Free fall acceleration in SR

Samshorn

Yes, and lacking a theory of gravity it's difficult to know with certainty what the errors might be, especially in circumstances where gravity plays an essential role. For the slingshot twins scenario one might think that, since we can make the coasting part of the journey as long as we want, we could ensure the gravitational effect is negligible, but that's not true, because if we posit a theory of gravity that doesn't deflect electromagnetic energy at all, we can't assume it would deflect a near-light-speed projectile very much either. To produce a gravitational slingshot and yet have no deflection of light, we would have to postulate a theory of gravity that couples with mass but not with other forms of energy, which is inconsistent with mass-energy equivalence of special relativity, to which we are supposedly adhering. The only way out would be to completely renounce any claim to empirical viability, and propose a theory of gravity in which hot objects fall differently than cold objects, etc. But if we renounce empirical constraints, then we're free to propose all kinds of crazy theories such as a theory in which gravity has no effect at all, and hence can't turn around any projectile. This is perfectly consistent with special relativity, it's just an empirical failure as a gravitational theory... but so is every other gravitational theory that doesn't satisfy the equivalence principle, which is the most precisely verified principle in physics.

DaleSpam

This is interesting. Do you mean this literally or is this hyperbole?

Samshorn

I meant it literally. One often hears that quantum field theory is the most precisely confirmed theory in all of physics, citing for example the computed value of the magnetic moment of an electron using Feynman diagrams up to 8th order, being accurate to within about 1 part in a billion. But the equivalence principle, or at least the equality of inertial and gravitational mass, has been established to 1 part in about 100 billion - and that was in 1964. Needless to say, that doesn't prove the equality is EXACT (as it must be in general relativity), but it sure doesn't give much reason to doubt it.

DaleSpam

Thanks, I was unaware of that! Do you have a reference, or at least the name of the experiment? It seems like one I should know, but don't.

Samshorn

One reference is a refinement of the classic Eotvos experiment, where they achieved precision of 1 part in 100 billion:

P. G. Roll, R. Krotkov, R. H. Dicke, Annals of Physics, 26, 442, 1964.

In 1971 Braginski improved this result by another order of magnitude:

Braginskiǐ, V. B.; Panov, V. I., Soviet Journal of Experimental and Theoretical Physics, Vol. 34, p.463.

I think more recently the precision has been improved still further, but don't have references.