Quantum Physics / The Cosmos


Planck’s Constant: The Number That Rules Technology, Reality, and Life

In 1878—before Einstein was born, before quantum mechanics, before we knew that our galaxy was one among many—a well-known physicist named Phillip von Jolly told young Max Planck, a student aspiring to a career in physics, “In this field, almost everything is already discovered, and all that remains is to fill a few unimportant holes.”

Little did von Jolly realize how seriously he had underestimated the depth and quantity of those “unimportant holes,” and he certainly had no idea that Planck was to play a vital role in helping to fill them. Fortunately for us, Planck was not turned off by Jolly’s remark, and replied that he was not so much interested in discovering new things as in understanding what was known. This might sound unusual, as most scientists are motivated by a combination of two things: a desire to understand, coupled with the urge to discover. Discovery and understanding go hand-in-hand; together they move science forward, and as science moves forward, the quality of our lives improves. Planck’s career was ultimately characterized by the discovery of something truly new, something which would lead to a deeper understanding of perhaps one of the great questions in all science: how the universe enables life to exist.

Chemistry tells us that the smallest amount of water is a water molecule, and any container of water consists of a staggering number of identical water molecules. In order to resolve an underlying problem in the theory of energy distribution, Planck wondered, What if energy worked the same way? What if there were a smallest unit of energy, just as there is a smallest unit of water? The idea that energy could be expressed in discrete units, or “quantized,” was fundamental to the development of quantum theory. Indeed, you might say that Planck put the “quanta” in quantum mechanics.

So what is this smallest unit of energy? Planck hypothesized the existence of a constant, now known as Planck’s constant, or h, which links a wave or particle’s frequency with its total energy. Today, we know that

h = 6.6262 x 10-34 Joule⋅second

Planck’s constant has had profound ramifications in three important areas: our technology, our understanding of reality, and our understanding of life itself. Of the universal constants—the cosmic numbers which define our Universe—the speed of light gets all the publicity (partially because of its starring role in Einstein’s iconic equation E = mc2), but Planck’s constant is every bit as important. Planck’s constant has also enabled the construction of the transistors, integrated circuits, and chips that have revolutionized our lives.

More fundamentally, the discovery of Planck’s constant advanced the realization that, when we probe the deepest levels of the structure of matter, we are no longer looking at “things” in the conventional meaning of the word. A “thing”—like a moving car—has a definite location and velocity; a car may be 30 miles south of Los Angeles heading east at 40 miles per hour. The concepts of location, velocity, and even existence itself blur at the atomic and subatomic level. Electrons do not exist in the sense that cars do, they are, bizarrely, everywhere at once, but much more likely to be in some places than in others. Reconciling the probabilistic subatomic world with the macroscopic everyday world is one of the great unsolved problems in physics—a not-so-unimportant hole that even von Jolly would have recognized as such.

Finally, Planck’s constant tells us how the universe is numerically fine-tuned to permit life to exist. Carl Sagan, one of the great popularizers of science, was fond of saying that “We are all star stuff”—the chemicals which form our bodies are produced in the explosions of supernovas. The fundamental nuclear reaction eventually leading to the explosion of a supernova is the fusion of four hydrogen atoms to produce a single atom of helium. In the process, approximately 0.7% of the mass is converted to energy via E=mc2. That’s not much, but there is so much hydrogen in the Sun that it has been radiating enough energy to warm our planet for more than four billion years—even from a distance of 93,000,000 miles—and will continue to do so for another five billion years.

This 0.7% is known as the efficiency of hydrogen fusion, and our understanding of it is one of the consequences of Planck’s investigations. It requires a great deal of heat to enable hydrogen to fuse to helium, and the hydrogen atoms in the sun are moving at different speeds, much like cars on a freeway move at different speeds. The slower-moving hydrogen atoms just bounce off each other; they are insufficiently hot to fuse. Higher speeds, though, mean higher temperatures, and there is a small fraction of hydrogen atoms moving at sufficiently high speeds to fuse to helium.

The 0.7% efficiency of hydrogen fusion is what is sometimes referred to as a “Goldilocks number.” Like the porridge that Goldilocks eventually ate, which was neither too hot nor too cold, but just right, the 0.7% efficiency of hydrogen fusion is “just right” to permit the emergence of life as we know it. The process of hydrogen fusion is an intricate high-speed, high-temperature ballet. The first step of this reaction produces deuterium, an isotope of hydrogen whose nucleus consists of one proton and one neutron. In this process, two protons slam into one another, causing one of the protons to shed its electrical charge and metamorphose into a neutron. If the efficiency of hydrogen fusion were as low as 0.6%, the neutron and proton would not bond to each other to form a deuterium atom. In this case, we’d still have stars—huge glowing balls of hydrogen—but no star stuff would ever form because the porridge would be too cold to create helium, the first step on the road to creating the elements necessary for life.

On the other hand, if hydrogen fusion had an efficiency of 0.8%, it would be much too easy for helium to form. The hydrogen in the stars would become helium so quickly that there wouldn’t be much hydrogen left to form the molecule most essential for life—water. Star stuff would be produced, but without water life as we know it would not exist. Maybe something else would take the place of water, and maybe life could evolve—but not ours.

Planck’s quantization of energy was an essential step on the road to the theory of quantum mechanics, which is critical to our understanding of stellar evolution. Science hasn’t filled in all the pieces of the puzzle of how life actually evolved, but quantum mechanics did begin to answer the question of how the pieces got there in the first place, and probably even Philipp von Jolly would recognize that as an important hole in our knowledge of the universe that desperately needed to be filled. But perhaps the greater lesson is this: The very moment when it feels like “almost everything is already discovered” may be the moment that the universe is about to yield up its biggest surprises—if you’re not afraid to dig in to a few holes.

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James Stein

    James D. Stein is a past member of the Institute of Advanced Studies and is currently a professor of Mathematics at California State University (Long Beach). His list of publications includes: How to Shoot from the Hip Without Getting Shot in the Foot (with Herbert L. Stone and Charles V. Harlow); How Math Explains the World (a Scientific American Book Club selection); The Right Decision (also a Scientific American Book Club selection); and How Math Can Save Your Life. He has been a guest blogger for Psychology Today and his work has been featured in the Los Angeles Times. His latest book is Cosmic Numbers: The Numbers That Define Our Universe. He lives in Redondo Beach, California.