Indirect experiments

I like how some advanced experiments in science are fantastically indirect. Take for example this experiment of measuring mass of proton (source).

For each hydrogen atom, the team replaced the atom's electron with a particle called a muon, which is 200 times more massive than an electron.

"Because the muon is so much heavier, it orbits very close to the proton, so it is sensitive to the proton's size," said team member Aldo Antognini, of the Paul-Scherrer Institute in Switzerland.

Muons are unstable, and they decay into other particles in just 2.2 microseconds. The team knew that firing a laser at the atom before the muon decays should excite the muon, causing it to move to a higher energy level—a higher orbit around the proton. The muon should then release the extra energy as x-rays and move to a lower energy level.

The distance between these energy levels is determined by the size of the proton, which in turn dictates the frequency of the emitted x-rays.

But based on the accepted proton radius, the experiment failed to produce x-rays at the anticipated frequency.