Where is Strong Equivalence Principle stronger than Weak Equivalence Principle? In my note, the two equivalence principles are stated as follows
Weak Equivalence Principle:
Gravitational and inertial masses are equal.
Strong Equivalence Principle:
There is no observable distinction between the local effects of gravity and acceleration.
I think the weak one will imply that the acceleration at a point and the gravitational field at that point are equal, thus we can remove the gravitational effect by using an accelerating frame. But, what does this differ from the strong version?
Is the change from at a point to local playing the role?
Best Answer
I'm not sure your note is correct in its statement of the two forms of the equivalence principle. They key distinction is this: the weak equivalence principle applies only to non-gravitational experiments, that is, experiments where gravitational interactions between the objects are not important. The strong equivalence principle extends this to include experiments where the objects may have strong self-gravity or important gravitational interactions.
For a concrete example, the Eöt-Wash group has carried out experiments to compare gravitational to inertial mass of bodies of different compositions. This tests the weak equivalence principle: does (say) nuclear binding energy fall the same way as proton rest mass? This was tested by comparing copper and uranium objects. An analogous test of the strong equivalence principle asks, does gravitational binding energy fall the same way as (say) proton rest mass? This is hard to test in the laboratory, because the gravitational binding energy of a laboratory-scale mass is minuscule. But lunar laser ranging allows us to compare how the Earth and the Moon fall - the Earth has considerably more gravitational binding energy per unit mass than the Moon. It turns out they fall the same way, to experimental accuracy, so the SEP looks solid.
How could the SEP be violated? Well, you could have some additional scalar field that coupled to gravity. This would be stronger in more strongly self-gravitating bodies and would affect how they fell.
The Eöt-Wash group's explanation: http://www.npl.washington.edu/eotwash/EquivalencePrinciple
A discussion of current tests of relativity, including both versions of the equivalence principle: http://relativity.livingreviews.org/Articles/lrr-2006-3/fulltext.html