PURSUING THE LIMITS OF FAILED SYMMETRY

General Relativity and quantum field theory are correct to the limits of observation, about 14 significant figures. They are incompatible where they overlap. Something postulated to be true is selectively false - and detectably so, but only outside theory. The greatest obstacle to understanding reality is not ignorance but the illusion of knowledge. Reality is not a peer vote. Empirical observation in existing apparatus using commercial materials can identify the failure.

Chiral algebras yield conformal field theory. How does non-linear dynamical symmetry chirality have linear algebraic consequences? Conformal field theory is typically explored in 2-D. In higher dimensions (e.g., Calabi-Yau, AdS/CFT correspondence, supersymmetric gauge theories, Sasaki-Einstein) it yields string theories having no empirical tests. Founding postulates can be empirically tested. They have no defense against falsification.

Every atom coordinate (+/-)M in a massed body is replaced with (-/+)M giving *M simultaneously reflected in all directions (geometric parity inversion). Translate centers of mass to coincide. Physics assumes rotations pinned to that point exactly transform *M back into M. If M is chiral, all series of rotations plus translations will fail. (Reflections, S_n improper axes of symmetry, are obviously forbidden). The math is unflawed, but it is incomplete.

If the vacuum is demonstrably not symmetric toward otherwise identical opposite geometric parity atomic mass distributions, physical theory is fundamentally wrong. Contradiction of prior observations is avoided. Divergence is only detectable for fermions in the chiral case, which as an atomic lattice is chemistry.

Physical theory postulates mirror symmetries: Newton (Green's function), General Relativity (Equivalence Principle), string theory (BRST invariance) and quantum gravitations overall, Calabi-Yau manifolds [1], standard model (arrives massless; Higgs is not detected), SUSY (invisible to LHC and XENON-100). The massed universe is not mirror-symmetric: electroweak force to fermions' anti-symmetric wavefunctions. Einstein-Hilbert action requires adding a parity-violating Chern-Simons term [2]. Defective postulates require inserted "symmetry breakings" during theory derivation.

Vacuum asymmetry toward otherwise identical opposite chirality atomic mass distributions has never been examined. Test mass is metaphoric left versus right shoes built of fermions, not massless boson photons pursuing null geodesic paths. Physics cannot calculate geometric parity divergence (chiral divergence in all directions) of a chiral atomic mass distribution and its mirror image. Crystallography and pure mathematics provide extreme inverse geometric parity self-similar atomic mass distributions to arbitrarily large sizes.

Socks and left shoes do not detect a left foot. Right shoes detect a left foot. A massed sector chiral vacuum background can be detected without contradiction of prior observations.

Big Bang intense chirality implies remnant chiral vacuum background active only toward fermionic mass [3]. A massed sector chiral vacuum background contradicts no prior data. Diastereotopic mass-vacuum interactions can exist. Noether's theorems couple continuous symmetries with conserved currents. Vacuum isotropy demands angular momentum conservation. Noether requires continuous symmetries or Taylor series' approximations.

Geometric parity is an explicit discontinuous symmetry. A massed sector chiral vacuum background allows minimum non-zero value for fermion angular momentum at large scale and small angular acceleration. Observed galaxy rotation versus increasing radius is remarkably modeled by MOND. The Tully-Fisher law relates spiral galaxies' visible mass distribution to asymptotically constant star and gas rotation velocities at large radii - the "dominating dark matter halos" regime. Milgrom acceleration critical value is g₀ ~(1.21±0.14)·10^-10 m/s². The universal MOND residual for fermionic matter can thus be sourced [4] as massed angular momentum with a minimum non-zero value from explicit symmetry breaking.

Chiral mass is divergent for matter vs. antimatter abundance, beta-decay rates [5], and neutrino-antineutrino reaction channels [6]. Massless photons are inert [7]. Opposite shoes detect a vacuum left foot by violating the Equivalence Principle (EP). Chemically and macroscopically identical, inverse geometric parity atomic mass distributions vacuum free fall non-identically: parallel minimum action trajectories, but with one test mass lagging the other in speed. Opposite circular polarizations of light traversing a materially homogeneous electronically chiral medium have different refractive indices (ORD) and different molar absorptivities (CD).

