So if we don't have access to CERN we won't find anything new or interesting. Cool.
Predominantly, (most of the time), new things, won't be discovered.
If you see a strange effect, such as a piece of paper, sticking to your fridge, for no reason.
It could be you have just invented/discovered, a new particle, or force of attraction, or property of Physics, that no one has discovered yet. Maybe it will lead to warp drives and/or mini-black holes, possibly even time-travel.
But, almost certainly, there is a rational explanation. Maybe the fridge has got something sticky on it, maybe the paper has got something sticky on it, maybe the paper was very light, and got statically charged up. Etc.
You can't just take a video of the paper sticking to your fridge, post it on youtube, then go on a scientific website, and proclaim you have found a new Physics something, and want your recognition, Noble prize, honorary Professorships, and most importantly, lots and lots of money, now.