Physics deal with measurements. The physical quantities are supposed to be results of measurements, either real, performed in the laboratory experiment, or imaginary, referring to some gedanken experiment as a part of the theory.
Origin of physical quantities
The ability to express some properties of physical objects with numbers refers to the measurement. Measurement implies counting, estimation of the number of repetition of some procedure that can be interpreted as comparison some properties of different object.
One of simplest physical properties is length. It may be measured by counting of number of steps necessary at walking from one side of the object to another. As the concept of length is established, the similar procedure can be applied also to measure distances that are too small or too big in compare to the human step; the length of an object can be compared to the length of some special object called etalon. (Should not be confused with ethanol). The ability to measure length makes it physical quantity
In the similar way can be treated the measurement of angles; in many cases it is converted to measurement of length.
Some processes repeat in the similar way again and again. Such processes are called periodic (or quasi–periodic, if some the deviation of one cycle from another is important), in analogy with property periodicity of functions in mathematical analysis. Each periodic process can be interpreted as clock, id set, device that measures time.
In general, ability to perform some procedure, that implies repeated operation, if such a procedure can be repeated giving the similar results, can be qualified as measurement; the result of the measurement can be interpreted as physical quantity.
Precision of measurements
The ability to make measurements can be attributed to the uniform metrics of the space-time, that allow perform similar experiments in various places and epochs. The quantum mechanics and general relativity determine the fundamental scale for the to the precision of measurements of the physical quantities, but the usually perforemed experiments, at east for century 21, are still very far from such a limit. In the most of theories, there is no need to consider the fundamental limit of precision of measurement of the physical, the errors due to the defects of the equipment prevail.
The most precise are measurements of time, of order of 18 decimal digits can be measured.
Other physical quantities are usually measured with less precision. Especially poor are measurements in the laser science; although the positions of the spectral lines (that come from spectroscopy may count several decimal digits, such quantities as gain. lifetime of the excited states or the effective cross-sections are usually known with only one or two decimal digits.