The Physical Constants Explained

What are the Physical Constants?

The physical constants are measurable properties of the physical universe that don’t change, everything else is relative to these constants.

Or, more technically, the physical constants are values that relate to phenomena in the universe that can be measured (directly or indirectly) as having a constant value (although some theories postulate that these constants could change under certain circumstances, and only a few constants are constant across all possible dimensions; see the PBS video on the constants changing below for more insight).

With that introduction in mind, there are a few types of physical constants including: universal constants, electromagnetic constants, physico-chemical constants, and the fundamental dimensionless constants (“true” constants).

Despite the constant types having different properties, all the constants are based on the same thing (the fundamental nature of our physical universe) and can be used to create “natural units” and “standard units.”

On this page, we give an overview of all physical constants (for non-physicists) with a focus on the fundamental physical constants.

The fundamental constants and quantities of the universe have been carefully dialed. This video is a great introduction to the constants, but make sure to pair it with the next video to understand how the concept of “constant” should be interpreted and weighted against true dimensionless constants.

TIP: Physical constants work just like mathematic constants. They are (generally speaking) not variables; they are constants. They are not relative to a frame of reference within a system (such as the universe); they are constant in all frames [this being only literally true for dimensionless constants]. The bottomline being: the constants do not change (in their respective dimensions). Constants are impressive and important, because almost everything in the universe is relative and dependent on frame of reference.

Are the Fundamental Constants Changing?

Where Do Constants Come From?

All constants are derived from the nature of mass-energy. For instance, the concept of light speed hinges on the constant speed of “pure massless energy” in a vacuum. The reduced Planck constant rests on the smallest movements of energy. The gravitational constant represents the constant force between two bodies due to their mass-energy. The same generally applies to the other physical constants, but we won’t go into the explanation of each constant here.

Check out the video below for a better understanding of the universal constants: the light speed constant, the Planck constant, and gravitational constant.

The Speed of Light is NOT About Light | Space Time | PBS Digital Studios

TIP: Visible light is a certain frequency of electromagnetic radiation. Mass-energy refers to a fundamental measurable property of electromagnetic force and the other forces. Thus, the speed of light (and the other constants, for their own reasons) are “derived from the nature of mass-energy”.

Cosmology and The Constants of Nature (John Barrow). There is no fun and simple video on the constants for beginners, but this mini-series on “Cosmology and the Constants of Nature” from the “Philosophy of Cosmology” project, a University of Oxford and Cambridge Collaboration, comes close.

Natural Units are Derived From the Constants

Constants can be used to give us natural units, we can use natural units as a measuring stick of sorts (Light units and Planck units for example). This is useful because time and space are relative to frame of reference, and that can make measuring things tricky.

Below, we give an explanation of the fundamental constants.

A Full List of Physical Constants

If you want to verify the constants for yourself, check out this list of fundamental physical constants from MIT (we don’t cover every constant here, as we want you to understand them conceptually, so use the MIT list for a full reference list of constants, or see this list).

For another basic guide see: Introduction to the constants for nonexperts.

Fundamental constants, physics and cosmology (Jean-Philippe Uzan)

The Universal Constants Overview

There are only a few universal constants used in most physics equations a non-physicist will encounter: the speed of light c, Planck’s constant h (and the related reduced Planck constant ℏ), and Newton’s gravitational constant G.

Most of the other constants can be explained by the nature of these, as the nature of these is derived from the nature of mass-energy itself.

In summary:

• Light speed (c) is the constant and only speed light (pure energy) can travel in a vacuum. Light speed is the max speed of the universe.
• The reduced Planck constant (ℏ) is the smallest unit of measurement energy can quantize to and is based on Planck’s constant (h). The Planck length, based on this unit, is the shortest distance energy can travel. The reduced Planck unit is the minimum unit of measurement in the universe.
• The gravitational constant (G) is the constant gravitational force between two bodies (this should not be confused with earth’s local gravity, express as ‘g’).

