You take a laser and turn it down super low so that only one photon goes through the experiment at a time. The individual photons go though a very closely spaced pair of slits. And hit a photographic screen on the opposite side. Each individual photon hits the screen leaving a single dot as if it was a particle, a miniature cannonball. However, if photons were little cannonballs then after several hundred photons you would see two clusters of dots ... one behind each of the two slits. But this is not what you see. What you see is a distribution of photons consistent with a wave going through the slits. See the picture I 'borrowed' from another website.
Now we get to the interesting part. IF we add a sensor to the experiment in between the slits and the photographic screen to find out if the photon went through the left slit, the right slit, or both THEN we get two clusters of dots like for little cannonballs. ( I didn't quickly find a picture I liked, so I used copy and paste to modify the picture from above and create the picture below. )
Never mind the exact details of this new sensor, suffice it to say that this part is tricky and a lot of physicists have reviewed and repeated the experiment. Details of the sensor is something that I don't consider myself qualified to comment on. The experiment has been performed to varying degrees with photons, electrons, atoms, and molecules by various researchers. Let me get back to that in a second or two (see item 1 below).
The new age philosopher gets excited about this experiment because the act of observing the photon affected it's behavior. It is important to note however that the experimenter still had no control over where the photon went. So while there was an effect, there is no control. This is an important distinction. All credible scientific sources and theories of which I am aware do not allow the observer to have control.
When I point this out, I am usually rebuffed with anecdotal stories of experiments where thoughts reduced crime, changed the shape of water crystals, or a hundred other things. I have looked into several of these and found no credible scientific evidence. One that comes up a lot is Dr. Emoto's "Messages from Water" or a similar publication by the same author. There are several issues with this including but not limited to:
1) Lack of peer repetition. I have found no publications from other researchers that substantiate the claims. There is however, a publication testing crystal formation at specific temperatures which appears to disprove Dr. Emoto's hypothesis. But the author (Libbrecht) was only testing for temperature, not the mood of the technician.
2) No blind tests. In fact, the good Doctor has been quoted as denouncing this procedure. So the person taking the picture of the water crystal knows exactly what to expect and can easily affect the results.
3) Limited data release. The good Doctor has chosen to only release one picture from 1 in 100 samples tested. This means that he could have chosen whatever he wanted to support any hypothesis. Full disclosure would require releasing a video of every sample.
If somebody wanted to substantiate the claims of Dr. Emoto, they could do a blind experiment where the photographers are given samples from three groups without knowing which group they are from. One group could be "love", another "hate" and the last unlabeled. Then it would be the photographer's job to determine which group the sample came from. The accuracy of their categorization would go a long ways to substantiate or disprove Dr. Emoto's claims.
So, why do new age philosophers gravitate towards the same examples regardless of the fact that they do not actually provide evidence of their claims or beliefs? I suppose it is the same reason we all do it, we want to believe what we want to believe and we want to be lazy about it too. But I do get frustrated having the same conversation over and over again ... especially when it is with the same person(s).