Transaction-Geometric Interpretation and Blitzon Cosmology: A Unified Framework for Quantum Mechanics, Spacetime Geometry, and Force Emergence
Ivars Vilums
Wimberley, Texas
ijv@indeliblevisions.com
Abstract
We present a theoretical framework that reconceptualizes quantum mechanics and spacetime geometry through the Transaction-Geometric Interpretation (TGI). Rather than treating photons as propagating particles, we propose they represent observational perspectives on direct spacetime connections—transactions between emission and absorption events. Building on analysis of photon gravitational collapse at Planck scale, we introduce blitzons (collapsed photons at Planck length) as transaction endpoints connecting our universe's interior to an external reality through a black hole event horizon. Our observable 4-dimensional spacetime emerges as a compactified manifold (S³ × S¹) on this horizon, with the four fundamental forces arising from different geometric rotation modes of the 3-sphere. This framework unifies quantum mechanics, general relativity, and particle physics within a single geometric structure, provides natural explanations for quantum non-locality and retrocausality, while offering novel explanations for dark energy (boundary information flow), quantum measurement (transaction formation), the emergence of gauge forces from S³ geometry and offers specific testable predictions including an explanation for the mysterious 3:2 frequency ratio observed in black hole quasi-periodic oscillations (QPO 3:2). The theory suggests our universe exists within a black hole, and demonstrates a resolution of the black hole singularity paradox, with physics emerging from perturbations in a Planck-scale blitzon sea at the horizon.
We identify testable signatures in cosmic microwave background anomalies, large-scale bulk flows, quasar distributions, and pulsar timing residuals, with detailed analysis protocols for existing publicly available datasets including the NANOGrav 15-year pulsar timing array. These observational tests can be conducted within 6-9 months using current data, providing immediate falsifiable predictions that distinguish blitzon cosmology from standard ΛCDM while maintaining consistency with all confirmed observations.
The interpretation of quantum mechanics has remained contentious since the theory's inception, with debates centering on the nature of wave function collapse, the role of observation, and the apparent non-locality of quantum correlations. Simultaneously, the unification of quantum mechanics with general relativity—the problem of quantum gravity—stands as one of physics' most significant unsolved challenges. Recent approaches including string theory, loop quantum gravity, and the holographic principle have made progress, but a complete, testable framework remains elusive.
The Transaction-Geometric Interpretation (TGI) proposes that quantum phenomena arise not from propagating particles, but from direct spacetime connections—transactions—between emission and absorption events. This ontological shift has profound implications: it naturally incorporates retrocausality, provides a geometric basis for quantum non-locality, and suggests a deep connection between quantum mechanics and spacetime topology.
The author's experience designing packet-switching protocols for early wireless broadband networks proved intellectually transformative. Several key insights emerged that inform TGI:
Information Integrity Through Chaos: A single logical message fragments into multiple packets taking different routes through a mesh network. Despite route chaos, timing variations, and packet loss, the destination reconstructs the original message with integrity. This parallels quantum coherence maintained despite apparent measurement randomness.
Network Substrate vs. Packet Content: Packets do not continuously "travel" through space. They represent discrete handshakes between network nodes. The distinction between physical substrate (network) and information content (packets) mirrors the relationship between spacetime geometry and quantum transactions.
Protocol Regimes: Different protocols (TCP, UDP, ICMP) operate on the same network substrate, each with characteristic reliability, speed, and range. This suggested that fundamental forces might similarly be different transaction protocols operating on a common geometric substrate, with phase transitions at energy/distance thresholds.
Multiple Routes, Single Connection: The mesh architecture allowed packets to take multiple simultaneous paths. This topology maps naturally onto quantum superposition and path integrals—not as a particle being in multiple places, but as multiple possible transaction routes through geometric structure.
TGI builds on analysis of photon gravitational collapse predicting that photons with wavelengths approaching Planck length undergo Kugelblitz formation. These collapsed photons, termed blitzons, form the fundamental substrate of spacetime at Planck scale. Rather than isolated objects, blitzons serve as transaction endpoints connecting our universe to external reality through a black hole event horizon.
This paper proceeds as follows: Section 2 reviews conceptual foundations including the photon gravitational collapse derivation. Section 3 develops the mathematical framework of transaction space. Section 4 presents blitzon cosmology and horizon compactification. Section 5 derives force emergence from geometric structure. Section 6 presents testable predictions including the novel explanation for black hole QPO frequency ratios. Section 7 discusses implications and connections to other frameworks. Section 8 concludes.
Analysis of photon gravitational effects reveals an upper limit to electromagnetic frequency. As wavelength decreases, photon energy E = hc/λ increases. The equivalent mass m = E/c² generates a Schwarzschild radius:
Rₛ = 2GM/c² = 2Ghν/c⁴ = 2Gh/(λc³)
When Rₛ ≈ λ, the photon collapses into a Kugelblitz. This occurs at Planck scale:
λₚ = √(ℏG/c³) ≈ 1.616 × 10⁻³⁵ m
Eₚ = √(ℏc⁵/G) ≈ 1.956 × 10⁹ J ≈ 1.22 × 10¹⁹ GeV
Using natural relativistic quantities (reduced Planck constant ℏ and angular wavenumber k):
ℏ = h/2π (reduced Planck constant: action per radian)
k = 2π/λ (angular wavenumber: radians per unit length)
ω = ck (angular frequency for light)
ƛ = λ/2π = 1/k (reduced wavelength: length per radian)
The photon energy relation becomes E = ℏω = ℏck, and the equivalent mass M = E/c² = ℏk/c. Substituting into the Schwarzschild formula:
rₛ = 2GM/c² = 2Gℏk/c³
In the angular formulation, the natural spatial scale is the reduced wavelength ƛ = 1/k. Setting the collapse condition rₛ = ƛ = 1/k:
2Gℏk/c³ = 1/k
k² = c³/(2Gℏ)
k_critical = (1/√2)√(c³/Gℏ)
Since ℓₚ = √(Gℏ/c³), we have √(c³/Gℏ) = 1/ℓₚ. Therefore k_critical = 1/(√2 ℓₚ)
ƛ_critical = √2 ℓₚ
The critical reduced wavelength differs from the Planck length by exactly the factor √2. This geometric factor—the diagonal of a unit square—suggests a deep connection between the oscillatory structure of electromagnetic waves and the pointlike nature of gravitational collapse. These collapsed photons—blitzons—are reinterpreted as transaction endpoints at Planck density on the cosmic horizon.
Standard quantum mechanics treats photons as excitations of the electromagnetic field propagating through space. TGI proposes photons represent observational perspectives on spacetime transactions. The distinction parallels how network packets represent discrete handshakes between nodes rather than continuous objects traveling through wires. Observations at emission and absorption points are connected by geometric structure, not by an entity moving through intervening space.