A table of universal constants (source):

Other Important Constants (Electromagnetic, physico-chemical, etc)

The other important constants are all a lot more heady and used less often in basic physics explainers. They include explainers for mass, charge, entropy, and other fundamental properties of particles or systems of particles. They include electromagnetic constants and physico-chemical constants.

There are a LOT of constants, and most require a deeper understanding of physics and chemistry then we cover on this site. Either soak in the basics below, or simply see a full list to learn more.

Electromagnetic and physico-chemical constants include (but aren’t limited to): Coulomb’s constant ke (constant electric force), and Boltzmann’s  constant k (constant heat energy of particles), magnetic constant (or permeability of free space constant) µ0, electric constant 1/µ0c2 ε0, characteristic impedance of vacuum √µ0/0 = µ0c Z0, elementary charge e, and more.

TIP: There are also conceptual constants that are important to physics such as the construct spacetime which is a theoretical combination of space and time. Space and time are relative, but spacetime is constant. Also important to physics, an inertial reference frame can be considered a sort of constant.

The Dimensionless Physical Constants

Beyond the constants mentioned above, there are also a set of constants what are “dimensionless” physical constants. This just means a constant not based on a human-created unit (like Pi). Light speed may be constant, but we are creating a unit around it, something like Pi (which is “a ratio”) works regardless of what system of units we are using.

Most of the non-dimensionless constants need to be the exact value or the universe breaks, however dimensionless physical constants (explained typically in values of Planck units for the sake of communication) represent values that simply aren’t dependent on human created units (again like Pi).

All the fundamental dimensionless constants are derived from “the mass of quantum particles”, and explained with the human-defined Planck, so just like the universal constants, the dimensionless constants are also derived from, and explained, by the nature of mass-energy.

Paul Dirac on Dimensionless Physical Constants and “Large Number Hypothesis”.

Wikipedia lists the dimensionless constants as:

• α, the fine structure constant, the coupling constant for the electromagnetic interaction (≈1/137.036). Also the square of the electron charge, expressed in Planck units, which defines the scale of charge of elementary particles with charge.
• μ or β, the proton-to-electron mass ratio, the rest mass of the proton divided by that of the electron (≈1836.15). More generally, the ratio of the rest masses of any pair of elementary particles.
• α_s, the coupling constant for the strong force (≈1)
• α_G, the gravitational coupling constant (≈10⁻⁴⁵) which is the square of the electron mass, expressed in Planck units. This defines the scale of the masses of elementary particles and has also been used to express the relative strength of gravitation.

Fine-structure constant. Typically I find “WikiAudio” stuff to be lame, but when it comes to things like the fine structure constant α, you might be surprised to know, there is a lack of simple jovial explainer videos.

For more reading check out the link below this quote:

“The most famous example is the “fine structure constant”, e²/ℏc. Here e is the electron charge, ℏ is Planck’s constant, and c is the speed of light. If you work out the units involved you’ll see it’s dimensionless, and experiments show that it’s about 1/137.03599. Nobody knows why it equals this. At present, it’s a completely mysterious raw fact about the universe!” – Learn more about dimensionless physical constants.

TIP: The term “fundamental constants” refers to either the universal constants (light speed, Planck, and gravity) and dimensionless constants (explained above), or just the dimensionless constants. The term fundamental is used because these constants are the core (AKA fundamental) constants in the universe. Some say the universal constants shouldn’t be called fundamental because the numerical values of these constants depend on the units used to express them. It is a technicality, but vital to understand when searching about constants on the internet. 9 times out of 10, outside of physics, when people say “constants”, they are talking about the big three universal constants light speed, Planck, and big G gravitational force.

UNSOLVED PHYSICS QUESTIONS: What is the minimum number of dimensionless physical constants from which all other dimensionless physical constants can be derived? Is there a theory which explains the values of all fundamental physical constants? Write your answer below.