## måndag 29 oktober 2018

### Why TGD?

1. Why TGD? (pdf-article)
2. How can TGD help to solve the problems of recent day theoretical physics?
3. What are the basic principles of TGD?
4. What are the basic guidelines in the construction of TGD?
The important is to catch the basic idea: technical details are not important, it is principles and concepts which really matter  + Problem solving. TGD itself and almost every new idea in the development of TGD has been inspired by a problem. Standard physics is plagued by problems deeply rooted in basic philosophical - even ideological - assumptions which boil down to -isms like reductionism, materialism, determinism - and locality.

Standard model summarize the recent understanding of physics. The attempts to extrapolate physics beyond standard model are often based on naive length scale reductionism and have produced Grand Unified Theories (GUTs), supersymmetric gauge theories (SUSYs). The attempts to include gravitation under the same theoretical umbrella with electroweak and strong interactions has led to superstring models and M-theory. These programs have not been successful, and the recent dead end culminating in the landscape problem (criticality lost?) of superstring theories and M-theory could have its origins in the basic ontological assumptions about the nature of space-time and quantum.

1. Why TGD?
The question requires an overall view about the recent state of theoretical physics.
• Thermodynamics, special relativity, and general relativity involve also postulates, which can be questioned, as in thermodynamics second law in its recent form, and the assumption about fixed arrow of thermodynamical time, since it is hard to understand biological evolution in this framework.
• In general relativity the  symmetries of special relativity are in principle lost and with Noether's theorem this means also the loss of classical conservation laws, even the definitions of energy and momentum are in principle lost.
• In quantum physics the basic problem is that the nondeterminism of quantum measurement theory   conflicts with the determinism of Schrödinger equation.

2. How can TGD help?  The view about space-time as 4-D surface in  fixed 8-D space-time is the starting point.
• motivated by the energy problem of general relativity
• fusion of the basic ideas of special and general relativities (a TOE).
This has led to other ideas:
• dark matter as phases of ordinary matter characterized by non-standard value of Planck constant, this has a strong operative function
• extension of physics in p-adic number fields  assumed to describe correlates of cognition and intentionality,
• zero energy ontology (ZEO) - quantum states are identified as counterparts of physical events (two times required).

These new elements generalize considerably the view about space-time and quantum + give possibility to understand living systems and consciousness in  physics.

3. TGD as a mathematical theory, basic principles.
A generalization of Einstein's geometrization program from space-time level to the level of "world of classical Worlds" as space of 4-surfaces.

The infinite-dimensional geometry fixes it uniquely.
It is the modes of the classical imbedding space spinor fields - eigenstates of four-momentum and standard model quantum numbers - that define the ground states of the super-conformal representations. It is these modes that correspond to the 4-D spinor modes of QFT limit.

+TGD as a generalized number theory with three separate threads.
• Number theoretical universality   from the need to fuse  p-adic physics and real physics to a coherent whole.
• Classical number fields (reals, complex numbers, quaternions, and octonions) have dimensions which correspond to those appearing in TGD. Basic laws of both classical and quantum physics could reduce to the requirements of associativity and commutativity.
• The  primes (and integer, rational, and algebraic number) can be generalized so infinite primes are possible.  Construction of infinite hierarchy of infinite primes using the primes of the previous level as building bricks to new level. This  is structurally identical with a repeated second quantization of supersymmetric arithmetic quantum field theory for which elementary bosons and fermions are labelled by primes.  Free many-particle states and also the analogs of bound states are obtained. The really hard part of quantum field theories - understanding of bound states - could have number theoretical solution.

• It is not yet clear if both visions (geometrization and number theory) are needed. In any case their combination has provided a lot of insights about   quantum TGD.

4. Guidelines in the construction of TGD.  The construction of physical theories is nowadays to a high degree guesses about the symmetries  and deduction of consequences. The very notion of symmetry has been generalized in this process. Super-conformal symmetries play even more powerful role in TGD than in superstring models and the gigantic symmetries of WCW  is a powerful 'proof'.

In TGD context string like objects are not something emerging at Planck length scale but  in scales of elementary particle physics. The irony is that although TGD is not string theory, string like objects and genuine string world sheets emerge naturally from TGD in all length scales.

Even TGD view about nuclear physics predicts string like objects.

The most important guidelines:
A kernel of WCW = a conjecture.
M4× CP2 as choice for the imbedding space
Number Theoretical Universality
'Quantum classical correspondence'  where classical theory is no approximation but  an exact part of quantum theory.

And  more technical guidelines:
• Strong form of General Coordinate invariance (GCI) is a very strong assumption, that gives the assumption that Kähler function is Kähler action for a preferred extremal as a counterpart of Bohr orbit. Strict determinism not required.   Strong form of GCI requires that the light-like 3-surfaces represent partonic orbits and space-like 3-surfaces at the ends of causal diamonds are physically equivalents as effective 2-D states. The intersections of these two kinds of 3-surfaces and 4-D tangent space data at them   code for quantum states.
• Quantum criticality means that Universe is analogous to a critical system with maximal structural richness.  Universe is at the boundary line between chaos and order. Quantum criticality fixes the basic coupling constant dictating quantum Dynamics.
• Finite measurement resolution using  von Neumann algebras.  Usually the measurement problem is a messy, ugly duckling in theoretical physics.
• Strong form of holography from strong form of GCI and TGD reduces to an almost topological QFT= a conjecture. Weak form of electric-magnetic duality is a TGD version of electric-magnetic duality discovered by Olive and Montonen.
• Generalized Feynman diagrams. TGD leads to a realization of counterparts of Feynman diagrams at the level of space-time geometry and topology. The highly non-trivial challenge is to give them precise mathematical content. Twistor revolution has made possible a considerable progress in this respect and led to a vision about twistor Grassmannian description of stringy variants of Feynman diagrams.
• The localization of spinor modes at string world sheets. There are three  reasons for the modes of the induced spinor fields to be localized to 2-D string world sheets and partonic 2-surfaces - or to the boundaries of string world sheets at them defining fermionic world lines.
Thanks to holography fermions behave like pointlike particles, which are massless in 8-D sense. General relativity emerges as an approximation due to frustration.
- gives em-charge as eigenstates. Spinor modes can have have well-defined electromagnetic charges - the induced classical W boson fields and perhaps also Z field vanish at string world sheets so that only em field and possibly Z field remain.
- acts as spacetime 'genes'.
- sign problems with partition, not necessary positive always. This is avoided in the 2D World sheet of TGD (many sheeted spacetime).

This is a very compressed text about TGD. Go to the sources for better info.
See the  article Why TGD? 2014.
Why TGD and What TGD is? 2018 (with spinor part), 49 pp.
A very short summary, a brief summary about TGD, 2018, 3 pp.

## söndag 24 februari 2013

Topological Geometro-Dynamics (TGD) is a unified theory of fundamental interactions. Quantum classical correspondence [by dimensional reduction] has been one of the guiding principles.

A different thinking in many questions is very much charachteristic of  TGD. Matti himself says that TGD is an oldfashioned quantum hadron model (as instance described by Björken), and the dimensions are emergent from microcosmos and gauge Lorentz invariance with its roots in the vacuum or zero point field. See also The model for hadron masses revisited.

The basic differencies of TGD in relation to other main theories:
• Poincare symmetry, Lorentz invariance, so it is more like a parallell to General Relativity of Einstein, still does not contradict it. TGD is more like a scaled up variant in 8D (GR^2) of GR.
• hadrons, as tripoints, three quarks, or pair of quark-antiquark, instead of strings
• tripoints are 3-surface, non-local points of mostly wave nature as they follow Kähler action
• Planck scale is not the basic scale, and Planck scale can be gigantic
• gravitational Planck constants, gravitational 'waves' (with respect to dark matter)
• there is no cosmological constant
• there is negative energy and magnetism that is vanishing, which make possible the Zero Energy Ontology (ZEO), and because electric currents vanish faster than magnetic dito there are left over magnetic 'bodies' as an effector. This is extremely important in biology
• fields are replaced with effects of spacetime sheets
• actions are made by Noether currents, not Ricci tensors
• time is an active force, creating entanglement and phases, also p-adic time. This is crucial in forming matrices with ZEO.
• the understanding of Feynman diagrams as generalized matrices in 2D (as partonic 2-surfaces) made of 3-surfaces and their matrices/braids. Lightlike 3-surfaces from  maxima of Kähler function define the matrices. This can even describe the black hole inside. Partons and partonic 2-surfaces as generalizations too, as are N-atoms and N-particles?

