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...The main survivors, Brans-Dicke-like theories, have extra gravity-like fields that interact with space-time to a greater or lesser degree -- and apparently to a lesser degree, enough to be difficult to distinguish from GR.
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I have been reading a little about general relativity based on Ernest Mach's strong principle, rather than Einstein's weak principle, of equivalence between inertial and gravitational mass. Is Ernest Mach's strong principle of equivalence part of any Brans-Dicke theory?
That is, is the equivalence principle strictly a local property, or is there a Brans-Dicke theory that makes it into a global property?