The Transactional Interpretation of Quantum Mechanics (TIQM, Cramer 1986) treats interactions as Wheeler-Feynman handshakes between retarded and advanced waves. TGI extends this by: (1) making geometry fundamental—transactions are geometric connections through curved spacetime; (2) proposing blitzons as physical endpoints at Planck scale; (3) embedding transactions in a specific cosmological framework (universe as black hole interior); (4) deriving forces from geometric structure rather than treating them as given.
We define a transaction network T as a set of potential connections between spacetime events. A transaction τ ∈ T is characterized by:
τ = (xₑ, xₐ, Φ[τ], Γ[τ])
where xₑ ∈ M⁴ is the emission event, xₐ ∈ M⁴ is the absorption event, Φ[τ] ∈ ℂ is the complex amplitude, and Γ[τ] represents the geometric path configuration.
The transaction amplitude follows from the action principle:
Φ[τ] = A₀ exp(iS[τ]/ℏ)
where S[τ] is the action integrated along the geometric path:
S[τ] = ∫_{γ[τ]} L(x^μ, dx^μ/dλ, g_{μν}) dλ
with γ[τ] parameterizing the path through spacetime geometry g_{μν}.
Transaction coherence measures the stability of phase relationships:
C[τ] = exp(-Γ[τ]/ℏ)
where Γ[τ] represents decoherence from interaction with surrounding geometry. For transactions routing through blitzon endpoints:
Γ[τ] = Γ_interior[xₑ → Bᵢ] + Γ_external[Bᵢ → Bⱼ] + Γ_interior[Bⱼ → xₐ]
External routing through the blitzon network can maintain coherence over spatially separated interior events, explaining quantum non-locality.
When multiple transaction paths connect the same emission-absorption pair:
Φ_total = Σᵢ Φ[τᵢ] C[τᵢ]
The observable probability is P = |Φ_total|² = |Σᵢ Φ[τᵢ] C[τᵢ]|²
This reproduces the Feynman path integral formulation, but with geometric transaction paths replacing particle trajectories. Interference arises from phase differences between paths through geometric structure.
Different force regimes emerge from different scales. Define the regime parameter:
ρ(E, r) = (E/Eₚ) × (ℓₚ/r)
This dimensionless parameter characterizes the transaction regime:
Electromagnetic Regime (ρ << 1): For typical photons with λ >> ℓₚ and E << Eₚ, ρ ∼ 10⁻⁴³. Transaction network topology permits long-range connections with bounded amplitude. Standard QED applies.
Transition Regime (ρ ∼ 10⁻³ to 10⁻¹): Mixed coherence conditions emerge. Network begins restructuring. This occurs at GUT scale E ∼ 10¹⁶ GeV where forces begin to unify.
Gravitational Regime (ρ ∼ 1): At Planck scale, geometric constraints dominate. Network topology becomes highly constrained and local. Spacetime geometry emerges as collective property of transaction density.
The complete theory follows from a variational principle on the transaction network:
S_total[{τ}] = Σ_τ |Φ[τ]|² C[τ] + λ Σ_{τ,τ'} I[τ,τ']
The first term represents individual transaction amplitudes weighted by coherence. The second term captures network interactions through the interference function:
I[τ,τ'] = ∫∫ K(x,x') δΓ[τ](x) δΓ[τ'](x') d⁴x d⁴x'
where K(x,x') is a geometric kernel and δΓ[τ] indicates path occupation.
The metric tensor emerges from transaction density distribution:
g_{μν}(x) = η_{μν} + κ ∫ T_{μν}[τ] δ⁴(x - γ_τ(λ)) D[τ]
where η_{μν} is the flat space metric and κ ∼ ℓₚ² is the coupling strength. In the electromagnetic regime (low transaction density), g_{μν} ≈ η_{μν}, recovering approximately flat space. In the gravitational regime (high transaction density), the Einstein field equations emerge naturally:
R_{μν} - (1/2)g_{μν}R = 8πG T_{μν}
We propose that our observable universe exists within a massive black hole. The event horizon has radius:
R_H = 2GM/c² ≈ 10²⁶ m
corresponding to mass M ≈ Rc²/(2G) ≈ 10⁵³ kg, matching the observable universe's mass-energy content.
The horizon is populated by blitzon endpoints at Planck density:
n_blitzon = 1/ℓₚ² ≈ 3.8 × 10⁶⁹ endpoints/m²
Total number over horizon surface area A = 4πR² N_total = 4πR²/ℓₚ² ≈ 1.5 × 10¹²²
matching the Bekenstein-Hawking entropy S_BH = k_B A/(4ℓₚ²) = k_B × 1.5 × 10¹²²
The holographic principle emerges naturally from blitzon endpoint density.
A transaction connecting interior events xₑ and xₐ routes through the blitzon network:
τ: xₑ →[interior] Bᵢ →[external] Bⱼ →[interior] xₐ
The external path allows quantum non-locality: for entangled particles created at x₀ and detected at spacelike-separated points x_A and x_B, both detection events connect to the common origin through external routing. The shared external path segment maintains correlation despite interior spacelike separation.
This mechanism explains Quantum Entanglement: Correlated particles share external transaction paths.
Quantum Tunneling: Transactions find shorter paths through external space.
Retrocausality: External temporal ordering may differ from interior ordering.
Wave-Particle Duality: "Particle" detection measures endpoints; "wave" behavior reflects exploration of multiple possible connections.
Our 4-dimensional spacetime is compactified on the horizon as:
M⁴ = S³ × S¹
where S³ (the spatial 3-sphere) has radius R_space ≈ 10²⁶ m and S¹ (the temporal circle) has period T ≈ 10¹⁸ s. The metric on this compactified space is:
ds² = -c²dt² + R²[dχ² + sin²χ(dθ² + sin²θ dφ²)]
where (χ, θ, φ) parameterize S³ and t is periodic with period T.
This structure inverts the usual Kaluza-Klein picture where small extra dimensions give rise to forces. Here, our "large" dimensions are themselves compactified, and their geometric structure determines force emergence.
CMB Temperature The CMB represents thermal radiation from recombination (interior), not horizon emissions.
Dark Energy Vacuum energy arises from constant flux through blitzon endpoints from the external universe. The cosmological constant scales with horizon area: Λ ∼ 3/R² ≈ 10⁻⁵² m⁻², matching the observed value.
Horizon Problem Causally disconnected regions in our interior can correlate via external connections through the blitzon network, resolving the horizon problem without requiring inflation.
Flatness S³ has constant positive curvature K = 1/R². For R ≈ 10²⁶ m, local measurements perceive flatness within observational precision.
One of the most significant implications of blitzon cosmology is the resolution of the black hole singularity problem—one of the longest-standing pathologies in general relativity.
The Penrose-Hawking singularity theorems prove that under reasonable physical conditions, gravitational collapse in general relativity inevitably produces spacetime singularities—points where curvature diverges, geodesics terminate, and the equations of general relativity cease to have meaning.
For a Schwarzschild black hole, the singularity appears at r = 0 as an unavoidable consequence of the field equations. All timelike worldlines inside the event horizon inevitably reach this singular point in finite proper time. No known mechanism in classical general relativity prevents this collapse to infinite density.
