In what sense is it correct to say that a measurement is always electromagnetic? 
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*Is it true or wrong that the interaction between the system to be measured and the measurement apparatus is always electromagnetic - even when looking at gravity or at nuclear interactions?


*Is it true or wrong that the bath in the (classical) measurement apparatus is always coupled to the outside world via electromagnetism?


*Is it true or wrong that in every measurement, i.e., in every comparison with a standard unit, the comparison is always done with the help of electromagnetism?
P.S. I tried to find something on the topic via Google scholar, but  I found nothing.
 A: Well, the human nervous system is an electromagnetic (or electromechanical) phenomenon, so anything that we perceive has to have been converted into electromagnetism first.
In 2011, Jenke and collaborators described an experiment where a beam of neutrons were put in a definite state in a gravitational potential by passing them between a horizontal mirror and absorber. That state was then altered by vibrating the mirror at an appropriate frequency.  In an accompanying article, Greene pointed out that this was the first example in the literature of a quantum-mechanical transition driven without an electromagnetic interaction: neutron reflection and absorption, which define the extrema of the gravitational-trap potential, are driven by strong interactions between the neutrons and their environments.  So that was ten years ago.
(Side note: I don't have good subscription access at the moment, so if I have in important detail wrong it's because I haven't read either of the linked articles in at least five years; corrections are welcome.)
But even there, the way you get a data-acquisition system to say "there are neutrons" is via a cascade of interactions that ends with electromagnetism.  Some detectors capture the neutrons and detect the gamma rays as the new nucleus cools.  More common designs turn neutrons into ionizing radiation, via strong (n,p) or (n,$\alpha$) reactions, and detect the ionization trails produced by the fast proton or alpha particle.  Or the absorbing material scintillates and the detector collects the light, in a photomultiplier or an avalanche photodiode.   Data acquisition is an electromagnetic business.