The basic objection against TGD is acc. to Matti, that induced metrics for space-time surfaces in M^4 × CP_2 form an extremely limited set in the space of all space-time metrics appearing in the path integral formulation of General Relativity. Even special metrics like the metric of a rotating black hole fail to be imbeddable as an induced metric. For instance, one can argue that TGD cannot reproduce the post-Newtonian approximation to General Relativity because it involves linear superposition of gravitational fields of massive objects. Holger B. Nielsen made this objection for at least two decades ago. Perhaps the strong objection against TGD is that linear superposition for classical fields is lost.
The linear superposition is however central starting point of field theories. Many-sheeted space-time circumvent this argument. The replacement of linear superposition of fields with the superposition of their effecs meaning that sum is replaced with set theoretic union for space-time sheets. This simple observation has far reaching consequences: it becomes possible to replace the dynamics for a multitude of fields with the dynamics of space-time surfaces with only 4 imbedding space coordinates as primary dynamical variables. See also Standing waves in TGD.

The continuity has also been an obstacle in a world where even the quantum fraction is geometric.

Discrete vs continuous controversy in physics - discrete and continuous features coexist in any natural phenomenon, depending on the scales of observation.

I quote from the TGD Intro (2007) about the main differencies from mainstream:

TGD was originally an attempt to construct a Poincare invariant theory of gravitation. Spacetime, rather than being an abstract manifold endowed with a pseudo-Riemannian structure, is regarded as a 4-surface in the 8-dimensional space.
• H=M^4_+ = the interior of the future light cone of the Minkowski space (to be referred as light cone)
• CP_2= SU(3)/U(2) is the complex projective space of two complex dimensions
The size of CP_2 which is about 10^4 Planck lengths replaces Planck length as a fundamental length scale in TGD Universe.

The identification of the spacetimes as a submanifolds leads to Poincare invariance broken only in cosmological scales and solves the conceptual difficulties related to the definition of the energy-momentum in General Relativity. Even more, sub-manifold geometry, being considerably richer in structure than the abstract manifold geometry behind General Relativity, leads to a geometrization of all basic interactions and elementary particle quantum numbers. In particular, classical electroweak gauge fields are obtained by inducing the spinor curvature of CP_2 to the spacetime surface.

Fig. 1. a) Future light cone of Minkowski space. b) CP_2 is obtained by identifying all points of C^3, space having 3 complex dimensions, which differ by a complex scaling \Lambda: z is identified with \Lambda x z.

This forces a generalization of the conventional spacetime concept to what might be called manysheeted spacetime or 'topological condensate'. The topologically trivial 3-space of General Relativity is replaced with a 'topological condensate' containing matter as particle like 3-surfaces "glued" to the topologically trivial background spacetime sheet by extremely tiny connected sum (wormhole) contacts having CP_2 size connecting the spacetime sheets. End quote.

The criticality.
One big problem in physics is the criticality, how a classic world can come from the quantum uncertainty. This problem does not differ so much from M-theory, but the solution does very much.
TGD can be seen as a model giving rise to GR as a simple 'mirror image', and also there is a double mirror. Time dimension also have this 'mirror image', and magnetism,  em-'force' can be vanishing? See How to perform WCW integrations in generalized Feynman diagrams? and "The relationship between TGD and GRT".  He writes (from the GRT abstract, and I have filled in other links):
Radically new views about ontology were necessary before it was possible to see what had been there all the time. Zero energy ontology states that all physical states have vanishing net quantum numbers. The hierarchy of dark matter identified as macroscopic quantum phases labeled by arbitrarily large values of Planck constant is second aspect of the new ontology.
1. Equivalence Principle in TGD Universe
2. Zero energy ontology
3. Dark matter hierarchy and hierarchy of Planck constants
4. The problem of cosmological constant
5. The generalized Feynman Diagrams
6. The families and massivation. The symmetries coming out from the microscopic massivation and time distortion or symmetry breaking. This last point I will not take up here.

1. The energy problem, is the equivalence principle holding in TGD?
The source of problems was the attempt to deduce the formulation of Equivalence Principle in the framework provided by General Relativity framework rather than in string model like context. The process shortly summarized:
a) Inertial and gravitational four-momenta are replaced with Super Virasoro generators of two algebras whose differences annihilate physical states = the super-conformal symmetries of quantum TGD.
b)  Number theoretical compactification providing a number theoretical interpretation of space spinors, and thus also of standard model quantum numbers.
c) The identification of the preferred extremals of Kähler action and  the formulation of quantum TGD in terms of second quantized induced spinors fields. This has turned out to be extremely useful for the development of TGD, made possible the  understanding of field equations, and led to a detailed understanding of quantum TGD at the fundamental parton level.

Absolute minimization of so called Kähler action is the fundamental variational principle of TGD and assigns to a given 3-surface X^3 a classical spacetime surface X^4(X^3) which is much like Bohr orbit going through a fixed point in wave mechanics characterized by classical non-determinism caused by enormous vacuum degeneracy and this forces a generalization of the notion of 3-surfaces in order to achieve classical determinism in a more general sense. 3-surfaces are in general unions of disjoint 3-surfaces with timelike separations rather than single time=constant snapshots of the spacetime surface. In particular, spacetime sheets with finite time duration, 'mindlike' spacetime sheets, are possible and are identified as geometric correlates of selves in TGD inspired theory of consciousness

2. Zero energy ontology (S-matrix is replaced with M-matrix definition "square root" of density matrix) allows to avoid the paradox implied in positive energy ontology, by the fact that gravitational energy is not conserved but inertial energy identified as Noether charge is. Energy conservation is always in some length scale in zero energy ontology. This principle is satisfied only by the outcomes of state function reduction.
To sum up, the understanding of Equivalence Principle in TGD context required quite many discoveries of mostly mathematical character: the understanding of the superconformal symmetries of quantum TGD, the discovery of zero energy ontology, the identification of preferred extremals of Kähler action by requiring number theoretical compactification, and the discovery that dimensional reduction allows to formulate quantum in terms of slicing of space-time surface by stringy word  sheets. See Tree like structure for the imbedding space
And later...
Gravitational four-momentum can be assigned to the curvature scalar as Noether currents and is thus completely well-defined [but non-conserved] unlike in GRT. Equivalence Principle requires that inertial and gravitational four-momenta are identical. This is satisfied if curvature scalar defines the fundamental action principle crucial for the definition of quantum TGD. Curvature scalar as a fundamental action is however non-physical and had to be replaced with so called Kähler action. The conservation of gravitational four-momentum seems to fail in cosmological scales. Also for vacuum extremals satisfying Einstein's equations gravitational four-momentum fails to be conserved and non-conservation becomes large for small values [lengths] of cosmic time.  My basic mistake looks now obvious. I tried to deduce the formulation of Equivalence Principle in the framework provided by General Relativity framework rather than in string model context.
But the conservation laws are questioned by many other too. This frame also gave a new interpretation of time.
The basic prediction of TGD is that the sign of energy depends on the time orientation of the spacetime surface.

Quantum states of 3-D theory in zero energy ontology correspond to generalized S-matrices. M-matrix might be a proper term, and is a "complex square root" of density matrix - matrix valued generalization of Schrodinger amplitude - defining time like entanglement coefficients. Its "phase" is unitary matrix. The counterpart of ordinary S-matrix is between zero energy states. I call it U-matrix. It has nothing to do with particle reactions. It is crucial for understanding consciousness via moment of consciousness as quantum jump identification. See Construction of Quantum Theory: S-matrix.