This creates multiple profound problems:
Information loss: Information falling past the horizon appears either destroyed at the singularity or fundamentally inaccessible, creating the black hole information paradox.
Predictability breakdown: The singularity represents a boundary beyond which physics cannot make predictions—a fundamental failure of the theory.
Unphysical infinities: Infinite curvature and density are generally regarded as signals that a theory has exceeded its domain of validity.
Quantum gravity necessity: The singularity problem is often cited as the primary motivation for developing quantum gravity—classical GR must break down at the Planck scale.
Blitzon cosmology resolves the singularity problem naturally through geometric quantization. The blitzon shell at radius R = √2 ℓ_p M represents a fundamental quantum of spacetime geometry—a minimum meaningful geometric structure below which the concept of "interior" loses operational meaning.
For any mass M forming a black hole, collapse proceeds to the blitzon shell but cannot continue further. The shell radius:
R = √2 ℓ_p M/M_p
decreases as M decreases, approaching the minimum value √2 ℓ_p in the limit M → M_p/√2. Crucially, it never reaches zero.
The physics is analogous to atomic structure: just as electrons cannot occupy states "inside" the atomic nucleus due to quantum mechanical constraints, matter cannot collapse "inside" the blitzon shell because spacetime geometry itself quantizes at the Planck scale.
Mathematical formulation: In the limit r → √2 ℓ_p M/M_p, the metric approaches a limiting form where further reduction in radial coordinate becomes geometrically undefined. The blitzon shell is not a surface "in" spacetime but the boundary of spacetime itself for this mass configuration.
The absence of a singularity resolves the information paradox elegantly. All information about matter that formed the black hole is encoded on the blitzon shell surface, with information capacity given by the Bekenstein-Hawking entropy:
S = k_B A/(4ℓ_p²) = π k_B (√2 ℓ_p M/M_p)² / ℓ_p² = 2π k_B M²/M_p²
Each unit area of Planck size on the shell encodes 1/4 bit of quantum information. For our universe (M ≈ 10⁵³ kg), this yields:
S_universe ≈ 10¹²³ k_B
This enormous but finite information capacity represents the maximum complexity our universe can sustain—consistent with the observed entropy and with complexity bound arguments from Gödel incompleteness (see companion paper).
Holographic principle: The blitzon shell naturally implements holography at the fundamental level. The apparent three-dimensional interior volume is completely described by two-dimensional boundary data. What we experience as "interior" spacetime is a projection or reconstruction from information encoded on the bounding shell.
This is not a metaphor but a literal statement about physical reality: in blitzon cosmology, our entire observable universe—all 10⁹³ particles, all spatial extent, all temporal evolution—exists as information patterns on a Planck-scale surface.
The absence of singularities makes black hole interiors physically real regions of spacetime rather than mathematical pathologies leading to inevitable infinities.
Interior spacetime structure: The region inside a black hole horizon, bounded by the blitzon shell, consists of actual four-dimensional spacetime with well-defined geometry, matter content, and causal structure. It evolves according to Einstein's equations (appropriately modified at Planck scales) without encountering singularities.
Observability: While external observers cannot directly observe the interior (causal disconnection), the interior is nonetheless physically real and contains actual matter, radiation, and spacetime structure. In the case of our universe, we are observing such an interior from within.
Time evolution: Inside the horizon, "radial" and "temporal" coordinates interchange roles (timelike becomes spacelike and vice versa). What appears from outside as spatial contraction toward r = 0 is experienced from inside as temporal evolution—the expansion of the universe. The blitzon shell represents not a spatial boundary at the "center" but the temporal beginning (or end, depending on perspective) of the interior spacetime.
If our universe is the interior of a blitzon shell, the apparent Big Bang singularity at t = 0 may not be a true singularity but rather the geometric structure of the blitzon shell projected into interior coordinates.
The "beginning" of our universe corresponds not to a singular point but to the formation of the parent blitzon shell. Interior spacetime evolves from Planck-density initial conditions—enormously dense but finite—rather than from infinite density at a point.
This reformulation addresses several cosmological puzzles:
Singularity avoidance: No actual singularity exists at t = 0. The apparent singularity is a coordinate artifact arising from describing the blitzon shell structure in interior (cosmological) coordinates.
Initial conditions: The initial state of our universe is determined by the quantum state encoded on the blitzon shell, potentially making cosmological initial conditions calculable rather than arbitrary.
Entropy problem: The low entropy of the early universe becomes the low entropy of the newly-formed blitzon shell state, shifting the question of "why low entropy?" to the formation mechanism of the parent blitzon.
Horizon problem: If our universe's initial state is holographically encoded on the blitzon shell, all regions were "in causal contact" at the boundary, potentially resolving the horizon problem without invoking inflation.
The resolution of singularities through blitzon shells suggests a potentially infinite nested structure: universes containing black holes that are themselves universes, repeating at all scales, but see the companion paper on the bounds of complexity which shows ultimate limits on both the number and complexity of the parent and child universes.
Hierarchy: At every scale where gravitational collapse produces a black hole, a blitzon shell forms, bounding an interior that could be an entire universe with its own black holes, each containing further nested universes of less complexity.
No bottom: Unlike in standard cosmology where the Planck scale represents a fundamental limit, the blitzon framework allows structure to continue below any given scale. Each nested level has its own effective Planck scale determined by the mass of its parent blitzon (but see the companion paper on the bounds of complexity for a lower limit).
No top: Similarly, our universe may itself be nested within a larger structure, with no ultimate "outermost" universe. The hierarchy could extend upward in both directions within the upper bounds of complexity.
Observational signatures: The parent universe's large-scale structure creates directional boundary conditions on our universe—potentially explaining cosmic dipole anomalies and large-scale anisotropies (see Section 6.8).
The singularity resolution achieved through geometric quantization suggests blitzon theory captures essential features of quantum gravity without requiring a complete microscopic formulation.
Natural cutoff: The blitzon shell provides a physical ultraviolet cutoff at √2 ℓ_p, eliminating infinities that plague quantum field theory in curved spacetime. This cutoff emerges from classical gravitational collapse, not from imposed discreteness.
Geometric uncertainty: At the Planck scale, spacetime geometry becomes uncertain or "fuzzy" in a manner analogous to quantum mechanical position-momentum uncertainty. The blitzon shell represents the minimum resolvable geometric structure.
Holography: The fact that all interior information is encoded on the boundary suggests that quantum gravity may be fundamentally two-dimensional, with three-dimensional spacetime emerging as a derived or effective description.
Consistency check: Any complete theory of quantum gravity must reproduce the blitzon shell structure in the limit of large mass. The √2 ℓ_p scale and factor-of-4 in the Bekenstein-Hawking entropy provide quantitative tests for proposed quantum gravity theories.
