Question

How local is local in the Hypothesis of Locality?

Answer 1

A while back I asked this question Freely falling frame and the use of special relativity? which I later answered using the Hypothesis of Locality which I used to state that E=−pμuμE=−pμuμ in any reference frame. My concern now is that the measurement of pμpμ cannot really be done at a point and relies on at least two separate space time events. So does my argument in the answer to the linked question stand, given this non-local measurement - either way please can you explain.

I guess I am asking: Can we use all the laws of special relativity at the point of the 'observer' in all GR reference frames - independent of how many derivatives they contain

Answer 2

the principle of locality states that an object is directly influenced only by its immediate surroundings. A theory which includes the principle of locality is said to be a "local theory". This is an alternative to the older concept of instantaneous "action at a distance"