12 Summary

The approach of Geometric Unity as a candidate physical theory of our world is to work with a variety of different bundles in both finite and infinite dimensions which are all generated from a single space X4.

The structure of the relationships may be summarized here:

We recall that there is a theory of sections above the infinite dimensional constructions on the right hand side involved with superspaces and so-called ‘induced representations’, but at this point cannot remember even the standard theory and so have not entered into it here and may do so in further work if there is sufficient interest and ability to recall. 54 12.1 Equations In Geometric Unity, we believe that the Einstein, Dirac, Yang-Mills and KleinGordon equations for the metric, Fermions, internal forces and Higgs sector respectively are not to be unified directly. Instead, the Einstein and Dirac equations are to be replaced by the reduced Euler Lagrange equations Π(dI 1 ω) = (δω) 2 = Υω = 0 (12.2) for a first-order Lagrangian after removal of redundancy through projections Π Then the Yang-Mills-Maxwell equations and Klein-Gordon equation for the Higgs follow from a second related Lagrangian Π(dI 2 ω) = D ∗ ωΥω = 0 (12.3) whose Euler Lagrange equation are automatically satisfied if the 1st order theory is satisfied. 12.2 Space-time is not Fundamental and is to be Recovered from Observerse. There has always been something troubling about the concept of Space-Time as the substrate for a dynamic world. In a certain sense, space-time is born as a frozen and lifeless corpse where the past is immutable and the quantum mechanically unknowable future hovers above it probabilistically waiting to be frozen in the trailing wake of four-dimensional amber which is our geometric past. To have a hope of contributing insight, GU must, it must recover this established structure as an approximation within the theory. But at its deepest level, it seeks to break free of the tyranny of the Einsteinian prison built on the bedrock of a single space with a common past. There is something very special about the arrow of time mathematically. Only in dimension n = 1 is R n always well ordered. For every dimension n > 1 there is no such concept without additional structure chosen (e.g. indifference curves and surfaces foliating the space of baskets in consumer choice theory). In our case we have moved to a world X4 in which we believe all signatures are in some sense ‘physically’ real, with X1,3 and X3,1 being the only two to be provably anthropic, and the others being disconnected and unreachable by the condition of non-degeneracy. Yet in Geometric Unity, hovering above the world we see, there is always a second structure Y 14 looming with multiple spatial and temporal dimensions beyond our own. This capacious augmentation of non-metric X4 as proto-spacetime allows us to wonder about the nature of time without a clear arrow being interpreted on a different space where the arrow is enforced by anthropics. However, we have found it quite challenging to think through the tension between two such worlds related by a bridge ג which must measure in order to observe. Thus, the idea of measurement and observation are forced to be 55 intrinsically tied and the concept of multi-dimensional arrowless time above is shielded from us living as if in Plato’s cave below. 12.3 Metric and Other Field Content are Native to Different Spaces. If the metric on X4 and the observed Bosonic and Fermionic fields are native to the same space, then there is likely a need to put both of them in the same quantum system. However, if they originate intrinsically from different spaces, then the possibilities for harmonizing them without putting them into the exact same framework increase. It may fairly be pointed out that we have a metric in the derived space Y that will have to be put in a common framework with the other fields, but even there we have a new twist. In this work we have not been considering unrestricted metrics on Y . In fact, almost all of the ‘metric’ information is built into the construction of Y , so that our subset of ‘metrics’ under consideration is really equivalent to the space of connections that split the long repeating exact sequence we have discussed between T Y and T ∗Y . This is not accidental but desired, as one of the goals of GU as connections, unlike metrics, have an adequate quantization theory as exhibited by QED, QCD and other theories. Hence the Zorro construction puts the only true metric field ג on a separate space from the main quantized structures, but uses a connection to derive the highly restricted metrics on Y . 