Physical Quantities and Measurement

Measurement

Physical Quantities and Measurement

Despite the mathematical beauty of some of its most complex and abstract theories, including those of elementary particles and general relativity, physics is above all an experimental science. It is therefore critical that those who make precise measurements be able to agree on standards in which to express the results of those measurements, so that they can be communicated from one laboratory to another and verified.

Introduction of Measurement

We start our study of physics by introducing some of the basic units of physical quantities and the standards that have been accepted for their measurement. We consider the pr

oper way to express the results of calculations and measurements, including the appropriate dimensions and number of significant figures. We discuss and illustrate the importance of paying attention to the dimensions of the quantities that appear in our equations. Later in the text, other basic units and may derived units are introduced as they are needed.

The Physical Quantities, Standards and Units

The building blocks of physics are the quantities that we use to express the laws of physics. Among these are length, mass, time, force, speed, density, resistivity, temperature, luminous intensity, magnetic field strength and many more. Many of these words, such as length and force are part of our everyday meanings of these words. The precise scientific definitions of length and force have no connection at all with the uses of these words in the quoted sentence.

We can define an algebraic quantity for instance, L for length, any way we choose and we can assume it is exactly known. However when we try to assign a unit to a particular value of that quantity, we run into the difficulty of comparing one length with another will agree on the units of measurement. At one time, the basic unit of length was the yard, determined by the size of the king's waistline. You can easily see the problems with such a standard, it is hardly accessible to those who need to calibrate their own secondary standards and it is not invariable to change with the passage of time.

Fortunately, it is not necessary to define and agree on standards for every physical quantity. Some elementary quantities may be easier to establish as standards and more complex quantities can often be expressed in terms of the elementary units. Length and time for example, were for many years among the most precisely measurable physical quantities and were generally accepted as standards. Speed, on the other hand, was less precisely measurable and therefore was treated as a derived unit (speed = length/time). Today, however, measurements of the speed of light have reached a precision beyond that of the former standard of length, we still treat length as a fundamental unit, but the standard for its measurement is now derived from the standards of speed and time.

The basic problem is therefore to choose the smallest possible number of physical quantities as fundamental and to agree on standards for their measurement. These standards should be both accessible and invariable, which may be difficult to satisfy simultaneously. If the standard kilogram, for instance, is to be an invariable object, it must be inaccessible and must be kept isolated beyond the effects of handling and corrosion.

Agreement or standards has been accomplished through a series of international meetings of the General Conference on Weights and Measures beginning in 1889, the 19th meeting was held in 1991. Once a standard has been accepted, such as the second as a unit of time, then we can apply the unit to a vast range of measurements from the lifetime of the proton (greater than 10⁴⁰ seconds) to the lifetime of the least stable particles that can be produced in our laboratories (about 10^-23 seconds). When we express such a value as 10⁴⁰ in units of seconds, what we mean is that the ratio between the lifetime of the proton and the time interval that is arbitrarily defined as the standard second is 10⁴⁰. To  accomplish such a measurement, we must have a way of comparing laboratory measuring instruments with the standard. Many of these comparisons are indirect, for no single measuring instrument is capable of operating precisely over 40 orders of magnitude. Nevertheless, it is essential to the progress of science that, when a researcher records a particular time interval with a laboratory instrument, the reading can in some way be connected to a calibration based on the standard second.

The quest for more precise or accessible standards is itself an important scientific pursuit, involving physicists and other researchers in laboratories throughout the world. In the United States, laboratories of the National Institute of Standards and Technology (formerly the National Bureau of Standards) are devoted to maintaining, developing and testing standards for basic researchers as well as for scientists and engineers in industry.