Thanks, Omph!
Looking forward to your upcoming modeling job.
I can see a relation between the “preference for local-interaction theories” and the Einsteinian/Minkowskian dictum that temporal simultaneity is nonambiguous ONLY in the case of spatial coincidence.
Has it been “demonstrated through observation” that conservation of momentum is true “across” the four forces as well as within each one, or is it more the case that (a) it is assumed, and (b) no disconfirming evidence has come up? To pick something out of the air, how do we know that something being operated on by the strong nuclear force isn’t falling, under gravitation, just a tad more slowly than it ought to?
The general question is impossible to answer affirmatively, of course; you can always envision a more complicated model of momentum nonconservation than ruled out by current experiments. There are various experiments that rule out some models, though. (I don’t know of any experiments done recently to do this explicit test, though this isn’t my field; but there are some whose results provide limits on momentum nonconservation.)
The specific case that you mention is a special case of the “Equivalence Principle,” an area of some enduring interest among physicists. The Equivalence Principle states that inertial mass (basically, the mass m in “F = m a” and “p = m v”) and gravitational mass (m in “F = m g”) are the same. In Newtonian gravity there’s no special reason this should be the case; after all, the electrostatic force law looks just the same as the Newtonian gravitation law, but with a completely different “mass” parameter. But General Relativity postulates that gravitational force is a result of geometry, so that in fact this equivalence is immediate. A variety of EP tests have been done. One sort of test which applies to your specific question is tests of gravitational forces on test masses of different nuclear composition. Heavy elements and light elements differ in their mass defects (the proportions of their masses due to strong nuclear forces), so you might expect to see differences in rates of fall if the strong force does not obey the same gravitational force laws; so far, no such differences have been seen. … Of course, you can now postulate a model for momentum nonconservation for which the equivalence principle also fails, and then these tests only tell you that they both fail the same way.
(Note that physicists look at the EP tests in the opposite way: as tests of general relativity, not of momentum conservation. But these are the sort of tests you might try, if you wanted to search for momentum nonconservation.)
Thanks, Omph–fascinating stuff to me!
Some of the experiments testing fundamental conservation laws are fascinating to learn about (even for a theorist). The experiments are often set up so that if the conservation is exact, the experimental result is zero. This allows some amazingly high-precision results (the exponent of r in the electrostatic force law has been experimentally determined to be 2.0, to something like 16 decimal places).