12.4 The Modified Yang-Mills Equation Analog has a Dirac Square Root in a Mutant Einstein-Chern-Simons like Equation Without the quadratic potential term in the earlier example of a GU Bosonic Lagrangian, we are left with an expression of the form: =< Shifted Torsion z}|{ Tω , ∗ |{z} Hodge Star ( Einstein Ricci Shiab z}|{ }· ω ( FBω |{z} Metric Curvature + C-S Like Terms z }| { 1 2 dBω Tω + 1 3 [Tω, Tω]) >g If we were to attempt to compare it to other Lagrangians, it would be seen as having some aspects of both the Einstein-Hilbert and Chern-Simons Lagrangians. The Einsteinian character comes from the fact that it produces a linear expression in the curvature tensor making use of Riemannian Projection via }· ω. The Chern-Simons-Palatini like properties come from the fact that it is a Lagrangian that takes connections and ad-valued 1-forms as its natural parameter space. 56 A comparison of the two expressions may be helpful to motivate some readers more familiar with one than the other: SCS ( Trivial z}|{ ∇0 , ∇A, Gauge Trans z }| { ε = Id) = 1 2 < A, ∗ Id ( 0 + d A + 2 3 A ∧ A) >M3 g l l l l l l SGU (∇g |{z} L-C , ∇$, ε) = < Tω, ∗ }· ω |{z} Einstein (FBω | {z } Rν ijµ

• 1 2 dBω Tω + 1 3 Tω ∧ Tω) >Y 14 g (12.4) Where ω = (ε, $) ∈ G = H n N and the connection 1-forms A = ∇A − ∇0 $ = ∇$ − ∇g (12.5) are measured relative to the trivial connection in the usual Chern-Simons theory, while Geometric Unity is inclined to use the spin Levi-Civita connection. The displaced torsion on the other hand Tω = ∇$ − ∇gℵ · ε = $ − ε −1 (d∇g ε) (12.6) is measured relative to the gauge transformed Levi-Civita spin-connection ∇Bω = ∇g · ε. The operator }· ω depends on the gauge transformation and, like the Einstein-Ricci projection, always kills off the Weyl curvature. Unlike the EinsteinRicci projection map, however, it does so in a gauge covariant fashion. In the Chern-Simons case, the ad-valued 1-form A is differentiated by the exterior derivative coupled to the trivial connection. Within Geometric Unity, it is differentiated by the exterior derivative coupled to ∇Bω , the Levi-Civita spin connection gauge transformed by ε. 12.5 The Failure of Unification May Be Solved by Dirac Square Roots. If we accept the colloquial description of the Dirac equation as the square root of the Klein-Gordon equation, we see that solutions of a first order operator can guarantee solutions of a more general second order equation. This was oddly at the fore when the so-called ‘Self-Dual’ Yang-Mills equation burst onto the scene in that F ± A = 0 d ∗ AFA = 0 (12.7) indicating that an equation linear in the curvature was powerful enough to guarantee the solution of a differential equation in the curvature via the Bianchi identity. This suggested to the author in the early 1980s in a seminar taught at the University of Pennsylvania that the Self-Dual equations were actually not so much meant to be Instanton equations, but were somehow more accurately the Einstein Field Equations in disguise as the square root of the YangMills-Maxwell equations. Confusing this picture was the fact that the Einstein equations are usually viewed as equations for a metric rather than a connection, and the fact that the self-duality operator does not work for signatures other 57 than (4, 0),(2, 2) and (0, 4), all of which are non-physical. However, we have now attacked both of these issues in the construction of the Observerse so as to be able to address the viability of the idea that the Einstein and Yang-Mills curvature equations are so related. Thus, in a Dirac pair, the Yang-Mills and Klein-Gordon equations would be assigned to a second order strata and the Einstein and Dirac equations to a first order strata, with a relationship between the two understood as above. In our case of fundamental physics, there are so far four basic equations for each of the known fundamental fields, Spin Name Field Order 0 Klein-Gordon Higgs Field φ 2 1 2 Dirac Lepton and Hadron Fields ψ 1 1 Yang-Mills Gauge Bosons A 2 2 Einstein Gravitons g 2 (12.8) In some sense, this can be replaced in GU by Naive Spin Name Field Order 0 Klein-Gordon w Potential Yang-Mills-Higgs Field φ 2 1 2 , 3 2 ‘Dirac-Rarita-Schwinger’ Lepton and Hadron Fields ν, ζ 1 ‘10 Yang-Mills Gauge Bosons $ 2 ‘10 ‘Chern-Simons-Einstein’ Tω 1 (12.9) suggests a Dirac Square Root Unification. That is, the two first order equations live inside a square root structure of a different equation that contains the two second order equations. In an extreme abuse of notation we might write Einstein-Dirac = p Yang-Mills-Higgs-Klein-Gordon (12.10) to be maximally suggestive of the kind of Dirac Square Root unification we have in mind. 12.6 Metric Data Transfer under Pull Back Operation is Engine of Observation. The metric tensor has traditionally been seen as an instrument of measurement of length and angle. This of course, is purely classical, arising as it does in both Special and General Relativity. The puzzle of Quantum measurement is, however, rather different, as it involves the application of Hermitian operators on Hilbert spaces to find eigenvectors as the possible post-measurement states, with their corresponding Eigenvalues as the experimental results. But in GU a different picture is possible. Consider X as if it were an old fashioned Victrola and the Metric as analogous to an old fashioned stylus with Y being a phonograph. What appears to be happening on the Victrola is largely a 58 Figure 6: Observation and The Observerse. function of where the stylus alights on the phonograph. From the point of view of the listener, each track or location on the phonograph is a different world, while from the perspective of the record manufacturer the album is a single unified release. In this way, the world of states of Y is merely being sampled and displayed as if it were the only thing happening on X. 12.7 Spinors are Taken Chimeric and Topological to Allow Pre-metric Considerations. It has been very difficult to get upstream from Einstein’s concept of space-time for a variety of reasons. In particular, the dependence of Fermions on the choice of a metric in fact appears to doom us to beginning with the assumption of a metric if we wish to consider leptonic or hadronic matter. Yet this dependence must be partially broken if we are to harmonize metric-generated gravity from within metric-dependent Quantum Field Theory. Many years ago, Nigel Hitchin demonstrated that, while the elliptic index of a Dirac operator in Euclidean signature was an invariant by the Atiyah-Singer index theorem, the dimension of the Kernel and Co-Kernel could jump under metric variation. Since that time Jean-Pierre Bourguignon and others have expended a great deal of work tracking Spinors under continuous variation of the metric. Given the odd way in which Spinors appear to be both intrinsically topological (e.g. the topological Aˆ-genus) but confoundingly tied to the metric, we have sought to search for the natural space over which the topological nature of spinors is most clearly manifest. In essence, this has lead us to attempt to absorb the metric structure into a new base space made of pure measuring devices but constructed from the purely topological representation of GL( f r + s, R) on the homogeneous spaces GL( f r + s, R)/Spin(r, s) 59 12.8 Affine Space Emphasis Should Shift to A from Minkowski Space. There appear to be many difficulties when attempting to do Quantum Field Theory in curved space. Thus there has always been a question in the author’s mind as to whether the emphasis on affine Minkowski space M1,3 is a linearized crutch to make the theorist’s model building easier, or whether there is something actually fundamental about affine space analysis. In some sense, GU attempts to split the difference here. We find the emphasis on Minkowski space misplaced, but not the focus on affine theory, as no matter how curved Space-time may be, there is always an affine space that is natural and available with a powerful dictionary of analogies to relate it to ordinary and super-symmetric Quantum Field Theory: Special Relativity/QFT to GU Relativity, QFT GU Analog Affine Space M1,3 A Model Space R 1,3 N = Ω1 (ad) Core Symmetries