Gravitational potential energy depends on the height chosen as the zero reference level, yet physicists say only differences in gravitational potential energy matter. Why is the reference level allowed to be arbitrary?

1. Gravitational potential energy depends on relative position, so a reference level must be chosen at which to set it equal to zero. 2. This choice is arbitrary because only differences in gravitational potential energy relate to work done and to physically measurable effects. 3. Earth's surface is simply a convenient, commonly used choice, not the only physically correct one, since a different reference level would give the same physics as long as differences are computed consistently. 4. Gravitational potential energy is a genuine, useful quantity and is not always zero, so neither of those claims explains the arbitrariness of the reference level. _Source: OpenStax College Physics (CC BY 4.0), Ch 7 "Work, Energy, and Energy Resources", section 7.3 Gravitational Potential Energy_