As long as you conduct all of your experiments locally, it would be difficult to detect. However, if things that vary with time (frequency of oscillations; photons, for example) are emitted in the past (say, from very far away), you would detect them as being different from what you expect. You "know" what to expect because you know the physical processes that cause them. (However, your calculations of these things depend on "constants," and if the constants aren't really constant-- why should they be??-- the whole issue is a mess to determine.)