Notes from "The Observational Foundations of Physics"

Section 1.3, Measurements and Standards, is a continuation of the setup for the arguments for Cook's thesis on how measurement affects the logical structure of physics. First, Cook states that the equations of physics are simply relationships between physical states or quantities. These relationships are congruent to the relationships between observations. I am a bit unclear as to what congruent means here, but aside from that the setup so far seems fairly obvious.

He continues onto a more lengthy discussion of the role that standards play in measurement. Every measurement consists of comparing some quantity to a standard quantity. When measuring the length of an object, for example, one simply compares the object's length to the length of a ruler (the standard). Our system of standards plays a significant role in shaping the nature of physical theories.

What was very surprising is that, traditionally, standards for all physical measurements can be derived from four independent standards: length, mass, time, and current. These standards have since been replaced by other physical constants and quantities, but the number of independent standards has remained the same. For example, length is measured as a ratio between the speed of light in free space to a unit of time, which is derived from a standard of frequency from a certain atomic process.

The standard of voltage comes from the standard of frequency and the Josephson effect with help from another fundamental constant, the ratio of Planck's constant to the unit of electronic charge. Mass currently (as of the book's publishing) escapes a relation to the standard of frequency, but it's conceivable that it could be related to energy, voltage, and current through the quantum Hall effect.

The shift from mechanical standards to electronic and quantum standards has greatly increased the precision with which we can measure physical quantities. It has also changed the nature of our physical theories, Cook claims.