where x ^ ^ f r e e is a value of x ^ ^ that the Object would have, were it not coupled to the Meter, and δ δ x B A ^ ^ [ F ^ ^ ] is the perturbation to the value of x ^ ^ caused by back action force, F ^ ^ . The uncertainty of the latter is proportional to Δ Δ F ∝ ∝ Δ Δ O − − 1 . Thus, there is a minimal value, or the limit to the precision one can get in such a measurement, provided that δ δ O ^ ^ and F ^ ^ are uncorrelated.