I understand that it’s impossible to bring a photon to a state of rest, therefore impossible to collect them into a cup to weigh them and calculate their mass. A guy in a pub explained to me, quite smugly, that photons are just expressions of energy and that’s that. From my understanding solar sails would be just large surface areas being hit by photons, pushing the spacecraft in a desired direction, just like normal ship sails are being pushed by wind. But air particles do have mass. How could photons push the spacecraft if they don’t weigh anything?
In: Physics
Momentum.
Normally we think of momentum as a property of mass. For low speed objects, momentum is the m*v, the mass times the velocity.
Which makes sense. A larger object going the same speed will hit harder. But also, the same object going faster will hit harder.
Momentum.
Whatever the momentum of the striking object, that gets transferred to the object being struck.
So if 2 kg of air molecules hits the ship sail going at 5 m/s, they give the ship 10 momentum units.
However, momentum gets weird when you get things going at or near the speed of light, or when things get smaller than atoms. (Technically the weirdness was always there, just too small to matter; but these are the situations where it does matter).
Now, let’s talk photons.
A photon has two properties – energy, and spin. Spin doesn’t matter for this, so we’ll ignore it. Energy determines everything else about the photon – with just the energy, you can calculate the momentum, the frequency, and the wavelength, each with a different formula.
For momentum, it’s e/c, the energy divided by the speed of light. The speed of light is 299,792,458 m/s, so a photon with 299,792,458 Joules of energy has 1 momentum unit.
To recap, that means a photon with 299,792,458 Joules will hit as hard as a 1 kg ball moving at 1 m/s.
This has the property that it adds nicely. Meaning if you hit an object with two 1-Joule photons, it’s the same as hitting with one 2-Joule photon. Meaning if you have all this energy you want to use to send photons, it’ll be the same whether you send as 1, or 1 million, or 1 googolplex photons, the effect is the same.
As to the energy photons have, well, they can have almost any energy. A red photon has 3*10^-19 Joules, and a blue photon has about 6*10^-19 Joules. The invisible ones flying through space (known as the CMB) have even less; meanwhile, x-rays have more, and some photons have even more. There’s not much to constrain what they can be other than “more than 0, less than infinity”.
Photons do not have a rest mass, otherwise they could not travel at the speed of light. They do have a momentum, defined by the most famous equation ever(‘s extended form) E^2 =c^2 p^2 +(m^2 c^4 ). This means that the energy of a photon equals the momentum of the photon times the speed of light. As a result, they can impart that momentum on objects when they reflect or are absorbed by them. So in reality solar sails are something that can exist. And not in theory, but in practice. As in we’ve made them. [and they work](https://en.m.wikipedia.org/wiki/IKAROS).
Solar sails do function (as described by other comments). In 2018 was some theorizing around ‘Oumuamua being an alien solar sail, which led to [this interesting preprint](https://arxiv.org/abs/2105.09435) against interstellar travel with solar sails. From the abstract:
>even if we neglect slowing (and damage) by interplanetary material, there exists an effective terminal velocity beyond which the sail barely accelerates. This velocity is much lower than the relativistic speeds proposed […]
‘Oumuamua would take two million years to cover the distance to the nearest extrasolar star (at just 4.22 light years distance).
Mass and energy are equivalent, meaning photons have momentum. They can then transfer that momentum to objects.
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