glasses. The program is on the WWW at http://rsp.math.brandeis.edu/3D-Filmstrip. The

Sine-Gordon Breather is confined in space (y-axis) but periodic in time (x-axis), and therefore naturally lives on the (1+1)-dimensional torus with a timelike dimension of the Event Horizon of the pion. ...]

... Thus, Eq. (4.59) can be thought of as a soliton and an antisoliton oscillation about their common center-of-mass. For this reason, it is called 'the doublet [ or Breather ] solution'. ... the energy of the doublet ...[ eq. 4.64 ]

E = 2 M sqrt( 1 - ( w^2 / A ) )

where [ eq. 4.65 ] M = 8 sqrt( A ) / B^2 is the soliton mass. Note that the mass of the doublet is always less than twice the soliton mass, as we would expect from a soltion-antisoliton pair. ... Dashen, Hasslacher, and Neveu ... Phys. Rev. D10, 4114; 4130; 4138 (1974). A pedagogical review of these methods has been written by R. Rajaraman ( Phys. Reports 21, 227 (1975 ... Phys. Rev. D11, 3424 (1975) ...[ Dashen, Hasslacher, and Neveu found that ]... there is only a single series of bound states, labeled by the integer N ... The energies ... are ... [ eq. 4.82 ]

E_N = 2 M sin( B'^2 N / 16 )

where N = 0, 1, 2 ... < 2 =" B^2" qdot =" 2" 2 =" 4" m =" -" 2 =" 4" g =" 0" http://www.valdostamuseum.org/hamsmith/sGmTqqbarPion.pdf

...[eq. 2.13b ] E = 8 sqrt(A) / B^2 ...[ is the ]... energy of the lump ... of sine-Gordon theory ... frequently called 'soliton...' in the literature ... [ Zeroth-order is the classical case, or classical limit. ] ...

... Coherent-state variation always gives the same result as the ... Zeroth-order weak coupling expansion ... .

The ... First-order weak-coupling expansion ... explicit formula ... is ( 8 / B^2 ) - ( 1 / pi ). ...".

Note that, using the VoDou Physics constituent mass of the Up and Down quarks and antiquarks, about

312.75 MeV, as the soliton and antisoliton masses, and setting B^2 = piand using the DHN formula,

the mass of the charged pion is calculated to be ( 312.75 / 2.25 ) MeV = 139 MeV

which is in pretty good agreement with the experimental value of about 139.57 MeV. Why is the value B^2 = pi ( or, using Coleman's eq. ( 5.14 ), the Thirring coupling constant g = 3 pi ) the

special value that gives the pion mass ?

Because B^2 = pi is where the First-order weak coupling expansion substantially coincides with the ( probably exact ) DHN formula. In other words,

The physical quark - antiquark pion lives where the first-order weak coupling expansion is exact.

Near the end of his article, Coleman expressed "Some opinions":

"... This has been a long series of physics lectures with no reference whatsoever to experiment.

This is embarrassing.

... Is there any chance that the lump will be more than a theoretical toy in our field? I can think of

two possiblities.

One is that there will appear a theory of strong-interaction dynamics in which hadrons are thought of as lumps, or, ... as systems of quarks bound into lumps. ... I am pessimistic about the success of such a theory. ... However, I stand ready to be converted in a moment by a convincing computation.

The other possibility is that a lump will appear in a realistic theory ... of weak and electromagnetic interactions ... the theory would have to imbed the U(1)xSU(2) group ... in a larger group without U(1) factors ... it would be a magnetic monopole. ...".

This description of the hadronic pion as a quark - antiquark system governed by the sine-Gordon - massive Thirring model should dispel Coleman's pessimism about his first stated possibility and relieve his embarrassment about lack of contact with experiment.

As to his second stated possibility, very massive monopoles related to SU(5) GUT are still within the realm of possible future experimental discoveries.

