In quantum mechanics, the precision of a measurement is not directly related to the phenomenon of redshift. Redshift refers to the shift of spectral lines towards longer wavelengths (lower energies) due to the expansion of the universe or the relative motion between an observer and a light source. It is a phenomenon studied in the field of cosmology and astrophysics, not within the realm of quantum mechanics.
In quantum mechanics, the precision of a measurement is typically related to the uncertainty principle, which states that certain pairs of physical properties, such as position and momentum or energy and time, cannot be simultaneously known with arbitrary precision. The more precisely you try to measure one property, the larger the uncertainty in the corresponding conjugate property.
For example, in the case of energy and time, the uncertainty principle states that the more precisely you try to determine the energy of a quantum system, the less precisely you can know the time at which that energy was measured. This relationship is mathematically described by the Heisenberg uncertainty principle.
Therefore, in quantum mechanics, precision is typically associated with minimizing the uncertainties in a measurement, rather than being directly connected to phenomena like redshift. Reducing the uncertainty in energy measurements involves techniques such as improving the energy resolution of detectors, enhancing the stability of experimental setups, and employing precise calibration methods.