Wikipedia, Noethers theorem, Constant of motion, conservation law, and conserved current, says;
A conservation law states that some quantity X in the mathematical description of a system's evolution remains constant throughout its motion — it is an invariant. Mathematically, the rate of change of X (its derivative with respect to time) vanishes,

$\frac{dX}{dt} = 0 ~.$
Such quantities are said to be conserved; they are often called constants of motion (although motion per se need not be involved, just evolution in time). The earliest constants of motion discovered were momentum and energy,
Here are some examples of research about Noether currents by other scientists:
1. Applications of Noether currents. Scale invariance. R. Corrado 1994: To illustrate the use of Noether’s theorem and the currents produced, we examine the case of scale transformations. As we shall see, these are not necessarily invariances of the action and we will have to determine what conditions are necessary for scale transformations to be a symmetry. Only the masses breaks scale invariance. Any operator with a dimensionful coupling constant breaks the scale invariance of the massless theory.
2. Continous symmetries and conserved currents. conservation of the Noether current holds in the quantum theory, with the current inside a correlation function, up to contact terms (that depend on the infinitesimal transformation). Conserved charges associated with this current are generators of the Lorentz group.
3. Symmetries and conservation Laws.  Lagrangian density with a symmetry can give 1. time translations, - time translation invariance implies that H is constant. This does not appear to be the case in our Universe, because it is expanding (the cosmological constant). The Hamiltonian generates translations in time. 2. spacetime translations - Noether currents are the components of the stress-energy tensor. The conserved charges (components of the total four-momentum) generate translations. 3. Rotations -  specified by a vector ~ pointing in the direction of the axis of rotation. Its magnitude is the angle of rotation. If e is small, under a rotation, the corresponded charges form the angular momentum of the system. The angular momentum generates rotations, rotation 3x3 matrix. 4. Lorentz transformations - In addition to rotations, the group of Lorentz transformations contains boosts (small velocity, corresponding charges are the components of the vector and generates boosts: for infinitesimal velocities and finite vectors where Λ is the corresponding 4×4 Lorentz transformation matrix. show that vectors M and  L transform correctly as vectors in R3 under rotations.
4. Noether currents and charges for Maxwell-like Lagrangians, Yakov 2003: Application of the Noether procedure to physical Lagrangians yields, however, meaningful (and measurable) currents. The well-known solution to this 'paradox' is to involve the variation of the metric tensor. The Noether current of the field considered on a variable background coincides with the current treated in a fixed geometry. Consistent description of the canonical energy–momentum current is possible only if the dynamics of the geometry (gravitation) is taken into account.
5. Nonlocal currents as Noether currents, Dolan & Roos 1980: The first two nonlocal currents in the general two-dimensional chiral models are derived as Noether currents. The associated infinitesimal field transformations are shown to obey a group integrability condition. A subset of the structure constants of the symmetry group responsible for these conserved currents is calculated.
6. GAUGE SYMMETRIES AND NOETHER CURRENTS IN OPTIMAL CONTROL. Torres, 2003: extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a semi-invariance notion, and the transformation group may also depend on the control variables.

3.  Dark matter hierarchy.
The dimensional reduction for preferred extremals of Kähler action - if they have the properties required by theoretic compactification - leads to string model with string tension which is however not proportional to the inverse of Newton's constant but to  p-adic length scale squared and thus gigantic [and dark], see p-Adic Mass Calculations: New Physics. This allowed to predict the value of Kähler coupling strength by using as input electron mass and p-adic mass calculations. In this framework the role of Planck length as a fundamental length scale is taken by CP2 size so that Planck length scale loses its magic role as a length scale.
The identification of gravitational four-momentum in terms of Einstein tensor makes sense only in long length scales. This resolves the paradoxes associated with objects like cosmic strings.

Dark matter hierarchy corresponds to a hierarchy of conformal symmetries Zn of partonic 2-surfaces and this hierarchy corresponds to an hierarchy of increasingly quantum critical systems in modular degrees of freedom. For a given prime p one has a sub-hierarchy Zp, Zp2=Zp× Zp, etc...
This mapping of integers to quantum critical systems conforms nicely with the general vision that biological evolution corresponds to the increase of quantum criticality as Planck constant increases. The group of conformal symmetries could be also non-commutative discrete group having Zn as a subgroup.
The number theoretically simple ruler-and-compass integers having as factors only first powers of Fermat primes and power of 2 would define a physically preferred sub-hierarchy of quantum criticality for which subsequent levels would correspond to powers of 2: a connection with p-adic length scale hypothesis suggests itself. Updated view here.

Particles of dark matter would reside at the flux tubes but would be delocalized (exist simultaneously at several flux tubes) and belonging to irreducible representations of Ga. What looks weird is that one would have an exact macroscopic or even astroscopic symmetry at the level of generalized imbedding space. Visible matter would reflect this symmetry approximately. This representation would make sense also at the level of biochemistry and predict that magnetic properties of 5- and 6-cycles [pentoses and hexoses] are of special significance for biochemistry. Same should hold true for graphene. Electron pairs are associated with 5- and 6-rings and the hypothesis would be that these pairs are in dark phase with na=5 or 6. Graphene which is a one-atom thick hexagonal lattice could be also an example of (conduction) electronic dark matter with na=6.

The idea about dark matter as a large Planck constant phase, requires na/nb= GMm/v0, v0=2-11 so that the values are gigantic. A possible interpretation is in terms of a dark (gravi)magnetic body assignable to the system playing a key role in TGD inspired quantum biology.  See Construction of Elementary Particle Vacuum Functionals.

The fundamental feature of the configuration space is that it has two kinds of degrees of freedom.  The degrees of freedom in which metric vanishes correspond to what I call zero modes and are purely TGD based prediction basically due to the non-point like character of particles identified as 3-surfaces. Zero modes are the counterparts of the classical macroscopic variables and in every quantum jump a localization in zero modes occurs; the state function reduction. This also means that the replacement of point like particle with 3-surface means giving up the locality of the physics at spacetime level: physics is however local at the level of configuration space containing 3-surfaces as its points. For instance, classical EPR nonlocality is purely local phenomenon at the level of configuration space. Besides allowing to get rid of the standard infinities of the interacting local field theories, the non-locality explains topologically the generation of structures, in particular biological structures which correspond to spacetime sheets behaving as autonomous units.

4. The cosmological constant.
Astrophysical systems correspond to [relativistic] stationary states analogous to atoms and do not participate [much] to cosmic expansion in a continuous manner but via discrete quantum phase transitions in which gravitational Planck constant increases. This from the dark matter hierarchy.
a) By quantum criticality of these phase transitions critical cosmologies are excellent candidates for the modeling of these transitions. Imbeddable critical (and also over-critical) cosmologies are unique apart from a parameter determining their duration and represent accelerating cosmic expansion so that there is no need to introduce cosmological constant = quantum phase transition increasing the size. See Could the value of fine structure vary in cosmological scales?
b) A possible mechanism driving the strings to the boundaries of large voids could be repulsive interaction, or  repulsive gravitational acceleration.
c) Cosmological constant like parameter does not characterize the density of dark energy but that of dark matter identi fiable as quantum phases with large Planck constant.
d) The Lambda problem:  large voids arequantum systems which follow the cosmic expansion only during the quantum critical phases.
e) p-Adic fractality predicts that cosmological constant is reduced by a power of 2 in phase transitions occurring at times corresponding to p-adic time scales. These phase transitions would naturally correspond to quantum phase transitions increasing the size of the large voids during which critical cosmology predicting accelerated expansion naturally applies.
f) On the average Lambda (k) behaves as 1/a^2 where a is the light-cone proper time. This predicts correctly the order of magnitude for observed value of Lambda.
g) What empty space is may be a consequence of cosmological constant absence. Such as stochastic quantization and a  holography  that  reduces everything to the level of 3-metrics and more generally, to the level of 3-D eld con figurations.  To a given 3-surface the metric of WCW assigns a unique space-time and this space-time serves as the analog of Bohr orbit and allows to realize 4-D general coordinate invariance in the space of 3-surfaces so that classical theory becomes an exact part of quantum theory. Both 4-D path integral and stochastic quantization for gravitation fail in this respect due to the local divergences (insuper-gravity situation might be di fferent). The preferred 3-surfaces circumvent this di fficulty, and give the GR^2. No emergence of space-time, no  'empty' space is there in TGD? In ZEO the S-matrix is replaced with M-matrix de fining a square root of thermodynamics.
Since the space-times allowed by TGD de ne a subset of those allowed by GR one can ask whether the quantization of GRT leads to TGD or at least sub-theory of TGD.
The arguments represented [in the article] however suggest that this is not the case.
A promising signal is that the generalization of Entropic Gravity (Verlinde's) to all interactions in TGD framework leads to a concrete interpretation of gravitational entropy and temperature, to a more precise view about how the arrow of geometric time emerges, to a more concrete realization of the old idea that matter-antimatter asymmetry could relate to di erent arrows of geometric time (not however for matter and antimatter but for space-time sheets mediating attractive and repulsive long range interactions), and to the idea that the small value of cosmological constant could correspond to the small fraction of non-Euclidian regions of space-time with cosmological constant characterized by CP2 size scale.

5. The helicity, vertices or spin.
The basic prediction of TGD is that the sign of energy depends on the time orientation of the spacetime surface ('negative energy' possible as a request or demand?), creating tensions and vortices as an S-matrix.

Generalized Feynman diagrams.
Zero energy ontology (ZEO) has provided profound understanding about how generalizedFeynman diagrams differ from the ordinary ones. The most dramatic prediction is that loop momenta correspond to on mass shell momenta for the two throats of the wormhole contact defining virtual particles: the energies of the energies of on mass shell throats can have both signs in ZEO. This predicts finiteness of Feynman diagrams in the fermionic sector. Even more: the number of Feynman diagrams for a given process is finite if also massless particles receive a small mass by p-adic thermodynamics. See topological torsion and thermodynamic irreversibility, by Kiehn and the TGD version. The mass would be due to IR cutoff provided by the largest CD (causal diamond) involved.
Generalized Feynman Diagrams as Generalized Braids String world sheets and partonic 2-surfaces provide a beatiful visualization of generalized Feynman diagrams as braids and also support for the duality of string world sheets and partonic 2-surfaces as duality of light-like and space-like braids. The dance metaphor.

The TGD inspired proposal (TGD as almost topological QFT) is  that generalized Feynman diagrams are in some sense also knot or braid diagrams allowing besides braiding operation also two 3-vertices. The first 3-vertex generalizes the standard stringy 3-vertex but with totally different interpretation having nothing to do with particle decay: rather particle travels along two paths simultaneously after 1→2 decay. Second 3-vertex generalizes the 3-vertex of ordinary Feynman diagram (three 4-D lines of generalized Feynman diagram identified as Euclidian space-time regions meet at this vertex). I have discussed this vision in detail here. The main idea is that in TGD framework knotting and braiding emerges at two levels.

1. At the level of space-time surface string world sheets at which the induced spinor fields (except right-handed neutrino, see this) are localized due to the conservation of electric charge can form 2-knots and can intersect at discrete points in the generic case. The boundaries of strings world sheets at light-like wormhole throat orbits and at space-like 3-surfaces defining the ends of the space-time at light-like boundaries of causal diamonds can form ordinary 1-knots, and get linked and braided. Elementary particles themselves correspond to closed loops at the ends of space-time surface and can also get knotted (for possible effects see this).

2. One can assign to the lines of generalized Feynman diagrams lines in M2 characterizing given causal diamond. Therefore the 2-D representation of Feynman diagrams has concrete physical interpretation in TGD. These lines can intersect and what suggests itself is a description of non-planar diagrams (having this kind of intersections) in terms of an algebraic knot theory. A natural guess is that it is this knot theoretic operation which allows to describe also non-planar diagrams by reducing them to planar ones as one does when one constructs knot invariant by reducing the knot to a trivial one. Scattering amplitudes would be basically knot invariants.

Black holes.
One outcome is a new view about black holes replacing the interior of blackhole with a space-time region of Euclidian signature of induced metric and identifiable as analogs of lines of generalized Feynman diagrams. In fact, black hole interiors are only special cases of Eucdlian regions which can be assigned to any physical system. This means that the description of condensed matter as AdS blackholes is replaced in TGD framework with description using Euclidian regions of space-time.

The effective superposition of the CP2 parts of the induced metrics gives rise to an effective metric which is not in general imbeddable to M4× CP2. Therefore many-sheeted space-time makes possible a rather wide repertoire of 4-metrics realized as effective metrics as one might have expected and the basic objection can be circumvented. In asymptotic regions where one can expect single sheetedness, only a rather narrow repertoire of "archetypal" field patterns of gauge fields and gravitational fields defined by topological field quanta is possible.
The skeptic can argue that this still need not make possible the imbedding of a rotating black hole metric as induced metric in any physically natural manner. This might be the case but need of course not be a catastrophe. We do not really know whether rotating blackhole metric is realized in Nature. I have indeed proposed that TGD predicts new physics new physics in rotating systems. Unfortunately, gravity probe B could not check whether this new physics is there since it was located at equator where the new effects vanish.

Ulla said... Seems this Firewall at the edge of Black holes, by Polchinski, has went through the blogosphere. Here Scott Aaronson.

Lubos saysuncritically promote the views of Joe Polchinski, Leonard Susskind, Raphael Bousso, and a few others. When it comes to the AMPS thought experiment, it just uncritically parrots the wrong statements by Polchinski et al.:

The interior (A) and the near exterior (B) have to be almost maximally entangled for the space near the horizon to feel empty; the near exterior (B) is almost maximally entangled with some qubits inside the Hawking radiation (C) because the Hawking radiation's ability to entangle the infalling and outgoing qubits. Because of the monogamy of the entanglement (at most one maximum entanglement may incorporate (B) at the same time), some assumptions have to be invalid. The unitarity should be preserved which means that the A-B entanglement has to be sacrificed and the space near the horizon isn't empty: it contains a firewall that burns the infalling observer.
That may sound good but, as repeatedly explained on this blog, this argument is wrong for a simple reason. The degrees of freedom in (A) and those in (C) aren't independent and non-overlapping. It is the very point of the black hole complementarity that the degrees of freedom in (A) are a scrambled subset of those in (C). The degrees of freedom in (A) are just another way to pick observable, coarse-grained degrees of freedom and "consistent histories" within the same Hilbert space. So the entanglement of (B) with "both" (A) and (C) isn't contradictory in any sense: it's the entanglement with the same degrees of freedom described twice.

It seems clear to me that this imbalanced perspective was incorporated to the article by the main "informers" among the scientists who communicated with Jennifer. This conclusion of mine partly boils down to the amazing self-glorification of Joe Polchinski in particular. So we're learning that if there's a mistake, the mistake is not obvious, AMPS is a "mighty fine paradox" that is "destined to join the ranks of classic thought experiments in physics" and it's the "most exciting thing that happened since [Bousso] entered physics". Holy cow. The mistake is obvious. AMPS simply assume that complementarity can't hold by insisting on separate parts of the wave function that are responsible for observations inside and outside. That's a wrong assumption, so it's not shocking that various corollaries such as the "firewall" at the horizon are wrong, too. This wrong assumed denial of complementarity is as wrong as the assumption that simultaneity has to be absolute – an assumption made by those who "debunk" Einstein's relativity; the error is in step 1 and means that they just didn't understand the original insights.

Matti Pitkanen said...
Blackholes  represent the singularity of general relativity as a theory. What happens for the space-time in the interior of black hole? This should be the difficulty from which to start from. Not the only one.

One could also start from the energy problem of general relativity.

Or from proton instability predicted by GUTs: why quark and lepton numbers seem to be conserved separately?

Or by asking whether it is really true that so many primary fields are needed (superposition of effects of fields replaces superposition of fields in many-sheeted space-time)?

Or what is behind the family replication phenomenon?
Or what is the deeper structure behind standard model symmetries?

I could continue the list: the answer to every question unavoidably leads to TGD.

Superstring theories were claimed to provide quantum theory of gravitation but the outcome was land scape and tinkering with blackholes after it had become clear that superstrings themselves do not tell anything about physics and one must make a lot of ad hoc assumptions to get QFT theory limit. After production of huge amount of literature super stringers are exactly in the same position as before the advent of superstring models.

It would be encouraging if people would gradually realize that we have not made much progress during these four decades. Some really new idea is needed to make genuine progress and we must open our minds for it. Maybe it is here already;-).

Ulla said...
Thanks, this was exactly the kind of list of problems leading to TGD I have asked for. You are welcome to continue on it :)

Under our current best-guess of a complete theory of physics, the maximum possible temperature is the Planck temperature, or 1.41679 x 10^32 Kelvins. However, it is common knowledge that our current theories of physics are incomplete.

The use of the so called "Planck units" is rather arbitrary, and I will point out why: Every model has its limitations. For instance, Newton's second law breaks down at speeds near c and need to be replaced by a Lorentz invariant version, so that the concept of relativistic energy rises from it. But, you see, the speed of light was known from Maxwell equations well before relativity. It was also known that Maxwell equations and Newton's laws doesn't always get along (there are some situations were the Lorentz force between a point charge and a magnet does not have a action-reaction partner). Also, and more obvious, Maxwell equations are not invariant under Galilean transformations, in which Newton's second law is based. So, we have two models for the same Nature, and they disagree... one of them carries a fundamental constant: the speed of light. Years later, we see that this very same speed is the limit of one of the models: the one that did not care about it.

Now, we have several models (quantum mechanics, general relativity, etc) and we can expect all of them to have a limit, to break down at some value of some physical observable.

So we must have a model based on Lorentz invariance, which is exactly what TGD is.

## Saturday, December 01, 2012

This is a blogpost directly from Matti Pitkänens blog. It seems that also Matti thinks that physics is only for physicists, and my efforts to give TGD lessons are in vain. I leave it for the readers to judge.
Matti also complains that the communication does not work, and I thought this would be one way to make things easier, not more difficult? Experts can go to Mattis blog, where they find the math and the physical phrases. I try to avoid them as far as possible here. I use more words, because words are my tool. The reader can determine if they form just a word-salat?

In an earlier blog discussion Hamed asked about some kind of program for learning TGD in roughly the same manner as I did it myself. I decided to write a brief summary about the basic steps leaving aside the worst side tracks since 35 years means too flat learning curve;-).

I wrote a summary about the very first steps, that is the steps made during the four years before my thesis and related to classical dynamics mostly. I could not avoid mentioning and even briefly explaining notions like the "world of classical worlds" (WCW), quantum TGD, Kähler action, modified Dirac equation, zero energy ontology, etc... since I want to relate the problems that I encountered during the first years of TGD to their solutions which came much later, some of them even during this year. I hope that I find time to write similar summaries about later stages in the evolution of TGD and add them to this text.

This summary does not provide any Golden Road to TGD. I do not even know whether it is possible to learn TGD. And certainly it is much more difficult to passively assimilate ideas of others than to actively discover and develop ideas by one self. The authority of the original discoverer - such as that of Witten's - can help enormously but I do not possess this kind of authority so that I must trust only on the power of the ideas themselves.

Since the text consists of five pages it is more practical to give only a link to the pdf file containing it.

Ulla said... I have stranded on the spacetime itself. I cannot decide which is the most easy way into TGD, and I think today it is wrong to start with introducing the classic concept of spacetime. There is clearly an interest in this, because my small 3 texts has got quite many visits. I have 30 texts written, but because of the uncertainty I have not published them yet.

Maybe the intro of some important problems would be a more logical way? As the three body problem?
Zero Energy Ontology etc. To link these to mainstream physics is also difficult for me.

Matti Pitkanen said...
The fact is that understanding of TGD requires understanding of basics of physics and mathematics. As a referee I have read so many unified theories by people who have read a couple of popular science books and got the impression that building a theory of everything requires just "creativity" that unified theories cannot be built in garage.

Physics and theoretical physics are disciplines, whose development has taken a about 500 hundred years, a life work of totally devoted brilliant people. Nowadays these 500 years can be compressed to 3-4 years in university classes. This is wonderful but during this time one of course gets only some important impressions, not much more. There is no hope of compressing 500 years to a couple of web articles. This would be however needed as a background to develop introduction to TGD for dummies;-).

Anyone can learn macro-economics but theoretical physics is a REALLY difficult discipline. Think only that the best mathematical brains have worked for 28 years in vain with superstring models. They did not get anywhere. We still have Einstein's theory as THE theory of gravitation.

The following old saying still applies. "God give me the wisdom to see what I cannot do and give strength to do what I can;-)". In my case this means that I cannot write a five page essay leading the reader to enlightment but I can improve endlessly the articulations of TGD so that who have the needed background can easily understand it when the Zeitgeist allows them to read an article about TGD in presence of colleagues.

Ulla said...
I did not talk of a 5 page essay. I talked about the basic questions leading to TGD. It is so enormously complex by itself. I have met so many questions now that need explanation in terms of mainstream thinking. The implicit part of TGD is one big obstacle. Also the different parts are so intwined in each other that it is almost impossible to start somewhere simple. This made me stop for a while, and now I have so little time for this. My aim is to continue, but I need advice what the best path would be. To simply repeat what you have said is nonsense. I need to UNDERSTAND it. As Hamed said, the most interesting part is the biology, but to reach there I need the physics first. Without university physics and most of the math :) I have only the words. And it is only an intro.

One thing that maybe went wrong is the Kaluza-Klein thinking about the cosmological constant? It led to string theory, but are there other ways out? Or is the try to mathematize the unknown wrong in itself?

I know you have the hierarchy.

http://www.scientificamerican.com/article.cfm?id=what-is-a-dimension-anyway

Matti Pitkanen said...

Unfortunately words are not enough when one is trying to talk about quantum physics or mathematics. In mathematics words are only a shorthand - program calls initiating processes in the brain of mathematician but not in brain of a layman. This mathematics is sometimes very simple but difficult to grasp without background. There is no concept so boringly simple as finite-D Hilbert space, but when you try to understand quantum theory without it you encounter mission impossible. Quantum superposition, quantum entanglement, and quantum jump: here are three notions whose understanding without Hilbert space is exceedingly difficult.

Complexity is very relative notion. Basic principles are simple but once you start to really develop and apply the theory, things become complex. So it is also with TGD: TGD is a TOE covering everything form CP_2 length scale to cosmology and one cannot expect simplicity at the level of implications.

The theory of von Neumann algebras is excellent example of this: the axioms look trivial but the mathematics generated by them looks formidable and fascinating at the same time.

If you look about text book about QED, something relatively simple by recent standards, you get absolutely scared by the complexity of the formulas. And they are only for electron-photon system!

I am sorry, but this is the situation. It is very very lonely here and also the air is very cold and thin;-). And it took 35 years to climb here;-). Maybe I should have thought twice.

Santeri Satama said...
Matti and Hamed, a learning strategy suggestion: to my knowledge there is no better way to learn a thing than to internalize it by trying to teach it to somebody else, "learn one thing, teach one other" as the saying goes; so if Hamed finds suitable "victim" at some stage of this process he could start trying to teach TGD - while simultaneously learning it with the help that Matti can can provide.

Good to see thins happening. The real test of TGD is can it be communicated to other theoreticians and even laymen, or will it remain the "Lonely God". ;)

PS: it's becoming almost impossible to post on this blog by passing the "not a robot" test. Which is both sad and funny.

Matti Pitkanen said... To Santeri:

You are right about learning. Unfortunately too often only the teacher learns;-).

11 said...
Dear Matti,

Did you think about future experiments to support or falsify your TGD?

Matti Pitkanen said...

To 11:

Experimental tests are very important. TGD makes a lot of predictions. Many of them are acutally successfully tested already. Mention only p-adic mass calculations which are based on extremely general assumptions.

a) No standard SUSY is one prediction but no one takes this as interesting because standard SUSY is already excluded in practice.

b) My hope was that the absence of Higgs and identification of Higgs like state as pion of M_89 physics could provide a killer test. It however turned out that TGD is consistent with Higgslike state allowing at QFT limit effective description of particle masses: this follows more or less from the existence of QFT limit. Experimentally the situation is still unsettled. Decays in two-gamma channel and to fermion pairs are both decisive.

c) An excellent candidate for a breakthrough prediction is M_89 hadron physics. The prediction of entire new hadron physics is sensational. The recent observations from LHC (made for the first time already two yeas ago and commented also here) have simplest interpretation as decay of string like magnetic flux tubes to partons.

