You appear to be principled, do you not feel hypocritical then using technology that owes its existence to theoretical physics?
You mean GPS? Yes, I am a pilot, and I have empirically determined that it just works. I'm not sure how, but it's approved as primary means of navigation for my profession, which includes descending in between mountains at night in cloud, with specimens of the general public on board. In total we had 4,000,000,000 passengers with zero deaths over 2017. That means something.
The fact that I don't yet understand how it works, or how it matches my observations of the earth being flat even from an airplane, doesn't mean that I am ignorant. (Not that you said that)
Planes used to navigate by NDB, and VOR, which both have considerable problems for navigation.
For example with the NDB and VOR we need to allow for 5 degree error. This is an 8 km error (!!!) if you are 60 miles from the beacon. I have seen this too, the needle on the instrument just waver, and for example if there is a thunderstorm nearby, the needle swings to the strike...
With a standard GPS system, we allow for a 1km error. That is valid anywhere, close to a waypoint, far from a waypoint, in mountains or over water, as long as the system does not give a warning in regard to position accuracy. (Aviation GPSes tell the pilot when their position is inaccurate). Once we go in to land, the allowed error drops down to 300 metres.
That is how precise we can use it, and there is no other navigation system available that comes close to how it performs.