Pairs of chemically identical opposite geometric parity atomic mass distributions occur as single crystals in enantiomorphic space groups P3121 and P2221 (quartz, benzil) plus P31 and P32 (glycine gamma-polymorph). They can measurably violate the Equivalence Principle in parity-retaining Eötvös experiments. They can detect both a chiral vacuum background and EP parity violation in parity-destroying calorimetric experiments.
©2005,2006,2007,2008,2009 Alan M. Schwartz. All Rights Reserved.
organiker atsign lycos dotsign com
PACS 04.80.Cc, 11.30.Er
Revised 03 September 2009

Calorimetric Equivalence Principle Test

The weak interaction is strictly left-handed. Parity Violating Energy Difference (PVED) experiments seek a measurable energy divergence between left-handed and right-handed molecules from weak interaction Z0 neutral current exchange between nucleus and electrons. Optimistic PVED is 8·10-12 eV. Room temperature energy background kT = 0.0257 eV. Carbon-carbon bond strength is 3.6 eV. Benzil PVED deltadeltaH(fusion) will not exceed 4·10-10 J/gram from the weak interaction.
Mendeleev Commun. 13(3) 129 (2003)
Angew. Chem. Int. Ed. 41(24) 4618 (2002)

If gravitation is parity-odd, like the Chern-Simons term added to Einstein-Hilbert action in quantized gravitations or teleparallel gravitation in Weitzenböck space, calculated deltadeltaH(fusion) between left-handed and right-handed benzil crystals is 8.99 J/gram or 8% energy/mass difference for a 10-13 difference/average Equivalence Principle mass/mass anomaly. EP parity violation arises from interaction with a measurably chiral vacuum background. A two day experiment has profound consequences for physics, chemistry, and biology. Somebody should look.
Einstein-Cartan theory
Einstein-Cartan theory revisited
Completely asymmetric Cartan tensor



    Table I.     Equivalence Principle Tests
EP Parity Calorimetry Experiment
    Figure 1.    Geometry of Parity Violation
    Table II.    Eötvös vs. Parity Calorimetry Experiments
    Table III.   Test Mass Property Magnitudes
Geometric Parity Divergence
    Figure 2.    Crystalline Benzil Helix Repeat Unit
    Table IV.    Benzil Differential Parity Enthalpy of Fusion
Net Active Mass
    Table V.     Postulated Gravitation Independence
    Table VI.    Solar Gravitation at Earth Orbit
    Table VII.   Horizontal Acceleration vs. Latitude
Parity Calorimetry Experiment Details


Any credible theory of gravitation - classical or quantized - must postulate, derive, or ignore the Equivalence Principle (EP):


The EP is true, gravitation is parity-even gerade, inertial and gravitational masses are inseparably coupled, the vacuum is achiral. Parity violations (e.g., the Weak Interaction) are extrinsic symmetry breakings.
The EP is not true, gravitation is parity-odd ungerade, inertial and gravitational masses can be decoupled, the vacuum is chiral (e.g., possessing a background pseudoscalar field in the massed sector that differentially interacts with opposite parity atomic mass configurations). Parity violations are intrinsic (space is a left foot) and can be demonstrated with chemically and macroscopically identical, opposite parity mass distributions (left and right shoes).

General Relativity postulates the EP. String theory derives it from state-operator correspondence and BRST invariance of graviton vertex operators. Symmetry of the Einstein curvature tensor and contingent energy-momentum tensor prohibit relativistic exchange of spin and orbital angular momenta. Detecting spin-orbit coupling in binary pulsar PSR J0737-3039A/B requires ~20 years of observation.

Conservation of angular momentum enforced by isotropic vacuum and Noethers' theorem would not obtain for opposite parity test masses. (Parity is not a Noetherian symmetry for being discontinuous and not approximated by a Taylor series.)

Contemporary Eötvös balance studies on chemical compositions (Adelberger) are sensitive to 5·10-14 difference/average over a three month run. Cryogenic 2.2°K Eötvös apparatus sensitive to 10-14 is being debugged (Newman). Gravitation theory is a geometry of mass distribution disregarding chemical composition. All chemical compositions empirically vacuum free fall identically.