This kind of objects should not appear at ultra high energies since they relate to low energy hadron physics. The only possibility is that hadrons of new hadron physics with large mass scale are in question. M_89 hadron physics is of course the natural candidate for this hadron physics.
Already RHIC observed these events and QCD definitely does not predict them. Therefore the notion of color glass condensate was introduced to save the situation but it is not QCD prediction if we are honest. Quark gluon plasma is the prediction of QCD.

More generally fractal copies of hadron physics and also leptohadron physics predicting pion like states consisting of color octet charged leptons are predicted. These states have been observed for all lepton families but since they do not fit with standard model the observations have been put under the rug.

Also "infrared" Regge trajectories for ordinary hadrons are possible and there is recent evidence in case of ordinary hadrons for them: the scale of mass splittins is about 20-40 MeV.

d) TGD explains family replication in terms of the topology of partonic 2-surface and this also means predictions of new physics. Do gauge bosons have analog of family replication meaning an exotic octet of mesons besides singlet for dynamical symmetry SU(3) assigned to the 3 families? And how massive are the fermions corresponding to higher genus: here there is a good argument supporting the guess that they are massive.

These are just few predictions and related to particle physics. There are myriads of predictions in cosmology and astrophysics and also in biology. This because TGD Universe is fractal. Basic quantitative tool is p-adic length scale hypothesis predicting a hierarchy of length scales coming as powers of sqrt(2).

The problem is the communication barrier due to the extremely arrogant attitudes of the academic researcher. For this I cannot do much. It would be a job of psychiatrist.

Fractality said...
Matti: Noble attempt at helping us laymen out in cultivating understanding of TGD. It is much appreciated. Do you think you could do something similar for TGD theory of consciousness?
ThePeSla said... Matti,

This post is an excellent attempt at trying to communicate these frontier ideas. I downloaded it in hard copy of 8 pages and read it carefully. If you are interested in my impressions where we may share some evolution in our approaches I have stated it there.

Professors, like Hoyle when I had tea with him- well he said students are always coming to him to comment on their theories-of course we talked about other things, down to earth and I mentioned supporting him briefly if I did not have other directions but certainly not the new Big Bang cosmology.

Still feel free to comment on my system if I have in discussing yours made it a little easier- then you can get down to maybe something more useful from my own.

I mentioned the scientific american article ulla had posted in facebook- there was a time when I did break from just those two ways to apply and see dimensions and it was an awakening moment.

I think your more careful formal approach is much more difficult than freely allowing the intuition and poetic magic to flow.

But where you say you cannot understand some things even in the asking clearly that is an achievement and perhaps some things in the context were not an error (holographic stuff and surfaces for example) but the context is such an error.

As to why the advanced culture of Finnish science does not support your project that is like some form of economics it would take another Gauss to begin to phantom although I made meager suggestions.

All in all a great posting, thank you. I do wish I had the training in the exponential type notations but perhaps they slow us down.

Matti Pitkanen said...

To Fractality:

I hope I can find time and energy to continue the summaries, also about TGD inspired theory of consciousness and quantum biology.

Thanks for Pesla for encouraging comments.
Fractality said...
Matti: Excellent. You are inducing quantum jump to the order of Einstein ;) Have you ever theorized as to the roles of biologically active compounds like serotonin and certain tryptamine alkaloids?
Matti Pitkanen said...

Not seriously. Just some general ideas about what makes information molecule information molecule.

Santeri Satama said... Not sure how relevant this is to above questions, but watching this vid about psychological time and internal "clock" so far unexplained (http://www.youtube.com/watch?feature=player_embedded&v=DKPhPz5Hqqc)
gave the idea that internal clock or time-sense could be based on Shnoll effect. Through "information molecules"?.

Would that be the expectation of your general view about the relation of geometric times and psychological times?

Matti Pitkanen said...

Thank you for asking. I cannot answer without bringing in magnetic bodies.

One of their basic tasks is go generate EEG rhythms which define the ticks of clocks with different basic units of time. It has been observer that the period of EEG decomposes to two parts such that during first half there is coherence and second half non-coherence.

Maybe this means that during the first half period "alpha" subself with say average lifetime/wakeup time of .05 seconds wakes up and dies in the beginning of second half period (roughly). We ourselves would do the same in time scale of 12+12 hours. Wake-sleep cycle would define a universal clock.

In standard picture one tries to understand basic EEG rhythms in terms of various brain circuits. I see this as hopeless project as trying to find standard SUSY at LHC;-) but modern Big Science is full of this kind of desperate projects.

I have talked in http://matpitka.blogspot.fi/2012/11/quantum-dynamics-for-moduli-associated.html about the recent views concerning the generation of the arrow of time. I do not bother to type the recent view about time.

Perhaps it is enought to say that in zero energy ontology the analog of clock pendulum emerges at very abstract level. The state function reductions at upper and lower boundary of causal diamond take place alternatively. This has as an analog the motion of clock pendulum: the highest position at right- that at left- that at right-..... This would correspond at the level of self sleep-wake-up cycles which would be universal aspect of consciousness.

As always I think that the understanding is rather satisfactory now;-) . I must of course confess that the understanding of the arrow of time has been an Odysseia similar to the understanding of the nature of possibly existing Higgs in TGD Universe;-).

Ulla said...
Matti, fortunately I have absolutely no intention to make things more complex than they need to be. I only try to make some introduction, nothing else.

I have seen enough of nonsense to realize this is difficult, and that's why I usually ask. I WANT to do this because TGD is really a good way to understand things. But the details necessary are troublesome, and they force me to read lots and lots of articles. I don't write for experts, but for common people with common knowledge. For them words like math phrases are just garbage and say absolutely nothing. I have to 'translate' TGD.

Cold and thin air is good for the brain. Why on Earth did you have to come in my way? You should not have had, if things worked well, as T said. Dammit.

I have no problems with the test, which maybe says something about me?

Ulla said...
Can I publish this discussion on my TGD Lessons?

Hamed said...

When I see the posting I encounter with many comments. I know more of these persons are very interested to understand TGD, but there is a big problem for them that are a lot of physics and mathematics for those that don’t know about basic physics and mathematics.
I have some suggestions for the readers and I request from Matti if anything between them is wrong, he correct and complete it.

Generally learning science is a process that needs patient but it is very enjoyable ;-). About TGD this seems hard, because TGD is not only a theory but a program, a lot of mathematical and physical ideas and principles had evolved more than 30 years. Although learning TGD is hard but it is possible if one has enough patient.
I encourage everyone even laymen that are working in other fields of science to learn TGD. Because the worldview of TGD makes deep influence on their thinking and this leads to progress and evolution in other fields of science too.
How the laymen can learn TGD? I try to answer it.
in learning consciousness and biological parts of TGD, although at first it seems that these parts doesn’t need mathematics or physics but as I tried it, when one goes further and asks some whys in the bases of them, at end it will be Revealed that it needs understanding Quantum TGD. Similarly understanding the bases of Quantum TGD without classical TGD is impossible.
But for a beginner it is useful at first to understanding the definitions of concepts of TGD from classical to Quantum and after it to biology and consciousness at the introductory level without going further. For this the overview articles of TGD is very good.
After this, I encourage them to learn basic concepts of physics and mathematics. For laymen I think it is possible to learn them without calculations because it is enough for their purposes. Unfortunately it is not enough for me ;-). The book “The road to reality” of Penrose is very good for this purpose.(for example it gives some good mathematical intuitions about Hilbert space for learning Quantum too) The prerequisite for learning the book is physics and mathematics of high school. The physical intuitions in this book are very useful even for teachers in physics.

Santeri Satama suggested to me to teach for better understanding. Yes, It will be useful for my learning and I will try as I can. I remember the quoting of Einstein “You do not really understand something unless you can explain it to your grandmother.” ;-). I am certain that I can’t explain anything of physics to my grandmother ;-) but I think I can do it at least for the readers of the blog and request from Matti to correct it.

Matti Pitkanen said... To Ulla:

To Hamed:

Thank you for a perspective of a person who is really working hard to understand the ideas of TGD. It would be nice to have the "Road to Reality" in bookshelf. This kind of books are God's gifts to human kind. Maybe someone writes someday this kind of book explaining hyperfinite factors, Kac Moody algebras and all that stuff which makes me feel unpleasant;-).

