Let’s say we had a nearby very small black hole, just a couple of light years away, that was in a direction perpendicular to the ecliptic. How much easier would it be to come up with a Unified Field theory than it is now? Given everything else being the same.
My gut reaction: not at all. There are two scenarios I can think of in which it would make a difference:
[ul][li]Gravitational waves behave substantially differently than we expect them to, due to quantum-gravitational effects; and we observe gravitational waves due to objects falling in to the black hole. This is pretty unlikely, though, given the indirect evidence we have for gravitational waves; the Universe would have to be conspiring against us pretty intensely for this to be the case.[/li][*] The black hole is really small, so that it’s putting out enough Hawking radiation that we could study it and notice any differences from the classical predictions. The problem with this is that larger black holes actually emit less Hawking radiation, so we’d need a relatively tiny black hole for this to work. If I’ve done my sums correctly, a black hole with a mass of about 10[sup]8[/sup] kg, or around the mass of a large sea-going ship, would be visible from Earth (bolometric magnitude of +25); but as far as we know, black holes that small can’t form naturally.[/ul]ETA: I should say that the influence of the black hole on objects in our solar system is just going to be like that of a star of the same mass at the same distance; which is to say, not much. We would need something, like gravitational waves or Hawking radiation, that originate near the black hole and travelled to us.
See, I had this whole theory cooked up where a civilization could advance much faster after a certain point because of such a thing. Damn. 
Are we going to be happy observers with an an energetic x-ray source in our near neighbourhood?
Not to mention that it would only last like 2.6 years (if I did that right).
See, there’s the rub. Although I imagine life in a place like that would evolve better DNA repair than we have.
Which would make it an even MORE useful tool for helping our physics, no? 