Table I. POSTULATED GRAVITATION INDEPENDENCE

Class Invariance  Conserved Quantity 

 Proper orthochronous
Lorentz symmetry 		  translation in space  linear momentum
 rotation in space  angular momentum
 translation in time  energy

Discrete symmetry  P, coordinates' inversion  spatial parity
 C, charge conjugation  charge parity
 T, time reversal  time parity
 CPT  product of parities

Internal symmetry  EM (U1) gauge transformation  electric charge

G parity

 isospin

 hypercharge

 lepton generation number

 baryon number

 quark color

 quark flavor
Perkins, DH, Introduction to High Energy Physics, 4th Ed. (Cambridge, NY: Cambridge University Press, 2000) pp. 63-93
http://www.shef.ac.uk/uni/academic/N-Q/phys/teaching/phy304/invariance.html

Linear and angular momenta, mass-energy, and electric charge are strongly conserved ("black holes have no hair"). CPT, baryon number, lepton generation number, and quark color are locally conserved. Processes that violate parity conservation can violate the remainder. Parity/chirality is a powerful inquiry.

Geometric spacetime is incompatible with quantum mechanics that dominates physics as virtual particle exchanges. General Relativity demands symmetry under all smooth coordinate transformations, resisting quantization. (General Relativity may be vulnerable to parity challenges as are weakly conserved quantities. Nobody has looked.) Relativity is accurate to eleven decimal places in the Global Positioning Satellite system[10]. Any relativistic classical field theory can be at best the classical limit of a relativistic quantum field theory. There are no known empirical exceptions to the Equivalence Principle. Good people continue to seek one by watching things fall:

Table II. EQUIVALENCE PRINCIPLE TESTS

Year Investigator  Sensitivity  Method

  500? Philoponus[11]  "small" Drop Tower
1590? Galileo[5]  2x10-2 Pendulum, Drop Tower
1686 Newton[6]      10-3 Pendulum
1832 Bessel[12]  2x10-5 Pendulum
1910 Southerns[13]  5x10-6 Pendulum
1923 Potter[14]  3x10-6 Pendulum
1918 Zeeman[15]  3x10-8 Torsion Balance
1922 Eötvös[16]  5x10-9 Torsion Balance
1935 Renner[17]  2x10-9 Torsion Balance
1964 Dicke,Roll,Krotkov[18]  3x10-11 Torsion Balance
1972 Braginsky,Panov[19]      10-12 Torsion Balance
1976 Shapiro, et al.[20]      10-12 Lunar Laser Ranging
1981 Keiser,Faller[21]  4x10-11 Fluid Support
1987 Niebauer, et al.[22]      10-10 Drop Tower
1989 Heckel, et al.[23]      10-11 Torsion Balance
1990 Adelberger, et al.[24]      10-12 Torsion Balance
1999 Adelberger, et al.[25]      10-13 Torsion Balance
2005? MiniSTEP[26]      10-18 Earth Orbit
Ciufolini & Wheeler Gravitation and Inertia (1995) pp. 117-119
http://einstein.stanford.edu/STEP/information/data/gravityhist2.html