>>11475494for one, if you make a strong enough electric field, it starts pulling particles out of the vacuum. second of all, quantum fluctuations are responsible for the casimir effect, which has been empirically measured. third, Drell-Yan processes rely on off-shell "particles", which are really just quantum field fluctuations, and those are observed. fourth, vacuum polarization. i probably should have listed this first. but in order to calculate the magnetic moment of the electron, it requires calculating using off-shell "particles" i.e. quantum fluctuations. and if you do the calculation (originally by Schwinger) you match experiment to 11 decimal places and it confirms that quantum fields, along with their fluctuations, exist, and if they did not (if you omitted off-shell loop diagrams) you would lose agreement within the first couple of decimal places