A left foot can only be detected by a right shoe; socks and left shoes will fit almost identically. Do (metaphoric) left and right shoes fall identically? Somebody should look. A parity calorimetry test offers a 33,000-fold improvement in EP anomaly sensitivity in only two days of measurements.


  500? Philoponus[20] "small" Drop Tower
1585 Stevin[19] 5·10-2 Drop Tower
1590? Galileo[2] 2·10-2 Pendulum, Drop Tower
1686 Newton[3]    10-3 Pendulum
1832 Bessel[21] 2·10-5 Pendulum
1910 Southerns[22] 5·10-6 Pendulum
1918 Zeeman[23] 3·10-8 Torsion Balance
1922 Eötvös[24] 5·10-9 Torsion Balance
1923 Potter[25] 3·10-6 Pendulum
1935 Renner[26] 2·10-9 Torsion Balance
1964 Dicke,Roll,Krotkov[27] 3·10-11 Torsion Balance
1972 Braginsky,Panov[28]    10-12 Torsion Balance
1976 Shapiro, et al.[29]    10-12 Lunar Laser Ranging
1981 Keiser,Faller[30] 4·10-11 Fluid Support
1987 Niebauer, et al.[31]    10-10 Drop Tower
1989 Heckel, et al.[32]    10-11 Torsion Balance
1990 Adelberger, et al.[33]    10-12 Torsion Balance
1999 Baeßler, et al.[34] 5·10-13 Torsion Balance
2008 Adelberger, et al. PDF 5·10-14 Torsion Balance
201? Schwartz 2·10-16 Parity Torsion Balance
201? Schwartz 3·10-18 Parity Calorimetry
201? MiniSTEP[35]    10-17 Earth Orbit
Ciufolini & Wheeler Gravitation and Inertia (Princeton University Press: Princeton, 1995) pp. 117-119


All compositions of matter validate the Equivalence Principle (EP). Empty spacetime is isotropic to massless photons locally and astronomically: vacuum refractive index = 1; no dispersion, no dichroism, no gyrotropy. Parity-violating massed sectors are neither required nor forbidden in metric-affine, Einstein-Cartan, teleparallel, and Riemannian geometry gravitations. Ashtekar has a parity violating term with the Immirzi coefficient.

An EP parity violation cannot originate in Newtonian gravitation (e.g., Green's function), metric gravitation (EP), or string theory (BRST invariance). Its falsifying presence is testable. The relevant probe of spacetime geometry is test mass geometry. Theory predicts what it is told to predict. Somebody should look.

Chemically identical, opposite parity mass distributions have opposite chirality in all directions (all atom coordinates are sign-reversed). They have unequal insertion energies into a chiral vacuum background - a left foot fitted with left and right shoes. That divergence ends when atom positions are randomized: melt, vaporize, dissolve, or burn. Energies of transition must be different for opposite parity insertions becoming identical achiral states. A pair of calorimeters can falsify GR and string theory.

The Earth inertially accelerates about its spin axis as it gravitationally accelerates in its solar orbit. Chiral vacuum interaction, (massinertial - massgravitational) divergence, will be modulated by shifting phase angles of inertial and gravitational acceleration with local time of day compared with opposite parity test masses' geographic orientation.

Chirality vanishes at lengths smaller than a screw's pitch. The smallest possible chiral emergent scale and densest self-similar lattice packing are desired. alpha-Quartz SiO3 chirality emergent scale is within a 0.304 nm diameter sphere. Benzil (C=O)-(C=O) torsion angle is within a 0.313 nm diameter sphere.

Quartz' atoms are densely packed, 79.62 atom/nm3. gamma-Glycine's atoms are very densely packed, 127.1 atoms/nm3, enantiomorphic space groups P31 and P31. Both are suitable for parity Eötvös experiments. Benzil's atoms are densely packed, 93.46 atoms/nm3 for a parity calorimetry experiment.

Benzil (parity calorimetry experiment) and alpha-quartz (both in enantiomorphic space groups P3121 and P3221) calculate as sweet spots given M. Petitjean, "On the root mean square quantitative chirality and quantitative symmetry measures", J. Math. Phys. 40, 4587 (1999). gamma-glycine (parity Eötvös experiment) in enantiomorphic space groups P31 and P32 also passes QCM calculation with CHI asymptotic to 1, COR =1, DSI = 0.

Two local differential scanning calorimeters located between 40°-50° latitude (optimal 44.95° latitude; WGS 84) preferably between 06 October and 01 April (optimal 03 January) are abutted and positioned so that their sample pans are located along a north-south line. Each holds a ~3 mm diameter ~17 mg solid single crystal sphere of benzil, one in space group P3121 (right-handed) and one in P3221 (left-handed). deltaH(fusion) for both are simultaneously run. The procedure is run with new crystals at 0600 hrs, noon, 1800 hrs, and midnight local time. Half-hour intervals would fill in the curve. If all deltadeltaHfusion at all times are not equal within experimental error (differential output would be maximum signal, null, maximum, null), the experiment is repeated the next day with the calorimeters aligned east-west to confirm. The deltadeltaHfusion will have a six hour phase shift on the second day if the signal is real.



Metric gravitation demands the two numbers must always be identical, or deltadeltaHfusion always equals zero. If there is a reproducible non-zero deltadeltaHfusion General Relativity (GR) was founded upon two empirically falsified postulates - the Equivalence Principle (EP) and the isotropy of space. Affine, teleparallel, and noncommutative gravitation are validated.

There are four possible outcomes for a parity calorimetry experiment in benzil:

  1. No net signal. deltadeltaHfusion = zero. Both single crystal deltaHfusion are identical to that of powdered racemic benzil. Values do not change versus time of day and N-S or E-W geographic orientation.
  2. Left- and right-handed crystals consistently fit with different energies into left-handed vacuum. The melts are achiral and identical. Opposite parities of chemically identical crystal melting to the common state must display different enthalpies of transition. deltaHfusion will be different from that of powdered racemic benzil, deltadeltaHfusion will be non-zero.
  3. The angle between Earth's inertial spin and gravitational orbit rotates 360°/24 hours. This sources a composition Eötvös experiment signal. Add parity benzil test masses aligned N-S or E-W and the coordinate frame cycles chiral, achiral, opposite chiral, achiral every 24 hours. A sinusoidal deltadeltaHfusion will appear.
  4. (2)+(3). The expected achiral nodes of (3) will display non-zero deltadeltaHfusion.

Differing (transition energy)/gram, is immediately testable. Allow both the DSCs to cool to obtain both deltaHcrystallization. Reheat to obtain both deltaHfusion again. If the net non-zero signal originated from opposite parity mass distributions - scrambled by melting - the enthalpies of crystallization and re-fusion will be identical/mass in each calorimeter and between calorimeters. The initially observed divergence arose from opposite parity mass distribution geometry.

An observed net signal is further validated by running each day's calorimeter orientation at hourly or shorter intervals to fill in the sine curve response of deltadeltaHfusion versus time of day. Those two plots would constitute inarguable evidence for a chiral vacuum background and Equivalence Principle parity violation. Helicity, optical chirality, and geometric chirality are insufficient.

Petitjean's rigorous parity divergence mathematics can be relaxed by employing benzil single crystal needles with wildly different moments of inertia rather than solid spheres. A 21 screw axis is simultaneously left- and right-handed. Elegant tests separately examine opposite chirality crystals of

space group P212121
Acta Cryst. C52 773 (1996)

and then opposite parity crystals of

space groups P3121 and P3221
Acta Cryst. C52 2465 (1996)

Their chemical compositions are essentially identical but their symmetries are wildly different.


