While the proof is too long to include here, we have shown that if the Finite Nature hypothesis is true, then there must be the equivalent of a single fixed reference frame for the entire Universe. Thus, microscopically, DM must violate translational and angular symmetry. It seems likely that some clever experiment will be able to detect those violations. Consideration of that problem indicates that it might be easier to detect initially if the apparatus were moving in a straight line (no spatial acceleration), without rotation, for a reasonable amount of time. Up to this time, no scientific experiment has ever been conducted while the experimental apparatus was moving in PTM, Pure Translational Motion [1] . Further, most scientific experiments involve averaging data over time while the Earth rotates and the laboratory moves in a complex trajectory. Satellites and other spacecraft that are touring the solar system, never move in PTM. While it is impossible to arrange for continuous PTM on Earth or in a space ship within the solar system, it is nevertheless feasible to build a mechanical platform that corrects, for short periods of time, for the complex motion of the laboratory. While that task is feasible anywhere on Earth (for a minute or two in a reasonably sized laboratory) the task would be conceptually simplified if conducted on a platform that rotated once per sidereal day and that was located at the South Pole. On that slowly rotating platform, another platform could move to take out the residual spatial acceleration of the Earth in orbit around the Earth-Moon center of gravity and of the motion of the Earth-moon system around the Sun. Thus, for periods of time from seconds to a couple of minutes or so, depending on the size of the apparatus, one could have an experimental volume of PTM space that is free of rotation and spatial acceleration. If such an experimental environment enhanced our ability to detect a fixed reference frame it is most likely that we would then be able to invent compact devices that detect and measures it and that work in any reference frame, under any circumstances. Hopefully we won’t need the kind of apparatus used to generate B0 particles.
What would it mean if there were a detectable fixed reference frame allowing us to measure absolute translational velocity and absolute angular orientation? Philosophically, quite a lot, but the mathematical laws of physics would remain largely unchanged. We would simply have to accept that, to a large extent, we had hoodwinked ourselves into believing that there must not be a fixed reference frame. If truth be told, we have merely failed to detect and measure such a thing.
There are other aspects of physics where we have a strong belief about some symmetry and that belief would have to be abandoned if there was just one experiment that violated that symmetry. Examples include translational symmetry (which implies that the laws of physics are the same in all unaccelerated reference frames) and rotational symmetry (which implies that the laws of physics are the same for any angular orientation). So far we do not know of any experimental evidence that violates those symmetries. On the other hand, we know of no competent experiments that might have detected such violations, given the consequences of strict conservation laws and the Variant of Noether’s Theorem.
Of course, there is also hope that experiments might be able to directly detecting the discreteness of length and time; measuring the units of length and time.