I feel that technical side is not terribly important but maybe this is illusion: to learn the conceptual thinking one must perhaps learn first the basic techniques such as the mathematics learned in theoretical physical classes during first few years.

Maybe this relates to basic fact about language: words as such have no meaning, they only induce self-organization patterns giving rise to the experience of meaning. The meaning of the word is quite different for a person with and for a person without the adequate background.

Ulla said...
Thanks Matti,

Hamed is right in the fact that consciousness needs the physical background to be right understood. Also every biological event need a physical explanation, and that is alone a huge task. We have as instance with Matti discussed the meaning of endorphins and serotonins, but without the physical background his explanations seems meaningless, even nonsensical. This is exactly what ordinary physicists encounter too, and this is why they say TGD is rubbish. They simply have not the patience to learn it from basics. Many times I feel I know more than them when I have tried to discuss things, but then again I have too many empty boxes of knowledge. The mainstream physicist have maybe what seems a coherent knowledge, but when I ask deep enough it turns out they too know very little. This is why I asked for a list of problems that show TGD as a possible solution.

Hamed is really very good for TGD. I hope time is ripe for it now, and he is not marginalized for it.

Matti Pitkanen said...

To Ulla;

Every generation of scientists plays again the evergreen "Emperor's new clothes" by H. C. Andersen.

## tisdag 24 januari 2012

### Geometrodynamics.

Geometrodynamics from wikipedia (short variant here) generally denotes a program of reformulation and unification which was enthusiastically promoted by John Archibald Wheeler in the 1960s and is today rather loosely used as a synonym for GR, and some authors use the phrase Einstein's geometrodynamics to denote the initial value formulation. Spacetimes are sliced up into spatial hyperslices, and the vacuum Einstein field equation is reformulated as an evolution equation describing how, given the geometry of an initial hyperslice (the "initial value"), the geometry evolves over "time". This is also what distinguishes TGD and GR, in the big structure, says Matti.

As described by Wheeler in the early 1960s, geometrodynamics attempts to realize three catchy slogans
• mass without mass,
• charge without charge,
• field without field.
Just LOOK. This is a pointing to thinking today?

"The vision of Clifford and Einstein can be summarized in a single phrase, 'a geometrodynamical universe': a world whose properties are described by geometry, and a geometry whose curvature changes with time – a dynamical geometry." The geometry of the Reissner-Nordström electrovacuum solution suggests that the symmetry between electric (which "end" in charges) and magnetic field lines (which never end) could be restored if the electric field lines do not actually end but only go through a wormhole to some distant location. He searched the momentum constraint in geometry and wanted to show that GR is emergent, like a logical necessity; he talked of spacetime foam; requres the Einstein-Yang-Mills-Dirac System."

Scattering and virtual particles are similar modern notions? A dynamic metric.

"Geometrodynamics also attracted attention from philosophers intrigued by the suggestion that geometrodynamics might eventually realize mathematically some of the ideas of Descartes and Spinoza concerning the nature of space."

Is this a bad way to say that Matti Pitkänens work is too spiritual? Not even the name mentioned. Still he is 'famous'. See Topological Geometrodynamics: What Might Be the Basic Principles.

Modern geometrodynamics.
Christopher Isham, (he got the Dirac medal 2011), Jeremy Butterfield, (his homepage here) + students have continued to develop quantum geometrodynamics.

Addendum: About the Dirac medal, se all Dirac Medal winners here, note the many famous names:
Professor Christopher Isham
Imperial College London
For his major contributions to the search for a consistent quantum theory of gravity and to the foundations of quantum mechanics.
Chris Isham is a worldwide authority in the fields of quantum gravity and the foundations of quantum theory. Few corners of these subjects have escaped his penetrating mathematical investigations and few workers in these areas have escaped the influence of his fundamental contributions. Isham was one of the first to put quantum field theory on a curved background into a proper mathematical form and his work on anti-de Sitter space is now part of the subject’s standard toolkit.
His early work on conformal anomalies has similarly gone from “breakthrough to calibration”, as all good physics does. He invented the concept of twisted fields which encode topological aspects of the spacetime into quantum theory, and which have found wide application. He did pioneering work on global aspects of quantum theory, developing a group-theoretic approach to quantization, now widely regarded as the “gold standard” of sophisticated quantization techniques. This work laid some of the foundations for the subsequent development of loop-space quantum gravity of Ashtekar and collaborators (the only well-developed possible alternative to string theory). He has also made significant contributions to quantum cosmology and especially the notoriously conceptually difficult “problem of time”.
On the foundations of quantum theory, Isham has made many contributions to the decoherent histories approach to quantum theory (of Gell-Mann and Hartle, Griffiths, Omnes and others), a natural extension of Copenhagen quantum mechanics which lessens dependence on notions of classicality and measurement in the quantum formalism. In particular, using a novel temporal form of quantum logic, he established the axiomatic underpinnings of the decoherent histories approach, crucial to its generalization and application to the quantization of gravity and cosmology.
His recent work has been concerned with the very innovative application of topos theory, a generalization of set theory, into theoretical physics. He showed how it could be used to give a new logical interpretation of standard quantum theory, and also to extend the notion of quantization, giving a firm footing to ideas such as “quantum topology” or “quantum causal sets”. Isham’s contributions to all of these areas, and in particular his continual striving to expose the underlying mathematical and conceptual structures, form an essential part of almost all approaches to quantum gravity.

From Wikipedia cont. "Topological ideas in the realm of gravity date back to Riemann, Clifford and Weyl and found a more concrete realization in the wormholes of Wheeler characterized by the Euler-Poincare invariant. They result from attaching handles to black holes.
Observationally, Einstein's general relativity (GR) is rather well established for the solar system and double pulsars. However, in GR the metric plays a double role: Measuring distances in spacetime and serving as a gravitational potential for the Christoffel connection. This dichotomy seems to be one of the main obstacles for quantizing gravity. Eddington suggested already 1924 in his book The Mathematical Theory of Relativity' (2nd Edition) to regard the connection as the basic field and the metric merely as a derived concept.
Consequently, the primordial action in four dimensions should be constructed from a metric-free topological action such as the Pontrjagin invariant of the corresponding gauge connection. Similarly as in the Yang-Mills theory, a quantization can be achieved by amending the definition of curvature and the Bianchi identities via topological ghosts. In such a graded Cartan formalism, the nilpotency of the ghost operators is on par with the Poincare lemma for the exterior derivative. Using a BRST antifield formalism with a duality gauge fixing, a consistent quantization in spaces of double dual curvature is obtained. The constraint imposes instanton type solutions on the curvature-squared Yang-Mielke theory' of gravity, proposed in its affine form already by Weyl 1919 and by Yang in 1974. However, these exact solutions exhibit a vacuum degeneracy'. One needs to modify the double duality of the curvature via scale breaking terms, in order to retain Einstein's equations with an induced cosmological constant of partially topological origin as the unique macroscopic background'.
Such scale breaking terms arise more naturally in a constraint formalism, the so-called BF scheme, in which the gauge curvature is denoted by F. In the case of gravity, it departs from the meta-linear group SL(5,R) in four dimensions, thus generalizing (Anti-)de Sitter gauge theories of gravity. After applying spontaneous symmetry breaking to the corresponding topological BF theory, again Einstein spaces emerge with a tiny cosmological constant related to the scale of symmetry breaking. Here the background' metric is induced via a Higgs-like mechanism. The finiteness of such a deformed topological scheme may convert into asymptotic safeness after quantization of the spontaneously broken model."

During the 1950s, Wheeler formulated geometrodynamics, a program of physical and ontological reduction of every physical phenomenon, such as gravitation and electromagnetism, to the geometrical properties of a curved space-time. Aiming at a systematical identification of matter with space, geometrodynamics was often characterized as a continuation of the philosophy of nature as conceived by Descartes and Spinoza. Wheeler's geometrodynamics, however, failed to explain some important physical phenomena, such as the existence of fermions (electrons, muons, etc.) or that of gravitational singularities. Wheeler therefore abandoned his theory as somewhat fruitless during the early 1970s.
Maybe he used the wrong concept for the unification? Why are forces making qubits?

