Have you ever done empirical test to validate your senses?

Every pilot has empirically tested their sense of balance and orientation, and found it to be deeply flawed and completely untrustworthy.

Pilots are trained to distrust both their senses and any particular instrument, in favor of reality and a general consensus of all instruments. When an altimeter reads a rapidly decreasing altitude, a compass is spinning in circles, an airspeed indicator is rising, but an attitude indicator reads straight and level flight, they are trained to ignore both their own senses and the attitude indicator telling them everything is alright, and trust the other instruments that are telling them they are in a spin and about to die.

Our pilot friend has no "perfect" sense or instrument available to him. Each of his senses can lie to him. Each of his instruments can lie to him. He knows that none of his instruments are perfectly infallible, but he flies anyway. Even though they are not absolutely perfect, the data they provide is sufficient to develop a reasonably accurate, functional worldview.

Physics can provide a much more accurate model of his flight, by considering many more factors than his onboard instrumentation can measure. For example, our pilot lacks the instrumentation necessary to determine how his aircraft will be affected by the change in gravitational pull induced by tidal forces, or the non-uniform nature of the earth's geologic composition. He has no instrumentation to measure the effects of centripetal force from the earth's rotation against the acceleration of his aircraft due to gravity.

But, does it really matter that his 560-ton aircraft is a pound heavier at the poles than at the equator? Will that difference have enough of an effect on the flight that he needs to consider it? Or is this inaccuracy something he can simply ignore, as it will not significantly affect the operation of his aircraft?

The theoretical limit of our empirical knowledge is the Heisenberg Uncertainty Principle. We can rationalize beyond that point, but we cannot empirically test such rationalizations. Long before we reach that point, though, the possible effects of our rationalizations will be far less than the "noise" in the system being tested, and thus indistinguishable from that noise.