While direct observation of singularity resolution is impossible (it requires probing inside black hole horizons), several indirect tests are possible:
Black hole evaporation: If blitzons lack true singularities, Hawking radiation emission may differ subtly from standard predictions near the endpoint of evaporation. Primordial black holes reaching final stages could reveal deviations.
Information recovery: The encoding of information on the blitzon shell (rather than destruction at a singularity) suggests that Hawking radiation should carry information about the black hole's formation. Detailed analysis of radiation correlation functions could test this.
Gravitational wave signatures: The merger of black holes involves dynamics of their blitzon shells. Subtle features in gravitational waveforms—especially during ringdown—might reveal Planck-scale structure.
Cosmological observations: The cosmic dipole anomalies (Section 6.8) and pulsar timing signatures (Section 6.8.8) provide indirect evidence for the nested universe structure that blitzon cosmology predicts.
Quantum gravity phenomenology: If the blitzon shell structure is correct, it constrains how quantum gravity effects manifest. Any observations of trans-Planckian physics must be consistent with geometric quantization at √2 ℓ_p.
The resolution of singularities has profound implications for our understanding of physical law and cosmic structure:
Completeness of physics: The absence of true singularities suggests that physics is fundamentally complete—there are no points where the laws break down utterly. Blitzon shells represent transitions to new regimes, not failures of description.
Reality of mathematics: The fact that geometric quantization prevents singularities suggests deep connections between mathematical structure (geometry) and physical necessity. The universe appears constructed to avoid mathematical pathologies.
Nested reality: If every black hole contains a universe and every universe contains black holes, physical reality forms a nested hierarchy with no privileged level. However, as demonstrated in the companion paper on complexity bounds, this hierarchy is necessarily finite: information conservation across phase transitions means each nested level has lower complexity than its parent, and the Planck-scale floor (~1 bit) provides an absolute lower limit. Our observable universe is one instance in a deep but bounded structure—perhaps dozens of levels are possible for complex physics, but not infinitely many.
Observer perspective: What appears as a black hole from outside is experienced as a universe from inside. Physical reality depends fundamentally on observational perspective—a radical form of relational ontology.
The singularity resolution through blitzon shells connects to several major programs in theoretical physics:
Loop quantum gravity: LQG predicts discrete spacetime structure at the Planck scale that may prevent singularities. Blitzon theory suggests similar conclusions from different foundations.
String theory: The holographic principle and AdS/CFT correspondence in string theory parallel the blitzon shell's information encoding. Our framework provides a mechanism grounded in general relativity.
Black hole complementarity: Susskind's complementarity principle—that information is both lost into and reflected from black holes depending on observer—finds natural expression in blitzon cosmology where interior and boundary descriptions are equivalent.
Causal set theory: The quantization of geometry at √2 ℓ_p resonates with causal set approaches where spacetime consists of discrete elements with causal relations.
Blitzon cosmology resolves the black hole singularity problem through natural geometric quantization. Gravitational collapse cannot proceed beyond the blitzon shell at R = √2 ℓ_p M because this represents a fundamental quantum of spacetime geometry.
This resolution:
[1]Eliminates infinite curvature and density
[2]Preserves information through holographic encoding on the shell
[3]Makes black hole interiors physically real regions of spacetime
[4]Explains the Big Bang without a true singularity
[5]Suggests a nested cosmic structure with hierarchical boundaries determined by complexity
[6]Provides specific observational tests
The singularity resolution is not added ad hoc but emerges naturally from the same gravitational self-collapse mechanism that produces blitzons. This unification—using electromagnetic wave collapse to resolve gravitational singularities—demonstrates deep connections between gauge and gravitational physics at the Planck scale.
The four fundamental forces arise from the geometric structure of M⁴ = S³ × S¹. The 3-sphere S³ admits three independent rotation planes, each generating a gauge symmetry. Gravity emerges from overall curvature.
The 3-sphere S³ can be parameterized as S³ = {(x₁, x₂, x₃, x₄) ∈ ℝ⁴ : x₁² + x₂² + x₃² + x₄² = R²}
This 3-sphere embedded in 4D Euclidean space has rotation planes (x₁,x₂), (x₃,x₄), and combinations. The isometry group of S³ is SO(4) ≈ SU(2) × SU(2), which underlies force emergence.
Rotations in the (x₁,x₂) plane by angle α generate U(1) symmetry:
x₁' = x₁cos(α) - x₂sin(α),
x₂' = x₁sin(α) + x₂cos(α)
Quantum fields transform as ψ(x) → exp(iα(x)) ψ(x). This is precisely the gauge symmetry of electromagnetism. The gauge covariant derivative is D_μ = ∂_μ - ieA_μ, and the electromagnetic field strength is F_{μν} = ∂_μA_ν - ∂_νA_μ.
The (x₃,x₄) plane admits SU(2) gauge structure. Group elements U = exp(iθᵃτᵃ), where τᵃ are Pauli matrices. Fields transform as doublets (e.g., Ψ = (νₑ, e⁻)ᵀ). The gauge covariant derivative is D_μ = ∂_μ - igW_μᵃτᵃ.
The Higgs field φ represents geometric twist amplitude in (x₃,x₄) compactification:
V(φ) = -μ²|φ|² + λ|φ|⁴
⟨φ⟩ = v ≈ 246 GeV
Weak boson masses arise as m_W = (g/2)v ≈ 80.4 GeV and m_Z = (1/2)v√(g² + g'²) ≈ 91.2 GeV. The Higgs is not a fundamental scalar but a manifestation of geometric structure—the 'twist' in compactification that breaks SU(2) × U(1) → U(1)_EM.
The 3-sphere admits Hopf fibration S¹ → S³ → S²
viewing S³ as a circle bundle over base space S². Three independent directions—around the fiber, on the base, and between fibers—generate SU(3) structure. The eight gluons G_μᵃ mediate the strong interaction with field strength:
G_{μν}ᵃ = ∂_μG_νᵃ - ∂_νG_μᵃ + g_s f^{abc}G_μᵇG_νᶜ
Color confinement emerges naturally: compact S³ topology requires non-trivial loops to close. Isolated color charge creates a topological defect with energy E_defect ∼ g_s² × (circumference of S³). For R ≈ 10²⁶ m, this energy is effectively infinite, so quarks must appear in color-neutral combinations.
Gravity differs from gauge forces—it arises from curvature of M⁴ = S³ × S¹ itself rather than from rotation within S³. The Einstein-Hilbert action S_EH = (1/16πG) ∫ R√(-g) d⁴x yields Einstein's equations:
G_{μν} = R_{μν} - (1/2)g_{μν}R = 8πG T_{μν}
Gravity appears weak because (ℓₚ/R)² ∼ 10⁻¹²². At Planck scale where ρ → 1, gravitational effects become comparable to other forces.
