What about the double-slit experiment? That's kind of a miracle isn't it? Point an electron gun at a pair of slits and then look at where they land on a screen behind. It doesn't matter how fast you fire the electrons, they will, over time, form an interference pattern. In other words, they are behaving like waves. OK, so now you're wondering, if they are behaving like waves, yet they're being fired one at a time, what is interfering with what? Does each electron interfere with itself, or do they interfere with each other, somehow "seeing" the other electrons both forward and backward in time?
Lets design an experiment to test these ideas. Now you flash a strobe light every time you fire an electron so you can figure out through which slit it passes. The interference pattern disappears.
I've heard any number of interpretations of quantum mechanics: An object isn't really there when you aren't observing it. There is a mystical connection between observer and observed. The distinction between subject and object is an illusion. And so on.
But at least in this case, I think the interpretation is much, much simpler. When you observe something, it changes. Suppose instead of using the term observe, we substitute the word probe. To probe is almost by definition to interfere with since a probe (as a noun) is almost always something material and solid. Granted, if you drop a sounder into the ocean to measure depth, for instance, the ocean floor won't change much in response, certainly less than measurement error or the local variance. But if you fire a photon at a sub-atomic particle, it will change the velocity of that particle, sometimes by a large amount.
The act of observation is the act of touching. When something is touched, it will always move or change in response.
The analogy to investigations of so-called "psi" phenomenon is (or should be) obvious. Lets use prayer as an example. I have at various times in my life, prayed with considerable regularity. While I no longer identify as Christian, I still pray, though less often than I used to. It was a great sense of relief when I stopped attending church because I could finally admit to myself that I am completely ignorant about spiritual matters. But then again, the whole point of a Supreme Being is that He or She or It is completely beyond us.
I don't know how many times I've heard of studies purporting to demonstrate the effectiveness of prayer. I don't know how many times I've heard skeptics try to debunk such claims and reference their own studies. But after all, if spiritual configurations (for lack of a better word) are as delicate as sub-atomic particles, should we be surprised if close observation destroys them? Should we be surprised if they behave in the same way as the double slit experiment and lose their magic as soon as they are seriously scrutinized?
I don't know the answer to these questions, because there is no answer. I guess it just comes down to faith.