View Full Version : Re: [Rated: speculation] Alternative to strings and Kaluza-Klein
John Gonsowski
Oct13-04, 07:03 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410090351.25162666-100000@posting.google.com>...\n\n> Dan Smith mentioned in his positing octonions, quaternions and\n> CP_2 in his comments. During last 25 years I have developed a\n> unification that I call Topological Geometrodynamics based\n> on the assumption that space-times are representable as\n> 4-surfaces in H= M^4xCP_2. Octonions and quaternion appear\n> in a number theoretic formulation of TGD too.\n\nI think you mean Tony Smith though there is a Dan Smith out there.\nTony\'s use of CP2 I believe was inspired by your\'s.\n\n> In contrast to Kaluza-Klein theories, classical gravitation\n> and gauge fields are unified in terms of induction of\n> M^4xCP_2 metric and spinor structure. Standard model\n> quantum numbers are understood in terms of isometry and\n> holonomy groups apart from family replication. Baryon and\n> lepton numbers correspond to different chiralities for\n> H-spinors induced to space-time surface and quark and\n> lepton numbers are separately conserved.\n\nTony Smith\'s use of CP2 is a Kaluza-Klein use. M4 for classical\ngravitation I think is consistent with what Tony does.\n\n> The basic (not the only one) conformal invariance is\n> naturally associated with metrically 2-dimensional light\n> like causal determinants (call them X^3_l) which by the\n> general coordinate invariance can be selected as\n> representatives of 3-spaces. This conformal invariance\n> implies effective 2-dimensionality: the physics is coded\n> by certain 2-dimensional sections X^2 of X^3_l so that a\n> formalism reduces to a form very reminiscent of conformal\n> field theories. Family replication corresponds to the\n> different genera (sphere, torus, etc.) for X^2 and there\n> is an argument explaining why only the 3 lowest genera are\n> realized.\n\nNow you\'ve really lost me which isn\'t very hard to do though getting\neffective 2-dimensionality from conformal invariance sounds\ninteresting.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410090351.25162666-100000@posting.google.com>...
> Dan Smith mentioned in his positing octonions, quaternions and
> CP_2 in his comments. During last 25 years I have developed a
> unification that I call Topological Geometrodynamics based
> on the assumption that space-times are representable as
> 4-surfaces in H= M^{4xCP_2}. Octonions and quaternion appear
> in a number theoretic formulation of TGD too.
I think you mean Tony Smith though there is a Dan Smith out there.
Tony's use of CP2 I believe was inspired by your's.
> In contrast to Kaluza-Klein theories, classical gravitation
> and gauge fields are unified in terms of induction of
> M^{4xCP_2} metric and spinor structure. Standard model
> quantum numbers are understood in terms of isometry and
> holonomy groups apart from family replication. Baryon and
> lepton numbers correspond to different chiralities for
> H-spinors induced to space-time surface and quark and
> lepton numbers are separately conserved.
Tony Smith's use of CP2 is a Kaluza-Klein use. M4 for classical
gravitation I think is consistent with what Tony does.
> The basic (not the only one) conformal invariance is
> naturally associated with metrically 2-dimensional light
> like causal determinants (call them X^{3_l}) which by the
> general coordinate invariance can be selected as
> representatives of 3-spaces. This conformal invariance
> implies effective 2-dimensionality: the physics is coded
> by certain 2-dimensional sections X^2 of X^{3_l} so that a
> formalism reduces to a form very reminiscent of conformal
> field theories. Family replication corresponds to the
> different genera (sphere, torus, etc.) for X^2 and there
> is an argument explaining why only the 3 lowest genera are
> realized.
Now you've really lost me which isn't very hard to do though getting
effective 2-dimensionality from conformal invariance sounds
interesting.
Matti Pitkanen
Oct14-04, 02:50 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>John Gonsowski <jcgonsowski@yahoo.com> wrote in message news:<e98e7f56.0410121523.3c02ffd0-100000@posting.google.com>...\n> Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410090351.25162666-100000@posting.google.com>...\n>\n> > Dan Smith mentioned in his positing octonions, quaternions and\n> > CP_2 in his comments. During last 25 years I have developed a\n> > unification that I call Topological Geometrodynamics based\n> > on the assumption that space-times are representable as\n> > 4-surfaces in H= M^4xCP_2. Octonions and quaternion appear\n> > in a number theoretic formulation of TGD too.\n>\n> I think you mean Tony Smith though there is a Dan Smith out there.\n> Tony\'s use of CP2 I believe was inspired by your\'s.\n>\n\nYou are right, of course. We had long discussions for long time ago.\nI discovered CP_2 around 1980 (S^2 preceeded it but turned out be not\nenough) and my thesis around 1982 used CP_2.\n\n\n> > In contrast to Kaluza-Klein theories, classical gravitation\n> > and gauge fields are unified in terms of induction of\n> > M^4xCP_2 metric and spinor structure. Standard model\n> > quantum numbers are understood in terms of isometry and\n> > holonomy groups apart from family replication. Baryon and\n> > lepton numbers correspond to different chiralities for\n> > H-spinors induced to space-time surface and quark and\n> > lepton numbers are separately conserved.\n>\n> Tony Smith\'s use of CP2 is a Kaluza-Klein use. M4 for classical\n> gravitation I think is consistent with what Tony does.\n\nYes. Kaluza-Klein like aspect is present however in the sense that\ncolor is not spin like quantum number but more analogous to rigid\nbody rotational degrees of freedom associated with these 2-D parton\nlike surfaces.\n\nAn important point is that CP_2 does not allow spinor structure in\nthe standard sense: one must couple imbedding space spinors to a\nmultiple of Kahler gauge potential to get a respectable spinor\nstructure. This gives the U(1) factor of standard model gauge group\nand makes CP_2 completely unique. The multiple of Kahler gauge\npotential is n=1 for quark chirality and n=3 multiple for lepton\nchirality: this gives correct em charges and correct trialities for\nleptonic/quark color partial waves. Most of these color partial waves\nrepresent states which are ultraheavy (mass scale about 10^(-4=\nPlanck masses from CP_2 size which is about 10^4 Planck lengths) since\ncolor\ncontributes to mass squared just as it would to in KK case.\n\nA further delicacy relates to the fact that the correlation between\ncolor and electroweak quantum numbers is not correct for the spinor\nharmonics of CP_2 appearing in the state construction. U and D type\nquarks correspond to different triality 1 representations for\ninstance. The construction of massless states as belonging to the\nrepresentations of Super Kac Moody algebra gives however the correct\ncorrelation: colored Kac Moody generators\nacting on the state take care of this. This is nothing but breaking of\nelectroweak gauge symmetries already at the level of CP_2 geometry\n(holonomy group U(2)_ew is not symmetry group!).\n\n\n\n\n> > The basic (not the only one) conformal invariance is\n> > naturally associated with metrically 2-dimensional light\n> > like causal determinants (call them X^3_l) which by the\n> > general coordinate invariance can be selected as\n> > representatives of 3-spaces. This conformal invariance\n> > implies effective 2-dimensionality: the physics is coded\n> > by certain 2-dimensional sections X^2 of X^3_l so that a\n> > formalism reduces to a form very reminiscent of conformal\n> > field theories. Family replication corresponds to the\n> > different genera (sphere, torus, etc.) for X^2 and there\n> > is an argument explaining why only the 3 lowest genera are\n> > realized.\n>\n> Now you\'ve really lost me which isn\'t very hard to do though getting\n> effective 2-dimensionality from conformal invariance sounds\n> interesting.