Planck and other physicists in the late 1800s and early 1900s were trying to understand the difference between classical mechanics — that is, the motion of bodies in the observable world around us, described by Sir Isaac Newton in the late 1600s — and an invisible world of the ultrasmall, where energy behaves in some ways like a wave and in some ways like a particle, also known as a photon.

"In quantum mechanics, physics works different from our experiences in the macroscopic world," explains Stephan Schlamminger, a physicist for the National Institute of Standards and Technology, by email. As an explanation, he cites the example of a familiar harmonic oscillator, a child on a swing set.

"In classical mechanics, the child can be at any amplitude (height) on the swing's path," Schlamminger says. "The energy that the system has is proportional to the square of the amplitude. Hence, the child can swing at any continuous range of energies from zero up to a certain point."

But when you get down to the level of quantum mechanics, things behave differently. "The amount of energy that an oscillator could have is discrete, like rungs on a ladder," Schlamminger says. "The energy levels are separated by h times f, where f is the frequency of the photon — a particle of light — an electron would release or absorb to go from one energy level to another."

In this 2016 video, another NIST physicist, Darine El Haddad, explains Planck's constant using the metaphor of putting sugar in coffee. "In classical mechanics, energy is continuous, meaning if I take my sugar dispenser, I can pour any amount of sugar into my coffee," she says. "Any amount of energy is OK."

"But Max Planck found something very different when he looked deeper, she explains in the video. "Energy is quantized, or it's discrete, meaning I can only add one sugar cube or two or three. Only a certain amount of energy is allowed."

Planck's constant defines the amount of energy that a photon can carry, according to the frequency of the wave in which it travels.

Electromagnetic radiation and elementary particles "display intrinsically both particle and wave properties," explains Fred Cooper, an external professor at the Santa Fe Institute, an independent research center in New Mexico, by email. "The fundamental constant which connects these two aspects of these entities is Planck's constant. Electromagnetic energy cannot be transferred continuously but is transferred by discrete photons of light whose energy E is given by E = *h*f, where h is Planck's constant, and f is the frequency of the light."