The momentum
of Light

Michele Diego

Now, how can light, which has no mass, have momentum and, therefore, be able to push an obstacle away?

It is night. A man on a hill is holding a lantern ready to be lit. On the opposite hill, another man, also holding a switched-off lantern as well, is waiting. As soon as he will see the other’s lantern switching on, he will light his up. The first man is Galileo Galilei, the second is his assistant. The goal of this operation is to measure the speed of light. Galileo thinks he will be able to measure the interval between the moment in which he will turn his lantern on, and the moment in which he will see the light coming from the one held by his assistant. Later, he will only need to know the distance between the lanterns to calculate the speed of light. It is a simple and effective idea, on paper, yet impossible to accomplish with the instruments of the time. If, for example, we suppose that the two are at a distance of two kilometers, then the light would take a thousandth of a thousandth of a second to travel the whole way – an unthinkable time to record if using human reflexes only.
Today we know that the speed of light in a vacuum is about three hundred thousand kilometers per second. Moreover: we know that nothing is faster than light. This limit did not derive from an empiric constatation, such as that we have yet to find an object traveling faster than light, but from the theoretical calculation contained in Einstein’s Theory of Relativity. Indeed, in his work, the German genius demonstrated how, in the Universe, there is a speed that cannot be exceeded. Moreover, objects with mass cannot even reach a similar speed. Light, having no mass, can move exactly at that limiting speed, which is why we define it as the ‘speed of light’.

Well, what is light, precisely? We commonly identify it as something that allows us to see the world around us. In reality, visible light is only a small portion of the entire spectrum – or, more precisely, the electromagnetic spectrum. This is because we have X-rays, radio waves, microwaves, Gamma rays, and more that are always part of it: they move at the speed of light, they are just not visible to our eyes. What separates X-rays, radio waves, and the other types of light we have mentioned, is the energy of the particles composing them, called photons. Very energetic photons create Gamma rays, and less energetic ones give us radio waves; visible light is made of photons with “average” energy, so to say. In short, we can imagine photons as particles transporting a certain amount of energy, and they compose light as we know it. However, we said that light has no mass. Therefore, photons have no mass: they are particles transporting energy, with no mass – we must keep this in mind, being it fundamental to understanding the rest.
Obviously, different technologies that use light exploit different photons to obtain different outcomes. Photography is basically the impression of matter through visible light. X-rays use photons that have little interaction with biological matter and, passing through it, allow us to “see” our inside. Microwave ovens in our kitchens use photons capable of exciting water molecules – which is why the food heats up, but the plate does not. Radio waves can travel very long distances without being absorbed by matter, so they are fundamental in telecommunications. Other technologies, for example, optic fibres, satellite communication, some medical treatments, etc. use other photons with different energies.
However, there are some more recent technologies that do not directly exploit photons’ energy, instead, they use their Quantity of Motion or momentum. So, what is the ‘momentum’ of an object? Intuitively, we can say that an object’s momentum is greater the more it is able to push an obstacle away. Therefore, a bicycle moving at 50 kilometers an hour, has less momentum than a car travelling at the same speed. In turn, a car traveling one hundred kilometers an hour has even more momentum than if it were travelling at fifty kilometres. With these simple examples, we can already recognise two fundamental aspects of momentum: it depends on an object’s speed and mass. In classic physics, indeed, momentum is precisely defined as the mass of an object times its velocity. Now, how can light, which has no mass, have momentum and, therefore, be able to push an obstacle away?
Once again, the answer comes from Einstein’s Relativity. In his calculation, the definition of momentum gets replaced by another, which includes the previous, and extends it, making it more generic, making it also valid for objects moving at an extreme speed, as does light. In the new Einsteinian definition, momentum is linked to the energy of an object, and not necessarily to its mass and speed. We have said that photons composing light have different energies and, therefore, although massless, still have momentum. Clearly, a single photon has very low energy, consequently, its momentum is small. The push we receive when a single ray of light hits us is obviously infinitesimal; nobody ever felt the pressure of solar light pushing them on their sun lounger when resting on the beach. Nevertheless, this pressure exists and can be used for various purposes, some of which are very futuristic.
A first example is the so-called optical tweezers, which are highly focalized laser beams capable of “imprisoning” small particles within, using the force impressed by light. In this way, it is possible to manipulate viruses, bacteria, living cells, DNA fragments, or small metallic particles, as you would do with tweezers. Another quite futuristic application uses the momentum of photons to push a new generation of spaceships forward. The idea is to build ships equipped with “sails” made of reflecting material on which photons will slam, pushing them. Something similar to what happens to a sailboat pushed by the wind. As much as this technology is in its earliest days, we already have examples of successful applications. Ikaros is a Japanese space probe [1] that used a nearly 200 squared meters sail to exploit the propulsion of solar photons in an interplanetary journey. In 2010 Ikaros took off from Earth and passed Venus, continuing its space navigation. The last contact with Ikaros was back in 2015. LightSail 2 is a smaller spaceship engineered by the non-profit organisation Planetary Society [2]. With its 30x10x10 cubical centimetres, it displays a 32 squared meters sail. For three years it has orbited Earth using solar light at an altitude of 720 kilometres (as a reference, think that the International Space Station, orbits at 400 kilometres of height). In 2022, it returned to the atmosphere after travelling for eight million kilometres.

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