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.

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    • http://www.facebook.com/zackalawi Zack Alawi

      Great article. Got a clear understanding of what happens on the Sun that allows life here on earth. .07% and Planck’s contribution to quantum mechanics. Although, I don’t see the correlation between Planck’s constant, h, and the .07% hydrogen efficiency. Is it that h allows the calculation of the efficiency?

      • Jim Stein

        Hi Zack! Here’s my understanding of how this happens. Planck’s constant also enables us to understand the way energy is distributed among atoms. It requires extremely high venergies for two hydrogen atoms to fuse — if they hit each other at too low an energy, they’ll be repelled electrically because they’ll both have the same electrical charge. Planck’s constant enables us to calculate the fraction of atoms that have sufficient energy to overcome what is called the electrostatic barrier.

    • Carole Brooks Platt

      I’m very impressed by the clarity here, so unusual and such a benefit to non-scientists who want to understand the cosmic dimension of things.

      • Aaron

        My thoughts exactly.

    • pixellated

      Good reading – re-enforced some basic things I know. Question though, what happened to the other 99.30%?

      • Jim Stein

        It’s still mass. When the atoms of hydrogen fuse to form helium, only a small amount (0.7%) of the original mass is converted into helium. The leftover mass goes into making up helium,.

        • Bob Shultz

          Hi Jim, I think you mean 0.7% of the original mass is converted to energy.

          (btw, speaking of numbers, do you think Yale took a step backwards when they dropped their numeric grading system in favor of an alphabetic one?)

          • Jim Stein

            Hi Bob,

            Of course you’re right about the 0.7%. Well, yet another typo on my long list.

            I absolutely agree with you about Yale. On the other hand, numeric grading was unfair to liberal arts majors. Science and math majors got scores of over 95 in a bunch of science, math, and logic courses — how can you get scores like that in history, lit, and philosophy?

    • http://www.facebook.com/xtiansimon Christian Simon

      The article brings to memory the industry announcements the past few years about “molecular gears” and three dimensional circuit boards. And how we know what we know about distant stars without ever actually going there to see them. Thanks.

    • philip

      Philipp in the original, or in English, Philip.

    • Jeff Michals-Brown

      Thank you, James Stein, for a very nice synthesis! A few minor details and a question.
      First, living things are mostly carbon, hydrogen, oxygen, nitrogen, phosphorus and sulfur with smaller amounts of a bunch of other things. Of these, hydrogen is original to the Big Bang, and all the others can be produced by normal fusion in stars of various masses at various stages of their lives. Normal, energy-producing fusion ends with iron-56 (which is at the bottom of the Curve of Binding Energy), if I recall, and heavier elements come only from supernovae. On the other hand, I suppose not much of the heavy elements produced in normal fusion would get out into the universe at large unless big stars blew up!
      Second, if the efficiency of hydrogen fusion were 0.6%, we wouldn’t have stars, would we? Hydrogen gas clouds would slowly condense, radiate away the heat from their gravitational collapse, and then end as cold, dark dense blobs of gas long before our (conceivable) time, right?
      Now my question: if hydrogen fusion efficiency WERE 0.8%, what would the universe be like?
      Thank you–this is fun!
      Jeff Michals-Brown

      • Jim Stein

        Hi Jeff,

        Wow, you sure have a good grounding in the basics. Normal fusion does produce the lighter elements up through iron, and supernovae the other elements. However, if the stars don’t explode, how do we get to access those lighter elements?

        My understanding is that too low a number for the efficiency of hydrogen fusion would result in the inability to produce deuterium, which is a critical step in the proton-proton chain, the primary path to hydrogen fusion. Too large a number would result in helium being produced too quickly, hydrogen would be quickly consumed, and without hydrogen there is no water.

    • Ed Atwood

      after watching the fabric of the cosmos..wow..what a show..is it possible that everything that goes into a black hole doesn’t really go away..it comes out somehow as dark matter..back into this reality..continueing to push the universe apart..the last part about black holes was way out for me..but hey just the univ of fla’s wastewater treatment plant operator passing the time…

    • Hakuin Suso

      I like reading items on physics that dumbs down the complicated math for people like me. However, it’s frustrating when terms like “life” are used in two or more different senses yet is presented as if it had only one meaning.

      We’re told that Planck’s career has deepened our understanding of how the universe enables life to exist. In fact, all it’s done is enable us to understand how particular elements are formed. How these all come together to create that something we call “Life” is not understood at all.

      For that matter, what Life “is,” is not really understood either. We could, for example, make a machine that consumes fuel, performs diverse functions, and actively interacts with its environment, yet we wouldn’t call it alive. But in one sense Mr. Stein would have us believe it is alive because it is made up of elements forged in the sun.

