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KF5JRV > TECH 12.12.16 14:26l 104 Lines 6791 Bytes #999 (0) @ WW
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Subj: Fundamental Constant Accuracy
Path: IW8PGT<CX2SA<N0KFQ<KF5JRV
Sent: 161212/1215Z 6873@KF5JRV.#NWAR.AR.USA.NA BPQ6.0.13
Throughout all of the formulations of the basic theories of physics and their
application to the real world, there appear again and again certain
fundamental invariant quantities. These quantities, called the fundamental
physical constants, and which have specific and universally used symbols, are
of such importance that they must be known to as high an accuracy as is
possible. They include the velocity of light in vacuum (c); the charge of the
electron, the absolute value of which is the fundamental unit of electric
charge (e); the mass of the electron (me); Planck's constant (h); and the
fine-structure constant, symbolized by the Greek letter alpha.
There are, of course, many other important quantities that can be measured
with high accuracy -- the density of a particular piece of silver, for
example, or the lattice spacing (the distance between the planes of atoms)
of a particular crystal of silicon, or the distance from the Earth to the
Sun. These quantities, however, are generally not considered to be fundamental
constants. First, they are not universal invariants because they are too
specific, too closely associated with the particular properties of the
material or system upon which the measurements are carried out. Second, such
quantities lack universality because they do not consistently appear in the
basic theoretical equations of physics upon which the entire science rests,
nor are they properties of the fundamental particles of physics of which all
matter is constituted.
It is important to know the numerical values of the fundamental constants with
high accuracy for at least two reasons. First, the quantitative predictions of
the basic theories of physics depend on the numerical values of the constants
that appear in the theories. An accurate knowledge of their values is
therefore essential if man hopes to achieve an accurate quantitative
description of the physical universe. Second, and more important, the careful
study of the numerical values of these constants, as determined from various
experiments in the different fields of physics, can in turn test the overall
consistency and correctness of the basic theories of physics themselves.
Definition, importance, and accuracy
The constants named above, five among many, were listed because they exemplify
the different origins of fundamental constants. The velocity of light (c) and
Planck's constant (h) are examples of quantities that occur naturally in the
mathematical formulation of certain fundamental physical theories, the former
in James Clerk Maxwell's theory of electric and magnetic fields and Albert
Einstein's theories of relativity, and the latter in the theory of atomic
particles, or quantum theory. For example, in Einstein's theories of
relativity, mass and energy are equivalent, the energy (E) being directly
proportional to the mass (m), with the constant of proportionality being the
velocity of light squared (c2) -- i.e., the famous equation E = mc2. In this
equation, E and m are variables and c is invariant, a constant of the
equation. In quantum theory, the energy (E) and frequency, symbolized by the
Greek letter nu (nu), of a photon (a single quantum unit of electromagnetic
energy such as light or heat radiation) are related by E = hnu. Here, Planck's
constant (h) is the constant of proportionality.
The elementary charge (e) and the electron mass are examples of constants
that characterize the basic, or elementary, particles that constitute matter,
such as the electron, alpha particle, proton, neutron, muon, and pion.
Additionally, they are examples of constants that are used as standard units
of measurement. The charge and mass of atomic and elementary particles may be
expressed in terms of the elementary charge (e) and the electron mass (me);
the charge of an alpha particle, the nucleus of the helium atom, is given as
2e, whereas the mass of the muon is given as 206.77 me.
The fine-structure constant (alpha) is an example of a fundamental constant
that can be expressed as a combination of other constants. The fine-structure
constant is equal to a numerical constant times the velocity of light times
the elementary charge squared divided by twice Planck's constant, or
µ0ce2/2h, µ0 being the so-called permeability of free space, numerically equal
to exactly 4pi x 10-7. (The system of measurement units used in this article
is the Système International d'Unités [International System of Units], or SI.)
Because this particular combination of constants always appears in theoretical
equations in exactly the same way, however, the fine-structure constant is
really a fundamental constant in its own right. For example, the
fine-structure constant is the fundamental constant of quantum
electrodynamics, the quantum theory of the interaction (mutual influence)
among electrons, muons, and photons. As such it is a measure of the strength
of these interactions. Another quantity that is a combination of other
constants is the Rydberg constant (symbolized Rinfinity), which is equal to
the product µ02c3e4me/8h3. It sets the scale (magnitude) of the various
allowed electron energy states or levels in atoms such as hydrogen.
The accuracy with which many of the fundamental constants can be currently
measured is a few parts in a million. By accuracy is meant the relative size
of the uncertainty that must be assigned to the numerical value of any
quantity to indicate how far from the true value it may be because of
limitations in experiment or theory. This uncertainty is a quantitative
estimate of the extent of the doubts associated with the value. The most
commonly used uncertainty, the standard deviation, symbolized by the Greek
letter sigma, is such that there is about a 68 percent chance that the true
value lies within plus or minus sigma. Furthermore, there is a 95 percent
chance that the true value lies between plus and minus two standard deviations
and a 99.7 percent chance that it lies between plus and minus 3 standard
deviations. (All uncertainties quoted in this article will be one standard
deviation.)
In practice, an uncertainty of one part per million (abbreviated ppm) is
rather respectable. It corresponds to determining the length of a United
States football field (100 yards, or about 91 meters) to within the thickness
of two of these pages (one page is about 0.0022 inch or 0.056 millimeter
thick). There are several quantities that have been measured with
uncertainties approaching one part in 1 000 000 000 000 (one in 1012); this
uncertainty corresponds to determining the distance from New York to San
Francisco to within one-tenth the thickness of a piece of paper.
73 Scott KF5JRV
KF5JRV.#NWAR.AR.USA.NA
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