All the big guns for this discussion are stored elsewhere,
The short form (Adobe Acrobat pdf).
The long form (history, rigor, subsidiary topics, clickable citations; on the Web)
Here we go... The Equivalence Principle (EP) *postulates* gravitational mass (try lifting a car) is fundamentally indistinguishable from inertial mass (try pushing a car). All local test bodies - ball bearings, feathers, photons - thereby fall identically in vacuum. General Relativity immediately follows as an inevitable consequence. Everything else is details.
If the EP is counter-demonstrated at will, General Relativity loses its founding postulate. Drop two things in vacuum, see one fall "sidways" or too fast/slow compared to the other, and General Relatvity is thereby falsified. Poof!
Do all local test bodies really fall identically in vacuum (pursue parallel geodesic trajectories)? We can cleverly measure the difference in trajectories between two (sets of) test bodies accurate to one in ten trillion relative (yup, 10^(-13) accuracy) with an Eotvos balance. Everything to date comes out a perfect null result within experimental error. General Relativity has a perfect track record no matter how weird its predictions seem.
Lots of people have looked very hard at almost everything
However... Every physical property originates in a mathematical symmetry, and vice-versa (Noether's theorem). A list of all symmetries gives a list of all test mass properties - and physics missed testing one against the Equivalence Principle! Nobody knows if right-handed objects vs. left-handed objects fall identically. More specifically, we must go beyond handedness (chirality; one coordinate axis inverted in a mirror image) to full parity (all three coordinate axes inverted).
Here's a picture of the difference.
Will parity pair test masses fall identically? Does a left shoe fit identically on a left or right foot? Is spacetime handed (chiral)? Nobody has ever looked! Wouldn't it be fine if Einstein made an omission in his theory? Euclid goofed that way.
Euclid postulated that given a straight line and a point not on that line, only one line could be drawn through that point parallel to the original line (not quite in those words). If you accept this you get plane geometry, and plane geometry contains no mistakes. If you don't assume Euclid's Fifth (Parallel) Postulate, you get elliptic (no parallel lines) or hyperbolic (infinite parallel lines) geometries. They also work perfectly, and with broader application.
General Relatvity models spacetime as general covariance (scale-independent symmetry under all smooth coordinate transformations). We calculate that parity pair tellurium single crystals are maximally unlike each other, arising from the discontinuous symmetry of parity. Can spacetime geometry fall to test mass geometry? Can Einstein and spacetime curvature be overthrown on a technicality as Euclid was shown to be a special case of more general geometries?
The parity Eotvos experiment would be an interesting adventure - conducted in existing apparatus run SOP by its academic keepers using commercial materals. Parity has embarassingly overturned physics theory in the past.
Everybody was really surprised!
Do you think test mass parity has one more surprise awaiting discovery? We've got the calculated numbers. The experiment can be done as are others of tis kind. So
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Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm
