To see a world in a grain of sand

And a heaven in a wildflower,

Hold infinity in the palm of your hand

And eternity in an hour

— William Blake

There is a universe in a grain of sand. Three of the four known forces of nature combine to hold together the nuclei of atoms and their electron clouds. Contained within the atomic and crystal structure of the sand and all atoms are all of the forces that exist in the universe.

The electromagnetic, strong and weak forces act on the small scale to give form to all substances, including the silicon dioxide that makes up quartz sand. Gravity contrarily acts on the large scale and holds the universe together.

The electromagnetic force governs atomic bonds that form by sharing or exchange of electrons. In crystals the arrangement of the atoms is a repeating and unvarying 3D array, the configuration of which depends on the electronic properties of the atoms.

The nucleus of an atom occupies only an insignificant fraction of its volume. The size of the nucleus relative to the electron cloud is comparable to that of a basketball in a large stadium. Therefore, the atoms in a solid crystal can be viewed as lumps of negative electric clouds.

The strong force binds protons and neutrons in the nucleus. It overcomes the electromagnetic repulsion of protons and permits the mediating effect of neutrons, allowing positively charged protons to remain stable while packed into the nucleus.

The weak force is responsible for radioactive decay when the strong force cannot maintain a stable nucleus.

These four forces are the only ones known to exist. They are responsible for the existence of matter in the only forms we know in this universe.

Physicists have calculated the roles of these forces with great precision to a startling conclusion: If any of the four were different by only a fraction of a percent, matter as we know it could not exist.

If the electromagnetic force were just a little weaker, electrons would not stay in their orbits around the nucleus, and there would be no atoms. A little stronger and electrons would spiral into the nucleus, and again there would be no atoms.

If the strong force was weaker, it could not hold the nucleus together, and if stronger, it would pack them too tight. Variation in the weak forces would affect the stability of the nucleus, and there would be no atomic nuclei in either case. Without atomic nuclei there would be no atoms, no planets, no stars and no galaxies.

There would be no us.

Cosmologists wonder about the coincidence that we just happen to exist in a Goldilocks universe that is just right for our existence.

But we can only exist in a universe where the atoms that comprise us can exist and make our existence possible.

There may be other universes where the strengths of these four forces are different, but we can never know of it directly. All of our senses have evolved within the familiar laws of physics of our universe, with its four fundamental forces.

There is a world, indeed a universe, in a grain of sand.

Richard Brill is a retired professor of science at Honolulu Community College. His column runs on the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.