Decay of an intensely chiral Big Bang false vacuum, differentially acting upon fermionic matter only, fueled cosmic inflation, selected matter over antimatter, froze the Weak interaction left-handed. Its trace remnant today, active only in the fermionic massed sector, biased biological homochirality, causes annual sinusoidal rates of chiral beta-decay, splits the degeneracy of chiral neutrino-antineutrino reaction channels, and remains detectable by inverse geometric parity atomic mass distributions. Cosmic microwave background photons' polarization decoupled from massed sector chirality long before the universe went transparent.

No EP violation has emerged since 1500s' Galileo Galilei and Simon Stevin. Anomalies will appear external to derivation. Geometric parity, outside physical theory founding postulates and obtainable by chemistry, is the obvious testable EP falsification. Test for it: Opposite shoes vacuum free fall non-identically.

Geometric parity is nonsuperposability of a set of points upon its mirror image along all coordinate axes.

Quantum field theories (QFT) with Hermitian Hamiltonians are invariant under the Poincaré group containing spatial reflections. Parity is a spatial reflection but is not a QFT symmetry. Covariance with respect to reflection in space and time is not required by the Poincaré group of Special Relativity or the Einstein group of General Relativity (GR). Noether's theorems require continuous symmetries or approximation by a Taylor series. Parity is irresolvably discontinuous and excluded. Physics is proudly blind to opposite shoes.

Parity effects appear in weak interactions. Gravitation is the weakest fundamental interaction by 24 orders of magnitude. Opposite shoes will vacuum free fall along identical trajectories at detectably different rates - a vacuum "chiral mass refractive index" not exceeding 10^-12 difference/average. One enantiomorph will vacuum free fall (nearly) unremarkably, as a pair of socks or a left shoe fit upon a left foot. The other enantiomorph will display the majority of the parity EP anomaly, as a right shoe poorly fits upon a left foot.

Metric and quantum gravitation theories unite the effects of a massive body and an accelerated inertial frame by postulating the EP (general relativity) or rationalizing it (string theory and BRST invariance).

Eötvös experiments detect no composition or field EP violations to 5·10^-14 difference/average [8]. Lunar laser ranging observes zero Nordtvedt effect. 1.74 solar-mass 465.1 Hz pulsar PSR J1903+0327 plus a 1.05 solar-mass star are a 95.17-day orbit binary system [9]. 15.3% (AP4 model radius) [10] vs. 0.0001% gravitational binding energy, 1.8·10¹¹ vs. 30 surface gees, 2·10⁸ gauss vs. 5 gauss magnetic field; compressed superfluid neutrons and superconductive protons [11] vs. proton-electron plasma, extreme isospin and lepton number divergence; and pulsar 11% (AP4) of lightspeed equatorial spin velocity are differentially EP-inert for orbit, periastron precession, and gravitation radiation orbital decay. 1.97 solar-mass 317.5 Hz PSR J1614-2230 and a 0.5 solar-mass He-C-O white dwarf contrast pulsars with Fermi-degenerate matter, 20% versus 0.01% gravitational binding energy [12], to no EP anomaly.

Divergent strong field relativistic and quantum measurable observables universally validate the EP. All atoms are anonymous unit masses in vacuum free fall. Chemical bonding is gravitationally invisible: covalent, ionic, metallic, hydrogen, aromatic, aromatic stacking, banana, pi-pi sigma, dative, halogen; carbanions, carbocations, radicals, carbenes; 3-center 2-electron, charge transfer, metal to ligand charge transfer, intervalence charge transfer, van der Waals.... All measurable observables are differentially inert in Einstein's elevator at laboratory, local, and cosmic scales. Mass distribution chirality can be observed and calculated, but it cannot be measured. The EP can be falsified without contradiction of prior observations in any venue at any scale.

Crystallographic space groups (pdf) are a group of automorphisms with a bounded fundamental region consistent with crystal lattice discrete translation symmetries. Two objects equivalent by affine transformation but not conjugate by an orientation-preserving transformation (no orientation-preserving map from the group to its mirror image exists) are an enantiomorphic pair [18]. 3-space periodic crystal lattices are 230 unique self-similar distributions of points. 65 Sohnke space groups permit chiral contents. 11 enantiomorphic pairs in the 65 are mathematically chiral independent of unit cell contents (pdf). Delete individual space groups containing racemic or opposite sense screw axes. Two usable enantiomorphic pairs remain, with right-handed 3₁ screw axes or left-handed 3₂ screw axes: P3₁21(#152) | P3₂21(#154),

-quartz. P3₁(#144) | P3₂(#145),

-glycine. These are our shoe boxes containing opposite shoes.

