# How do Photons Move Solar Sails?

Ok so, this is something that I've been researching for quite some time now and, no matter where on the internet I end up at, no matter how many sources I visit and read, this still doesn't make even a little bit of sense to me and it's actually driving me insane.

Light (or Photons I guess I should so but w/e, same diff) has the ability to move solid objects. It can do this in one of two different ways. The first way is by transferring momentum onto whatever it is that they run into, and the second way is by increasing the kinetic energy of the gas molecules around the object so much, that they move whatever's in front of them outwards.

The second method is the one that I'm very familiar with and understand well. The first method however, is the one that I still can't wrap my head around.

Like seriously, how does this even work anyway? Photons have no mass whatsoever and they don't interact with electrons or the electromagnetic force even a little bit. HOW are they capable of imparting momentum onto solid objects and causing them to move? Is there a transformation of electromagnetic energy to kinetic energy going on here? Do the Photons steal some mass from the Sun and impart it onto the Solar Sail? Is energy being converted into momentum (is that even possible?)? Seriously, what is actually going on here?

There are two misconceptions that you seem to have:

• Photons do not have mass and therefore cannot have momentum.
• Photons do not interact with electrons.

Neither one of these are true.

### Momentum of photons

Photons do in fact have momentum. In regular old Newtonian physics, the relationship between momentum, mass, and velocity is $$p = mv$$. However, this turns out to be a special case that only holds for particles moving with speeds much less than $$c$$, the speed of light. More generally, it turns out that for any particle, regardless of its speed, $$E^2 = p^2 c^2 + m^2 c^4,$$ where $$E$$ is the energy of the particle, $$p$$ is its momentum, and $$m$$ is its mass. From this equation, it should be obvious that so long as a particle has energy $$E \neq 0$$, it will also have momentum $$p$$ even if $$m \neq 0$$.

This is what happens with photons. They have both energy and momentum, and when they impact the solar sail, they transfer some energy and some momentum to it.

### Photons do not interact with electrons

This is also incorrect. In fact, a photon can interact directly with any particle that has charge. In the case of your solar sail, this means that on a microscopic level, each photon interacts with an electron (or a proton) in the sail material, imparting some momentum to it. That electron (or proton) is then displaced from its equilibrium location, exerting a force on the rest of its neighbors, causing them to move in the direction of the original photon; which then causes some momentum transfer to the neighbors' neighbors, and so on.

• Look buddy, imma level with you. I'm an absolute twat when it comes to physics and I can't even recite one third of the periodic table to save my life. I appreciate your answer very much, but do you mind simplifying it just a little bit (and by a little bit, I actually mean so much to the point that a 5 year old could understand it)? Nov 18, 2021 at 18:17
• @CrystalKing A big simplification: photons "are" electromagnetic waves, which means they are traveling oscillations in the electric & magnetic "force fields". Charged particles are accelerated by these force fields. So when the wave arrives at a charged particle, it makes it move. Nov 18, 2021 at 22:13

Photons have no mass whatsoever

This is true, but not relevant. Even though they have no mass, they do have momentum. The general relationship between mass, energy, and momentum is:

$$m^2 c^2 = E^2/c^2 - p^2$$

For $$p=0$$ this gives the famous $$E=mc^2$$, but for $$m=0$$ we get $$p=E/c$$. So photons have momentum that is directly proportional to their energy.

So if a photon of energy $$E$$ is absorbed by an object then, the photon's momentum goes from $$p=E/c$$ to $$0$$, or $$\Delta p_\gamma=-E/c$$. So by conservation of momentum, the momentum of the object increases by $$\Delta p_\text{obj} = E/c$$.

they don't interact with electrons or the electromagnetic force even a little bit

This may be the source of your confusion. Photons certainly do interact with electrons, and photons are the electromagnetic force carrier. So a photon will interact with the electrons or protons in the object's material. This interaction is exactly what leads to the exchange of momentum.

• This is a nice-sounding answer, but it still doesn't tell me what explicitly is happening when an object is moved by a storm of photons. Do the photons transfer some of their energy to the object as kinetic energy? These equations tell me nothing. Also when I said that Photons don't interact with electrons, I meant that they don't spark the electric force that you see from two electrons close to each other that allows for anything to be physically touched. A photon (to my knowledge at least) won't be attracted or repelled by an electron Nov 18, 2021 at 18:11

Let me give you an example of how photons behave with matter in this experiment studying the diffraction of single photons at a time by a double slit. It is the "single photon" that is relevant,

The little dots one sees are the impact of the photons on the screen material. They leave a particle footprint. Hitting the screen material, each photon transfers its momentum and energy to the material, as shown mathematically by the answers. The atoms and lattice of the material interact with the photon either by changing energy levels of electrons and atoms, or various inelastic collisions.

The accumulation of photons from left to right starts displaying the classical light interference pattern.

• But... where do the Photons even get that momentum from in the first place? How someone with no mass have momentum anyway? What actually happens when a Photon hits an object? Nov 18, 2021 at 19:42
• @CrystalKing photons follow the rules of special relativity, as explained in the answers. The algebra of special relativity has to do with four vectors and if you really want to know what is happening you have to understand it hyperphysics.phy-astr.gsu.edu/hbase/Relativ/vec4.html . although galilean transformation work for low velocities, photons because of zero mass have very large velocity c (velocity of light in vacuum) and one has to use four vectors Nov 18, 2021 at 19:55
• Really nice answer. Nov 22, 2021 at 16:18