Further material about the sine-Gordon doublet Breather and the massive Thirring equation can be found in the book Solitons and Instantons (North-Holland 1982,1987) by R. Rajaraman, who writes:

"... the doublet or breather solutions ... can be used as input into the WKB method. ... the system is ... equivalent to the massive Thirring model, with the SG soliton state identifiable as a fermion. ... Mass of the quantum soliton ... will consist of a classical term followed by quantum corrections. The energy of the classical soliton ... is ... [ eq. 7.3 ]

E_cl[f_sol] = 8 m^3 / L The quantum corrections ... to the 'soliton mass' ... is finite as the momentum cut-off goes to infinity and equals ( - m / pi ). Hence the quantum soliton's mass is [ eq. 7.10 ]

M_sol =( 8 m^3 / L ) - ( m / pi ) +O(L). The mass of the quantum antisoliton will be, by ... symmetry, the same as M_sol. ... The doublet solutions ... may be quantised by the WKB method. ... we see that the coupling

constant ( L / m^2 ) has been replaced by a 'renormalised' coupling constant G ... [ eq. 7.24 ] G = ( L / m^2 ) / ( 1 - ( L / 8 pi m^2 )) ... as a result of quantum corrections. ... the same thing had happened to the soliton mass in eq.

( 7.10 ). To leading order, we can write [ eq. 7.25 ] M_sol = ( 8 m^3 / L ) - ( m / pi ) = 8 m / G ... The doublet masses ... bound-state energy levels ... E = M_N, where ... [ eq. 7.28 ] M_N = ( 16 m / G ) sin( N G / 16 ) ; N = 1, 2, ... <> 8 pi / G . ... The

classical solutions ... bear the same relation to the bound-state wavefunctionals ... that Bohr orbits bear to hydrogen atom wavefunctions. ... Coleman ... show[ed] explicitly ... the SG theory equivalent to the charge-zero sector of the MT

model, provided ... L / 4 pi m^2 = 1 / ( 1 + g / pi )...[ where in Coleman's work set out above such as his eq. ( 5.14 ) , B^2 = L / m^2 ]...Coleman ... resurrected Skyrme's conjecture that the quantum soliton of the SG model may be

identified with the fermion of the MT model. ... ".

WHAT ABOUT THE NEUTRAL PION?

The quark content of the charged pion is u_d or d_u , both of which are consistent with the sine-Gordon picture.

Experimentally, its mass is 139.57 Mev.

The neutral pion has quark content (u_u + d_d)/sqrt(2) with two components, somewhat different from the sine-Gordon picture, and a mass of 134.96 Mev.

The effective constituent mass of a down valence quark increases (by swapping places with a strange sea quark) by about

DcMdquark = (Ms - Md) (Md/Ms)2 aw V12 == 312x0.25x0.253x0.22 Mev = 4.3 Mev.

Similarly, the up quark color force mass increase is about

DcMuquark = (Mc - Mu) (Mu/Mc)2 aw V12 == 1777x0.022x0.253x0.22 Mev = 2.2 Mev.

The color force increase for the charged pion DcMpion± = 6.5 Mev.

Since the mass Mpion± = 139.57 Mev is calculated from a color force sine-Gordon soliton state, the mass 139.57 Mev already takes DcMpion± into account.

For pion0 = (u_u + d_d)/ sqrt 2 , the d and _d of the the d_d pair do not swap places with strange sea quarks very often because it is energetically preferential for them both to become a u_u pair. Therefore, from the point of view of calculating DcMpion0, the pion0 should be considered to be only u_u , and DcMpion0 = 2.2+2.2 = 4.4 Mev.

If, as in the nucleon, DeM(pion0-pion±) = -1 Mev, the theoretical estimate is

DM(pion0-pion±) = DcM(pion0-pion±) + DeM(pion0-pion±) == 4.4 - 6.5 -1 = -3.1 Mev, roughly consistent with the experimental value of -4.6 Mev.

