###### By Don Lincoln, Fermilab

## Max Planck was a German theoretical physicist, and one of the legends of quantum mechanics. He was one of the original architects of the first quantum revolution. In 1899, he introduced what is called the Planck constant, which is what is called a unit of electromagnetic action. Planck’s constant is written in lower case *h*. So, what is it all about?

### Planck Units

According to currently popular theoretical bias, the smallest possible size is called the Planck length, and it is 1.6 × 10^{−35} meters. There is a shortest time, called the Planck time, and that is 5.4 × 10^{−44} seconds. There is a hottest temperature, called the Planck temperature, and it is 1.4 ×10^{32} kelvin. There is also a Planck energy, a Planck charge, a Planck mass, and a whole bunch of other similar units.

A unit of electromagnetic action probably doesn’t mean anything to you, but it is a constant that relates the frequency of light to the energy of a photon of light with that frequency.

### Photoelectric Effect

Actually, we can partially thank Einstein for that, as this was the equation of the photoelectric effect. But Einstein’s paper on the photoelectric paper was released in 1905 and Planck’s paper came out six years earlier. He was working on a conundrum of late 19th century physics.

According to the prevailing physics of the time, a glowing object should have been much, much, bluer than is actually observed. Planck used the same equation that Einstein did, but in a different context. He also said that the energy of light was proportional to frequency.

Since blue light is high frequency, each individual blue photon has a lot of energy. If there is a certain amount of blue light energy and if every blue photon has more energy than say, for example, red light, then that means that there must be fewer blue photons than red ones.

### Spectrum of Microwaves

That might be a little hard to visualize but imagine that blue photons carry twice the amount of energy than red ones. If there are equal amounts of blue and red light energy, then there will be half as many blue photons as red ones.

The details of Planck’s work are much more complicated than that, but that’s the big idea. And his work accurately predicted the shape of the spectrum of microwaves of the big bang. His work had nothing to do with astronomy and everything about glowing things in general.

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### Solving Potential Miscommunication in Measurement

In any event, in his paper that accurately predicted the color of hot and glowing objects, he thought about another issue, and that was about units of measure and how they were arbitrary. Planck was trying to solve the potential for miscommunication in the most scientific way possible. The way he did that was to start with five known and well measured scientific quantities. These are quantities that any scientifically advanced society can measure.

The first is the speed of light, which we’ve encountered before. The second the gravitational constant, which Newton defined in his theory of gravity. The third is the reduced Planck constant, which is just Planck’s constant divided by 2 *pi*. The fourth is the Boltzmann constant, which arises in thermodynamics and equates the energy and temperature of a gas. The fifth and final fundamental parameter is the Coulomb constant, which arises in electricity situations, most famously in Coulomb’s law, which predicts the force between two electrically charged objects.

Each of those parameters can be measured in any system of units. For instance, the speed of light is about 300,000 kilometers per second or 186,000 miles per second, but either way, the speed of light has units of length divided by time.

### Natural Units that Will Retain Their Meaning for Good

What Planck realized was that he could take ratios of these five fundamental constants and cancel units, leaving the one unit he wanted for. For instance, the units for the speed of light is length per time. The units for the Gravitational constant are length cubed divided by mass and time squared. The reduced Planck constant has units of length squared times mass, divided by time. Don’t worry if you can’t hold all that in your head. Neither can I. I just have to write it down.

But if you multiply the reduced Planck constant times the gravitational constant and divide it by the speed of light cubed, the result is a number that has units of length squared. Then you take the square root of that and you can get a quantity with units of length. This is called the Planck length. In the metric system, it is 1.6 × 10^{−35} meters. In the American system, it is 5.2 × 10^{−35} feet. And you can repeat the exercise, coming up with Planck mass, Planck time, Planck temperature, Planck charge, and on and on and on. Very cool.

The numbers one gets in different unit systems are different, but it’s super important to remember that in both systems, they are measuring the same physical length or time or energy. From that, scientists using different systems of measurements can come up with scientifically motivated conversion factors.

Planck himself said in his paper to the Prussian Academy of Sciences, “These necessarily retain their meaning for all times and for all civilizations, even extraterrestrial and non-human ones, and can therefore be designated as ‘natural units’.”

### Common Questions about the Planck Constant and What It Is Good For

**Q: Who was Max Plank?**Max Plank was a German theoretical physicist, a legendary in the field of quantum mechanics. He introduced the Planck constant, a unit of electromagnetic action.

**Q: What were the details of Planck’s work?**In addition to using Einstein’s question of the photoelectric effect same equation, yet in a different context, Planck also predicted the shape of the spectrum of microwaves of the big bang.

**Q: What are the five measured scientific quantities units that Planck took their ratio?**These are five fundamental constants and cancel units, including the speed of light, the gravitational constant, the reduced Planck constant, the Boltzmann constant, as well as the Coulomb constant.