\n\n\nThe story behind this quite recent realization involves 15 years work\nin the construction of metric and spinor structure of the\nconfiguration space of 3-surfaces coding for physics predicted by TGD:\ngeometry for the "world of classical worlds" analogous to Wheeler\'s\nsuperspace or loop space of closed string models. Spinor structure\nrequires infinite-D gamma matrices realized in terms of super charges\nconstructed using fermionic oscillator operators of free second\nquantized induce spinor fields at space-time surface. Hence fermion\nstatistics has purely geometric interpretation in infinite-D context.\nConfiguration space spinors are fermionic Fock states: spin up/down,\nfermion number 1/0.\n\n\nMathematical arguments for effective 2-dimensionality derive from the\nclassical non-determinism of the fundamental variational principle.\n\na) The first observation pointing to the notion of effective\n2-dimensionality was the discovery of called CP_2 type extremals.\nThey are imbeddings of CP_2 to M^4xCP_2 for which M^4 projection is\nlightlike random curve. Classically lightlike randomness is nothing\nbut Virasoro conditions. The only sensible interpretation is that this\nrandomness corresponds to a gauge symmetry, at least mathematically.\nThis degeneracy drops effectively one coordinate direction away and\nsuggests that 3-surfaces become effectively 2-D. CP_2 type extremals\nare excellent candidates for representatives of elementary\nparticles. That the induced metric has Euclidian signature does not\nmatter since Poincare symmetries act in imbedding space rather than in\nspace-time.\n\n\nb) Pieces of these CP_2 type extremals can be used to build "wormhole\ncontacts" between parallel space-time sheets. Here you encounter one\nvariant of causal determinant. The wormhole contacts have Euclidian\nsignature and the space-time sheets Minkowskian. There must exist a\n3-surface\nwhich separate these regions. At this region the signature of the\nmetric is neither Minkowskian 1-1-1-1 nor Euclidian -1-1-1-1(nor both)\nand thus 0-1-1-1:\nhence light-likeness. Black hole horizon is of course one example of a\nlightlike causal determinant and effective 2-dimensionality implies\nthat horizon at fixed value of time codes for all information about\nphysical states.\n\nc) A further important piece in the story is the classical\nnon-determinism of the basic variational principle involving Maxwell\naction for the Kahler form of CP_2 projected to the space-time\nsurface. There is a huge vacuum degeneracy due to the fact that\ninduced gauge field vanishes identically when the Kahler gauge\npotential is pure gauge. This occurs when the CP_2 projection of\nspace-time surface belongs to a 2-dimensional Lagrange manifold Y^2.\nThe analog in the case of (P,Q) phase space would be p= f(q). Now one\nhas\n\nP^i = partial_i f(Q^1,Q^2), i=1,2,\n\nwhere P^i and Q^i are so called Darboux coordinates for CP_2. Also\nthe non-vacuum extremals obtained as deformations of vacuum extremals\n(absolute minima of Kahler action which tend to develop Kaehler\nelectric fields to minimize the action) inherit this degeneracy. A\nconsiderable fraction of this degeneracy due to classical\nnon-determinism should have interpretation as a gauge degeneracy, at\nleast in the mathematical sense.\n\nThe fact that time direction becomes non-dynamical for 3-D lightlike\ncausal determinants suggests that this degeneracy must make 3-surfaces\neffectively 2-dimensional.\n\n\nThere are various physical arguments for effective 2-dimensionality.\n\na) Physically the result is understandable as follows. By general\ncoordinate invariance and quantum gravitational holography 3-D causal\ndeterminants code the physics: quantum gravitational holography can be\ntranslated also to the\nstatement that space-time surfaces are like Bohr orbits: once you know\nthe point through which the orbit goes and the direction of orbit you\nknow the orbit. The above mentioned gauge invariance eliminates\neffectively one\ndimension (but only effectively).\n\nb) If you would take very seriously the fact that our sensory data\nseems\nalways to be about two-dimensional surfaces, you would say heureka:\nthe physics is such that everything can be expressed in terms of these\n2-D partons and everything reduces to the task of identifying the\nunderlying conformal field theory.\n\nc) Particle-field duality. Fields in the interior of space-time\nsurface\ncorresponds to field aspects. Lightlike causal determinants carrying\nspinorial shock waves correspond to particle, or more precisely\nparton, aspect and the physical evolution of shock wave is coded to\ninitial data given at\n2-surface X^2. Click caused by photon in detector is like bang created\nby an acoustic shock wave in my ears.\n\nd) Consider for simplicity a 4-surface with 3-D space-like section\nX^3 and lightlike boundary X^3_l. You could argue that the information\nabout physical state must be coded wither by X^3 or by X^3_l. This\nleaves only the possibility that it is coded by the 2-D intersection\nX^2 of X^3 and X^3_l, the "parton".\n\n\n\n\nThere are also number theoretic arguments supporting the effective\n2-dimensionality.\n\na) You could also regard 8-D space M^4xCP_2 as a space possessing an\noctonionic structure in its tangent space and say that space-time\nsurfaces are maximal associative sub-manifolds. This means that\ntangent space spans at every point quaternionic subalgebra. One could\nhope that the absolute minimization of Kahler action is equivalent\nwith associativity: perhaps someone could prove this conjecture to\nbe correct/wrong.\n\nb) You can generalize the notion of commuting observables to\nnumber theory level to the statement that physics is coded by\ncommutative sub-manifolds of\nspacetime. The tangent spaces of commutative manifolds must define\nAbelian subalgebras of octonionic M^4xCP_2. Only 2-surfaces for\nwhich tangent space defines a complex subalgebra of octonions are\npossible. There are good reasons to believe that existence of complex\nconjugation at each point implies a global Z_2 conformal symmetry of\nparton 2-surface. This symmetry, known as hyperellipticity,\nguarantees that the partons in incoming and outgoing states can have\nonly three lowest topologies: sphere, torus, sphere with two handles.\nThree particle families, also bosonic ones, are predicted. The reason\nis that elementary particle vacuum functionals in conformal modular\ndegrees of freedom of X^2 vanish for hyperelliptic surfaces with genus\nlarger than 2.\n\n\nStill one point: the effective 2-dimensionality is only effective. The\ndata about the interior of space-time surface is coded to say\nS-matrix. The normal components T^{n alpha} of Maxwell energy\nmomentum tensor for induced Kahler field define a flow analogous to a\nhydrodynamic flow at the lightlike 3-surfaces and contain information\nabout the forces caused by other partons. The induced spinor fields\nare parallelly translated along the flow lines of this flow defining a\nbraiding flow. Higgs mechanism can be understood as loss of\ncorrelations (finite correlation length/time means massivation) due to\nthe mixing caused by this flow.\n\nA somewhat surprising outcome is that at the fundamental space-time\nlevel TGD is more like "anyonic shydrodynamics" than field theory.\nField equations are indeed essentially hydrodynamical in the sense\nthat they state local conservation of four-momentum and classical\ncolor charges. Quantum field theory approximation would appear at\nMinkowski space level when one finds that S-matrix elements have\napproximate decomposition into vertices and propagators in Minkowski\nspace and goes on to postulate quantum fields with local\ninteractions.\n\n\n\nMatti Pitkanen\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>John Gonsowski <jcgonsowski@yahoo.com> wrote in message news:<e98e7f56.0410121523.3c02ffd0-100000@posting.google.com>...
> Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410090351.25162666-100000@posting.google.com>...
>
> > Dan Smith mentioned in his positing octonions, quaternions and
> > CP_2 in his comments. During last 25 years I have developed a
> > unification that I call Topological Geometrodynamics based
> > on the assumption that space-times are representable as
> > 4-surfaces in H= M^{4xCP_2}. Octonions and quaternion appear
> > in a number theoretic formulation of TGD too.
>
> I think you mean Tony Smith though there is a Dan Smith out there.
> Tony's use of CP2 I believe was inspired by your's.
>
You are right, of course. We had long discussions for long time ago.
I discovered CP_2 around 1980 (S^2 preceeded it but turned out be not
enough) and my thesis around 1982 used CP_2.
> > In contrast to Kaluza-Klein theories, classical gravitation
> > and gauge fields are unified in terms of induction of
> > M^{4xCP_2} metric and spinor structure. Standard model
> > quantum numbers are understood in terms of isometry and
> > holonomy groups apart from family replication. Baryon and
> > lepton numbers correspond to different chiralities for
> > H-spinors induced to space-time surface and quark and
> > lepton numbers are separately conserved.
>
> Tony Smith's use of CP2 is a Kaluza-Klein use. M4 for classical
> gravitation I think is consistent with what Tony does.
Yes. Kaluza-Klein like aspect is present however in the sense that
color is not spin like quantum number but more analogous to rigid
body rotational degrees of freedom associated with these 2-D parton
like surfaces.
An important point is that CP_2 does not allow spinor structure in
the standard sense: one must couple imbedding space spinors to a
multiple of Kahler gauge potential to get a respectable spinor
structure. This gives the U(1) factor of standard model gauge group
and makes CP_2 completely unique. The multiple of Kahler gauge
potential is n=1 for quark chirality and n=3 multiple for lepton
chirality: this gives correct em charges and correct trialities for
leptonic/quark color partial waves. Most of these color partial waves
represent states which are ultraheavy (mass scale about 10^(-4=
Planck masses from CP_2 size which is about 10^4 Planck lengths) since
color
contributes to mass squared just as it would to in KK case.
A further delicacy relates to the fact that the correlation between
color and electroweak quantum numbers is not correct for the spinor
harmonics of CP_2 appearing in the state construction. U and D type
quarks correspond to different triality 1 representations for
instance. The construction of massless states as belonging to the
representations of Super Kac Moody algebra gives however the correct
correlation: colored Kac Moody generators
acting on the state take care of this. This is nothing but breaking of
electroweak gauge symmetries already at the level of CP_2 geometry
(holonomy group U(2)_ew is not symmetry group!).
> > The basic (not the only one) conformal invariance is
> > naturally associated with metrically 2-dimensional light
> > like causal determinants (call them X^{3_l}) which by the
> > general coordinate invariance can be selected as
> > representatives of 3-spaces. This conformal invariance
> > implies effective 2-dimensionality: the physics is coded
> > by certain 2-dimensional sections X^2 of X^{3_l} so that a
> > formalism reduces to a form very reminiscent of conformal
> > field theories. Family replication corresponds to the
> > different genera (sphere, torus, etc.) for X^2 and there
> > is an argument explaining why only the 3 lowest genera are
> > realized.
>
> Now you've really lost me which isn't very hard to do though getting
> effective 2-dimensionality from conformal invariance sounds
> interesting.
The story behind this quite recent realization involves 15 years work
in the construction of metric and spinor structure of the
configuration space of 3-surfaces coding for physics predicted by TGD:
geometry for the "world of classical worlds" analogous to Wheeler's
superspace or loop space of closed string models. Spinor structure
requires infinite-D \gamma matrices realized in terms of super charges
constructed using fermionic oscillator operators of free second
quantized induce spinor fields at space-time surface. Hence fermion
statistics has purely geometric interpretation in infinite-D context.
Configuration space spinors are fermionic Fock states: spin up/down,
fermion number 1/0.
Mathematical arguments for effective 2-dimensionality derive from the
classical non-determinism of the fundamental variational principle.
a) The first observation pointing to the notion of effective
2-dimensionality was the discovery of called CP_2 type extremals.
They are imbeddings of CP_2 to M^{4xCP_2} for which M^4 projection is
lightlike random curve. Classically lightlike randomness is nothing
but Virasoro conditions. The only sensible interpretation is that this
randomness corresponds to a gauge symmetry, at least mathematically.
This degeneracy drops effectively one coordinate direction away and
suggests that 3-surfaces become effectively 2-D. CP_2 type extremals
are excellent candidates for representatives of elementary
particles. That the induced metric has Euclidian signature does not
matter since Poincare symmetries act in imbedding space rather than in
space-time.
b) Pieces of these CP_2 type extremals can be used to build "wormhole
contacts" between parallel space-time sheets. Here you encounter one
variant of causal determinant. The wormhole contacts have Euclidian
signature and the space-time sheets Minkowskian. There must exist a
3-surface
which separate these regions. At this region the signature of the
metric is neither Minkowskian 1-1-1-1 nor Euclidian -1-1-1-1(nor both)
and thus 0-1-1-1:
hence light-likeness. Black hole horizon is of course one example of a
lightlike causal determinant and effective 2-dimensionality implies
that horizon at fixed value of time codes for all information about
physical states.
c) A further important piece in the story is the classical
non-determinism of the basic variational principle involving Maxwell
action for the Kahler form of CP_2 projected to the space-time
surface. There is a huge vacuum degeneracy due to the fact that
induced gauge field vanishes identically when the Kahler gauge
potential is pure gauge. This occurs when the CP_2 projection of
space-time surface belongs to a 2-dimensional Lagrange manifold Y^2.
The analog in the case of (P,Q) phase space would be p= f(q). Now one
has
P^i = partial_i f(Q^1,Q^2), i=1,2,
where P^i and Q^i are so called Darboux coordinates for CP_2. Also
the non-vacuum extremals obtained as deformations of vacuum extremals
(absolute minima of Kahler action which tend to develop Kaehler
electric fields to minimize the action) inherit this degeneracy. A
considerable fraction of this degeneracy due to classical
non-determinism should have interpretation as a gauge degeneracy, at
least in the mathematical sense.
The fact that time direction becomes non-dynamical for 3-D lightlike
causal determinants suggests that this degeneracy must make 3-surfaces
effectively 2-dimensional.