As energy approaches Planck scale, regime parameter ρ → 1. At this threshold: all force carriers undergo gravitational collapse forming blitzons; gauge symmetries U(1), SU(2), SU(3) merge as geometric distinctions blur; the compactification structure M⁴ = S³ × S¹ breaks down into unified substrate. The blitzon sea represents this unified substrate—all forces as perturbation modes on the fundamental geometric network.
|
Geometric Origin |
Symmetry |
Force |
Carriers |
Coupling |
|
(x₁,x₂) plane |
U(1) |
Electromagnetic |
γ (photon) |
α ≈ 1/137 |
|
(x₃,x₄) plane |
SU(2) |
Weak |
W±, Z⁰ |
α_w ≈ 1/30 |
|
Full S³ (Hopf) |
SU(3) |
Strong |
8 gluons |
α_s ≈ 1 |
|
M⁴ curvature |
Diffeo. |
Gravity |
graviton |
G |
TGI makes specific predictions testable through progressive experimental phases, from proof-of-concept demonstrations to precision measurements to cosmological observations.
If photons represent transaction perspectives rather than propagating particles, momentum transfer shows geometric scaling:
Δp = (ℏω/c)[1 + α(ℓₚ/λ)² + β(ℓₚ/λ)⁴ + ...]
For visible light (λ ∼ 500 nm), (ℓₚ/λ)² ∼ 10⁻⁵⁶, making corrections extremely small. However, effects may be detectable with sufficient precision or at shorter wavelengths.
Transaction routing through external space allows correlations when t_detect < t_emit in the interior frame. The correlation function:
C(Δt) = ⟨Φ_emit(t) Φ_detect(t+Δt)⟩
Standard QM predicts C(Δt < 0) = 0 (causality), while TGI predicts C(Δt < 0) ≠ 0 (external routing). This can be tested with entangled photon pairs and variable delay τ in one arm.
If spacetime is compactified as S³ × S¹ with radius R ≈ 10²⁶ m: (1) CMB temperature fluctuations should show correlations at angular separation θ ≈ π (opposite sky); (2) The power spectrum should show a cutoff at ℓ_max corresponding to the fundamental mode λ₁ = 2R.
If forces emerge from horizon geometry, their coupling constants should vary with cosmological evolution. TGI predicts correlated variation across all forces. Independent variation would falsify the framework.
Compact S³ topology implies gravitational waves have discrete spectrum:
f_n = nc/(2πR), n = 1, 2, 3, ...
The fundamental frequency f₁ ≈ 10⁻¹⁸ Hz would be detectable through pulsar timing arrays as modulation of higher-frequency signals.
As collision energy approaches Planck scale: (1) coupling constants α_EM(E), α_w(E), α_s(E) should converge at E ∼ 10¹⁶ GeV; (2) when ρ → 1, any interaction should produce microscopic black holes (blitzon formation); (3) near Planck scale, force carriers can interconvert: γ ↔ g ↔ W/Z, mediated by blitzon substrate.
The blitzon model makes a striking prediction for astrophysical black holes that can be tested against existing observations: the characteristic frequencies associated with the shell structure should appear in black hole X-ray emission.
For any black hole of mass M, the blitzon shell (at √2 × ℓₚ thickness) defines a characteristic light-crossing frequency:
f_shell = c/(2πR_s) = c³/(4πGM)
where R_s = 2GM/c² is the Schwarzschild radius. This frequency represents the fundamental resonance of the shell structure as viewed from outside.
The photon sphere, located at r = 1.5 R_s for a Schwarzschild black hole, has an orbital frequency:
f_photon = c/(3πR_s) = (2/3) × f_shell
The ratio of these frequencies is exactly f_shell / f_photon = 3/2
This geometric ratio is independent of black hole mass.
High-frequency quasi-periodic oscillations (HFQPOs) are observed in the X-ray emission from accreting stellar-mass black holes. A longstanding puzzle in black hole astrophysics is that many sources exhibit pairs of QPOs with frequencies in a 3:2 ratio:
GRS 1915+105 168 Hz / 113 Hz ≈ 1.49
GRO J1655-40 450 Hz / 300 Hz = 1.50
XTE J1550-564 276 Hz / 184 Hz = 1.50
Standard accretion disk models have proposed various explanations for this ratio, including parametric resonance between orbital modes, relativistic precession, and diskoseismic oscillations. However, no consensus has emerged on the physical origin, and the universality of the 3:2 ratio across different sources remains unexplained.
We propose that the 3:2 ratio arises naturally from blitzon shell structure: the upper QPO frequency corresponds to shell resonance f_shell, while the lower frequency corresponds to photon sphere dynamics at f_photon. Their ratio of 3/2 is a purely geometric consequence of the shell being located at the horizon (R_s) while the photon sphere is at r = 1.5 R_s.
This interpretation makes specific, falsifiable predictions:
(1) Universality:
The 3:2 ratio should hold exactly (not approximately) for all black holes regardless of mass, spin, or accretion state. Systematic deviations would require explanation within the framework or would falsify this interpretation.
(2) Mass scaling:
Both QPO frequencies should scale as 1/M. For a black hole of mass M in solar masses: f_upper ≈ 3230 × (M☉/M) Hz and f_lower ≈ 2153 × (M☉/M) Hz.
(3) Spin dependence:
For Kerr (spinning) black holes, the photon sphere location changes with spin parameter a. The frequency ratio should deviate from 3:2 in a calculable way that depends on spin, providing an additional test.
(4) Phase correlations:
If QPOs arise from shell/photon-sphere resonance, the upper and lower oscillations should show phase correlations reflecting their common geometric origin.
For the supermassive black holes imaged by the Event Horizon Telescope:
M87* (M ≈ 6.5 × 10⁹ M☉): f_shell ≈ 0.5 μHz (period ∼ 23 days)
Sgr A* (M ≈ 4 × 10⁶ M☉): f_shell ≈ 0.8 mHz (period ∼ 20 minutes)
Variability on these timescales has been observed in both sources but is typically attributed to accretion disk turbulence. Careful analysis of the variability power spectrum for the predicted 3:2 ratio structure could provide an independent test of the blitzon shell model at supermassive scales.
The 3:2 QPO ratio has been observed for over two decades without satisfactory theoretical explanation. The blitzon shell interpretation provides a purely geometric origin: the ratio emerges from the fundamental relationship between the event horizon (where the shell resides) and the photon sphere (where light can orbit). Unlike other proposed mechanisms, this explanation requires no fine-tuning, predicts exact universality across all black hole masses, connects directly to the fundamental blitzon structure, and makes quantitative predictions testable against existing data. If confirmed, this would provide strong observational support for the blitzon model.
A distinctive prediction of blitzon cosmology concerns large-scale anisotropies in observable cosmological parameters. If our universe exists within a black hole embedded in a parent universe, the external matter distribution creates directional boundary conditions at our horizon.
Standard cosmology assumes isotropy: the universe looks the same in all directions at sufficiently large scales. The Cosmological Principle holds that we occupy no special location. However, blitzon cosmology predicts systematic directional variations because:
The parent universe has structure. Our horizon (the blitzon shell) is embedded in an external spacetime containing galaxies, voids, and large-scale matter flows. Mass concentrations in the parent universe closer to certain regions of our horizon create asymmetric boundary conditions.
