Despite lacking mass, particles of light called photons do carry momentum—enough to potentially carry a spacecraft from Earth around the solar system. But how do we calculate this momentum?
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The discovery of the photon, the basic unit of light, did not come until the earliest years of the 20th Century, but with it would come a whole new field of research: quantum physics.
It is perhaps surprising to learn that despite lacking mass, photons do possess momentum. In fact, a beam of photons intense enough could close a door or, say, knock a person off their feet. Of course, this would require an incredibly intense and collimated beam of light.
Despite its limited influence, the momentum of light is suggested for a wide range of uses. Arguably, one of the most exciting is in the field of space exploration.
In space where there is no resistance to be countered or friction to diminish the force of a push, the momentum of photons has been suggested as a propulsion mechanism for space vehicles equipped with a large solar sail, catching photons from the sun just as mariners once used the push of the wind.
In the vacuum of space, the sails made of large light mirrors would gradually recoil and could actually carry a spacecraft through the solar system.
Of course, all this leads to the joint questions: how did we discover photons have momentum, and how can we measure photon momentum?
The Origin of the Photon
As the 1900s rolled around, the debate between researchers over whether light was a particle or a wave had seemed over, with the consensus being that it is a wave. That would be complicated when Einstein, inspired by the work of German physicist Max Planck, discovered the photoelectric effect.
Planck believed that light came in discrete units of energy or quanta, with Einstein confirming this in 1905 when he discovered that incident light on metal would cause the release of photons.
These photons would only be released if the wavelength and frequency of the light were at a certain value. It didn’t matter how much low-frequency light was incident on metal, it would not release electrons. Just a tiny amount of high-frequency light and electrons would immediately be released, however.
To realize how counter-intuitive this is, imagine a ping-pong ball placed in a bucket, analogous to an electron around an atom of metal. It doesn’t matter how much water fills the bucket, the ping pong ball will not spill over the rim unless the water is at a certain temperature.
The discovery of quanta of energy would of course lead to the development of quantum physics, which would subsequently deliver a raft of counter-intuitive results, including the revelation that light is neither particle nor wave, but in reality something with properties of both.
What the photoelectric effect also demonstrated was that the energy of photons, a term that wouldn’t be widely used for these units of light until 1926, was directly tied to their frequency and wavelength. This gave rise to the equation: energy equals Planck’s constant (h)times the speed of light (c ), divided by wavelength (λ), or E = hν = hc/λ.
However, this and the photoelectric effect have another consequence. The fact that photons have energy and a finite speed also means that they have momentum, despite being completely mass-less. We can calculate the momentum of a photon (p)³ therefore with the equation p=h/λ=E/c.
How To Measure Photon Momentum
Photon momentum is tiny, even when photons are in tremendous numbers, so measuring it is tricky. One potential method to measure it is using the photoelectric effect itself; it is momentum, after all, that knocks electrons out of the metal it falls upon. That means that every time you walk through an automatic light-activated door that functions thanks to Einstein’s photoelectric effect, you are measuring the momentum of photons.
Perhaps the most famous experiment to determine the momentum of photons comes from Compton scattering, which works on the basis that energy and momentum both are a conserved quantity. The recoils of x-ray photons with decreased energies from electrons in materials were visible due to the fact these photons have a short wavelength and large momentum. The momentum is transferred when they collide with electrons, a relatively light fundamental particle.
Compton scattering helped prove the Compton effect, which showed that the momentum of photons is given by p=h/λ. As Planck’s constant (h) is so small, this equation also demonstrates why the momentum carried by photons is so minuscule, also explaining why electrons recoil from photons, but your bedroom mirror does not when you open the curtains or turn on the light.
Comets have tails of gas and dust that grow when passage close to the sun causes icy material to sublimate, turning straight from gas to dust and escaping from its icy nucleus and surface. These tails are generally thought to trail the main body of the comet, but the truth is somewhat different. The tails of comets actually always point away from the sun. This is because they recoil from photons from our central star when these photons confer momentum to them.
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References and Further Reading
The Photoelectric Effect, Britannica, [https://www.britannica.com/science/photoelectric-effect]
Photons, Britannica, [https://www.britannica.com/science/photon]
Photon Momentum, Introduction to Quantum Physics, Lumen Physics, [https://courses.lumenlearning.com/physics/chapter/29-4-photon-momentum/]
Compton Scattering, MIT, [https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/lecture-notes/MIT6_007S11_lec37.pdf]
Comet Tails, Case Western University, [http://burro.astr.cwru.edu/Academics/Astr221/SolarSys/Comets/tails.html]