How was the equation $E=hf$ discovered?

Was the proportional expression between energy and frequency of light $E\propto f$ discovered only by experiment? Or is there some logical(theoretical) senses affected?

Skip to content
# [Physics] Discovery of $E=hf$

#### Related Solutions

### EDIT: Real History vs. Physicist's History

###### Related Question

historyphotonsquantum mechanics

How was the equation $E=hf$ discovered?

Was the proportional expression between energy and frequency of light $E\propto f$ discovered only by experiment? Or is there some logical(theoretical) senses affected?

Newton's 1st and 2nd laws weren't particularly revolutionary or surprising to anyone in the know back then. Hooke had already deduced inverse-square gravitation from Kepler's third law, so he understood the second law. He just could not prove that the bound motion in response to an inverse square attraction is an ellipse.

The source of Newton's second law was Galileo's experiments and thought experiments, especially the principle of Galilean relativity. If you believe that the world is invariant under uniform motion, as Galileo states clearly, then the velocity cannot be a physical response because it isn't invariant, only the acceleration is. Galileo established that gravity produces acceleration, and its no leap from that to the second law.

Newton's third law on the other hand *was* revolutionary, because it implied conservation of momentum and conservation of angular momentum, and these general principles allow Newton to solve problems. The real juicy parts of the Principia are the specific problems he solves, including the bulge of the Earth due to its rotation, which takes some thinking even now, three centuries later.

The real history of scientific developments is complex, with many people making different contributions of various magnitude. The tendency in pedagogy is to relentlessly simplify, and to credit the results to one or two people, who are sort of a handle on the era. For the early modern era, the go-to folks are Galileo and Newton. But Hooke, Kepler, Huygens, Leibniz and a host of lesser known others made crucial contributions along the way.

This is especially pernicious when you have a figure of such singular genius as Newton. Newton's actual discoveries and contributions are usually too advanced to present to beginning undergraduates, but his stature is immense, so that he is given credit for earlier more trivial results that were folklore at the time.

To repeat the answer here: Newton did not discover the second law of motion. It was well known at the time, it was used by all his contemporaries without comment and without question. The proper credit for the second law belongs almost certainly to the Italians, to Galileo and his contemporaries.

But Newton applied the second law with genius to solve the problem of inverse square motion, to find the tidal friction and precession of the equinoxes, to give the wobbly orbit of the moon (in an approximation), to find the oblateness of the Earth, and the altitude variation of the acceleration of gravity g, to give a nearly quantitative model of the propagation of sound waves, to find the isochronous property of the cycloid, and a host of other contributions which are so brilliant ad so complete in their scope, that he is justly credited as founding the modern science of physics.

But in physics classes, you aren't studying history, and the applications listed above are too advanced for a first course, and Newton did indeed *state* the second law, so why not just give him credit for inventing it?

Similarly, in mathematics, Newton and Leibniz are given credit for the fundamental theorem of calculus. The proper credit for the fundamental theorem of calculus is to Isaac Barrow, Newton's advisor. Leibniz does not deserve credit at all. The real meat of the calculus however is not the fundamental theorem, but the organizing principles of Taylor expansions and infinitesimal orders, with successive approximations, and differential identities applied in varied settings, like arclength problems. In this, Newton founded the field.

Leibniz gave a second set of organizing principles, based on the infinitesimal calculus of Cavalieri. Cavalieri was Galileo's contemporary in Itali, and he either revived or rediscovered the ideas originally due to Archimedes in "The Method of Mechanical Theorems" (although he might not have had access to this work, which was only definitively rediscovered in the early 20th century. One of the theorems in Archimedes reappear in Kepler's work, suggesting that perhaps the Method was available to these people in an obscure copy in some library, and only became lost at a later date. This is pure speculation on my part. Kepler might have formulated and solved the problem independently of Archimedes. It is hard to tell. The problem is the volume of a cylinder cut off by a prism, related to the problem of two cylinders intersecting at right angles). Cavalieri and Kepler hardly surpassed Archimedes, while Newton went far beyond. Leibniz gave the theory its modern form, and all the formalism of integrals, differentials, product rule, chain rule, and so on are all due to Leibniz and his infinitesimals. Leibniz was also one of the discoverers of the conservation of mechanical energy, although Huygens has his paws on it too, and I don't know the dates.

The mathematicians' early modern history is no better. Again, Newton and Leibniz are given credit for theorems they did not produce, and which were common knowledge.

This type of falsified history sometimes happens today, although the internet makes honest accounting easier. Generally, Witten gets credit for everything, whether he deserves it or not. The social phenomenon was codified by Mermin, who called it "The Matthew principle", from the biblical quote "To those that have, much will be given, and to those that have not, even the little they have will be taken away." The urge to simplify relentlessly reassigns credit to well known figures, taking credit away from lesser known figures.

The way to fight this is to simply cite correctly. This is important, because the mechanism of progress is not apparent from seeing the soup, you have to see how the soup was cooked. Future generations deserve to get the recipe, so that we won't be the only ones who can make soup.

Well, you are mixing things in your question, you say:

. I'm just curious to know the proper historical development of this non-trivial fact of reality

This is historical:

The Nobel Prize in Physics 1921 was awarded to Albert Einstein "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".

No semiclassical explanations at the time , because the link you give is not historical, it is decades after the detection of the photoelectric effect and its interpretation as the photon being a discrete particle.

You yourself give the historic path.

Now there is a solid quantum mechanical theory called the standard model of particle physics, where the photon has its niche as a point particle on par with electrons and neutrons in the Lagrangian .

This model has been validated by innumerable data, and the chase for physics beyond the standard model goes into making photons into string excitations, not continuous classical electromagnetic waves.

Now wavepackets, that your first reference states, are necessary in the Quantum Field Theory of describing nature, which works with quantum "events" in effect. So I do not see anything revolutionary:

Do we count indivisible photons or discrete quantum events experienced by detectors?

One could ask this for all elementary particles, and certainly they are quantum entities, not classical particles .

Certainly there are hundreds of other historically important papers that are going under the rug here

Do you have any links? I do not think they exist, which is the reason Einstein got his Nobel.

In conclusion, any semiclassical arguments have to face all the bulk of data of the self consistent current model that describes particle data, i.e. embed them in the new format, because these are data too , in addition to the photon being an elementary particle.

## Best Answer

The relationship $E = h f$ was proposed by Max Plank in 1899 or 1900 as a way to "fix" a major problem in the existing understanding of the how light was emitted by hot bodies (the so called "ultraviolet catastrophe"). The conventional story holds that Plank did not consider this as fundamental.

^{1}Later Albert Einstein took the idea as a way to explain the photo-electric effect in 1905, bringing the principle that light energy actually

camein discrete chucks to the forefront. This work was among that cited by the committee in awarding Einstien's Nobel prize.The discovery of Compton Scattering in 1923 gave the "photon" a firm place in modern physics.

Quantum field theories eventual came to explain the photon as an excitation of the electromagnetic field.

^{1}I can't say if that is true or not, but it is the way the Lore goes.