Addendum: Wikipedia, the talk page for discussing improvements to the John Archibald Wheeler article.

## information regarding geometrodynamics is not accurate

This is a good article on J.A. Wheeler. However, the information regarding geometrodynamics is not accurate, especially the following statement: "Wheeler abandoned it as fruitless in the 1970s".As a matter of fact, Wheeler kept using the term "geometrodynamics" to describe Einstein's theory of general relativity till his last days. For example, in Gravitation and Inertia, a book written with the Italian physicist I.Ciufolini in 1995(and which was missing from the bibliography), the authors keep referring to "Einstein Geometrodynamics"(the title of Chapter 2) throughout the the book: Chapter 3 is entitled " Tests of Einstein Geometrodynamics", Chapter 5 is "The Initial-Value Problem in Einstein Geometrodynamics" and Chapter 7:"Some Highlights of the past and a Summary of Geometrodynamics and Inertia".This proves that Wheeler did not abandon the concept at all in the 1970s!
John A. Wheeler, 1990, "Information, physics, quantum: The search for links" in W. Zurek (ed.) Complexity, Entropy, and the Physics of Information. Redwood City, CA: Addison-Wesley.
Addendum about quantum geometrodynamics, hard linked to time and quantum gravity: Claus Kiefer, 2008. Quantum geometrodynamics: whence, whither? Total search here. Abstract:
Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.
And this is actually published; Gen.Rel.Grav.41:877-901, 2009 DOI:10.1007/s10714-008-0750-1
Scalar perturbations in cosmological models with dark energy - dark matter interaction

Look: Does time exist in quantum gravity?
Comments: 10 pages, second prize of the FQXi "The Nature of Time" essay contest

Cosmological constant as result of decoherence. This means non-commutative geometry?

An earlier article (Adrian P. Gentle, Nathan D. George, Arkady Kheyfets, Warner A. Millerfrom 2004; Constraints in quantum geometrodynamics, http://arxiv.org/abs/gr-qc/0302044

And about time and geometrodynamics, by the same authors
http://arxiv.org/abs/gr-qc/0302051
http://arxiv.org/abs/gr-qc/0006001
http://arxiv.org/abs/gr-qc/9412037
http://arxiv.org/abs/gr-qc/9409058

A geometric construction of the Riemann scalar curvature in Regge calculus. Jonathan R. McDonald, Warner A. Miller http://arxiv.org/abs/0805.2411

and
A Discrete Representation of Einstein's Geometric Theory of Gravitation: The Fundamental Role of Dual Tessellations in Regge Calculus http://arxiv.org/abs/0804.0279

Quantum Geometrodynamics of the Bianchi IX cosmological model
Arkady Kheyfets, Warner A. Miller, Ruslan Vaulin 2006 http://arxiv.org/abs/gr-qc/0512040

and from 1995,
Quantum Geometrodynamics I: Quantum-Driven Many-Fingered Time
Arkady Kheyfets, Warner A. Miller http://arxiv.org/abs/gr-qc/9406031

All actually published.

References:
• Anderson, E. (2004). "Geometrodynamics: Spacetime or Space?". arXiv:gr-qc/0409123 [gr-qc]. This Ph.D. thesis offers a readable account of the long development of the notion of "geometrodynamics". University of London, Examined in June by Prof Chris Isham and Prof James Vickers. 226 pages including 21 figures. 396 cit.
This thesis concerns the split of Einstein's field equations (EFE's) with respect to nowhere null hypersurfaces. Areas covered include A) the foundations of relativity, deriving geometrodynamics from relational first principles and showing that this form accommodates a sufficient set of fundamental matter fields to be classically realistic, alternative theories of gravity that arise from similar use of conformal mathematics. B) GR Initial value problem (IVP) methods, the badness of timelike splits of the EFE's and studying braneworlds under guidance from GR IVP and Cauchy problem methods.

Abstract
The work in this thesis concerns the split of Einstein field equations (EFE’s) with respect to nowhere-null hypersurfaces, the GR Cauchy and Initial Value problems (CP and IVP), the Canonical formulation of GR and its interpretation, and the Foundations of Relativity. I address Wheeler’s question about the why of the form of the GR Hamiltonian constraint “from plausible first principles”. I consider Hojman–Kuchar–Teitelboim’s spacetime-based first principles, and especially the new 3-space approach (TSA) first principles studied by Barbour, Foster, ´O Murchadha and myself. The latter are relational, and assume less structure, but from these Dirac’s procedure picks out GR as one of a few consistent possibilities. The alternative possibilities are Strong gravity theories and some new Conformal theories. The latter have privileged slicings similar to the maximal and constant mean curvature slicings of the Conformal IVP method.
The plausibility of the TSA first principles are tested by coupling to fundamental matter. Yang–Mills theory works. I criticize the original form of the TSA since I find that tacit assumptions remain and Dirac fields are not permitted. However, comparison with Kuchaˇr’s hypersurface formalism allows me to argue that all the known fundamental matter fields can be incorporated into the TSA. The spacetime picture appears to possess more kinematics than strictly necessary for building Lagrangians for physically-realized fundamental matter fields. I debate whether space may be regarded as primary rather than spacetime. The emergence (or not) of the Special Relativity Principles and 4-d General Covariance in the various TSA alternatives is investigated, as is the Equivalence Principle, and the Problem of Time in Quantum Gravity.
Further results concern Elimination versus Conformal IVP methods, the badness of the timelike split of the EFE’s, and reinterpreting Embeddings and Braneworlds guided by CP and IVP knowledge.
Mielke, Eckehard W. (2010, July 15). Einsteinian gravity from a topological action. SciTopics. Retrieved January 17, 2012, from http://www.scitopics.com/Einsteinian_gravity_from_a_topological_action.html
Topological ideas in the realm of gravity date back to Riemann, Clifford and Weyl and found a more concrete realization in the wormholes of Wheeler characterized by the Euler-Poincare invariant. They result from attaching handles to black holes.
Observationally, Einstein's general relativity (GR) is rather well established for the solar system and double pulsars. However, in GR the metric plays a double role: Measuring distances in spacetime and serving as a gravitational potential for the Christoffel connection. This dichotomy seems to be one of the main obstacles for quantizing gravity. Eddington suggested already 1924 in his book The Mathematical Theory of Relativity' (2nd Edition) to regard the connection as the basic field and the metric merely as a derived concept.
Consequently, the primordial action in four dimensions should be constructed from a metric-free topological action such as the Pontrjagin invariant of the corresponding gauge connection. Similarly as in the Yang-Mills theory, a quantization can be achieved by amending the definition of curvature and the Bianchi identities via topological ghosts. In such a graded Cartan formalism, the nilpotency of the ghost operators is on par with the Poincare lemma for the exterior derivative. Using a BRST antifield formalism with a duality gauge fixing, a consistent quantization in spaces of double dual curvature is obtained. The constraint imposes instanton type solutions on the curvature-squared Yang-Mielke theory' of gravity, proposed in its affine form already by Weyl 1919 and by Yang in 1974. However, these exact solutions exhibit a vacuum degeneracy'. One needs to modify the double duality of the curvature via scale breaking terms, in order to retain Einstein's equations with an induced cosmological constant of partially topological origin as the unique macroscopic background'.
Such scale breaking terms arise more naturally in a constraint formalism, the so-called BF scheme, in which the gauge curvature is denoted by F. In the case of gravity, it departs from the meta-linear group SL(5,R) in four dimensions, thus generalizing (Anti-)de Sitter gauge theories of gravity. After applying spontaneous symmetry breaking to the corresponding topological BF theory, again Einstein spaces emerge with a tiny cosmological constant related to the scale of symmetry breaking. Here the background' metric is induced via a Higgs-like mechanism. The finiteness of such a deformed topological scheme may convert into asymptotic safeness after quantization of the spontaneously broken model.
Although many details remain to be seen, topological actions are prospective in being renormalizable and, after symmetry breaking, are inducing general relativity as an "emergent phenomenon" for macroscopic spacetime.
Older ref.