A Decisive Experiment Comparing Vertical and Horizontal Light Travel Times in Gravitational Fields: Testing the Gravitational-Potential Dependence of Light Speed

We propose a ground-operated decisive experiment to compare the round-trip travel times of laser light along vertical (radial) and horizontal (transverse) paths of equal geometric length, using a single high-precision atomic clock fixed on the ground. The experiment is motivated by a phenomenological hypothesis: in a weak gravitational field, the speed of light increases with gravitational potential as v(r)=c(1−GM/(c2r))v(r)=c(1−GM/(c2r)), while atomic clock rates also depend on the potential, making local measurements of cc always yield cc (explaining the null result of Michelson–Morley type experiments). By keeping the clock on the ground, the vertical path integrates the light speed over varying heights, whereas the horizontal path experiences constant light speed. The model yields a predicted time difference ΔTmodel≈−GMc3(H/R)2ΔTmodel≈−c3GM(H/R)2 (negative, i.e., vertical travel time shorter), while general relativity predicts a positive difference ΔTGR≈+2GMc3⋅H/RΔTGR≈+c32GM⋅H/R. For height H≳2H≳2 km, ∣ΔTmodel∣∼10−18∣ΔTmodel∣∼10−18 s, within the reach of current optical lattice clocks. The experiment can decisively discriminate between the two theories by the sign of the measured time difference. AcknowledgmentsThe author thanks auxiliary AI tools for linguistic revision, typesetting and numerical verification. All original physical ideas, model derivations and conclusions are independently completed by the author.