Mathematician Michel Petitjean's published (pdf) QCM software [19] ab initio, from relative atomic coordinates only, calculates CHI - the normalized global minimum for all translations and rotations for all correspondences permitted by a graph. QCM requires anonymous countable N points' relative coordinates and body finite inertial moments. The overall extreme is CHI = 1 (normalized geometric parity divergence, [0 - 1]), COR = 1 (identity element only; N! maximum), DSI = 0 (self-similarity; [0 - 1]).

CHI asymptotic to 1 given COR = 1 DSI = 0 is a connection among eigenvalues, special functions, their representation theory with solid angles, and exponentials of fractions of

at a characteristic scale. Graphic intercept arises from a solid angle subtended by a polyhedron vertex angle

(supplement of its dihedral angle) of a formula unit's three consecutive atoms (

-quartz' averaged six O-Si-O paths) or dihedral angle (benzil), Eq. 1. Larger angles give smaller intercepts and larger CHI at a given lattice ball radius (scaled as log₁₀, radius in angstroms, and angle in degrees). All proposed enantiomorphic test masses qualify as the most extreme case.

Space groups P3₁21 and P3₂21: The quartz group includes

-quartz, [20], berlinite and analogues, cinnabar, tellurium, metallic selenium, others. Opposed solid single crystals of right- and left-handed quartz enable a parity-conserving Eötvös experiment sensitive to EP parity violation. A semi-empirical approach to calculating geometric parity divergence strictly agrees [23]. Quartz' atoms are densely packed, 79.64 atoms/nm³.

Benzil, C₆H₅-(C=O)-(C=O)-C₆H₅, is achiral when molten, gas phase, or dissolved. Solid state crystal lattice forces twist and stack benzil molecules into homochiral helices, space groups P3₁21 or P3₂21 [Acta Cryst. B43 398 (1987)].

A parity-destroying (by melting the crystal lattice) calorimetry experiment measures divergent vacuum insertion energies plus EP parity violation as single crystals' divergent enthalpies of fusion, shoes fitted into the vacuum left foot then melted into identical fitted socks without any chemical alteration. Benzil's atoms are densely packed, 93.43 atoms/nm³.

Space groups P3₁ and P3₂: Glycine

-polymorph [21] mesitylglyoxylic acid, 2,2-bis(hydroxymethyl)propionic acid, 1,2,4-thiadiazole-3,5-dicarbonitrile.

-Glycine's atoms are very densely packed, 127.07 atoms/nm³. It has 62.7% a-quartz' lattice volume/atom and 59.8% its material density, providing 2.67 times more structure/mass.

A chiral vacuum background appears in two independent ways. Right and left shoes fall through it differently. Right and left shoes insert into it with different energies. The former is a parity Eötvös experiment requiring exotic apparatus, 90 days, and PhD staff. Both together are a parity calorimetry experiment requiring two differential scanning calorimeters (DSCs), 2 days, and technicians.

EP violation as divergent rather than parallel trajectories disturbingly defines a privileged direction in space. EP violation as divergent acceleration magnitudes is unremarkable.

EP parity divergence is geometric, not compositional or electronic. Optical chirality is progressive rotation of the plane of linearly polarized light with passage through a medium. It is the imaginary part of the complex gyrotropy tensor. The quantitative electronic chirality scalar is time-reversal even, mirror-reflection odd:

Optical chirality is an artifact of orbitals, spin polarization, and interrogation frequency (J. Appl. Cryst. 19 108 (1986)). Chiroptical methods (specific rotation, optical rotatory dispersion; circular dichroism) are electromagnetic probes of three irreducible tensor components: pseudoscalar (chirality persists in disordered solution); vector (pyroelectric lattice); pseudodeviator (lattice symmetry). The last two allow mirror planes (gyrotropy without chirality) [13]. Silver thiogallate, AgGaS₂ in achiral space group I-42d(#122), has 522°/millimeter optical rotation along [100] at 497.4 nm [14].