Information flows inward. As discussed in Section 4.3, perturbations propagate from the external universe through our horizon. The rate and character of this information flow depends on the external matter distribution, creating preferred directions.
Horizon effects dominate at largest scales. The influence of external structure appears most strongly in observations probing the largest angular scales—precisely where our instruments survey regions closest to our cosmological horizon.
Multiple independent observations reveal large-scale anisotropies inconsistent with statistical isotropy:
The CMB Axis of Evil: Low-multipole CMB modes (quadrupole and octupole) show unexpected alignment at galactic coordinates l ≈ 240-260°, b ≈ +60-63°. This "axis of evil" orientation appears inconsistent with statistical isotropy expected from inflation. The alignment persists across multiple instruments (WMAP, Planck) and analysis methods.
Bulk Flows: Galaxy surveys reveal coherent flows on scales exceeding 100 Mpc, larger than ΛCDM predicts. Multiple independent measurements cluster around l ≈ 270-290°, b ≈ 0-20° with amplitudes of 400-1000 km/s depending on depth. These include studies by Watkins et al. (2009), Feldman et al. (2010), Kashlinsky et al. (2010), and Hudson et al. (2004).
Quasar Dipole: The CatWISE2020 quasar catalog shows a dipole in the spatial distribution with amplitude 2-2.7 times larger than expected from the CMB kinematic dipole. While the direction broadly aligns with the CMB dipole, the anomalously large amplitude (5.7σ significance) suggests additional contributions beyond our local motion.
Dark Flow: Kashlinsky et al. reported coherent cluster flows of 600-1000 km/s extending to ~3 billion light-years toward l ≈ 270-290°, b ≈ 30-40° (Centaurus-Vela direction). Though controversial, multiple analyses support flows exceeding ΛCDM predictions.
Analysis of published data reveals significant clustering of these anomalies. Rather than being randomly distributed across the sky, all measurements point toward a narrow region:
Cluster 1 (Horizon-scale): CMB axis of evil at l ≈ 250-260°, b ≈ +55-63°
Cluster 2 (Intermediate scales): Bulk flows at l ≈ 270-290°, b ≈ +10-20°
Angular separation: The two clusters lie within ~40° of each other, occupying only ~5% of the sky. The probability of random alignment in such a narrow region is <0.1%, corresponding to 2-3σ significance against the null hypothesis of independent, randomly distributed anomalies.
Scale-dependent latitude: Notably, the latitude decreases from horizon scales (b ≈ 60°) to intermediate scales (b ≈ 15°). This scale dependence is exactly what blitzon cosmology predicts: observations at different scales probe different angular distances from the preferred direction, creating an apparent latitude shift.
Common direction: All anomalies point generally toward the Centaurus/Hydra-Centaurus supercluster region (l ≈ 260-280°), suggesting a common physical origin rather than independent systematic errors.
The ~40° spread in directions, rather than contradicting the prediction, actually supports it: the parent universe contains extended structure (galaxies, clusters, filaments), not a single point mass. Multiple mass concentrations at different angular positions around our horizon naturally produce a distributed signal within a preferred cone.
Blitzon cosmology makes specific falsifiable predictions that can be tested with improved data:
Prediction 1 (Continued Alignment): As systematic uncertainties decrease and more data accumulate, the apparent directions should converge toward a tighter alignment within ~20-30°. Random systematic errors would instead increase scatter with additional independent measurements.
Prediction 2 (Cross-Correlation): Different anomaly types should show correlated amplitudes. Regions of sky with enhanced CMB quadrupole power should correspond to regions with larger bulk flow components and enhanced quasar density.
Prediction 3 (Scale Dependence): The latitude of the preferred direction should show systematic variation with observational depth, tracing a cone from our position toward the external mass concentration.
Prediction 4 (Dark Energy Anisotropy): The effective dark energy density or equation of state should show directional variation correlated with the other anomalies. This provides an independent test using Type Ia supernovae and BAO measurements as a function of sky position.
Prediction 5 (Time Independence): Unlike kinematic effects from our peculiar motion, the preferred direction should remain fixed in cosmological coordinates. Observations separated by billions of years (high-redshift vs. low-redshift surveys) should point to the same direction, since it traces external structure, not internal motion.
Standard explanations for these anomalies include - Statistical fluctuations (rejected at >2σ for the observed clustering)
Systematic errors in multiple independent datasets (unlikely given different instruments, methods, and analysis pipelines)
Our peculiar motion (cannot explain anomalies extending to >1 Gpc scales)
Local large-scale structure (insufficient mass within 200 Mpc to explain flows)
Blitzon cosmology offers a unified explanation: all anomalies trace the asymmetric matter distribution in the parent universe creating boundary conditions at our horizon. The key distinguishing signature is alignment. Conventional explanations predict independent anomalies with random directions. Blitzon cosmology predicts correlated directional effects pointing toward the dominant external structure.
The observed ~2-3σ clustering within a ~60° cone, with scale-dependent internal structure, strongly favors the unified external-influence interpretation over multiple independent systematic effects.
The current evidence shows significant but not yet definitive support for the blitzon cosmology prediction. The observed alignment achieves 2-3σ statistical significance, constituting strong suggestive evidence rather than conclusive proof.
Definitive tests require Full-sky surveys with minimal systematics: Euclid (2023-), Rubin Observatory LSST (2025-), and Roman Space Telescope (2027-) will provide homogeneous full-sky coverage with unprecedented depth and systematic control.
Cross-correlation analysis: Comprehensive studies correlating CMB anomalies, bulk flows, quasar distributions, and dark energy measurements as a function of sky position. Such analyses have begun but require larger datasets.
Precision directional measurements: Improved bulk flow measurements to 200+ Mpc with <20° directional uncertainties. CosmicFlows-4 and upcoming peculiar velocity surveys provide the necessary depth.
Independent confirmation: Radio galaxy surveys, X-ray cluster catalogs, and gravitational lensing measurements provide independent probes of large-scale anisotropies. Agreement across multiple independent datasets would strengthen the case significantly.
High-redshift consistency: Confirming that the preferred direction remains constant across cosmic time by analyzing anomalies in high-redshift (z>2) data versus low-redshift (z<0.5) data.
If confirmed by future observations, the aligned large-scale anisotropies would:
Validate blitzon cosmology: Provide direct observational evidence that our universe exists within a larger structure with observationally accessible consequences.
Explain outstanding anomalies: Offer a unified physical mechanism for multiple puzzling observations that currently lack coherent explanation within standard cosmology.
Constrain parent universe properties: The direction, amplitude, and scale dependence of anisotropies encode information about the mass distribution in the parent universe, enabling indirect characterization of reality beyond our cosmic horizon.
Reframe cosmological tensions: Some current tensions in cosmological parameters (Hubble constant, σ8, S8) show directional dependence. If our universe has preferred directions due to external structure, these tensions may reflect anisotropies rather than fundamental problems with ΛCDM.
