Theory 29/Metrology
Uncertainty Has a Floor
The claim
The uncertainty of a measurement that is averaged over time reaches a minimum set by the ratio of averaging time to drift time, rather than decreasing indefinitely with more averaging.
01The mechanism
Averaging reduces noise but accumulates drift; the two balance at an optimum, and beyond it more data make the estimate worse.
02Predictions
- P1Uncertainty should show a minimum with averaging time.
- P2Longer averages should increase error past the optimum.
03Refutation
Uncertainty decreasing monotonically with averaging would remove the drift term.