Spin(1, 3) H = Γ∞(PH ×Ad H) Inhomogeneous Poincare Group G Extension = Spin(1, 3) n R1,3 = H n N Fermionic Extension Space-Time SUSY (ν, ζ) ∈ Ω 0 (/S) ⊕ Ω 1 (/S) (12.11) This also makes more sense from the so-called super-symmetric perspective. If, historically, supercharges are to be thought of as square roots of translations, then in the context of a ‘superspace’ built not on M1,3 but on A, supercharges would have an honest affine space to act and translate where they would appear as square roots of operators or gauge potentials. This would also allow a framework where Supersymmetry12 could be formally active without the introduction of artificial superpartners which have been remarkable in their failure to materialize at expected energies. In this framework, the supercharges may already be here in the form of the ν and ζ fields as this would not be space-time supersymmetry. 12.9 Chirality Is Merely Effective and Results From Decoupling a Fundamentally Non-Chiral Theory Consider a stylized system of equations for a world Y with metric g, having scalar curvature R(y), and endowed with a non-chiral Dirac operator operating on full Dirac Spinors,  −Λ(y) /∂A /∂A −Λ(y)   ψL(y) ψR(y)  = 0 R(y)  1 0 0 1  = 4  Λ(y) 0 0 Λ(y)  (12.12) 12The author finds supersymmetry unnecessarily confusing as an as-if symmetry and is uncomfortable saying much more about it. 60 which are nonetheless decomposed into chiral Weyl component-spinors. Solving both of these equations together yields a system of coupled equations: /∂AψL(y) = R(y) 4 ψR(y) (12.13) /∂AψR(y) = R(y) 4 ψL(y) (12.14) leading to a stylized massive Dirac Equation with mass m = R(y) 4 for any fixed background metric for which the scalar curvature R(y) is approximately constant in a region under study. However, in any region where the scalar curvature was zero or sufficiently close to zero, R(y) ≈ 0 (12.15) the differential equations would decouple as they are only linked by the scalar curvature term of order zero. /∂AψL(x) ≈ 0 (12.16) /∂AψR(y) ≈ 0 (12.17) This however, is not the end of the story when the tangent bundle has further structure. In the neighborhood of an embedding such as we have in: ג : X1,3 −→ Y 7,7 (12.18) we have ג ∗ (T Y 7,7 ) = T X1,3 ⊕ N 6,4 ג (12.19) from our previous discussion. However at the level of the chiral Weyl halves of the total Dirac Spinor we have two decompositions: ג ∗ (/S 64 L (T Y )) = Luminous Light Standard Model Family Matter z }| { (/S 2 L (T X) ⊗ /S 16 L (Nג) ⊕ ((/S 2 R(T X) ⊗ /S 16 R (Nג(( ג ∗ (/S 64 R (T Y )) = (/S 2 L (T X) ⊗ /S 16 R (Nג) ⊕ ((/S 2 R(T X) ⊗ /S 16 L ((גN( | {z } Dark Decoupled Looking Glass Matter (12.20) requiring a different view of chirality as both Left and Right handed spinors emerge from the branching rules of both Weyl halves confusing the picture. Left handed spinors on Y do not remain exclusively Left handed on X. It may be asked what the relevance of the above stylized toy example is to the model under discussion. Quite simply, for every field on Y in the Observerse, there is both a naive spin and a true spin. The naive spin of a differential form valued in another bundle is taken to be the spin of the form field if the tensored 61 bundle were taken formally to be purely auxiliary. Thus, for example, an advalued one form would carry naive spin 1 whether or not the ad bundle was derived from the structure bundle of the base space on which it lives. Thus, for example, our bundle Ω1 (Y, ad) of ad-valued 1-forms has naive spin one, but this disguises the fact that it also contains an invariant subspace that derives from Λ1 ⊗ Λ 1 ⊂ Λ 1 ⊗ Λ ∗ . This space of naive spin 1 would appear to be truly spinless from the point of view of Y . Thus, in some sense, the field playing the role of the fundamental mass for the generalized Dirac equations is actually part of the gauge potential. This sets up a three way linkage: Cosmological ‘Constant’ Λ ↔ Spinless Gauge Field ↔ Fermion Mass (12.21) and it is in such ways that GU seeks to attack non-anthropic fine tuning problems by having the same fields do multiple service. In essence here, a fundamentally non-chiral world of Dirac Spinors in this simplified example would appear chiral in regions of low scalar gravity. From beings made of such chiral matter, they would naturally view the universe as being mildly chiral much the way each of the two hands in Escher’s drawing is separately approximately symmetric about its middle digit. But raised high, the symmetry breaks down as digits two and four are only approximately symmetric in most people, and one and five are undeniably different. Yet it is not only the two middle fingers which are beautiful and symmetric about themselves, because the proper symmetry is left pinky to right pinky, left thumb to right thumb etc. and not left pinky to left thumb, right pinky to right thumb which is not broken as a symmetry, but simply accidental as well as being false. 