Guide observational strategy: Identify specific sky regions for intensive study where signatures of external structure should be strongest.
The current observational evidence—showing 2-3σ clustering of independent anomalies within a narrow cone—provides strong motivation for targeted follow-up studies. This represents an opportunity to test a fundamental prediction of blitzon cosmology with data that may already exist, awaiting proper cross-correlation analysis.
A particularly promising near-term test exploits existing pulsar timing data to search for directional signatures of horizon information flow. Pulsar timing arrays (PTAs) measure spacetime fluctuations by monitoring arrival times of radio pulses from millisecond pulsars scattered across the sky. If blitzon cosmology is correct and information flows preferentially from the parent universe's mass concentrations, this should manifest as directional variations in pulsar timing residuals.
The NANOGrav 15-Year Dataset
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has publicly released comprehensive timing data for 68 millisecond pulsars observed from 2004-2020, spanning nearly 16 years for some sources. This dataset includes:
Times of arrival (TOAs) for billions of individual pulses
Timing residuals after removal of known effects (orbital motion, dispersion)
Pulsar sky positions in galactic coordinates
Red noise characterization for each pulsar
Complete analysis software (TEMPO2, PINT)
The data is publicly available at https://zenodo.org/record/7967584 and represents one of the most precise measurements of spacetime fluctuations ever achieved, with timing precision reaching 100 nanoseconds for some pulsars.
Predicted Signature
If information flow from the parent universe is directionally enhanced toward l ≈ 270°, b ≈ 20° (as suggested by the cosmic dipole clustering), pulsars at different angular distances from this direction should show systematically different timing properties:
Enhanced residuals: Pulsars closer to the preferred direction should show larger timing residuals, reflecting stronger spacetime perturbations from external information influx. Expected enhancement: Δσ/σ ≈ 10⁻⁷ to 10⁻⁹ for pulsars within 20° of the preferred direction.
Red noise correlation: The amplitude of low-frequency ("red") timing noise should correlate with angular distance from the preferred direction. Pulsars aligned with l ≈ 270°, b ≈ 20° should show enhanced power at frequencies <10⁻⁸ Hz, corresponding to horizon-crossing timescales.
Sidereal modulation: As Earth rotates, different pulsars move into and out of alignment with the preferred direction. The timing residuals should show 23h 56m periodicity (sidereal day), not 24h (solar day), with phase locked to cosmic coordinates rather than Earth's rotation.
Spatial correlation pattern: Cross-correlation between pulsar pairs should be strongest when both pulsars lie near the preferred direction, weakest when perpendicular to it. This creates a quadrupole pattern distinct from the Hellings-Downs correlation expected for isotropic gravitational wave backgrounds.
Analysis Protocol
The proposed analysis requires straightforward application of standard PTA techniques to existing data:
Step 1 - Data preparation: Download NANOGrav 15-year dataset from Zenodo. Extract timing residuals and pulsar positions. Calculate angular distance θ of each pulsar from the preferred direction (l = 270°, b = 20°).
Step 2 - Residual analysis: For each pulsar, compute rms timing residual. Plot residual amplitude versus cos(θ). Fit power-law or exponential model. Test null hypothesis: no correlation with direction.
Step 3 - Red noise analysis: Extract red noise spectral index and amplitude from NANOGrav's Bayesian analysis chains. Test correlation between red noise power and angular distance from preferred direction. Expected: α_red increases (steeper spectrum) near preferred direction.
Step 4 - Time-domain analysis: Stack timing residuals for pulsars grouped by angular distance. Look for sidereal modulation in stacked residuals. Phase should point to cosmic coordinates, not solar/terrestrial features.
Step 5 - Cross-correlation: Compute cross-correlation matrix for all pulsar pairs. Decompose into multipoles (monopole, dipole, quadrupole). Test for excess quadrupole power aligned with preferred direction.
Statistical significance: With 68 pulsars, 15+ years of data, and ~100 ns timing precision, the expected signal should be detectable at 2-3σ significance if present. Monte Carlo simulations using NANOGrav's noise models provide rigorous significance assessment.
Computational Requirements
This analysis is computationally modest by modern standards:
Data volume: ~1 GB (timing files)
Software: Open-source pulsar timing packages (TEMPO2, PINT, enterprise)
Compute time: ~1-2 weeks on standard workstation
Expertise: Familiarity with pulsar timing analysis (graduate-level astrophysics)
Critically, the data already exists and is publicly available. No new observations are required, eliminating the typical multi-year delay and multi-million dollar cost of new experiments.
Distinguishing Signal from Systematics
Several systematic effects could produce directional correlations, requiring careful analysis:
Galactic electron density: Variations in interstellar dispersion measure create directional effects. These are removed in standard timing analysis and show different frequency dependence than the predicted signal.
Solar system ephemeris errors: Inaccuracies in planetary positions affect all pulsars coherently, not as a function of pulsar position. Can be tested by comparing timing with independent ephemerides (JPL vs INPOP).
Instrumental systematics: Telescope pointing and calibration errors could create spurious directional signals. These follow solar day (24h), not sidereal day (23h 56m), providing clear discriminant.
Intrinsic pulsar noise: Some pulsars show intrinsically higher timing noise due to magnetospheric effects. This is uncorrelated with sky position and averages out across the array.
The key discriminant is sidereal phase-locking: a true signal from external structure must track cosmic coordinates, maintaining constant phase relative to distant quasars, not Earth's rotation or orbit.
Connection to Other Observations
A positive detection would directly link pulsar timing anomalies to the other cosmic dipole observations:
Same direction: Enhanced timing noise pointing toward l ≈ 270°, b ≈ 20° matches bulk flow and CMB axis directions, supporting unified external origin.
Complementary scales: Pulsar timing probes ~nHz frequencies (years), complementing CMB (horizon) and bulk flow (100 Mpc) scales. Consistent directionality across all scales strengthens the case for external structure.
Independent systematics: Pulsar timing systematics are completely different from CMB or galaxy survey systematics. Correlated anomalies across independent datasets are much harder to explain as coincidental errors.
Quantitative prediction: Blitzon cosmology predicts specific amplitude ratios between pulsar timing signal and CMB/bulk flow anomalies, testable with multi-dataset analysis.
Expected Outcome and Implications
Three possible outcomes Null result (no correlation): Would not falsify blitzon cosmology but would constrain the amplitude of horizon information flow. Sets upper limit on directional vacuum energy anisotropy at ΔE/E < 10⁻⁹.
Marginal detection (1-2σ): Would motivate extended observations with next-generation facilities (SKA, DSA-2000) and refined analysis methods. Provides target sensitivity for future experiments.
Clear detection (>3σ): Would constitute strong evidence for directional spacetime anisotropy, supporting blitzon cosmology prediction. Combined with CMB and bulk flow data, would reach ~4-5σ total significance for the unified external-structure hypothesis.
