# Does light weigh anything?

Does light have a mass?
12 June 2018

## Question

Does light weigh anything?

Chris Smith put this question about light to materials scientist Jess Wade...

Jess - Yeah, this is great. I think firstly we need to think about light in two ways. We need to think about it as it being a wave which we’re all quite happy with, which reflects and kind of bounces off things and defracts and gives us great colours, and then we also need to think about it as being a particle. And then this is quite complicated and it comes from some great work done at the beginning of the 1900s to show that light comes to us as these tiny little packets of energy called photons, and photons move in waves and that’s exciting.

But these photons we define in physics, and I hope Fran agrees with me. We define that photons have no mass right?

Fran - Yes.

Jess - So photons don’t have any mass but they’re travelling incredibly quickly, at unsurprisingly…

Chris - The speed of light.

Jess - … the speed of light.

Chris - Is that why we say they have no mass because they couldn’t travel at the speed of light they wouldn’t have enough energy, because it would take an infinite amount of energy to travel at the speed of light if they weighed anything?

Jess - Exactly that. And it helps us out with an awful lot of equations that photons don’t have any mass.

Chris - So is it fudge, or is it that really the case?

Jess - I think the thing that makes everyone think photons should have mass is, we always say: E = mc squared. And photons have this phenomenal amount of energy (E) so therefore they should have some tiny amount of this m to give them this thing. But what we’re not actually thinking about is E = mc squared only really holds when you have no momentum, so = mc squared holds an invariant frame when the momentum is zero. So, in a photons case, all of its energy is coming from its momentum and that gets us round whether you think it’s fudging or not.What we can say, and what I think Fran might chip in with is photons behave like they have mass. So photons do - am I right?

Chris - They can give things a push can’t they? Because there’s this YORP (the Yarkovsky–O'Keefe–Radzievskii–Paddack effect) where light hits things…

Jess - Classic. Classic effect.

Chris - Well it’s well known. It pushes asteroids around in the solar system, and probably dislodged the asteroid that did the dinosaurs by giving them a nudge because that light falling on things gives them a push.

Fran - Yeah. So they have a momentum but they don’t have mass, which in general relativity is possible. I was just going to chip in on the is it a fudge question? People actually do experiments to try to work out if the photon might have a really really tiny mass. Because you can never rule out maybe it’s got a mass that’s just like one billion billion billionth of the mass of an electron or something. I think the limits lower than that now, and the limits are very very small at this stage.

Jess - It sounds like the beginning of your PhD: this is farcical, we don’t think it exists. Go and have fun for four years.

Fran - but it literally is in the beginning of my PhD.