It is usually quite hard to decouple things in physics: everything affects everything else, and isolating the effects you are trying to measure, from the noise of everything else around them, is difficult. That is why the really iconic experiments are done at a very low temperature, in a very carefully controlled magnetic field, in order to decouple things from their surroundings as much as possible. That is when you find out the really interesting things in physics. When you succeed in decoupling something completely from the magnetic field, you get a superconductor.
But decoupling your experiments from gravity is (apparently) theoretically impossible. That is why particle physicists have to be really creative in order to decouple their experiments from gravity. Firstly, they make sure to do their experiments horizontally. Relativists will do vertical experiments, in order to test the effects of gravity on basic physical properties, like the frequencies of quantum transitions, but particle physicists will do their utmost to avoid anything vertical. Even so, it is not possible to ensure that the gravitational field around an experiment is completely uniform. A typical experiment of a few metres in diameter can easily introduce a systematic error of 1 part per million or so due to gravitational effects.
Many such experiments have indeed exhibited “anomalies” of this order. I have pointed out a few, including the muon g-2 anomaly and CP violation of neutral kaon decay, and computed the magnitude of the anomaly in each case, in order to verify that it agrees with experiment. Which it does. But so far I have failed to communicate to particle physicists that what they have detected is a general relativistic effect. They appear to have completely decoupled gravity from particle physics in their brains. But decoupling them in their brains is not the same as decoupling them in reality. Gravity and particle physics are coupled in the vast majority of particle physics experiments, if not all.
The only experiments that I know of in which gravity actually is decoupled from particle physics are experiments on superfluids. A superfluid expels the gravitational field, and decouples itself from gravity completely (or so it seems to me). Not that I would recommend particle physicists to work with superfluids – on the contrary, what particle physicists need to do is to couple their particles properly to gravity – the last thing they need to do is to decouple them any more than they are already.
As I have demonstrated elsewhere, the (theoretical) decoupling of particle physics from gravity occurred in approximately 1973. From that point onwards, all vestiges of the original (gravitational) definition of mass were expunged from the theory, although it took another 40 years or so to get rid of this as a practical definition of mass. The old practical definition exhibited curious anomalous behaviour at the level of about 1 part per billion per year, which eventually made it unsuitable for the new theory. But there is an alternative possibility – the experimental anomalies may describe real physics more accurately than the new theory.