ParameterComposition EötvösParity Calorimetry
Duration and labor 90 days; 2160 hrs plus prep. 2 days; 2 hrs plus prep.
Data workup intensive and statistical subtract two numbers
Shielding and isolation hard vacuum, temperature,
magnetic, electromagnetic,
vibration, mass gradient;
torsion fiber relaxation...
Configuration leveling, balance, sample join,
light pressure, moments of
inertia, oscillation damping,...
align calorimeters,
weigh test masses
Precision laser interferometer 0.1% precision adequate
Active mass fraction 0.002398 maximum 0.9997 minimum
Signal source 10-13 mass/mass 8.99 joules/gram energy/mass
Sensitivity, mass/mass 10-13 3·10-18
Net output observed needs new theory teleparallel gravitation
External verification $2 million Eötvös balance two commercial calorimeters

A chiral non-rotating body translating through a medium will experience a consistent torque,

HK Moffat, Six lectures on general fluid dynamics and two on hydromagnetic dynamo theory, pp. 175-6 in R Balian & J-L Peube (eds), Fluid Dynamics (Gordon and Breach, 1977)
3.5 megabytes
pdf pp. 25-27, calculation of the chiral case.

Opposite parity mass distributions will detect (absolutely and by contrast) any interactive vacuum background. This is not a parity violation experiment.

Optical chirality is a local spectral artifact. It does not detect opposite geometric parity mass distributions. Achiral crystals can powerfully rotate the plane of plane polarized light. AgGaS2 in non-polar achiral tetragonal space group I-42d (#122) has immense optical rotatory power: 522°/millimeter along [100] at 497.4 nm. Chiral crystals can have directions of zero optical rotation alpha-Quartz 56.16° from crystallographic [0001] has zero optical rotation.

Composition chirality is irrelevant. All atoms are identical anonymous unit masses when in vacuum free fall. Chemical bonding is irrelevant. Magnetism is irrelevant, polarized spins or aligned orbital angular momenta.


PropertyFraction of
Rest Mass
rest mass 100%
crystal lattice
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     0.000000046% Earth***
    0.0000000019% moon
*(nuclear mass)/(atomic mass), corrected for isotopic abundance
**globally aligned undecatiplet
***Iron core rather than homogeneous body.

All chirality eventually vanishes with decreasing volume elements. Given a screw, chirality vanishes at lengths smaller than its pitch. Best efforts are then homochiral atomic helices (crystallographic screw axes) with sub-nanometer emergent scale (0.323 nm diameter sphere for alpha-quartz, 0.465 nm diameter sphere for benzil.)


Geometric parity divergence is chirality simultaneously calculated in all directions atom by atom. Atoms are anonymous and identical unit masses; only their relative distribution in 3-space is of concern. Nuclear positions are empirically indistinguishable from atomic positions. Comparison of separate macroscopic bodies can only be achieved if every atom can be locally assigned coordinates relative to the others and globally compared between bodies. Single crystal test masses satisfy these requirements. Test masses must be solid spheres - no drilling, no hollowing - given the math of quantitative geometric parity divergence and to eliminate direction bias.

There are 11 pairs of opposite parity space groups of 65 chiral space groups in 230 3-space periodic crystallographic space groups total. Howard Flack (e.g., the Flack parameter) is authoritative,

Helv. Chim. Acta 86 905 (2003) (pdf)

Explicit calculations demonstrate opposite parity space groups P3121 (right-handed screw axes) and P3221 (left-handed screw axes) always give quantitative geometric parity divergence rapidly asymptotic to theoretical maximum - CHI->1; COR=1, DSI=0 - with increasing radius. Slope is -2 by theory. The smaller the intercept the faster CHI->1.

J. Math. Phys. 40(9) 4587 (1999)
Chem. Mater. 15 464 (2003)
Benzil Benzil, without hydrogens alpha-Quartz
Cinnabar, mercury sublattice

Consider opposite parity P3(1,2)21 crystal lattices whose formula units are achiral molecules. Dissolution, melting, sublimation, and combustion destroy the crystal lattices and their mass distribution parity divergence. The solid state inertial-gravitational mass divergence must disappear during the phase transition - parity differential enthalpies of solution, fusion, sublimation, and combustion. Diastereotopic insertion energies into chiral vacuum are observable when parity divergence vanishes.

Benzil is an achiral molecule in solution, molten, or gas phase. Crystal lattice forces rotationally distort the molecule and stack it into homochiral helices giving either space group P3121 or space group P3221 for the solid,


Benzil, crystal and vacuum

Benzil melts between 94-95 C, 112 joules/gram enthalpy of fusion (latent heat of melting). 8.99 joules/gram is an 8% divergence. Differential scanning calorimeters (NOT oscillatory!) have 0.1% precision. 10-13 parity mass divergence detectable in three months is 10-15 parity energy divergence detectable in 15 minutes.


210.2322 g/mol
melting point
melting point
Enthalpy of fusion
mp = 94.82°C
112.0 J/g
  26.77 cal/g
23.546 kJ/mol
  5.6276 kcal/mol
Enthalpy of fusion
mp = 94.85°C
110.6 J/g
  26.44 cal/g
23.26 kJ/mol
  5.559 kcal/mol
Enthalpy of fusion
mp = 94.86°C
112.0 J/g
  26.76 cal/g
23.54 kJ/mol
  5.626 kcal/mol
Differential enthalpy
of parity divergence
8% for 10-13 g/g parity anomaly
E = (10-16 kg)(299,792,458 m/sec)2
E= 8.99 joules


The largest active mass fraction composition divergence Adelberger et al. examine is nuclear binding energy of titanium vs. beryllium. Newman examines magnesium vs. beryllium. All other property contrasts are much smaller. Most of the loaded mass is inert in a composition experiment. Correcting for isotopic abundance and their respective nuclear binding energies,

J.H. Gundlach, New J. Phys. 7 205 (2005)
R. Newman, Class. Quantum Grav. 18 2407 (2001)

     p  =  938.271998 MeV
     n  =  939.565330 MeV
     Be =    6.462844 MeV/baryon binding energy
     Mg =    8.265129 MeV/baryon binding energy
     Ti =    8.714634 MeV/baryon binding energy
     [Ti - Be]/[(30.9300n + 26p)/56.9300] = 0.002398 of total mass is active mass  
     [Mg - Be]/[(17.3202n + 16p)/33.3202] = 0.001919 of total mass is active mass  

Mass distribution parity divergence of atomic nuclei for benzil is 0.999713 of total mass. That is a factor of 417 better than Adelberger and 520 better than Newman. A 10-13 sensitivity composition Eötvös experiment is a 2-3·10-18 sensitivity calorimetry parity experiment for improved signal amplitude and active mass. A factor of 33,000 or 41,000 improvement is significant.

We are informed that Adelberger's Be/Ti comparison also tests baryon number (neutrons versus protons). Baryon number through Noether's theorem couples to an internal symmetry, SU(3) "winding number." Conserved quantities arising from internal symmetries cannot first-order source an observable. Given the scholarly publication we run its numbers and contrast net active mass with a parity Eötvös experiment in quartz,

Phys. Rev. Lett. 100 041101 (2008) (PDF)
[(1.001077) - (0.99868)/(0.5)(1.001077 + 0.99868)][(8)(4.84]= 0.0928 g active mass

In alpha-quartz with CHI=1 and active mass from atomic nuclear positions only,
(0.999726)(1)[(8)(4.84)]= 38.709 g active mass
38.709/0.0928 = 417 times the active mass

3·10-14 composition sensitivity, given the same magnitude of anomaly coupling, becomes 7·10-17 geometric sensitivity. It cannot do worse than null. Somebody should look.

"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong," Richard Feynman.


A parity calorimetry experiment requires two calorimeters, one for each space group of crystal. The calorimeters are oriented geographic north-south one day then east-west the next day. For each orientation a paired opposite parity enthalpy of fusion of benzil is run at local 0600 hrs, noon, 1800 hrs, and midnight to cycle maximum signal, null, maximum, and null signals from the phase angle of Earth's inertial spin and gravitational orbit. A real net signal, deltadeltaHfusion, will be sinusoidal during each day and phase-shifted 90° between days.

There is no parity Nordtvedt effect. Natural quartz is flawed and racemic, as are all chiral minerals. The Earth masses 5.9742·1024 kg. Wet biomass is 3.6·1014 kg. Water is not chiral. All chiral protein amino acids are L-configuration. All chiral natural sugars are D-configuration. Of the very small (dry chiral biomass)/(total Earth mass), meat and wood cancel.

A non-null EP parity experiment does NOT contradict any existing observation.


Equivalence Principle (EP) composition tests contrast properties coupled to symmetries through Noether's theorem. Required were continuous symmetries or approximation by a finite or countably infinite number of independent infinitesimal generators (Taylor expansion) consistent with smooth Lie groups. Other dependencies, given a larger infinite number of generators (GR and the Bianchi identities), were acceptable.

Parity is the only external symmetry with no continuous or summed infinitesimal approximation. It is excluded from Taylor expansions, smooth Lie groups, and Noether's theorem.

The existence of a symmetry operator implies the existence of a conserved observable. Given G is the Hermitian generator of nontrivial unitary operator U (e.g., parity), then if U commutes with Hamiltonian H so does G [H,G]=0. If U commutes with H it is a symmetry and a conserved quantity. Any system that is initially in an eigenstate of U evolves over time to other eigenstates having the same eigenvalue.

U = cpsi     then,
Uexp(-itH)psi = exp(-itH) Upsi   [U commutes with H]
                     = exp(-itH) cpsi
                     = c exp(-itH)psi

so exp(-itH)psi is again an eigenstate of U, with the same eigenvalue c. Discrete symmetries also give conserved quantities in classical mechanics (e.g., bifurcation theory of dynamical systems). Parity the symmetry is coupled to geometric parity the property without Noether's theorem.


ClassInvarianceConserved Quantity
translation in time
translation in space
linear momentum
rotation in space
angular momentum
P, coordinates' inversion spatial parity
C, charge conjugation charge parity
T, time reversal time parity
CPT product of parities

of spacetime

U(1) gauge transformation electric charge
U(1) gauge transformation lepton generation number
U(1) gauge transformation hypercharge
U(1)Y gauge transformation weak hypercharge
U(2) [U(1)xSU(2)] electroweak force
SU(2) gauge transformation isospin
SU(2)L gauge transformation weak isospin
PxSU(2) G-parity
SU(3) "winding number" baryon number
SU(3) gauge transformation quark color
SU(3) (approximate) quark flavor
Standard Model

EP tests exploit external symmetries' observables. Internal symmetries' observables (gauged using fiber bundle theory, e.g., charge conjugation) transform fields amongst themselves leaving physical states (translation, rotation) invariant. A local gauge transformation always exists to make the local gauge-field vanish. Two vector potentials differing only by a gauge transformation give the same field. EP tests opposing properties coupled to internal symmetries are empirical first order default nulls.


to sun,
106 km
2008 02 January 147.096603 0.613347
2009 04 January 147.095552 0.613356
2010 03 January 147.098040 0.613335
2011 03 January 147.105761 0.613271
2012 05 January 147.097207 0.613342
2013 02 January 147.098161 0.613334
average 147.09855 0.613331
1 AU 03 April 149.598 0.593007
2008 04 July 152.104160 0.573627
2009 04 July 152.091131 0.573725
2010 06 July 152.096448 0.573685
2011 04 July 152.102197 0.573642
2012 05 July 152.092424 0.573715
2013 05 July 152.097426 0.573678
average 152.097298 0.573679
1 AU 03 October 149.598 0.593007
Average July acceleration is 93.5% of January acceleration.
Earth-sun distance calculator
GMsun = 1.3271243994·1011 km3/sec2
1 astronomical unit = 149,598,000 km
1 mile = 1609.344 meters

and surface inertial centripetal acceleration (sidereal day, WGS 84; sea level unless noted) of Earth's rotation.

r = (6378136.46)[1-([sin2(lat)]/298.257223563)] meters
a = (3.380199)(cosine[lat])/sqrt[1-(0.006694380)cosine2(lat)] cm/sec2
   horizontal component of a = a[sin(lat)]


