Regarding experiments, I did one yesterday. I went out in my yard at 10 a.m. and recorded the relative position of the sun. Then I did the same 4 hours later. Guess what? Either my yard moved or the sun did, or maybe both. Motion can be measured : - D
Discussion
The motion of the Earth cannot be measured, which is why relativity was proposed. The movement of the sun across the sky isn't exclusive to any model. Heliocentrism says the Earth is moving, geocentrism says it is the sun that moves.
All measurements ever taken demonstrate that the Earth doesn't move. We don't feel it, we can't measure it... that's why relativity was proposed - exactly as is being explain by Brian in this video.
You can prove it by hanging a pendulum in a large room. Or buying a laser gyro.
It is very easily demonstrable.
The question that he makes at the end is basically the same as asking "where does inertia come from?"
It's a mystery for quantum physics to decipher. We only know that inertia exists.