There are various physical arguments for effective 2-dimensionality.
a) Physically the result is understandable as follows. By general
coordinate invariance and quantum gravitational holography 3-D causal
determinants code the physics: quantum gravitational holography can be
translated also to the
statement that space-time surfaces are like Bohr orbits: once you know
the point through which the orbit goes and the direction of orbit you
know the orbit. The above mentioned gauge invariance eliminates
effectively one
dimension (but only effectively).
b) If you would take very seriously the fact that our sensory data
seems
always to be about two-dimensional surfaces, you would say heureka:
the physics is such that everything can be expressed in terms of these
2-D partons and everything reduces to the task of identifying the
underlying conformal field theory.
c) Particle-field duality. Fields in the interior of space-time
surface
corresponds to field aspects. Lightlike causal determinants carrying
spinorial shock waves correspond to particle, or more precisely
parton, aspect and the physical evolution of shock wave is coded to
initial data given at
2-surface X^2. Click caused by photon in detector is like bang created
by an acoustic shock wave in my ears.
d) Consider for simplicity a 4-surface with 3-D space-like section
X^3 and lightlike boundary X^{3_l}. You could argue that the information
about physical state must be coded wither by X^3 or by X^{3_l}. This
leaves only the possibility that it is coded by the 2-D intersection
X^2 of X^3 and X^{3_l}, the "parton".
There are also number theoretic arguments supporting the effective
2-dimensionality.
a) You could also regard 8-D space M^{4xCP_2} as a space possessing an
octonionic structure in its tangent space and say that space-time
surfaces are maximal associative sub-manifolds. This means that
tangent space spans at every point quaternionic subalgebra. One could
hope that the absolute minimization of Kahler action is equivalent
with associativity: perhaps someone could prove this conjecture to
be correct/wrong.
b) You can generalize the notion of commuting observables to
number theory level to the statement that physics is coded by
commutative sub-manifolds of
spacetime. The tangent spaces of commutative manifolds must define
Abelian subalgebras of octonionic M^{4xCP_2}. Only 2-surfaces for
which tangent space defines a complex subalgebra of octonions are
possible. There are good reasons to believe that existence of complex
conjugation at each point implies a global Z_2 conformal symmetry of
parton 2-surface. This symmetry, known as hyperellipticity,
guarantees that the partons in incoming and outgoing states can have
only three lowest topologies: sphere, torus, sphere with two handles.
Three particle families, also bosonic ones, are predicted. The reason
is that elementary particle vacuum functionals in conformal modular
degrees of freedom of X^2 vanish for hyperelliptic surfaces with genus
larger than 2.
Still one point: the effective 2-dimensionality is only effective. The
data about the interior of space-time surface is coded to say
S-matrix. The normal components T^{n \alpha} of Maxwell energy
momentum tensor for induced Kahler field define a flow analogous to a
hydrodynamic flow at the lightlike 3-surfaces and contain information
about the forces caused by other partons. The induced spinor fields
are parallelly translated along the flow lines of this flow defining a
braiding flow. Higgs mechanism can be understood as loss of
correlations (finite correlation length/time means massivation) due to
the mixing caused by this flow.
A somewhat surprising outcome is that at the fundamental space-time
level TGD is more like "anyonic shydrodynamics" than field theory.
Field equations are indeed essentially hydrodynamical in the sense
that they state local conservation of four-momentum and classical
color charges. Quantum field theory approximation would appear at
Minkowski space level when one finds that S-matrix elements have
approximate decomposition into vertices and propagators in Minkowski
space and goes on to postulate quantum fields with local
interactions.
Matti Pitkanen
John Gonsowski
Oct15-04, 11:03 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410131853.3097ec78-100000@posting.google.com>...\n> > Tony Smith\'s use of CP2 is a Kaluza-Klein use. M4 for classical\n> > gravitation I think is consistent with what Tony does.\n>\n> Yes. Kaluza-Klein like aspect is present however in the sense that\n> color is not spin like quantum number but more analogous to rigid\n> body rotational degrees of freedom associated with these 2-D parton\n> like surfaces.\n\nI can see the standard model bosons doing for CP2 what gravitons do\nfor the 4 familiar spacetime dimensions.\n\n> An important point is that CP_2 does not allow spinor structure in\n> the standard sense: one must couple imbedding space spinors to a\n> multiple of Kahler gauge potential to get a respectable spinor\n> structure. This gives the U(1) factor of standard model gauge group\n> and makes CP_2 completely unique. The multiple of Kahler gauge\n> potential is n=1 for quark chirality and n=3 multiple for lepton\n> chirality: this gives correct em charges and correct trialities for\n> leptonic/quark color partial waves. Most of these color partial waves\n> represent states which are ultraheavy (mass scale about 10^(-4=\n> Planck masses from CP_2 size which is about 10^4 Planck lengths) since\n> color contributes to mass squared just as it would to in KK case.\n>\n> A further delicacy relates to the fact that the correlation between\n> color and electroweak quantum numbers is not correct for the spinor\n> harmonics of CP_2 appearing in the state construction. U and D type\n> quarks correspond to different triality 1 representations for\n> instance. The construction of massless states as belonging to the\n> representations of Super Kac Moody algebra gives however the correct\n> correlation: colored Kac Moody generators\n> acting on the state take care of this. This is nothing but breaking of\n> electroweak gauge symmetries already at the level of CP_2 geometry\n> (holonomy group U(2)_ew is not symmetry group!).\n\nI\'m kind of surprised that you work with the supersymmetry algebras. I\nthink Tony Smith\'s approach to this kind of stuff is summed up in this\nsci.physics.research post from a couple years ago though I feel a\nlittle funny quoting him so much here in a forum he visits also: "It\nmay be important to note that some of the relevant symmetric spaces\nsuch as BDI (p=2) for D5 / D4xU(1) and EIII for E6 / D5xU(1) and EVII\nfor E7 / E6x U(1) are Hermitian and therefore have related bounded\ncomplex homogeneous domains... and that the harmonic structures of\nsuch complex domains, such as Poisson kernels, Bergman kernels, etc.,\nare useful (probably necessary) for building models that do real\nphysics. However, spaces like E6 / F4 (type EIV) and E8 / E7xSU(2)\n(type EIX) have no Kahler structure, and no nicely directly related\nbounded complex homogeneous domains. Although the space E6 / F4 is not\ncomplex (it has no Kahler structure), it has octonionic/complexified\noctonionic strucure, and may be related to some Cayley-Dickson-doubled\nversion of the nice harmonic complex structures of the Hermitian\nspaces."\n\n> > Now you\'ve really lost me which isn\'t very hard to do though getting\n> > effective 2-dimensionality from conformal invariance sounds\n> > interesting.\n>\n> The story behind this quite recent realization involves 15 years work\n> in the construction of metric and spinor structure of the\n> configuration space of 3-surfaces coding for physics predicted by TGD:\n> geometry for the "world of classical worlds" analogous to Wheeler\'s\n> superspace or loop space of closed string models...\n> The first observation pointing to the notion of effective\n> 2-dimensionality was the discovery of called CP_2 type extremals.\n> They are imbeddings of CP_2 to M^4xCP_2 for which M^4 projection is\n> lightlike random curve...\n> You could also regard 8-D space M^4xCP_2 as a space possessing an\n> octonionic structure in its tangent space and say that space-time\n> surfaces are maximal associative sub-manifolds...\n> Higgs mechanism can be understood as loss of> correlations (finite\n> correlation length/time means massivation) due to the mixing caused by this > flow...\n> Quantum field theory approximation would appear at\n> Minkowski space level when one finds that S-matrix elements have\n> approximate decomposition into vertices and propagators in Minkowski\n> space and goes on to postulate quantum fields with local\n> interactions...\n\nSmith\'s model is a many-worlds one with closed strings and a\nvector-half spinor-half spinor triality. He does have an 8-D space\nincludine the co-associative CP2. The conformal degrees of freedom are\nwhat allows contact with CP2 (and the imaginary part of complex\nspacetime), I guess the mapping mostly comes out effectively two\ndimensional. Conformal symmetry does seem to have some nice side\neffects for the Higgs Mechanism, S-Matrix and other things.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410131853.3097ec78-100000@posting.google.com>...
