eli5 – if photons have no mass, how can they be used to push hypothetical “solar sails”?
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Momentum (aka oomph) was originally defined as mass X velocity. The assumption being that you have more “oomph” is you are faster or heavier.
Modern physics finds that it is more sensible to define “oomph” with a different equation. One reason for this is the fact that photons (which have no mass) clearly have oomph; they are able to push stuff (albeit only a little). So, momentum isn’t actually defined as mass times velocity anymore.
They don’t have mass but they have momentum.
It is possible because the mass was defined to be energy by einstein.
Solar sails are not hypothetical. IKAROS launched in 2010 used solar sales and practically demonstrated they work.
The answer is that photons have momentum.
The momentum is what is preserved in collisions. That is what Newton’s laws of motion are about.
In our everyday life momentum is mass * velocity. Mass in this context is the rest mass or invariant mass and it is the only thing we need to care about at a speed low compared to the speed of light.
At high-speed what is called relativistic mass is also relevant. A photon does have a relativistic mass.
The idea of mass–energy equivalence from relativity is to some degree known to most people that is what the E =mc^2 equation stands for.
That equation is for an object at rest for a moving object the formula i
E ^2 = ( m * c^2 )^2 + (p * c)^2
p is the momentum. So even if the rest mass m is zero the energy of the photons results in momentum this is called the Energy–momentum relation.
So rest mass is not required for momentum, mass is just what results in the momentum at the speed we are used to on earth.
You need some energy to push the sail. Things that have mass slow down when they hit the sail. Light doesn’t do that. How much energy light has depends on how much there is and the frequency (a little bit like how fast the wind in the sail is). When the light bouces off a solar sail it has a lower frequency. The light’s colour has shifted a little bit to the outer part of the rainbow.
We think that only things with mass can push when hitting something because we are used to everyday interactions with massive objects, including ourselves. Turns out photons can pack some punch too, because they have energy, and Einstein proved that energy is equivalent to mass in a certain sense which is what his famous equation (E = mc2) is all about. The more energetic a photon is (the shorter its wavelength) the more push it has to give.
I’ve copied a comment I made a while back because I think it’s a good explanation but bear in mind there are some errors.
**tl;dr:**
My understanding is that we know that photons have Energy, Velocity, and Frequency. We know that Energy can be represented as a product of Velocity and Something1 or Frequency and Something2. Energy’s units include mass, but Velocity’s and Frequency’s don’t, so the units of Something1 and Something2 must include mass. Well, Something1 is called Momentum in other contexts, so to be consistent it must be Momentum here, but expressed differently. Through experiments, we see that it’s just an unavoidable thing in the Universe which helps us to tie things together.
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Well, through experiments, we have determined that there are other properties of a wave or of the universe that come into play. All light with frequency F1 has energy E1, all light with frequency F2 has energy E2, etc., in such a nice way that we can say that there is Something2 is some constant value in the universe that can represent the energy of a photon when multiplied by its frequency. Let’s call this constant Planck’s constant (h-bar). So, E = Frequency * h-bar, and h-bar has units of kgm2s-1.
Through other experiments (not involving light), we see that Energy is Velocity * Momentum, and photons have Energy and Velocity, so they must have Momentum (since physics is supposed to work the same everywhere, more or less). So, their Momentum necessarily has units of Mass, but how? Well, through other experiments (involving light) we see that the Momentum of light can be represented as a product between other things.
Momentum has units of kgms-1 (Mass * Velocity), which can be seen as a product of things with units kgm2s-1 and m-1. Why these in particular? Well, we know that there’s a property of a photon that has units m, so this can fit in nicely. The property in question is the wavelength of light. If we can divide something by the wavelength of a photon, we’ll get something else which, when multiplied with Something, will return Momentum.
Light is a Wave and thus is a Vector because it has Magnitude and Direction. This Magnitude can be represented as 2*pi/wavelength, because Math. This Magnitude has units of m-1, so perhaps this can be multiplied by Something to return Momentum. This mean that Something needs to have units of kgm2s-1 since the Magnitude has m-1. Well, we already know of Something with those units: h-bar. And, through experiments, we see that it’s Momentum is simply h-bar * Magnitude.
What does mass have to do with that!? Momentum is what makes things move.
Things with mass can be thought of as light travelling in a circle, even if it doesn’t spin around to trigger your object recognition and object permanence, it is still energy moving in a direction.
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