Universal constants

Summary: Universal constants help describe the universe and are believed to be fixed for all times and places in the universe.

A universal constant is a physical quantity whose value remains fixed throughout the universe for all time. However, most constants are known only approximately; humans started measuring them relatively recently and it is an assumption that they are—and have always been—fixed. There may be other assumptions that scientists and mathematicians have implicitly made that turn out to be false and undermine the universality of these constants. For example, the ratio of the circumference of a circle to its diameter in Euclidean space is π, but with Albert Einstein’s conceptualization that the universe could have non-Euclidean geometry, this circumference-to-diameter ratio in the real world may be some value not equal π.

The international Committee on Data for Science and Technology defines and modifies physical constants and quantifies their levels of certainty. Three constants in particular are fundamental to the current understanding of the physical world. Together, they underlie the mathematics of gravity, relativity, and quantum physics. They are G (the gravitational constant), c₀ (the velocity of electromagnetic radiation in a vacuum (in other words, the speed of light), and h (Planck’s constant).

Universal Constant: “G”

G first appeared in Isaac Newton’s famous equation F=Gm₁m₂/r² which quantifies the force (F) of gravitation between two masses (m₁ and m₂), where r is the distance between their centers of mass. G is approximately 6.67×10^-11m³kg^-1s^-2 (meters-cubed per kilogram per second-squared), which is a very small number. Gravity is thus a very weak force. Although every mass is attracted to every other mass, the effects of gravity are obvious only when the masses involved are very large (such as with planets).

Using another of Newton’s equations, F=ma, it follows that the acceleration due to gravity on Earth is the same for all masses. This acceleration is known as g and its value is around 9.81 ms^-2 at sea level. This value varies with distance from the Earth’s center of mass (r in the equation above), so acceleration due to gravity decreases to around 9.78 ms^-2 at the top of Mount Everest. Knowing g to be about 9.81 ms^-2 and the radius of the Earth to be roughly 6,378,000 meters, one can use G to show that the mass of the Earth is about 5.98×1024 kg. One can also estimate the mass of the Sun and other celestial bodies, such is the applicability of G.

Universal Constant: “C0”

The velocity of light in a vacuum, c₀, is probably the most widely known universal constant. Since the length of a meter is defined by it, c₀ is fixed at exactly 299,792,458 ms^-1. The constancy (or invariance) of c₀ is a principle that was made famous by Albert Einstein in his theory of special relativity. Einstein’s principle states that no matter how fast you or the light source are travelling, you will always measure c0 to be 299,792,458 ms-1. This principle is counterintuitive, but both the constancy of c₀ and related predictions of relativity theory have been verified empirically. From relativity theory, it is known that as velocity increases, measurements of time and space change because duration and displacement are relative—they depend on how fast one is moving. The amounts by which they change are determined by c₀.

What is actually traveling at c₀ in electromagnetic radiation are massless particles called photons.

As carriers of the electromagnetic force, all light, electricity, and magnetism are the result of photon motion. The relationship between the photon energies and the frequency of their electromagnetic radiation is the basis of quantum physics and the third constant, h.

Universal Constant: “h”

Named after Max Planck, h has an approximate value of 6.63×10^-34 kgm²s^-1. The units of h can be understood as joule-seconds, also known as “action.” This unit is distinct from power, which is joules per second; for example, 10 joules expended every second for 10 seconds is 100 joule-seconds.

The first appearance of h was in the Planck’s relation E=hv. Planck discovered that photons only had certain discrete energy values, the E=hv equation relates the energy (E) of the photon to the frequency (v) of its electromagnetic radiation. The fact that h exists implies that energy comes in discrete lumps, not in a continuous stream. The unit of h appears in a number of important and fundamental relations, such as Werner Heisenberg’s uncertainty principle and Niels Bohr’s model of the atom.

Bibliography

Carnap, Rudolf. An Introduction to the Philosophy of Physics. New York: Dover Publications, 1995.

Feynman, Richard. Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher. Jackson, TN: Perseus Books, 1995.

———. The Character of Physical Law. Cambridge, MA: MIT Press, 2001.

Finch, Steven. Mathematical Constants. Cambridge, England: Cambridge University Press, 2003.

Fritzsch Harald. The Fundamental Constants: A Mystery of Physics. Translated by Gregory Stodolsky. Singapore: World Scientific Publishing, 2009.

Magueijo, Joao. Faster Than the Speed of Light: The Story of a Scientific Speculation. Jackson, TN: Perseus Books, 2002.