> > Tony Smith's use of CP2 is a Kaluza-Klein use. M4 for classical
> > gravitation I think is consistent with what Tony does.
>
> Yes. Kaluza-Klein like aspect is present however in the sense that
> color is not spin like quantum number but more analogous to rigid
> body rotational degrees of freedom associated with these 2-D parton
> like surfaces.
I can see the standard model bosons doing for CP2 what gravitons do
for the 4 familiar spacetime dimensions.
> An important point is that CP_2 does not allow spinor structure in
> the standard sense: one must couple imbedding space spinors to a
> multiple of Kahler gauge potential to get a respectable spinor
> structure. This gives the U(1) factor of standard model gauge group
> and makes CP_2 completely unique. The multiple of Kahler gauge
> potential is n=1 for quark chirality and n=3 multiple for lepton
> chirality: this gives correct em charges and correct trialities for
> leptonic/quark color partial waves. Most of these color partial waves
> represent states which are ultraheavy (mass scale about 10^(-4=
> Planck masses from CP_2 size which is about 10^4 Planck lengths) since
> color contributes to mass squared just as it would to in KK case.
>
> A further delicacy relates to the fact that the correlation between
> color and electroweak quantum numbers is not correct for the spinor
> harmonics of CP_2 appearing in the state construction. U and D type
> quarks correspond to different triality 1 representations for
> instance. The construction of massless states as belonging to the
> representations of Super Kac Moody algebra gives however the correct
> correlation: colored Kac Moody generators
> acting on the state take care of this. This is nothing but breaking of
> electroweak gauge symmetries already at the level of CP_2 geometry
> (holonomy group U(2)_ew is not symmetry group!).
I'm kind of surprised that you work with the supersymmetry algebras. I
think Tony Smith's approach to this kind of stuff is summed up in this
sci.physics.research post from a couple years ago though I feel a
little funny quoting him so much here in a forum he visits also: "It
may be important to note that some of the relevant symmetric spaces
such as BDI (p=2) for D5 / D4xU(1) and EIII for E6 / D5xU(1) and EVII
for E7 / E6x U(1) are Hermitian and therefore have related bounded
complex homogeneous domains... and that the harmonic structures of
such complex domains, such as Poisson kernels, Bergman kernels, etc.,
are useful (probably necessary) for building models that do real
physics. However, spaces like E6 / F4 (type EIV) and E8 / E7xSU(2)
(type EIX) have no Kahler structure, and no nicely directly related
bounded complex homogeneous domains. Although the space E6 / F4 is not
complex (it has no Kahler structure), it has octonionic/complexified
octonionic strucure, and may be related to some Cayley-Dickson-doubled
version of the nice harmonic complex structures of the Hermitian
spaces."
> > Now you've really lost me which isn't very hard to do though getting
> > effective 2-dimensionality from conformal invariance sounds
> > interesting.
>
> The story behind this quite recent realization involves 15 years work
> in the construction of metric and spinor structure of the
> configuration space of 3-surfaces coding for physics predicted by TGD:
> geometry for the "world of classical worlds" analogous to Wheeler's
> superspace or loop space of closed string models...
> The first observation pointing to the notion of effective
> 2-dimensionality was the discovery of called CP_2 type extremals.
> They are imbeddings of CP_2 to M^{4xCP_2} for which M^4 projection is
> lightlike random curve...
> You could also regard 8-D space M^{4xCP_2} as a space possessing an
> octonionic structure in its tangent space and say that space-time
> surfaces are maximal associative sub-manifolds...
> Higgs mechanism can be understood as loss of> correlations (finite
> correlation length/time means massivation) due to the mixing caused by this > flow...
> Quantum field theory approximation would appear at
> Minkowski space level when one finds that S-matrix elements have
> approximate decomposition into vertices and propagators in Minkowski
> space and goes on to postulate quantum fields with local
> interactions...
Smith's model is a many-worlds one with closed strings and a
vector-half spinor-half spinor triality. He does have an 8-D space
includine the co-associative CP2. The conformal degrees of freedom are
what allows contact with CP2 (and the imaginary part of complex
spacetime), I guess the mapping mostly comes out effectively two
dimensional. Conformal symmetry does seem to have some nice side
effects for the Higgs Mechanism, S-Matrix and other things.
Matti Pitkanen
Oct17-04, 11:21 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>John Gonsowski <jcgonsowski@yahoo.com> wrote in message news:<e98e7f56.0410151715.669e737f-100000@posting.google.com>...\n\n> I\'m kind of surprised that you work with the supersymmetry algebras. I\n> think Tony Smith\'s approach to this kind of stuff is summed up in this\n> sci.physics.research post from a couple years ago though I feel a\n> little funny quoting him so much here in a forum he visits also: "It\n> may be important to note that some of the relevant symmetric spaces\n> such as BDI (p=2) for D5 / D4xU(1) and EIII for E6 / D5xU(1) and EVII\n> for E7 / E6x U(1) are Hermitian and therefore have related bounded\n> complex homogeneous domains... and that the harmonic structures of\n> such complex domains, such as Poisson kernels, Bergman kernels, etc.,\n> are useful (probably necessary) for building models that do real\n> physics. However, spaces like E6 / F4 (type EIV) and E8 / E7xSU(2)\n> (type EIX) have no Kahler structure, and no nicely directly related\n> bounded complex homogeneous domains. Although the space E6 / F4 is not\n> complex (it has no Kahler structure), it has octonionic/complexified\n> octonionic strucure, and may be related to some Cayley-Dickson-doubled\n> version of the nice harmonic complex structures of the Hermitian\n> spaces."\n\nYou are wondering why I work with super symmetric algebras. As I\nalready explained 2-D conformal symmetry is naturally associated with\n3-D lightlike 3-surfaces which by General Coordinate Invariance can\nbe chosen as causal determinants and are metrically 2-D. The reason\nis that the basic dynamical principle assigns a space-time X^4(X^3)\nto a given 3-surface X^3 for Diff^4 to act on, and X^4(X^3) is\nanalogous to Bohr orbit. All diffeomorphs of X^3 along X^4(X^3) are\ngauge equivalent. The uniques of dimension two for conformal symmetry\nmeans that space-time dimension 4 is unique and gives maximally rich\nconformal invariance since the basic objects are effectively 2-D\nrather than 1-D as in string models.\n\n\nSuper algebras emerge naturally in infinite-D geomery.\n\na) Quantum states of the Universe correspond to the modes of classical\nspinor fields in infinite-D configuration space of 3-surfaces: the\n"world of classical worlds". This space has Kahler metric and spinor\nstructure and decomposes into union of infinite-dimensional symmetric\nspaces having constant curvature, which must vanish unless it is\ninfinite so that Einstein equations are satisfied. The spaces in the\nunion are labelled by zero modes having interpretation as non-quantum\nfluctuating classical observables characterizing size and shape of\n3-surface and allow to understand quantum measurement theory\ngeometrically. This is nothing but cosmological principle in\ninfinite-D context: all 3-surfaces with same zero modes are\nmetrically equivalent.