12.10 Three Generations Should be Replaced by 2+1 model of two True Generations and one Effective Imposter Generation At the time of this writing, the author is not convinced that we have three true generations of matter which differ only by mass. We instead posited here that the so-called third generation of matter is instead part of pure Rarita-Schwinger Spin− 3 2 matter on Y and its Spin− 1 2 appearance on X is the result of branching rules under pull back from Y where it is native: ג ∗ ( /R(T Y )) = /R(ג ∗ (T Y )) = /R(T X ⊕ Nג= (   /R(T X) ⊗ /S(Nג( ⊕ /S(T X) ⊗ /R(Nג( ⊕ /S(TX) ⊗ /S(Nג( | {z } Imposter Third Generation   (12.22) Thus, part of the field ζ ∈ Ω 1 (Y, /SR) is an ordinary second generation spinor in Ω0 (Y, /SL ) via the Dirac gamma matrix contraction while the complement /RR(T Y ) corresponding to the sum of the highest weights contains the imposter 62 third generation which is only revealed under decomposition as in the above. Thus, it is not a true generation as it has a different representation structure than the other two beyond its obvious mass difference.13 12.11 Final Thoughts To sum up, let us revisit the Witten synopsis to see what GU has to say about it: Figure 7: Edward Witten Synopsis. As we have seen, Geometric Unity may be considered an alternative narrative that tweaks familiar concepts in various ways. As the author sees it, it is really a collection of interconnected ideas about shifting our various perspectives. Given the apparent stagnation in the major programs, GU has sought an alternate interpretation of either or both of the two incompatible models for fundamental physics of the Standard Model or General Relativity. In our opinion this represents a rather general perspective on the likely reasons for the impasse in fundamental physics encountered over the five decades since the early 1970s. At almost every level, it appears to us as if the instantiations of the most important general ideas and insights hardened prematurely into assumptions that now block progress. In most cases, our shift in perspective is usually not a rejection of the current models at the level of ideas so much as a rejection of the pressure to communicate ideas concretely through instantiations. In essence, we see an intellectual disagreement between the tiny group of physicists who have sought to discover physical law and the vast majority of theorists who attempted to work out its consequences. What good is a beauty principle that works only in the hands of Einstein, Dirac, Yang, and a handful of others, while leading to failure and madness for others? Yet, in these matters, we have come to side with Dirac’s widely misunderstood perspective on the relationship between, instantiation, beauty, theory and experiment. In essence, a beautiful 13Note: we are speaking loosely here as if mass eigenstates and flavor eigenstates were one and the same. 63 theory is not its instantiation, but those who do not seek physical law cannot be forced to accept this critical issue. To rephrase Witten’s paragraph then in light of Geometric Unity, it might be rewritten as follows: “To Summarize the strongest claims of the strongest form of Geometric Unity, the basic assertions would be: i) Space-time X1,3 arises as a pseudo-Riemannian manifold from maps ג between two spaces Xn and Y n2+3n 2 (X) = Met(X) where Y is constructed from X at a topological level. ii) Over Y is a bundle C with a natural metric which is (semi-canonically) isomorphic to T Y , and one whose structure bundle carries a complex representation Spin(n 2 + 3n 2 , C) −→ U(2 n2+3n 4 , C) (12.23) on Dirac spinors with structure bundle PH for H