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Information Theory and Relativity: established connections for spacetime emergence
The intersection of information theory and relativity represents one of physics' most profound theoretical developments, with established frameworks demonstrating that spacetime geometry emerges from information-theoretic principles. The 511 keV electron rest mass scale appears as a fundamental boundary where classical electromagnetic descriptions fail and quantum field theory becomes essential, while the Lorentz factor directly controls information accessibility between reference frames.
Information-theoretic formulations of relativity
Modern physics has developed several rigorous frameworks connecting information theory to both special and general relativity. The most significant breakthrough came from Jacobson's thermodynamic derivation (Physical Review Letters, 1995), which showed Einstein's field equations emerge directly from the thermodynamic relation δQ = TdS applied to local Rindler horizons. This approach uses the Unruh temperature T = ℏa/2πck_B for accelerated observers and identifies entropy with horizon area: S = A/4G_ℏ.
Erik Verlinde's entropic gravity (JHEP, 2011) extended this paradigm by proposing gravity emerges as an entropic force from information changes on holographic screens. His framework uses F = T∇S with the same temperature relation, deriving Newton's laws from pure information-theoretic principles. While controversial, this approach has over 1000 citations and sparked extensive theoretical development.
The holographic principle provides perhaps the most concrete information-relativity connection. The Ryu-Takayanagi formula (PRL, 2006) shows entanglement entropy SA = Area(γA)/4G_ℏ, where γA is the minimal bulk surface. This demonstrates spacetime geometry literally encodes quantum entanglement structure, with AdS/CFT correspondence providing explicit realizations where (d+1)-dimensional gravity equals d-dimensional conformal field theory.
Electron rest mass as electromagnetic confinement scale
The 511 keV electron rest mass represents a fundamental scale in electromagnetic theory where classical and quantum descriptions meet. The classical electron radius re = e²/(4πε₀mec²) ≈ 2.82 × 10⁻¹⁵ m marks where electrostatic self-energy equals rest mass energy. At this scale, classical electromagnetic calculations diverge, requiring quantum field theory renormalization.
Historical work by Abraham, Lorentz, and Poincaré (1902-1906) attempted purely electromagnetic mass models. Poincaré introduced non-electromagnetic "stresses" contributing ~1/3 of electron energy to prevent electromagnetic instability. Modern QED calculations (Hönemann et al., 2018; Duhr et al., 2024) provide precise self-energy corrections, confirming the 511 keV scale as the boundary where perturbative expansions require careful treatment.
A.O. Barut's self-field QED (Physical Review A) demonstrates radiative effects can emerge from matter self-interaction without field quantization, treating 511 keV as the characteristic scale for electromagnetic interactions. Wave packet studies show electron localization becomes impossible below this scale - packets spread in ~10⁻¹⁶ seconds, demonstrating fundamental limits on electromagnetic confinement.
The 511 keV scale in atomic physics
While extensively studied in positronium physics and astrophysical contexts, the 511 keV scale's role as a fundamental atomic physics boundary appears underexplored in literature. The scale primarily appears through:
Positronium formation occurs above 6.8 eV threshold, with subsequent decay producing characteristic 511 keV photons. The galactic 511 keV emission line observed by INTEGRAL/SPI remains a major astrophysical puzzle, suggesting widespread positron annihilation processes.
Relativistic atomic effects become significant when binding energies approach the electron rest mass. For highly charged ions with Z > 70, K-shell binding energies can exceed 100 keV, making relativistic Dirac-Fock calculations essential. The 511 keV scale thus marks where non-relativistic atomic physics definitively fails.
The literature gap regarding 511 keV as a quantum-classical transition scale suggests opportunity for theoretical development. While the electron rest mass provides a natural atomic energy scale, explicit connections to correspondence principles remain unexplored.
Lorentz factor and information exchange
The Peres-Terno framework (Reviews of Modern Physics, 2004) established that quantum information transforms non-covariantly under Lorentz boosts. The Lorentz factor γ directly controls information accessibility - different inertial observers extract different amounts of information from identical quantum states. This represents a fundamental departure from non-relativistic quantum mechanics.
Entanglement transformation under Lorentz boosts (Alsing-Milburn, 2002; Jordan et al., 2007) shows γ can create maximal entanglement from finite transformations. The mathematical framework demonstrates von Neumann entropy S(ρ), mutual information I(A:B), and entanglement measures like concurrence all exhibit explicit γ-dependence.
The information causality principle (Pawłowski et al., Nature 2009) establishes that accessible information cannot exceed transmitted information, with relativistic light-cone structure enforcing fundamental limits. The Lorentz factor appears in constraints governing information transfer between spacelike-separated regions, preserving causal ordering through time dilation effects.
Martin-Martinez's framework (2011) shows relativistic quantum information requires quantum field theory formulation. Unruh-DeWitt detectors demonstrate γ-dependent information extraction from quantum fields, with entanglement harvesting protocols explicitly depending on detector acceleration through the Lorentz factor.
Synthesis and implications
These established frameworks reveal deep connections between information theory and spacetime structure. The 511 keV scale emerges as a fundamental boundary where electromagnetic self-energy calculations require quantum corrections, potentially marking transitions between classical and quantum regimes. The Lorentz factor controls information flow and accessibility, making information itself observer-dependent in relativistic contexts.
For spacetime emergence theories, these results suggest: (1) Gravitational dynamics emerge from thermodynamic/information-theoretic principles applied to causal horizons; (2) The 511 keV scale represents electromagnetic confinement limits relevant to particle mass generation; (3) Relativistic effects fundamentally alter information processing, with γ controlling the degree of information isolation between reference frames; (4) Holographic principles demonstrate spacetime geometry encodes quantum information structure.
These peer-reviewed foundations provide solid grounding for mathematical relationships in spacetime emergence theories, though significant theoretical development remains needed to fully connect the 511 keV scale to quantum-classical transitions in atomic systems.