\n\nCartan gave the list of finite-D symmetric spaces and a TOE inspired\nguess is that there is only a single item in the corresponding list in\nthe infinite-D context(;-). As found by Dan Freed, already loop spaces\nKahler geometries are unique and allow an infinite-dimensional\nisometry group (local gauge group itself). The problem is that\ncurvature scalar is infinite for them. In higher dimensions\nconsistency conditions are certainly stronger.\n\n\nb) Infinite-D spinor structure requires complexified gamma matrices\nand these are expressible in terms of fermionic oscillator operators\nfor the second quantized free induced spinor fields at space-time\nsurfaces. By effective 2-dimensionality everything reduces to these\n2-D boundary surfaces, partons, macroscopic boundaries, blackhole\nhorizons, etc...\n\n\nc) These gamma matrices generate super algebra: now they however\ncarry fermion number rather than being Majorana like. They correspond\nto super counterparts for Hamiltonians of \\$delta M^4_+CP_2\nallowing degenerate symplectic structure. There is also Super\nKac-Moody\nalgebra associated with isometries and holonomies of the imbedding\nspace. These two super algebras define two different tangent space\nbasis for the configuration space, and general coordinate invariance\nin infinite-D context encourages to think that corresponding Virasoro\nalgebras have the same central extension. If so, then the analog of\ncoset construction gives Virasoro algebra with a vanishing central\nextension: in string models this requires critical dimension. In TGD\nthis requires D=4 for space-time and there are good arguments that\nM^4xCP_2 is also mathematically the only option that works.\n\nVirasoro generators are *differences* of super Kac-Moody and\nsuper-canonical generators. Physical states are constructed by first\ncreating ground state using super-canonical algebras: its conformal\nweight is negative and has arbitrarily large magnitude. Then Super\nKac-Moody algebra is applied to increase the conformal weight so that\nit becomes non-negative. Although no sparticles are predicted,\ninfinite number of massless modes results. Higgs mechanism massivates\nthem but it requires a lot of thought to show that no light exotics\nare predicted. One must however remember that the 2-surfaces can have\narbitrary size so that elementary particles correspond to a very\nrestricted special case.\n\nI have started just now to disetangle the structure of particle states\n(see the chapter "Massless states and particle Massivation" of TGD at\nhttp://www.physics.helsinki.fi/~matpitka/tgd.html#mless .)\n\n\n\nd) The non-stringy effects relate to the presence of the\nsuper-canonical algebra. One of the most fascinating aspects is the\nconnection with Riemann Zeta. Number theoretic arguments strongly\nsuggest that super-canonical conformal weights are expressible in\nterms of zeros of Riemann Zeta: Riemann hypothesis z=1/2+iy follows a\nconsistency condition since also complex conjugate of weight must be a\nweight (note that the real part 1/2 relates very closely to N-S\nrepresentations). Physical states must have real conformal weights and\nthis gives rise to "conformal confinement": physical states are\ncreated by operators for which net super-canonical conformal weight is\nreal. If partons have a net conformal weight, their conformal weights\nmust sum up to a real conformal weight. Conformal confinement might\nunderly behind color confinement.\n\n\nMatti Pitkanen\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>John Gonsowski <jcgonsowski@yahoo.com> wrote in message news:<e98e7f56.0410151715.669e737f-100000@posting.google.com>...
> I'm kind of surprised that you work with the supersymmetry algebras. I
> think Tony Smith's approach to this kind of stuff is summed up in this
> sci.physics.research post from a couple years ago though I feel a
> little funny quoting him so much here in a forum he visits also: "It
> may be important to note that some of the relevant symmetric spaces
> such as BDI (p=2) for D5 / D4xU(1) and EIII for E6 / D5xU(1) and EVII
> for E7 / E6x U(1) are Hermitian and therefore have related bounded
> complex homogeneous domains... and that the harmonic structures of
> such complex domains, such as Poisson kernels, Bergman kernels, etc.,
> are useful (probably necessary) for building models that do real
> physics. However, spaces like E6 / F4 (type EIV) and E8 / E7xSU(2)
> (type EIX) have no Kahler structure, and no nicely directly related
> bounded complex homogeneous domains. Although the space E6 / F4 is not
> complex (it has no Kahler structure), it has octonionic/complexified
> octonionic strucure, and may be related to some Cayley-Dickson-doubled
> version of the nice harmonic complex structures of the Hermitian
> spaces."
You are wondering why I work with super symmetric algebras. As I
already explained 2-D conformal symmetry is naturally associated with
3-D lightlike 3-surfaces which by General Coordinate Invariance can
be chosen as causal determinants and are metrically 2-D. The reason
is that the basic dynamical principle assigns a space-time X^4(X^3)
to a given 3-surface X^3 for Diff^4 to act on, and X^4(X^3) is
analogous to Bohr orbit. All diffeomorphs of X^3 along X^4(X^3) are
gauge equivalent. The uniques of dimension two for conformal symmetry
means that space-time dimension 4 is unique and gives maximally rich
conformal invariance since the basic objects are effectively 2-D
rather than 1-D as in string models.
Super algebras emerge naturally in infinite-D geomery.
a) Quantum states of the Universe correspond to the modes of classical
spinor fields in infinite-D configuration space of 3-surfaces: the
"world of classical worlds". This space has Kahler metric and spinor
structure and decomposes into union of infinite-dimensional symmetric
spaces having constant curvature, which must vanish unless it is
infinite so that Einstein equations are satisfied. The spaces in the
union are labelled by zero modes having interpretation as non-quantum
fluctuating classical observables characterizing size and shape of
3-surface and allow to understand quantum measurement theory
geometrically. This is nothing but cosmological principle in
infinite-D context: all 3-surfaces with same zero modes are
metrically equivalent.
Cartan gave the list of finite-D symmetric spaces and a TOE inspired
guess is that there is only a single item in the corresponding list in
the infinite-D context(;-). As found by Dan Freed, already loop spaces
Kahler geometries are unique and allow an infinite-dimensional
isometry group (local gauge group itself). The problem is that
curvature scalar is infinite for them. In higher dimensions
consistency conditions are certainly stronger.
b) Infinite-D spinor structure requires complexified \gamma matrices
and these are expressible in terms of fermionic oscillator operators
for the second quantized free induced spinor fields at space-time
surfaces. By effective 2-dimensionality everything reduces to these
2-D boundary surfaces, partons, macroscopic boundaries, blackhole
horizons, etc...
c) These \gamma matrices generate super algebra: now they however
carry fermion number rather than being Majorana like. They correspond
to super counterparts for Hamiltonians of $\delta M^{4_}+CP_2
allowing degenerate symplectic structure. There is also Super
Kac-Moody
algebra associated with isometries and holonomies of the imbedding
space. These two super algebras define two different tangent space
basis for the configuration space, and general coordinate invariance
in infinite-D context encourages to think that corresponding Virasoro
algebras have the same central extension. If so, then the analog of
coset construction gives Virasoro algebra with a vanishing central
extension: in string models this requires critical dimension. In TGD
this requires D=4 for space-time and there are good arguments that
M^{4xCP_2} is also mathematically the only option that works.