a real form of U, with no internal symmetry groups. There is an inhomogeneous extension G of the gauge group H of PH acting on the space of connections A(PH) where the stabilizer of any point A0 ∈ A gives rise to a non-trivial endomorphism τA0 : H −→ G. iii) Fermions on X4 are pullbacks ג ∗ (ν) and ג ∗ (ζ) of unadorned non-chiral Dirac spinors ν ∈ Ω 0 (Y, /S) and 1-form valued spinors, ζ ∈ Ω 1 (Y, /S) on Y . In low gravitational regimes, the equations governing the fractional spin fields decouple leading to emergent effective chirality that disguises the non-chiral fundamental theory, and leading to Witten’s representations R and R¯ which are not isomorphic exactly as according to the branching rules for Spinors. The cosmological constant is actually the Vacuum Expectation Value (VEV) of a Field which plays the role of a fundamental mass, leading to the light Fermions being light in low gravity regimes. iv) If Super-symmetry is considered, it lives on the inhomogeneous gauge group and not the inhomogeneous Lorentz or Poincare group where gauge potentials take over from Galilean transformations and the affine space A plays the role of the Minkowski space M1,3 . The lack of internal symmetries indicates why naive super-partners have not been seen as space-time SUSY may be implementing over the wrong group. v) Gravity ג lives on X while the fields of the standard model are native to Y leading to a reason for General Relativity to appear classical on X in contrast to the Quantum nature of the SM fields ω tied to Y . vi) Gravity is the engine of observation, so that where gravity is localized in different sections גa, גb, it pulls back different content while vii) Gravity on Y is replaced by a cohomological theory involving an obstruction δ 2 ω = Υ combining elements of Einstein-Grossman, Dirac and Chern-Simons theories, while there is a new 2nd order theory replacing Yang-Mills, Higgs and Klein-Gordon theories so that the cohomological theory δ 2 ω = Υ = 0 is a ‘Dirac square root’ of the 64 second order theory. viii) The branching rules of ν leads to the appearance of one family of Fermions. ix) ζ branches as a second family due to gamma matrix multiplication on Y as T Y ⊗ /SY = /SY ⊕ /RY with a Rarita-Schwinger remainder. The Spin 3 2 portion of ζ breaks down under pull back to reveal a third ‘imposter generation’ that is merely effective, as it has different representation behavior in the full theory. x) The first order theory has a rich moduli of classical solutions and Υ = 0 carries an elliptic deformation complex in Euclidean signature once the redundant Euler-Lagrange equations are discarded.14” We would like to end this speculative foray with a quote from the man whose question provided the impetus for this excursion. “The relativity principle in connection with the basic Maxwellian equations demands that the mass should be a direct measure of the energy contained in a body; light transfers mass. With radium there should be a noticeable diminution of mass.The idea is amusing and enticing; but whether the almighty is laughing at it and is leading me up the garden path — that i cannot know.” -Albert Einstein While we believe in the story of Geometric Unity, we find the above, now as then, to be sage words in all such endeavors. Appendix: Other Elements of Shiab Constructions Continuing on from our earlier discussion of Shiab operator construction, the author simply wanted to note some of the gadgetry that has come up in the construction of these operators in past years. Most of this is obvious, but the fact that there are two products on the Unitary group Lie algebras given by matrix commutators, and anti-commutators multiplied by i, is an example of something that can be easily forgotten. The author may have forgotten other tools in the Shiab workshop over the years as well. Wedge The wedge product passes to bundle valued forms from the usual DeRham complex. Hodge Star As we have assumed our manifold to be oriented from the beginning, every time a metric g on Y is chosen it induces a non-vanishing volume form dvol 14The so-called Seiberg-Witten equations were first found this way around 1987 as the simplest toy model to proxy this moduli problem. 