Short answers, pulled from the story.
The metre is defined by the speed of light, a constant that has never changed since the beginning of the universe. This definition replaced the physical bar of platinum-iridium that was once stored in a vault in France. The International System of Units now defines the metre without reference to any physical object to ensure measurements remain exact and unchanging.
The kilogram was redefined in 2019 in terms of the Planck constant, a fundamental quantum constant. This change ended the era where the kilogram was defined by a physical cylinder kept in a vault. The redefinition ensures the unit remains stable regardless of the deterioration or destruction of any single artefact.
Charles Sanders Peirce proposed defining the metre using the wavelength of a spectral line in the late 19th century. This proposal to tie a unit to an experimental standard independent of a physical artefact directly influenced the Michelson, Morley experiment. The idea helped establish a more reliable standard for measurement.
The British systems of English units and later imperial units are still used in the United States and a few Caribbean countries. In Britain, road signs still show distances in miles and speed limits are in miles per hour. The international yard was defined in 1960 by the governments of the United States, United Kingdom, Australia, and South Africa as being exactly 0.9144 metres.
The representational theory defines measurement as the correlation of numbers with entities that are not numbers. Stanley Smith Stevens elaborated this theory, suggesting that numbers need only be assigned according to a rule. True measurement requires a structural similarity between the mathematical system and the qualitative system.
Quantum measurements alter the state of the system itself, changing the quantum state into one with the single measured quantum value. This process is referred to as state-vector reduction or collapse of the wavefunction. The measurement appears to act as a filter, creating a paradox that challenges our understanding of reality.