Virasoro generators are *differences* of super Kac-Moody and
super-canonical generators. Physical states are constructed by first
creating ground state using super-canonical algebras: its conformal
weight is negative and has arbitrarily large magnitude. Then Super
Kac-Moody algebra is applied to increase the conformal weight so that
it becomes non-negative. Although no sparticles are predicted,
infinite number of massless modes results. Higgs mechanism massivates
them but it requires a lot of thought to show that no light exotics
are predicted. One must however remember that the 2-surfaces can have
arbitrary size so that elementary particles correspond to a very
restricted special case.
I have started just now to disetangle the structure of particle states
(see the chapter "Massless states and particle Massivation" of TGD at
http://www.physics.helsinki.fi/~matpitka/tgd.html#mless .)
d) The non-stringy effects relate to the presence of the
super-canonical algebra. One of the most fascinating aspects is the
connection with Riemann \Zeta. Number theoretic arguments strongly
suggest that super-canonical conformal weights are expressible in
terms of zeros of Riemann \Zeta: Riemann hypothesis z=1/2+iy follows a
consistency condition since also complex conjugate of weight must be a
weight (note that the real part 1/2 relates very closely to N-S
representations). Physical states must have real conformal weights and
this gives rise to "conformal confinement": physical states are
created by operators for which net super-canonical conformal weight is
real. If partons have a net conformal weight, their conformal weights
must sum up to a real conformal weight. Conformal confinement might
underly behind color confinement.
Matti Pitkanen
John Gonsowski
Oct19-04, 11:51 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410170629.2872c69f-100000@posting.google.com>...\n\n> You are wondering why I work with super symmetric algebras. As I\n> already explained 2-D conformal symmetry is naturally associated with\n> 3-D lightlike 3-surfaces which by General Coordinate Invariance can\n> be chosen as causal determinants and are metrically 2-D...\n> Super algebras emerge naturally in infinite-D geomery...\n> I have started just now to disetangle the structure of particle states\n> (see the chapter "Massless states and particle Massivation" of TGD at\n> http://www.physics.helsinki.fi/~matpitka/tgd.html#mless .)...\n> Conformal confinement might underly behind color confinement...\n\nOk I think I\'m understanding this to the point I\'m capable of.\nHistorically, you had your basic model and you were working on your\nprime number stuff. The superalgebras were part of your prime number\nresearch but you hoped to later fit them into your overall model. You\nhave since fit them in but are still working on some details.\n\nUsing a sphere, a torus and a two-handle sphere for the three\ngenerations sounds somewhat like what Tony Smith does when he uses 0,\n1 and 2 CP2 to S4 connections for the three generations. He then uses\ncomplex domains from Lie Algebras to do diffusion equations for mass\ncalculations and it looks like you use superalgebras and your topology\nmodel to do the mass calculations. That conformal confinement sounds\nsimilar to what Smith does with Kerr-Newman equations and the\nconformal degrees of freedom.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410170629.2872c69f-100000@posting.google.com>...
> You are wondering why I work with super symmetric algebras. As I
> already explained 2-D conformal symmetry is naturally associated with
> 3-D lightlike 3-surfaces which by General Coordinate Invariance can
> be chosen as causal determinants and are metrically 2-D...
> Super algebras emerge naturally in infinite-D geomery...
> I have started just now to disetangle the structure of particle states
> (see the chapter "Massless states and particle Massivation" of TGD at
> http://www.physics.helsinki.fi/~matpitka/tgd.html#mless .)...
> Conformal confinement might underly behind color confinement...
Ok I think I'm understanding this to the point I'm capable of.
Historically, you had your basic model and you were working on your
prime number stuff. The superalgebras were part of your prime number
research but you hoped to later fit them into your overall model. You
have since fit them in but are still working on some details.
Using a sphere, a torus and a two-handle sphere for the three
generations sounds somewhat like what Tony Smith does when he uses 0,
1 and 2 CP2 to S4 connections for the three generations. He then uses
complex domains from Lie Algebras to do diffusion equations for mass
calculations and it looks like you use superalgebras and your topology
model to do the mass calculations. That conformal confinement sounds
similar to what Smith does with Kerr-Newman equations and the
conformal degrees of freedom.
Matti Pitkanen
Oct20-04, 02:55 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n[Moderator\'s note: This is drifting ever more into highly speculative\nrealms. Followups should be more focused on facts. -usc]\n\n\nJohn Gonsowski <jcgonsowski@yahoo.com> wrote in message news:<e98e7f56.0410190705.21f47448-100000@posting.google.com>...\n> Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410170629.2872c69f-100000@posting.google.com>...\n>\n> > You are wondering why I work with super symmetric algebras. As I\n> > already explained 2-D conformal symmetry is naturally associated with\n> > 3-D lightlike 3-surfaces which by General Coordinate Invariance can\n> > be chosen as causal determinants and are metrically 2-D...\n> > Super algebras emerge naturally in infinite-D geomery...\n> > I have started just now to disetangle the structure of particle states\n> > (see the chapter "Massless states and particle Massivation" of TGD at\n> > http://www.physics.helsinki.fi/~matpitka/tgd.html#mless .)...\n> > Conformal confinement might underly behind color confinement...\n>\n> Ok I think I\'m understanding this to the point I\'m capable of.\n> Historically, you had your basic model and you were working on your\n> prime number stuff. The superalgebras were part of your prime number\n> research but you hoped to later fit them into your overall model. You\n> have since fit them in but are still working on some details.\n>\n\nI encountered p-adic numbers entered around 1993, 15 years after the\nbasic idea about space-time as 4-D surface in M^4xS. The inspiration\ncame from the observation that p-adic thermodynamics allows to\nunderstand the ratios of elementary particle mass scales to Planck\nmass in terms of thermal expectations of Virasoro generator L_0. The\nBoltzmann weights exp(L_0/T) (L_0 has integer spectrum) p-adically\nsensible only if they are powers of p: exp(L_0/T)= p^n, p the prime\ncharacterizing the p-adic number field in question. Thus the\n"conformal temperature" has values T= log(p)/k: k=1 is the correct\nchoice.\n\nThermal mass^2 expectations are calculated as p-adic numbers and\nmapped to real numbers by what I call canonical identification\nmapping p-adics to reals continuously: in the expansion x= SUM_n\nx_np^n of p-adic number one just replaces n by -n to get its real\ncounterpart.\n\n\nMass scales come out as proportional to M^2(p)\\propto 1/p. I found\nthat elementary particles tend to correspond to primes p =about 2^k, k\nprime. In particular, Mersenne primes are favoured. For instance,\nintermediate gauge bosons/U and D quark/electron correspond to\nMersenne primes M_n= 2^n-1, n= 89/107/127. For instance electron and\nintermediate boson mass scales are in a ratio sqrt(M_89/M_127)= about\n2^[(127-89)/2]=2^{19}.\n\nI have spent a lot of effort in attempt to understand why the p-adic\nmodel works, and I see as the only viable explanation that real\nphysics is algebraically continuable to various p-adic number fields.\nThis poses extremely strong conditions also on the mass scales. Also\nthe evolution of\ncosmological constant to its present small value from its gigantic\nprimordial value can be understood as stepwise process in which p-adic\nmass scale comes down from Planck scale in half octaves. One can say\nthat cosmological constant depends on the (p-adic) length scale\ncharacterizing the size of the space-time sheet: the larger the\nspace-time sheet, the smaller the cosmological constant. Also\ncoupling constants depend on p-adic length scale and this evolution\nreplaces continuous coupling constant evolution: for each p-adic prime\np, the coupling constants and analogous to critical temperature.