Sears and Zemansky 13th ed.
Summary of Chapter ! (page 26):
"Physical quantities and units: Three fundamental physical quantities are mass, length, and time. The corresponding basic SI units are the kilogram, the meter, and the second. Derived units for other physical quantities are products or quotients of the basic units. ... "
'Physical quantities' means the modern authors are speaking of rules of measurement. "Derived units for other physics quantities ..." means the same authors are speaking of a derivation process which is not the same as citing rules of measurement.
(Going back to pages 4 & 5)
"Some physical quantities are so fundamental that we can define them only by describing how to measure them. Such a definition is called an operational definition. Two examples are measuring a distance by using a ruler and measuring a time interval by using a stopwatch. In other cases we define a physical quantity by describing how to calculate it from other quantities that we can measure."
"Time
From 1889 until 1967, the unit of time was defined as a certain fraction of the mean solar day, the average time between successive arrivals of the sun at its highest point in the sky. The present standard, adopted in 1967, is much more precise. It is based on an atomic clock, which uses the energy difference between the two lowest energy states of the cesium atom. When bombarded by microwaves of precisely the proper frequency, cesium atoms undergo a transition from one of these states to the other. One second (abbreviated s) is defined as the time required for9,192,631,770 cycles of this microwave radiation (Fig. 1.3a)."
"Length
In 1960 an atomic standard for the meter was also established, using the wavelength of the orange-red light emitted by atoms of krypton in a glow discharge tube. Using this length standard, the speed of light in vacuum was measured to be 299,792,458 m s. In November 1983, the length standard was changed again so that the speed of light in vacuum was defined to be precisely 299,792,458 m s. Hence the new definition of the meter (abbreviated m) is the distance that light travels in vacuum in 1 299,792,458 second (Fig. 1.3b). This provides a much more precise standard of length than the one based on a wavelength of light."
[With no explanation there is a third "so fundamental" ... "physical quantitiy" introduced.]
"Mass
The standard of mass, the kilogram (abbreviated kg), is defined to be the mass of a particular cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures at Sèvres, near Paris (Fig. 1.4). An atomic standard of mass would be more fundamental, but at present we cannot measure masses on an atomic scale with as much accuracy as on a macroscopic scale. The gram (which is not a fundamental unit) is 0.001 kilogram."
I knew textbooks had changed by becoming less rigorous. This introduction not only lacks rigor, but, is deliberately claiming it has presented material that it has not presented.
From the summary: "Three fundamental physical quantities are mass, length, and time."
Mass was not introduced as a fundamental physical quantity. It was placed, without explanation, following the "operational definitions" of length and time. It was given, by placement alone, the appearance of being associated with length and time. Length and time are the names used by physicists of the two properties of empirical evidence. Those two properties " ... are so fundamental that we can define them only by describing how to measure them." (The word define is an example of the adoption of layperson type of terminology.) There is not a third property involved in communicating empirical evidence. Mass is not associated with length and time. It is not a property that is " ... so fundamental that we can define it only by describing how to measure it. " It is associated with all other properties of mechanics that are learned from empirical evidence and must receive their definitions in terms of the only two fundamental physical quantities limited to being represented by their rules of measurement, length and time. The equation f/m=a gives us guidance that empirical evidence shows that the units of force divided by the units of mass must reduce to the units of acceleration. The properties of acceleration are length and time because acceleration is the form that empirical evidence arrives in. The 'a' in f/m=a is the empirical evidence.
James Putnam
