Courtesy links: If photons have no mass, how can they have momentum? How is it possible photons have no mass but have energy?

I saw two other questions asked about why photons have momentum and energy even though they do not have a rest mass. I now wanted to ask about Planck's constant. An object's action has dimensions of $M L^2 T^{-1}$. I do not see this being followed by photons. A constant action of $6.6 \cdot 10^{-31} \text{g} \, \text{m}^2 \text{s}^{-1}$, called Planck's constant $h$ has some connection with photons. The energy of photons is $E = h f$, where $f$ is the frequency of the photons. Where does this constant come from?

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    $\begingroup$ physics.stackexchange.com/a/730230/292464 read this to understand energy in relativistic cases. As for where planck's constant came from , read about ultraviolet catastrophe. $\endgroup$
    – user292464
    Oct 7, 2022 at 15:51
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    $\begingroup$ Planck’s constant is the quantum of action. Asking “where it comes from” is asking why action is quantized. We can imagine a universe in which it isn’t, but it would look nothing like our universe. $\endgroup$
    – Ghoster
    Oct 7, 2022 at 15:53
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    $\begingroup$ Planck's constant has some connection with photons? Have you learned that the energy $E$ and frequency $f$ of a photon are related by $E=hf$? $\endgroup$
    – Ghoster
    Oct 7, 2022 at 15:58
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    $\begingroup$ planck's constant was discovered in the context of photons, but is a lot more fundamental a quantity than just "governing how the energy of photons is quantized" $\endgroup$ Oct 7, 2022 at 19:56
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    $\begingroup$ I think it is fair to ask "Where does Planck's constant come from?", but the answer is a trivial "We don't know." right now, at least not on the level of first principles. $\endgroup$ Oct 7, 2022 at 22:09

1 Answer 1


h is a "fundamental" constant, like the speed of light, c.

Its size sets the dimension (scale) of quantum phenomena, whose cornerstone is the (then, a century ago) counterintuitive noncommutativity relation $[x,p]=i\hbar$.

Phenomena with action much-much-much larger than ℏ normally don't reflect this peculiar feature, and are then described by classical mechanics, an approximate, "easy" theory that dominated our description of our world for centuries, before the discovery of QM, and much of engineering to this day.

The characteristic dimensions of photons, are its wavelength (λ) and its momentum (p) understood to be inversely related to each other a century ago, $$ p\lambda = h . $$
This relation leads to the small scale of the photon momentum emitted in atomic energy level transitions, since $E= c p = h c/\lambda= h f$ .

In engineering units (SI), describing planets and mosquitoes, h is small, dramatizing the fact that quantum behavior is elusive and took delicate technology and precision to explore it when the time came a century + ago.

In short, h is the fundamental action dimension "atom" of our present description of the world. It didn't come from anyplace: our world comes from it.


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