\n\nThe selection of preferred primes near powers of two would be\nanalogous to a Darwianian selection: primes near prime powers of two\nare very fit and Mersennes are the fittest. Of course, the notions of\nselection and evolution do not have much content in the standard\nmodel framework. The attempt to formulate the idea about evolution as\na quantum jump sequence replacing again and again the entire 4-D\nspace-time (more precisely, quantum superpositions of 4-D space-times)\nwith a new one leads to a theory of consciousness, which has been\ncrucial for the development of quantum TGD itself.\n\n> Using a sphere, a torus and a two-handle sphere for the three\n> generations sounds somewhat like what Tony Smith does when he uses 0,\n> 1 and 2 CP2 to S4 connections for the three generations. He then uses\n> complex domains from Lie Algebras to do diffusion equations for mass\n> calculations and it looks like you use superalgebras and your topology\n> model to do the mass calculations. That conformal confinement sounds\n> similar to what Smith does with Kerr-Newman equations and the\n> conformal degrees of freedom.\n\nUnfortunately, my understanding of the model of Tony Smith is so\npoor that I cannot make a comparison. The approaches seem to have only\nthis structural similarity. Of course, the assumption that various\nparticle families do not belong to a representation of single gauge\ngroup is also shared: I have the feeling that no one is anymore trying\nto put muons and electrons into same multiplet.\n\nBy the way, the New Scientist of this week (16 October 2004) contains\nan interesting article about surprising findings related to quark\ngluon plasma. The plasma was expected to behave like a dilute gas but\nbehaves like a liquid having a density 30-50 times higher than\npredicted, and perhaps contains still hadrons floating around like\nice cubes in water near freezing point. This inspires a light hearted\nquestion whether the conformal confinement is indeed there and forces\nquarks and gluons to behave like a single coherent entity even when\ncolor force does not require this. Conformal confinement would be\nhalfway between topological (say quarks as magnetic monopoles of\nopposite charge) and purely dynamical confinement.\n\n\nWith Best Regards,\nMatti Pitkanen\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>[Moderator's note: This is drifting ever more into highly speculative
realms. Followups should be more focused on facts. -usc]
John Gonsowski <jcgonsowski@yahoo.com> wrote in message news:<e98e7f56.0410190705.21f47448-100000@posting.google.com>...
> Matti Pitkanen <matpitka@luukku.com> wrote in message news:<76de666b.0410170629.2872c69f-100000@posting.google.com>...
>
> > You are wondering why I work with super symmetric algebras. As I
> > already explained 2-D conformal symmetry is naturally associated with
> > 3-D lightlike 3-surfaces which by General Coordinate Invariance can
> > be chosen as causal determinants and are metrically 2-D...
> > Super algebras emerge naturally in infinite-D geomery...
> > I have started just now to disetangle the structure of particle states
> > (see the chapter "Massless states and particle Massivation" of TGD at
> > http://www.physics.helsinki.fi/~matpitka/tgd.html#mless .)...
> > Conformal confinement might underly behind color confinement...
>
> Ok I think I'm understanding this to the point I'm capable of.
> Historically, you had your basic model and you were working on your
> prime number stuff. The superalgebras were part of your prime number
> research but you hoped to later fit them into your overall model. You
> have since fit them in but are still working on some details.
>
I encountered p-adic numbers entered around 1993, 15 years after the
basic idea about space-time as 4-D surface in M^{4xS}. The inspiration
came from the observation that p-adic thermodynamics allows to
understand the ratios of elementary particle mass scales to Planck
mass in terms of thermal expectations of Virasoro generator L_0. The
Boltzmann weights \exp(L_0/T) (L_0 has integer spectrum) p-adically
sensible only if they are powers of p: \exp(L_0/T)= p^n, p the prime
characterizing the p-adic number field in question. Thus the
"conformal temperature" has values T= log(p)/k: k=1 is the correct
choice.
Thermal mass^2 expectations are calculated as p-adic numbers and
mapped to real numbers by what I call canonical identification
mapping p-adics to reals continuously: in the expansion x= SUM_nx_{np}^n of p-adic number one just replaces n by -n to get its real
counterpart.
Mass scales come out as proportional to M^2(p)\propto 1/p. I found
that elementary particles tend to correspond to primes p =about 2^k, k
prime. In particular, Mersenne primes are favoured. For instance,
intermediate gauge bosons/U and D quark/electron correspond to
Mersenne primes M_n= 2^n-1, n= 89/107/127. For instance electron and
intermediate boson mass scales are in a ratio \sqrt(M_{89}/M_{127})= about
2^[(127-89)/2]=2^{19}.
I have spent a lot of effort in attempt to understand why the p-adic
model works, and I see as the only viable explanation that real
physics is algebraically continuable to various p-adic number fields.
This poses extremely strong conditions also on the mass scales. Also
the evolution of
cosmological constant to its present small value from its gigantic
primordial value can be understood as stepwise process in which p-adic
mass scale comes down from Planck scale in half octaves. One can say
that cosmological constant depends on the (p-adic) length scale
characterizing the size of the space-time sheet: the larger the
space-time sheet, the smaller the cosmological constant. Also
coupling constants depend on p-adic length scale and this evolution
replaces continuous coupling constant evolution: for each p-adic prime
p, the coupling constants and analogous to critical temperature.
The selection of preferred primes near powers of two would be
analogous to a Darwianian selection: primes near prime powers of two
are very fit and Mersennes are the fittest. Of course, the notions of
selection and evolution do not have much content in the standard
model framework. The attempt to formulate the idea about evolution as
a quantum jump sequence replacing again and again the entire 4-D
space-time (more precisely, quantum superpositions of 4-D space-times)
with a new one leads to a theory of consciousness, which has been
crucial for the development of quantum TGD itself.
> Using a sphere, a torus and a two-handle sphere for the three
> generations sounds somewhat like what Tony Smith does when he uses 0,
> 1 and 2 CP2 to S4 connections for the three generations. He then uses
> complex domains from Lie Algebras to do diffusion equations for mass
> calculations and it looks like you use superalgebras and your topology
> model to do the mass calculations. That conformal confinement sounds
> similar to what Smith does with Kerr-Newman equations and the
> conformal degrees of freedom.
Unfortunately, my understanding of the model of Tony Smith is so
poor that I cannot make a comparison. The approaches seem to have only
this structural similarity. Of course, the assumption that various
particle families do not belong to a representation of single gauge
group is also shared: I have the feeling that no one is anymore trying
to put muons and electrons into same multiplet.
By the way, the New Scientist of this week (16 October 2004) contains
an interesting article about surprising findings related to quark
gluon plasma. The plasma was expected to behave like a dilute gas but
behaves like a liquid having a density 30-50 times higher than
predicted, and perhaps contains still hadrons floating around like
ice cubes in water near freezing point. This inspires a light hearted
question whether the conformal confinement is indeed there and forces
quarks and gluons to behave like a single coherent entity even when
color force does not require this. Conformal confinement would be
halfway between topological (say quarks as magnetic monopoles of
opposite charge) and purely dynamical confinement.
With Best Regards,
Matti Pitkanen
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