3.66 45 550 mph east
ground speed
1.46490 60 0.866025 1.691516
1.58993 55 0.819152 1.940941
1.66673 50 0.766044 2.175761
1.69294 45 0.70711 2.394172
1.69294 44.951894 0.706513 2.396188
1.66770 40 0.642788 2.594484
1.59175 35 0.573576 2.775137
1.46736 30 0.500000 2.934715
1.29826 25 0.422618 3.071958
1.08960 20 0.342020 3.185778
0.84770 15 0.258819 3.275266
0.57993 10 0.173648 3.339705
0.29446   5 0.087156 3.378578
0   0 0 3.391570

g = (978.032677)[1+(0.00193185139)sin2(lat)]/sqrt[1-(0.00669437999)sin2(lat)] cm/sec2
dg/dh = 0.000308766[1-(0.0014665)sin2(lat)] cm/sec2-meter
dg/ds = -0.0008109[cos[(2)(lat)]+(0.0022)cos[(4)(lat)]-(0.0033)cos[2(lat)]sin2(lat)] cm/sec2-km

r = geocentric radius
a = total centripetal acceleration
lat = latitude
g = gravitational acceleration
h = altitude above sea level
s = distance


A 10-13 difference/average mass/mass divergence is a (c2)(10-13) energy/mass divergence, or 8.99 joules/gram. Racemic benzil powder enthalpy of fusion is 112 joules/gram. 8.99/112 = 8%. Differential scanning calorimeters are accurate to 1% and precise to 0.1%. Benzil is an achiral molecule. Melting its crystal lattice destroys - not racemizes - its parity divergence.

Benzil must be crystallized from solution. Czochralski melt pull and Bridgman-Stockbarger directional solidification both give plastic deformation. Atom positions are distorted in crystal lattices.

Differential scanning calorimeters require 10-15 milligram samples. That is a benzil solid sphere 2.5-3 mm in diameter, d=1.23g/cm3. Subdued light: benzil is homolytically cleaved between its carbonyls at wavelengths of 430 nm and shorter.

On a good day, sort space groups by hemihedral facets. Otherwise, single edge razor blade to cut needles into cubes. Needle length is crystallographic c-axis. View along the c-axis between crossed linear polarizers to sort into left-handed and right-hand crystals. Benzil optical rotation of ±23º/mm at the sodium D-line, 589 nm.

Run trimmed cubes through a crystallographer's air grinder to shape spheres. Change the abrasive paper between left-handed and right-hand runs. On filter paper within a Buchner funnel quick ethanol-water wash and suck dry to polish the surfaces. Eight balls of each parity do the two days' runs.

Benzil has vapor pressure of 1 torr @ 128 C. To prevent heat-flow errors from sublimation, encapsulate the tared sphere in conformal aluminum foil.


If inertial and gravitational masses periodically uncouple for opposite parity mass distributions their vacuum free fall minimum action trajectories will be non-parallel. One parity will fall like everything else - a left shoe or sock on a left foot. The other parity will fall differently - a right shoe on a left foot. The horizontal component will exert a periodic differential torque if they are mounted on opposite sides of a vertical rotor.
  Eötvös vertical torsion balance rotor loaded with two opposed sets of test masses and hanging from a tungsten fiber (top).

The preferred test masses are seedless solid single crystal spheres of space group P3121 and P3221 alpha-quartz. The two control experiments are each quartz parity against amorphous fused silica test masses. Fused silica has a lower density than crystalline alpha-quartz. Gold plating on fused silica must be marginally thicker (+a) on a marginally smaller radius (R-a) solid sphere to balance mass and moments of inertia. "a" is directly proportional to radius. For R=1, a=0.0087810

a3 - 3Ra2 + 3R2a - [(d0 - d1)/(d2 - d1)] = 0

a = fused silica radial decrement
R = quartz radius
d0 = density of quartz, 2.649 g/cm3 nominal
d1 = density of fused silica, 2.203 g/cm3 nominal
d2 = density of gold, 19.283 g/cm3 nominal (x-ray density)
  Densities should be temperature-adjusted.