A detection would transform the cosmic dipole anomaly from puzzling coincidence to coherent pattern spanning multiple independent datasets and physical scales—exactly the signature expected if our universe exists within a larger structure with observationally accessible consequences.
Timeline and Feasibility
This analysis can proceed immediately Months 1-2: Data download, software setup, preliminary analysis
Months 3-4: Detailed correlation analysis, systematic error assessment
Months 5-6: Monte Carlo simulations, significance testing, paper preparation
Total time to publication: ~6-9 months from project start, assuming no complications. This is remarkably fast compared to typical multi-year astrophysics projects requiring new observations.
The combination of (1) publicly available high-quality data, (2) straightforward analysis methodology, (3) clear predicted signature, and (4) multiple systematic discriminants makes this one of the most immediately actionable tests of blitzon cosmology currently available.
Holographic Principle TGI provides concrete realization. The Bekenstein-Hawking bound S = A/(4ℓₚ²) emerges naturally from blitzon endpoint density. Our 3D+1 interior is holographically encoded on the 2D horizon.
String Theory Potential complementarity. String theory postulates 10-11 dimensions with 6-7 compactified at Planck scale. TGI inverts this: our 4 dimensions are compactified at cosmic scale. Strings might be transaction pathways through the blitzon network.
Loop Quantum Gravity LQG quantizes spacetime geometry into discrete spin networks. TGI offers similar discretization (blitzon endpoints) but with different ontology—not quantum geometry itself, but a transaction network from which geometry emerges.
AdS/CFT The interior-horizon duality parallels bulk-boundary correspondence.
External Universe: What physics governs reality beyond our horizon?
Singularity: Does the transaction network modify classical singularity structure?
Fermions: How do quarks and leptons fit? Possibly as topological defects in the blitzon network.
Precise Coupling Calculations: Exact derivation of α, α_w, α_s from geometric parameters.
We have presented the Transaction-Geometric Interpretation, a comprehensive framework that reconceptualizes quantum mechanics and spacetime geometry. By treating photons and force carriers not as propagating particles but as observational perspectives on direct spacetime transactions, TGI provides natural explanations for quantum non-locality, retrocausality, and wave-particle duality.
Blitzon cosmology extends this framework: collapsed photons at Planck scale form transaction endpoints on a black hole horizon. Our 4-dimensional spacetime emerges as the compactified manifold M⁴ = S³ × S¹, with forces arising from geometric structure. The 3-sphere rotation modes generate U(1) electromagnetic, SU(2) weak, and SU(3) strong gauge symmetries, while gravity emerges from overall curvature.
The framework provides natural explanations for the holographic principle, CMB anisotropies, dark energy, cosmic horizons, and a solution to the singularity paradox. The novel prediction that the mysterious 3:2 frequency ratio in black hole QPOs arises from the geometric relationship between shell and photon sphere frequencies offers a concrete, testable connection to existing astrophysical observations.
TGI makes specific testable predictions accessible through progressive experimental phases. The framework remains fully falsifiable—null results would constrain or eliminate TGI, while positive results would require an ontological shift in conceptualizing reality.
The profound implication: our universe exists as the interior of a black hole in an external reality we cannot directly observe. Physics as we know it—quantum mechanics, relativity, particle physics—emerges from perturbations in a Planck-scale blitzon sea. We are, in a precise sense, living inside geometry itself.
Gratitude to Aubrey McIntosh for sustained intellectual partnership spanning four decades, from micro-fluidic gas chromatograph collaboration (Ohio Medical Products, 1979-1981) through algorithm optimization (1984 Fast CRC routine) to consultation on theoretical physics concepts including post-manuscript review of photon collapse analysis (1990). His analytical rigor and dimensional analysis helped ground speculative ideas in established physics principles.
Deep appreciation to Thomas D. Ditto (1943-2025), with whom the author shared almost daily teleconferences over several years. These wide-ranging conversations covered holography and interferometry, practical matters, reminiscences, and eventually the DICER project. Ditto's innovative Dittoscope concept for space-based holographic telescopes inspired NASA's DICER mission. The years of technical discussions about diffractive optics and wave phenomena informed understanding of how distributed optical elements produce coherent results—directly relevant to transaction network concepts. Ditto's passing on March 14, 2025 (π day) was the loss of a close friend and intellectual companion.
Gratitude also to DICER team members: Heidi Newberg (Rensselaer Polytechnic Institute), Leaf Swordy, Shawn Domagal-Goldman, Richard K. Barry (NASA Goddard), L. Drake Deming (University of Maryland), and Frank Ravizza (Lawrence Livermore National Laboratory).
Thanks to the AI assistant for helping organize and clarify the mathematical exposition of these ideas.
[1]Cramer, J.G. "The Transactional Interpretation of Quantum Mechanics." Rev. Mod. Phys. 58, 647-687 (1986).
[2]Wheeler, J.A. & Feynman, R.P. "Interaction with the Absorber as the Mechanism of Radiation." Rev. Mod. Phys. 17, 157-161 (1945).
[3]Bekenstein, J.D. "Black Holes and Entropy." Phys. Rev. D 7, 2333-2346 (1973).
[4]Hawking, S.W. "Particle Creation by Black Holes." Commun. Math. Phys. 43, 199-220 (1975).
[5]'t Hooft, G. "Dimensional Reduction in Quantum Gravity." arXiv:gr-qc/9310026 (1993).
[6]Susskind, L. "The World as a Hologram." J. Math. Phys. 36, 6377-6396 (1995).
[7]Maldacena, J. "The Large N Limit of Superconformal Field Theories and Supergravity." Adv. Theor. Math. Phys. 2, 231-252 (1998).
[8]Hopf, H. "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche." Math. Ann. 104, 637-665 (1931).
[9]Vilums, I. "Gravitational Collapse of Photons at the Planck Scale." Companion paper (2025).
[10]Vilums, I. "The Photon as Spacetime Connection: A Transaction-Geometric Interpretation." Companion paper (2025).
[11]McClintock, J.E. & Remillard, R.A. "Black Hole Binaries." In Compact Stellar X-ray Sources, Cambridge University Press (2006).
[12]Strohmayer, T.E. "Discovery of a 450 Hz QPO from the Microquasar GRO J1655-40." Astrophys. J. Lett. 552, L49 (2001).
[13]Abramowicz, M.A. & Kluźniak, W. "A precise determination of black hole spin in GRO J1655-40." Astron. Astrophys. 374, L19 (2001).
[14]Remillard, R.A. & McClintock, J.E. "X-Ray Properties of Black-Hole Binaries." Ann. Rev. Astron. Astrophys. 44, 49-92 (2006).
[15]Vilums, I.J. U.S. Patent No. 4,878,735: Optical Imaging System Using Lenticular Tone-Plate Elements (1989).
[16]Newberg, H., Swordy, L., Ditto, T.D., et al. "Diffractive Interfero Coronagraph Exoplanet Resolver (DICER)." NASA NIAC Phase I Grant 80NSSC23K0588 (2023).