Let the uncertainty in the mass m be denoted by Δ Δ m . Let the error in the position of the pointer be Δ Δ q . Adding the load m to the box imparts a momentum p that we can measure with an accuracy Δ Δ p , where Δ Δ p Δ Δ q ≈ h . Clearly Δ Δ p ≤ ≤ t g Δ Δ m , and therefore t g Δ Δ m Δ Δ q ≥ ≥ h . By the redshift formula (which follows from the principle of equivalence and the time dilation), the uncertainty in the time t is Δ Δ t = c − − 2 g t Δ Δ q , and Δ Δ E = c 2 Δ Δ m , and so Δ Δ E Δ Δ t = c 2 Δ Δ m Δ Δ t ≥ ≥ h . We have therefore proven the claimed Δ Δ E Δ Δ t ≥ ≥ h .