-Quartz has no measurable optical chirality 56.16° from crystallographic [0001] (Ann. Phys. (Leipzig) 20 703 (1934)). Optical chirality cannot assemble a parity Eötvös experiment.

The Flack parameter is global detection of the chiral direction and relative enantiomeric excess of a non-centrosymmetric periodic crystal lattice. The Flack parameter is best resolved in a lattice containing both heavy and light atoms. It is not an absolute measure of atomic mass distribution chiral divergence, one crystal lattice composition compared to another composition.

Friedel's law says the scattering intensity |F(hkl)|² from crystal plane (hkl) equals |F(-h -k -l)|² where "F" is the calculated structure factor. However, atoms' inner electrons resonantly absorb x-rays and re-emit them with a delay. Reflections then have a phase shift called anomalous dispersion. Atomic scattering factors have imaginary parts due to anomalous dispersion, breaking Friedel's law.

"I" is the square of the scaled observed structure factor. If x ~ 0, the absolute chirality of the structure refinement is likely correct. If x ~ 1, the inverted structure is likely correct. If x ~ 0.5, the crystal may be racemic or twinned.

2-Norbornanone has [

]_D = 29.8° cm³/g-dm. 2-Norbornenone has [

]_D = 1146.° cm³/g-dm. The molecules are superposable except for olefinic hydrogens. Optical chirality does not measure geometric chirality within similar structures [15].

Chiroptical methods do not measure mass distribution chirality [16]. Even qualified local chiral atomic mass distributions may not sum to global chirality. Opposite chirality species cancel in a racemate. A solid ball is gaplessly dissected into N = 2 (or more) congruent homochiral pieces by the Coupe du Roi [17]. Global geometric criteria are required.

An Eötvös torsion pendulum is a symmetric ~6 cm diameter rotor vertically suspended from a meter of ~20 micrometer diameter tungsten filament (a hair is ~50 micrometers diameter) in a vibration-isolated; electrically, magnetically, and electromagnetically-shielded ultra-high vacuum chamber. It carries two mass-balanced and moments of inertia-balanced sets of 180°-opposed test masses totaling ~40 grams. The rotor link above [26] displays two parity Eötvös experiments:

EP violation exerts nanoscopic periodic torque with interferometric rotation detection as the Earth gravitationally orbits the sun (m_g, gravitational test mass) and inertially rotates about its axis (m_i, inertial test mass). EP composition tests null to
2|m_g - m_i|/|m_g + m_i| = 5·10^-14 difference/average sensitivity.

Geocenter orbital acceleration varies from 0.6133 cm/sec² ~03 January 2010 perihelion to 0.5737 cm/sec² ~06 July 2010 aphelion averaging 0.5930 cm/sec² at one astronomical unit. Given World Geodetic System 1984, 44.95° latitude affords maximum 1.693 cm/sec² horizontal component of Earth's inertial spin at sea level. Geoid gravity is 980.6 cm/sec² (differentially inactive in these experiments). Small imposed accelerations demand large contrasted property concentration and divergence for detectable EP violation.

An Eötvös experiment contrasts net active mass. Nuclear binding energy is the largest studied composition divergence, but it is a very small fraction of total mass loaded in a composition dipole. Weighted for isotopic abundance and respective nuclear binding energies, formula unit versus formula unit,

[Ti - Pt] is MICROSCOPE. It is a hopeless EP test made worse for the alloys to be used: PtRh10 (90% Pt, 10% Rh) versus titanium alloy TA6V (90Ti_6Al_4V).

Atomic mass distribution in 3-space defines a geometric parity test mass. Ignoring electrons entirely, quartz is 0.99973 active mass (nuclei relative positions in space). Parity Eötvös experiments are 400 to 500 times as sensitive as the best composition Eötvös experiments for the same test mass total loading for the same EP divergence.

