Science is inherently atheistic

[T0 Th3 M4X]

I think you're on the right path with what you're saying.  The "sciences" generally focus on what is observable in the natural world. We use controls to test things in the present to gain knowledge about how the world currently, or at some point, existed.  The reason we don't include supernatural is because if it was something that could be demonstrated, it couldn't logically be studied in a controlled environment, since we can't predicts the behavior through naturals means.

I'll try to use a neutral example.  If we believe ghosts like to hang out in a mansion, but in a specific room.  We could set up cameras and various other equipment in that room, but what if suddenly they started floating through walls to avoid the cameras?  What if they had powers that could manipulate the cameras or even not appear at all.  What if they had mind controlling powers that could make you believe they weren't there?  

I know that's kind of a silly example and I'm not saying you should believe in ghosts. What I am trying to say is that our ability to study these creatures in the natural world would be very difficult because we wouldn't know to control them.  They are not bound by our laws, but rather whatever else it is that drives them.

For the record, I don't believe in vampires that turn into bats, Frankenstein monsters, or people turning into werewolves when the moon is full.

I'm not clear why ghosts would be any more difficult to study than any other living thing. The biologist Medawar said that given the most stringent control of environment, the organism will do as it damn well pleases. And that's for standard biology. But we can do science nonetheless.

If we can detect ghosts, we can learn their properties and behaviors. That would then open up new physics (potentially) and even more science.

So science doesn't *require* a commitment to 'physical' things: just to testability of ideas and analysis of data.

But, of course, the actual observations DON'T lead us to believe in ghosts or any new physics associated with them, nor anything typically terms 'supernatural'.

You're pretty much on point. The simple answer is they are not bound by natural law.  Ghosts may not have been the best example, but I didn't want to pull anybody's strong personal beliefs into it so they didn't feel like I was picking on them.  If you could establish natural laws, then you could study them based on those laws, assuming you could set parameters that they couldn't violate.