Abstract: The charged pion, made up of Up plus antiDown or Down plus antiUp quarks, is described in terms of the sine-Gordon and massive Thirring models. When the quark and antiquark are seen as Kerr-Newman black holes each having constituent mass about 312 MeV, the pion is seen as resulting from their merger, whch produces a black hole with toroidal event horizon representing a sine-Gordon meson whose mass can be calculated. The charged pion mass calculation gives a charged pion mass of about 139 MeV, which is substantially consistent with experimental results.

The quark content of a charged pion is a quark - antiquark pair: either Up plus antiDown or Down plus antiUp. Experimentally, its mass is about 139.57 MeV.

The quark is a Naked Singularity Kerr-Newman Black Hole, with electromagnetic charge e and spin angular momentum J and constituent mass M 312 MeV, such that e^2 + a^2 is greater than M^2 (where a = J / M).

The antiquark is a also Naked Singularity Kerr-Newman Black Hole, with electromagnetic charge e and spin angular momentum J and constituent mass M 312 MeV, such that e^2 + a^2 is greater than M^2 (where a = J / M).

According to General Relativity, by Robert M. Wald (Chicago 1984) page 338 [Problems] ... 4. ...:

"... Suppose two widely separated Kerr black holes with parameters ( M1 , J1 ) and ( M2 , J2 ) initially are at rest in an axisymmetric configuration, i.e., their rotation axes are aligned along the direction of their separation.

Assume that these black holes fall together and coalesce into a single black hole.

Since angular momentum cannot be radiated away in an axisymmetric spacetime, the final black hole will have momentum J = J1 + J2. ...".

The neutral pion produced by the quark - antiquark pair would have zero angular momentum, thus reducing the value of e^2 + a^2 to e^2 .

For fermion electrons with spin 1/2, 1 / 2 = e / M (see for example Misner, Thorne, and Wheeler, Gravitation (Freeman 1972), page 883) so that M^2 = 4 e^2 is greater than e^2 for the electron. In other words, the angular momentum term a^2 is necessary to make e^2 + a^2 greater than M^2 so that the electron can be seen as a Kerr-Newman naked singularity.

Since the magnitude of electromagnetic charge of each quarks or antiquarks less than that of an electron, and since the mass of each quark or antiquark (as well as the pion mass) is greater than that of an electron, and since the quark - antiquark pair (as well as the pion) has angular momentum zero, the quark - antiquark pion has M^2 greater than e^2 + a^2 = e^2.

( Note that color charge, which is nonzero for the quark and the antiquark and is involved in the relation M^2 less than sum of spin-squared and charges-squared by which quarks and antiquarks can be see as Kerr-Newman naked singularities, is not relevant for the color-neutral pion. )

Therefore, the pion itself is a normal Kerr-Newman Black Hole with Outer Event Horizon = Ergosphere at r = 2M ( the Inner Event Horizon is only the origin at r = 0 ) as shown in this image http://www.valdostamuseum.org/hamsmith/sGmTqqbarPion.pdf

from Black Holes - A Traveller's Guide, by Clifford Pickover (Wiley 1996) in which the Ergosphere is white, the Outer Event Horizon is red, the Inner Event Horizon is green, and the Ring Singularity is purple. In the case of the pion, the white and red surfaces coincide, and the green surface is only a point at the origin.

According to section 3.6 of Jeffrey Winicour's 2001 Living Review of the Development of Numerical Evolution Codes for General Relativity (see also a 2005 update):

"... The black hole event horizon associated with ... slightly broken ... degeneracy [ of the axisymmetric configuration ]... reveals new features not seen in the degenerate case of the head-on collision ... If the degeneracy is slightly broken, the individual black holes form with spherical topology but as they approach, tidal distortion produces two sharp pincers on each black hole just prior to merger. ... Tidal distortion of approaching black holes ...

... Formation of sharp pincers just prior to merger ..

... toroidal stage just after merger ...

At merger, the two pincers join to form a single ... toroidal black hole.