Benzil differential enthalpy of fusion calorimetry (below) allows a maximum geometric parity divergence Eötvös signal of 10^-12 difference/average. Geometric parity Eötvös experiments offer thousands of times better overall sensitivity than the most divergent composition Eötvös experiments, even in principle,

Other composition Eötvös experiments have smaller active mass content and vanishingly small net active mass divergence,

A parity Eötvös experiment is geometric parity-conserving. A parity calorimetry experiment is geometric parity-destroying. It melts opposite shoes into identical achiral socks. A time-varying EP parity violation is summed with a constant differential chiral vacuum background insertion,

Property	Fraction of Rest Mass

rest mass	100%
crystal lattice nuclear mass distribution parity divergence	99.9775% (Te) 99.9771% (HgS) 99.9769% (PdSbTe) 99.9730% (AlPO₄) 99.9726% (SiO₂) 99.9713% (benzil) 99.9708% (*glycine)
nuclear binding energy (low Z)	0.76% (₂He⁴)
neutron versus proton mass	0.14%
electrostatic nuclear repulsion	0.06%
electron mass	0.03%
unpaired spin mass	0.005% (⁵⁵Mn**)
nuclear antiparticle exchange	0.00001%
Weak Force interactions	0.0000001%
Gravitational binding energy	0.0000000319% Earth*** 0.00000000185% moon

H_fusion(enthalpy of fusion) is 112 J/g. A 5·10^-14 relative Eötvös signal is

DSC precision is 0.1%. A borderline detectable parity Eötvös experiment output is 40 times DSC baseline sensitivity. A parity EP experiment has 400 to 500 times the relative active mass of the best composition Eötvös experiment. State of the art composition Eötvös experiment sensitivity is 5·10^-14 relative. Unremarkable parity calorimetry experiment sensitivity is 16,000 to 20,000 times better, 3·10^-18 relative.

Two horizontally abutted DSCs' sample ports define a north-south line. Each holds a ~3 mm diameter ~17 mg benzil single crystal sphere with sample carriers crimped against sublimation. One sample port consistently contains one crystal in space group P3₁21 and the other sample port one crystal in P3₂21.

H_fusion are simultaneously run. New crystals run at half-hour intervals for 24 hours inclusive local time. If

H_fusion is not equal to zero within experimental error, repeat the run the next day with east-west alignment.

H_fusion will have a six hour phase shift on the second day when the sample ports are aligned east-west. Calibration and controls are

H_fusion of finely powdered racemic benzil.

Earth's inertial spin and gravitational orbit offer rich interaction at 44.950 latitude (WGS84; Earth is a slightly oblate spheroid). "Vacuum propellers" are notoriously nonphysical - but not for us. A rigid chiral mass distribution translating through an interactive medium experiences torque. Inverse geometric parities experience opposite torques.

Otherwise identical single crystal quartz balls, space groups P3₁21 / P3₂21, and an amorphous fused silica ball are coated with superconductor and Meissner effect-levitated in hard vacuum re levitated superconducting dual sphere gravimeters. Balls counter-rotating with diurnal phasing (fused silica as control) validate massed sector interactive vacuum background inert to photons.

All aether and Lorentz invariance tests used photons. A divergent mass effect is not prohibited.

The parity gyroball experiment reduces to vacuum phase single molecules observed with (Fourier transform) microwave spectrometry for diurnally-varying relative rotation state populations. A preferred molecular rotor has a large fraction of its skeletal atoms being stereocenters rendered equivalent by rotation axes. Point group D2 twistane, tricyclo[4.4.0.0^3,8]decane, C₁₀H₁₆, has four identical chiral centers that arise from geometry.

Rigidly mount two vacuum propellers at opposite ends of a short stiff axle. Random McMurry coupling of racemic synthetic intermediate twist-2-one creates 25% right-right, 50% right-left, 25% left-left pairings. Rotationally rigid twistylidene dimer rotors are accessible and elegant.

The table lists calculated properties for candidate molecular rotors in vacuum. CHI validates the C₂₀H₂₈ dimers and their epoxides (permanent dipole moment for stronger microwave transitions). CHI and moments of inertia were calculated from HyperChem mm+ minimized structures.