65 compatible with the metric and orientation. This in turn induces a Hodge Star operator ∗ : Ωi (B) −→ Ω d−i (B) (12.24) which passes to forms valued in arbitrary bundles B over Y . Contraction Various forms of contraction can be defined either with co-variant against contravariant tensors in the obvious way or via the wedge and star operations between forms as in: φ ∨ µ = ∗(φ ∧ ∗µ) (12.25) Adjoint Bundle Bracket As with any Lie Group, U(64, 64) carries a Lie Bracket structure. Given that it lives embedded within the Clifford Algebra ClC(7, 7) = C(128), it can be constructed from the matrix algebra product in the usual fashion: [a, b] = a · b − b · a (12.26) Symmetric Product Unlike most Lie Algebras, there is a second symmetric product on u(n) gotten from taking: {a, b} = i(a · b + b · a) (12.27) Volume Form The analog of the Hodge Star operator is multiplication with the Clifford Volume form λ. Appendix: Thoughts on Method A few words are in order about what the author sees as unbridgeable differences with the mainstream of the community of professional physicists. Experiment and The Scientific Method The author understands the scientific method differently from many others and particularly from many within the world of String Theory. In essence there are general ideas and multiple instantiations of those ideas. The author believes that many who put their faith in the scientific method do not understand the danger of being pressured to discard ideas because one of their instantiations was invalidated by experiment. This is, in essence, the very point Dirac raised 66 in his 1963 Scientific American Article where he warned that beauty rather than the scientific method should be used as a guide to progress: “It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.” It is the misinterpretation of this very clear point that the author finds chilling. Dirac was clearly not saying that if a theory is beautiful, it need not agree with experiment, and yet he is frequently lampooned as such. Why is this? The author believes there is a principle, by which the scientific communities push most members for hyper explicit claims so as to learn the general idea and to wed the author to a prediction that can be easily falsified. Should the author succumb to associating her or his more general idea with a particular instantiation that fails to be confirmed, that idea is now ‘up for grabs’. Further, established players can speak more generally allowing different members different privileges. The author is proud to be able to offer algebraic predictions as to the ‘internal quantum numbers’ of new particles but would need the help of Quantum Field Theorists to see whether these can be sharpened further to include energy scales. The author is not equipped to undertake that effort alone but considers the predictions already offered to be considerably more explicit than many of the current contenders for a theory of everything on a relative basis. The author’s experience is that in calling such quantum numbers ‘predictions’ is that those farthest away from making such predictions are paradoxically the most likely to complain viciously about the lack of an energy threshold so as to deflect criticism from their own theory’s failure to be able to make such claims. Isolation

It is the experience of this author that almost no professional mathematicians and physicists have any concept what it is like to be isolated from the community for 20 years or more at a time. Geometry and field theory are languages that in this author’s experience, decay exceedingly rapidly when there is no one with which to speak them, and it is nearly impossible to find it actively maintained anywhere outside of the profession.

It has been over 25 years since the current author was in a professional environment where anyone else was conversant in the topics discussed here. My apologies are offered for any inconvenience caused, but the author’s ability to converse with the professional community, but, in full candor, the ability to communicate was likely to get even further degraded via additional years of isolation. 67 Appendix: Locations Within GU We collect here for convenience the usual ingredients that constitute fundamental physics and give their intended address within the framework of Geometric Unity. Usual Name GU Location Higgs Field ג