The inner hole of the torus subsequently [ begins to] close... up (superluminally) ... [ If the closing proceeds to completion, it ]... produce[s] first a peanut shaped black hole and finally a spherical black hole. ...".

In the physical case of quark and antiquark forming a pion, the toroidal black hole remains a torus. The torus is an event horizon and therefore is not a 2-spacelike dimensional torus, but is a (1+1)-dimensional torus with a timelike dimension.

The effect is described in detail in Robert Wald's book General Relativity (Chicago 1984). It can be said to be due to extreme frame dragging, or to timelike translations becoming spacelike as though they had been Wick rotated in Complex SpaceTime.

As Hawking and Ellis say in The LargeScale Structure of Space-Time (Cambridge 1973):

"... The surface r = r+ is ... the event horizon ... and is a null surface ...

... On the surface r = r+ .... the wavefront corresponding to a point on this surface lies entirely within the surface. ...".

A (1+1)-dimensional torus with a timelike dimension can carry a Sine-Gordon Breather, and the soliton and antisoliton of a Sine-Gordon Breather correspond to the quark and antiquark that make up the pion.

Sine-Gordon Breathers are described by Sidney Coleman in his Erica lecture paper Classical Lumps and their Quantum Descendants (1975), reprinted in his book Aspects of Symmetry (Cambridge 1985), where Coleman writes the Lagrangian for the Sine-Gordon equation as ( Coleman's eq. 4.3 ):

L = (1 / B^2 ) ( (1/2) (df)^2 + A ( cos( f ) - 1 ) )

file:///Users/Shared/Pion%20PDF/sGmTpion.html (4 of 11)5/25/06 10:35 AM

June 2006 update

and Coleman says:

"... We see that, in classical physics, B is an irrelevant parameter: if we can solve the sine-Gordon equation for any non-zero B, we can solve it for any other B. The only effect of changing B is the trivial one of changing the energy and momentum assigned to a given soluition of the equation. This is not true in quantum physics, becasue the relevant object for quantum physics is not L but [ eq. 4.4 ]

L / hbar = (1 / ( B^2 hbar ) ) ( (1/2) (df)^2 + A ( cos( f ) - 1 ) )

An other way of saying the same thing is to say that in quantum physics we have one more dimensional constant of nature, Planck's constant, than in classical physics. ... the classical limit, vanishingf hbar, is exactly the same as the small-coupling limit, vanishing B ... from now on I will ... set hbar equal to one. ...

... the sine-Gordon equation ...[ has ]... an exact periodic solution ...[ eq. 4.59 ]...

f( x, t ) = ( 4 / B ) arctan( ( n sin( w t ) / cosh( n w x ))

where [ eq. 4.60 ] n = sqrt( A - w^2 ) / w and w ranges from 0 to A. This solution has a simple physical interpretation ... a soliton far to the left ...[ and ]... an antisoliton far to the right. As sin ( w t ) increases, the soliton and antisoliton mover farther apart from each other. When sin( w t ) passes thrpough one, they turn around and begin to approach one another. As sin( w t ) comes down to zero ... the soliton and antisoliton are on top of each other ... when sin( w t ) becomes negative .. the soliton and antisoliton have passed each other. ...[

This stereo image of a Sine-Gordon Breather was generated by the program 3D-Filmstrip for Macintosh by Richard Palais. You can see the stereo with red-green or red-cyan 3D glasses. The program is on the WWW at http://rsp.math.brandeis.edu/3D-Filmstrip. The

Sine-Gordon Breather is confined in space (y-axis) but periodic in time (x-axis), and therefore naturally lives on the (1+1)-dimensional torus with a timelike dimension of the Event Horizon of the pion. ...]