Molecule	CHI	Moments of inertia, amu-Å

phenylalanine	0.103146	198.137	1153.73	1182.48
twistane	0.709172	228.401	349.101	352.793
hexadecafluorotwistane	0.714376	1640.94	2150.10	2208.38
chiral di-2-twistylidene	0.462493	703.060	1774.35	1938.04
meso-di-2-twistylidene	0.000000	702.402	1760.13	1996.00
chiral di-2-twistylidene epoxide	0.455900	733.022	1874.77	2058.85
meso-di-2-twistylidene epoxide	0.000092	738.745	1877.88	2130.11

FT microwave spectroscopy seeks a diurnal divergence of rotational state populations for paired homochiral rotors versus the meso-pair. A chiral vacuum background will diverge the two homochiral rotors' responses. Diurnal divergence validates a massed sector interactive vacuum background inert to photons.

A 5·10^-14 gram/gram divergence is a 4.49 joule/gram divergence. Twistylidene dimer rotors, C₂₀H₂₈, are MW = 268.436. Boltzmann's constant estimates rotational divergence as molecular temperature. If the sample cell is at 100°C, 373.15°K, it is a 28% absolute temperature increase.

(4.49 J/g)(268.436 g/mol)/(6.022·10²³ molecules/mole)(1.3806510^-23 J/kelvin) = 145 kelvin/molecule

The historic EP test drops two objects from a tall tower and differentially compares their free fall trajectories. Fallturm Bremen is a 110 meter vacuum free fall, 4.74 seconds one way, or 9 seconds with a bottom catapult launch. The 146 meter tower's core 123 meter vacuum tube is pumped down to 7.5 millitorr. A drop capsule contains an interior drop capsule in hard vacuum.

Robert Reasenberg and James Phillips, Harvard-Smithsonian Center for Astrophysics, are fabricating a 400-second vacuum free fall sounding rocket capsule promising 1000X (pdf) greater sensitivity than an Eötvös balance, (arxiv:1001.4752, Class. and Quantum Grav. 27(9) 095005 (2010)). They plan to oppose aluminum versus lead test masses. Grant funding embraces 100% guaranteed failure of a composition EP test but rejects plausible success of a geometric EP test.

A parity Eötvös experiment opposing enantiomorphic space group single crystal alpha-quartz test masses risks success in falsifying the Equivalence Principle. Parity calorimetry in benzil proceeds in kind. Inverse parity gyroballs and parity-paired plus anti-paired molecular propellers are sensitive to all massed sector interactive vacuum backgrounds. A Galilean drop is absolutely definitive. A broad swath of physical theory postulating isotropic vacuum validated by photons could be selectively falsified without contradiction by inverse geometric parity atomic mass distributions. Somebody should look, for the worst it can do is succeed.

Uncle Al denounces academic physicists who reject challenging spacetime geometry with test mass geometry. They are cowards and worse - managers and bureaucrats covering their bums with abstract performance metrics, measuring what is Officially True not important, procuring performance bonuses for pursuing process not product. Scientists pursue discovery. Discovery is product. On a good day, discovery is ghastly wicked insubordination.

Contemporary physics is an abusive hegemony of beige, as Tommy Aquinas knew the necessary answer but lacked a route to it. Science is poisoned by deformed decisions valuing theory over falsifying experiment. Cognition stratifies.

Young Marlon Brando was grizzly. His studio plugged actors into scripts, making movies and money. Grizzly Brando was a singing gangster in Guys and Dolls. The toughest US criminals were gelded in a Salvation Army meeting. A song said it all,

Promotion within hierarchal management is quantitatively worse than random choice. Physics is staring down extraordinary empirical failures: quantum gravitations; Standard Model, SUSY, and the Higgs meson; dark matter. Physics is a coward for not examining a subtle universal falsification of its assumptions to be performed in existing apparatus. Hey physics... you would still have teleparallel gravitation, authored by A. Einstein, et al.

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[26] Adapted from http://www.npl.washington.edu/eotwash/experiments/equivalencePrinciple/newWashPendulum.jpg

PURSUING THE LIMITS OF FAILED SYMMETRY

Uncle Al, 09 July 2011

CONTENTS

I. Failure of theory

II. Different in a different way

III. Shopping for shoes

IV. Fitting shoes on feet

V. Parity Eötvös experiment

VI. Parity calorimetry experiment

VII. Parity Gyroballs

VIII. Parity Molecular Rotors

X. Parity Galilean Drops

XI. Commentary and Polemic

References