      We can describe how all the elements that comprise a physical body are created in the stars, but putting them together in a box doesn’t make life. But don’t suppose I’m taking a religious approach and stipulating this is god’s doing. I’m not. And neither should physicists use science to make claims that science cannot support. Science as we know it, has no idea how life came to be in the universe.

    • http://www.facebook.com/people/Rod-Thomson/1440670509 Rod Thomson

      Just came across this blog. Love it. But I’m probably not the normal reader. I’m a Christian and one who believes the Bible is what it says it is. And I am a mere layman in all areas of science. No formal training. (Degree in journalism and been a journalist my whole life.) But the more I read from people much smarter than me, the less science seems in conflict with religion when simply presented as scientific facts. I’m not meaning to start too big a conversation, or in the wrong place, but I would like others’ insights on whether Planck’s Constant is consistent or inconsistent (or neither) with existence of a Creator.

      Thanks for any input and for the explanation.

      • Stephen A. Halkovic III

        Good day Rod Thomson,

        I’m Stephen A. Halkovic III and had left the field of astrophysics in the mid-eighties because of the realization of the current biases of the Big Bang theorists about Christian ideas. Their need to establish an origin has more to do with establishing a religion and has nothing to do with science. Planck was a Christian and his ideas came from his Christian mind. However there is an overwhelming majority of anti-Christian and anti-Semitics in today’s world scientific community. I do have a blog that I’m not publicizing because I use it more to rant at the stupidity of the Big Bang Theories short comings and close mindedness. Planck’s constant doesn’t conflict with any of the teachings of Jesus Christ. The Judaic tradition states; “In the beginning God created the heaven and the earth.” Genesis 1;1 Because the time is fixed and not infinite then the ancient Greek philosopher Zeno’s paradoxes questioning the idea of infinity and this world stipulate that there must be a smallest distance or no distance can ever be traversed. Planck’s constant is an answer of what that ‘distance’ which is actually associated with energy; E=hv (E=the energy of a photon, h= Planck’s constant, and v=the photon’s frequency). It’s very interesting because (for those who haven’t read the First Book of Moses) “God said ‘Let there be Light.’ and there was light.” Genesis 1;3 I hope that is enough to validate your faith and know that the Big Bang theorists are perverting the good work of true believers.

        Good Bless, PPP,


        • Gamer_Czar

          I agree with you Stephen! God’s Word was not written to be a “science” book.

        • rail

          shut up, ignorant theist

      • arthur brogard

        of course none of it is inconsistent with the existence of a creator.

        all depends upon definitions.

        a definition I like is that god is all. and all is god.

        science is one of the ways in which god becomes conscious of god.

      • walter

        This is a interesting discussion and yes it does line up with what God is conveying to the world. There is a parallel dimension that many have not the ability to access because they lack the energy needed to decay the firewall that’s protecting its reality from visible light. Unfortunately the world that we currently reside in possess not the “Mind of Christ” to unlock the mysteries. However the chosen that possess this mind is unveiling in this season. God bless

    • http://www.facebook.com/bruce.camber Bruce Camber

      I am a rather simple person. I wondered what would happen when we multiply the Planck constant by 2… just how many times would it take to get to one meter. We found 117. We (five high school geometry classes) continued multiplying until we got to the edges of the observable universe. That took another 85-to-89 steps. We have a former NASA wizard helping us with that calculation and he arrived at successive multiplications. Yesterday he arrived at 202.34. Earlier this year, a brilliant astrophysicist of some global acclaim told me 206. So, in about 202.4 – to – 206 steps we see the ordered universe.

      Two questions: Is progression of successive multiplications base-2 (as opposed to base-ten scientific notation)? And, is there such a thing as Planck number 1 to 205 documented anywhere? We are looking and can’t seem to find it so assume our logic is faulty somewhere. Would you like to check our math? It is all online now.

    • makori benard magati

      i am totally pleased by that smart explanation sir.thanks very much.

    • Anonymous

      Truly fascinating stuff. Yet in all our endeavors to define, explain, and discover the actual foundation of what we call reality, there is always a missing element that drives us to further analysis and discovery.

      Consider how everything we explore is always in the framework of externalization. We assume without question reality is an objective state. We require our five physical senses to define what we think we are observing.

      Yet, if we “think” about this process, we are forced to conclude that it is in fact only our ability to subjectively experience reality that has any reality.

      Planck’s Constant, Einstein’s E=MC2 and all the other formulas that define the relationships of matter and energy we know only tells us why things appear as they do, not how they came to be in the first place. That is all still theory.