... Thus, Eq. (4.59) can be thought of as a soliton and an antisoliton oscillation about their common center-of-mass. For this reason, it is called 'the doublet [ or Breather ] solution'. ... the energy of the doublet ...[ eq. 4.64 ]

E = 2 M sqrt( 1 - ( w^2 / A ) )

where [ eq. 4.65 ] M = 8 sqrt( A ) / B^2 is the soliton mass. Note that the mass of the doublet is always less than twice the soliton mass, as we would expect from a soltion-antisoliton pair. ... Dashen, Hasslacher, and Neveu ... Phys. Rev. D10, 4114; 4130; 4138 (1974). A pedagogical review of these methods has been written by R. Rajaraman ( Phys. Reports 21, 227 (1975 ... Phys. Rev. D11, 3424 (1975) ...[ Dashen, Hasslacher, and Neveu found that ]... there is only a single series of bound states, labeled by the integer N ... The energies ... are ... [ eq. 4.82 ]

E_N = 2 M sin( B'^2 N / 16 )

where N = 0, 1, 2 ... < 2 =" B^2" qdot =" 2" 2 =" 4" m =" -" 2 =" 4" g =" 0" http://www.valdostamuseum.org/hamsmith/sGmTqqbarPion.pdf

...[eq. 2.13b ] E = 8 sqrt(A) / B^2 ...[ is the ]... energy of the lump ... of sine-Gordon theory ... frequently called 'soliton...' in the literature ... [ Zeroth-order is the classical case, or classical limit. ] ...

... Coherent-state variation always gives the same result as the ... Zeroth-order weak coupling expansion ... .

The ... First-order weak-coupling expansion ... explicit formula ... is ( 8 / B^2 ) - ( 1 / pi ). ...".

Note that, using the VoDou Physics constituent mass of the Up and Down quarks and antiquarks, about

312.75 MeV, as the soliton and antisoliton masses, and setting B^2 = piand using the DHN formula,

the mass of the charged pion is calculated to be ( 312.75 / 2.25 ) MeV = 139 MeV

which is in pretty good agreement with the experimental value of about 139.57 MeV. Why is the value B^2 = pi ( or, using Coleman's eq. ( 5.14 ), the Thirring coupling constant g = 3 pi ) the

special value that gives the pion mass ?

Because B^2 = pi is where the First-order weak coupling expansion substantially coincides with the ( probably exact ) DHN formula. In other words,

The physical quark - antiquark pion lives where the first-order weak coupling expansion is exact.

Near the end of his article, Coleman expressed "Some opinions":

"... This has been a long series of physics lectures with no reference whatsoever to experiment.

This is embarrassing.

... Is there any chance that the lump will be more than a theoretical toy in our field? I can think of

two possiblities.

One is that there will appear a theory of strong-interaction dynamics in which hadrons are thought of as lumps, or, ... as systems of quarks bound into lumps. ... I am pessimistic about the success of such a theory. ... However, I stand ready to be converted in a moment by a convincing computation.

The other possibility is that a lump will appear in a realistic theory ... of weak and electromagnetic interactions ... the theory would have to imbed the U(1)xSU(2) group ... in a larger group without U(1) factors ... it would be a magnetic monopole. ...".

This description of the hadronic pion as a quark - antiquark system governed by the sine-Gordon - massive Thirring model should dispel Coleman's pessimism about his first stated possibility and relieve his embarrassment about lack of contact with experiment.

As to his second stated possibility, very massive monopoles related to SU(5) GUT are still within the realm of possible future experimental discoveries.

Further material about the sine-Gordon doublet Breather and the massive Thirring equation can be found in the book Solitons and Instantons (North-Holland 1982,1987) by R. Rajaraman, who writes:

"... the doublet or breather solutions ... can be used as input into the WKB method. ... the system is ... equivalent to the massive Thirring model, with the SG soliton state identifiable as a fermion. ... Mass of the quantum soliton ... will consist of a classical term followed by quantum corrections. The energy of the classical soliton ... is ... [ eq. 7.3 ]

E_cl[f_sol] = 8 m^3 / L The quantum corrections ... to the 'soliton mass' ... is finite as the momentum cut-off goes to infinity and equals ( - m / pi ). Hence the quantum soliton's mass is [ eq. 7.10 ]

M_sol =( 8 m^3 / L ) - ( m / pi ) +O(L). The mass of the quantum antisoliton will be, by ... symmetry, the same as M_sol. ... The doublet solutions ... may be quantised by the WKB method. ... we see that the coupling

constant ( L / m^2 ) has been replaced by a 'renormalised' coupling constant G ... [ eq. 7.24 ] G = ( L / m^2 ) / ( 1 - ( L / 8 pi m^2 )) ... as a result of quantum corrections. ... the same thing had happened to the soliton mass in eq.

( 7.10 ). To leading order, we can write [ eq. 7.25 ] M_sol = ( 8 m^3 / L ) - ( m / pi ) = 8 m / G ... The doublet masses ... bound-state energy levels ... E = M_N, where ... [ eq. 7.28 ] M_N = ( 16 m / G ) sin( N G / 16 ) ; N = 1, 2, ... <> 8 pi / G . ... The

classical solutions ... bear the same relation to the bound-state wavefunctionals ... that Bohr orbits bear to hydrogen atom wavefunctions. ... Coleman ... show[ed] explicitly ... the SG theory equivalent to the charge-zero sector of the MT

model, provided ... L / 4 pi m^2 = 1 / ( 1 + g / pi )...[ where in Coleman's work set out above such as his eq. ( 5.14 ) , B^2 = L / m^2 ]...Coleman ... resurrected Skyrme's conjecture that the quantum soliton of the SG model may be

identified with the fermion of the MT model. ... ".

WHAT ABOUT THE NEUTRAL PION?

The quark content of the charged pion is u_d or d_u , both of which are consistent with the sine-Gordon picture.

Experimentally, its mass is 139.57 Mev.

The neutral pion has quark content (u_u + d_d)/sqrt(2) with two components, somewhat different from the sine-Gordon picture, and a mass of 134.96 Mev.

The effective constituent mass of a down valence quark increases (by swapping places with a strange sea quark) by about

DcMdquark = (Ms - Md) (Md/Ms)2 aw V12 == 312x0.25x0.253x0.22 Mev = 4.3 Mev.

Similarly, the up quark color force mass increase is about

DcMuquark = (Mc - Mu) (Mu/Mc)2 aw V12 == 1777x0.022x0.253x0.22 Mev = 2.2 Mev.

The color force increase for the charged pion DcMpion± = 6.5 Mev.

Since the mass Mpion± = 139.57 Mev is calculated from a color force sine-Gordon soliton state, the mass 139.57 Mev already takes DcMpion± into account.

For pion0 = (u_u + d_d)/ sqrt 2 , the d and _d of the the d_d pair do not swap places with strange sea quarks very often because it is energetically preferential for them both to become a u_u pair. Therefore, from the point of view of calculating DcMpion0, the pion0 should be considered to be only u_u , and DcMpion0 = 2.2+2.2 = 4.4 Mev.

If, as in the nucleon, DeM(pion0-pion±) = -1 Mev, the theoretical estimate is

DM(pion0-pion±) = DcM(pion0-pion±) + DeM(pion0-pion±) == 4.4 - 6.5 -1 = -3.1 Mev, roughly consistent with the experimental value of -4.6 Mev.

## 1 Comments:

https://dorigo.wordpress.com/2006/08/03/top-mass-now-at-12-uncertainty/

1. nc - August 9, 2006

I’m interested in comparing this to Tony Smith’s prediction at http://valdostamuseum.org/hamsmith/TCZ.html :

“The Truth Quark, through its strong interaction with Higgs Vacua, may have two excited energy levels at 225 GeV and 173 GeV, above a ground state at 130 GeV. The 173 GeV excited state may exist due to appearance of a Planck-energy vaccum with = 10^19 GeV in addition to the low-energy Standard Model vacuum with = 252 GeV.”

The new value of 171.4 +/- 2.1 is fully compatible with the 173 excited state Tony Smith gives.

Post a Comment

<< Home