We assume that relativistic foreshortening is merely an illusion of spacetime perspective. Here is an experiment to find out if it is real.

Special Relativity contains the beta factor that goes toward zero as velocity approaches lightspeed,

beta = sqrt[1-(v^2)/(c^2)] = sqrt[1-(v/c)^2]

where "v" is the velocity of the observed frame relative to the observer and "c" is lightspeed. As observed by a stationary observer, a moving body alters its mass, length parallel to its direction of movement, and rate of time flow,

M = m/(beta)
L = l(beta)
T = t(beta)

Where uppercase is the observed value and lowercase is the rest value. The relativistic projection of time ratchets by empirical demonstration. Relativistic clocks run slow compared to local clocks. A relativistic beam of a radioisotope or an unstable particle launched, propagated, and recovered is seen to have decayed proportionately less than a stationary sample. There is no paradox in the Twin Paradox, and acceleration fore and aft has nothing to do with the observed results (added small perturbation in the same sense vs. overall flight given linear acceleration, the Equivalence Principle, and GR).

The projection of space is held to be a figment of observation. Nobody has done an experiment where the "flattening" of space parallel to the direction of relativistic propagation has ratcheted consequences.

A tetrahedral carbon chiral center "flattened" by a factor of 70 at 0.9999c doesn't have much pucker at all. One might expect a degree of racemization (reopening in either direction) upon unflattening. Acceleration and deceleration of a suitable chiral ion (as low a mass as possible) does not imply heating or additional chemistry. Supersonic molecular beams from expansion into vacuum are deeply cryogenic in their own frame.

http://www.mazepath.com/uncleal/racem.png
http://www.mazepath.com/uncleal/racem.htm

This image contains three stereograms of N,N,2,5-tetramethylpyrrolidinium with two chiral centers. Carbon is pale blue, hydrogen is white, nitrogen is dark blue and has a positive charge. The chiral left-left or (S,S) isomer is first. The chiral right-right or (R,R) isomer is in the middle. The achiral left-right (R,S) isomer is third. Since the mirror image of left is right, that last molecule has a mirror plane of symmetry normal to and bisecting the plane of the ring through the nitrogen. The slight ring pucker is reversible top to bottom and races around the ring by thermal vibration, averaging to a flat ring. The methyls are spinning and average their hydrogen's orentations.

We take a beam of the resolved left-left ion and boost it to 0.9999c in the Relativistic Heavy Ion Accelerator, then reverse the timing to decelerate it and collect as a salt. Give that the flying ions are randomly tumbling as viewed in our reference frame, billions and billions of potential flattenings and racemizations will (or will not) transpire to an equilibrium mixture of all three species. We then measure the optical rotation, [alpha]D, for the product vs. the starting material.

The Gedankenexperiment is mildly interesting. Reduction to practice is highly unlikely. Particle physics doesn't know organic chemistry exists.
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Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz3.pdf