      The objective universe we perceive is totally void at it’s quantum foundation. Here, there are no dimensions that define objects in space, for all exists everywhere at the same time as probabilities of what may or may not become objectified.

      Now consider thought. Here too all exists as probabilities that may or may not become objectified. We don’t know where our thoughts come from, or where they go, or how they exist at all, yet from some of them, much of our objective experience is created.

      The possibility exists therefore that our thoughts and quantum existence are directly related and are from the same source; the only source that is totally subjective; conscious awareness.

      Experience itself cannot exist until it is created subjectively, as an idea or a thought. Without this, all the formulas and definitions of reality do not exist. Weird, but true. Try experiencing anything without first thinking about it. It is impossible by default.

      I read an interesting book on this if anyone is interested at http://www.therealitycode.com. Fact truly is stranger than fiction.

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    • ashish p rao

      Very good explanation, sir. I came to this blog in the search of a decent explanation of the Planck constant. I have found the answer through various sites such as yours. The reason I wanted to know what the planck constant is to understand the math behind the Heisenberg Uncertainty Theory. I still havent understood the math behind the uncertainty theory. I know what the theory is, but I can’t understand the math.
      Someone, please help me.

    • Doctor Demento

      Thanks for a truly outstanding presentation of what is often very confusing material. I’ve been teaching these concepts for over 20 years at the college level and this is one of the best explanations of the history, theory, and implications of Planck’s work. Many thanks for your essay!


      superb and simple explanation of a concept normally too difficult for a laymen to comprehend. How many geniuses out there can do this… explain, in the simplest terms, the most complex and difficult theories and their ramifications… one way or another, for mankind on this planet? Very few I’d wager! Bravo James Stein! Thankyou!

    • http://www.filmbreak.com/projects/energeia Patrick Drake


    • FMHenry

      If two 10 watts electromagnetic signals were transmitted from Earth to Mars…(the first
      was at 10 MHz and the second was at 3 GHz)…assuming zero losses for both signals
      what would the power of the signals received at the surface of Mars ???

    • Fred

      Yes well written but how exactly is the theoretical and measured value of Planck’s constant derived ?

    • arthur brogard

      i liked reading this but i’m damned if i can understand all the fulsome praise of the ‘clear explanation’ etc…
      nothing much is explained of the ‘finding’ of the constant.
      establishing its existence, finding its size, proving it.
      he just says Planck theorized and then jumps immediately to ‘now we know it is…’
      no explanation there.
      But, yes, some explanation of the sun’s processes. good. clear. interesting.

    • https://www.youtube.com/watch?v=w7BO_hqe_q0 Alone: bad. Friend: good!


      Everyone has the wrong idea of what energy, forces and fields are.
      Energy is a particle vibration or movement.
      You cannot have energy without a mass, energy is mass vibrating.
      Energy cannot be out on its own. (a supposed mass-less particle is a particle nonetheless, but there are no mass-less particles, so that’s irrelevant)

      Same thing goes for forces.
      A force is a group of particles arranged in a field pulling each other… and all of the particles absolutely have to be physically connected.

      A force (a group of connected particles) can only push very short distances and in rare circumstances like same pole magnets.

      But the point is… a force has to have particles involved.
      A force cannot be out on its own.

      Most of mainstream physics is a misconception.

      There is no such thing as pure energy.
      Again… Energy is a vibration on a particle (or particle movement).

      Can energy be converted into mass?
      Ummm… no, energy already has mass involved, it is a particle vibration or movement. There is no pure energy and you are not going to convert energy into mass.

      Think of a guitar string. If you pluck it… that is the energy. If you remove the guitar string from the scenario… can you still have the energy? No, of course not.

      Can you convert the guitar string vibration into mass? No… that is ridiculous.

      Look at what everything really is…

      Dimensions and units…
      mass = [M] = kilograms
      length = [L] = meters
      time = [T] = seconds
      frequency = [T^-1] = seconds ^-1
      speed = [L] / [T] …… = m/s
      acceleration = [L] / [T^2] …. = m / s^2
      momentum = [M] [L] / [T] … = kg_m / s
      force = [M] [L] / [T^2] . = kg_m / s^2
      energy = [M] [L^2] / [T^2] = kg_m^2 / s^2
      power = [M] [L^2] / [T^3] = kg_m^2 / s^3

      Notice mass [M] is not equal to energy [M] [L^2] / [T^2] …the vibration is missing

      Here is what Einsteins famous equation really looks like…

      [M] [L^2] / [T^2] = [M] [L^2] / [T^2]

      Energy already is a mass times speed^2.

      How would you go about converting a mass times speed^2 into a mass times speed^2.