How can light have momentum if it doesn’t have mass?
Momentum does not require mass!
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Hey Crazies.
I get these comments all the time and I’m tired of responding individually.
I’m making a video instead!
Ok, so, momentum.
The first time students see it, it’s written like this.
The "v" stands for velocity and the "m" stands for mass.
The "p" is short for a Latin word meaning "to go to" or seek.
It’s a nice simple relationship.
You can have more momentum by moving faster or by having more mass.
But momentum isn’t really relevant unless there are at least two objects.
It only matters for these cars if they run into each other.
That’s something you might call a collision for obvious reasons.
We even categorize them based on how much kinetic energy is retained during the collision.
Unfortunately, this gives students all sorts of wrong impressions.
Misconception number one!
These so-called collisions don’t require physical contact.
All that matters is that the objects exchange forces.
Sure, this collision involved physical contact.
But there are many forces in this universe and not all of them require contact,
like Newtonian gravity for example.
Orbits are a kind of continuous collision.
You can model this motion using momentum exchanges and it works.
Besides, if we want to get super technical, there’s no such thing as physical contact.
At least in the way most people understand it.
All contact forces are just complex manifestations of the electromagnetic force.
Are you pushing on something?
That’s just electric repulsion between atoms on the outside of two solids.
Pulling on something?
That’s just electric attraction between molecules in a solid.
Buoyant force?
That’s electric repulsion again, but in fluids instead of solids.
Friction?
Actually, we’re still trying to work out some of the details on that one.
My point is the word "collision" is a very misleading word.
They’re interactions, not collisions.
Misconception number two!
Momentum does not require mass.
This equation is not a fundamental definition.
It’s a special case for slow moving objects with rest mass.
It’s pretty good for things with speeds less than about 10% the speed of light.
Any faster than that and you’ll need the version from special relativity.
This gamma factor adjusts it so it’s more accurate.
Even then, it still only works for objects with rest mass.
Surprise! Light doesn’t have any of that.
So even this equation fails for light.
That doesn’t mean that light has rest mass.
It means the equation sucks.
The one for light looks like this.
But, hold up a second.
If we really want to understand how light can have momentum, we need to answer a better question:
Um... what the heck is momentum?
That’s the one!
When these cars run into each other, they each exert a force on the other.
With Newton’s second law, we could plug in a mass and get an acceleration.
That changes the speeds of each car for as long as that force is exerted,
which is mainly just during the collision.
So can light exert forces on things?
Oh yes, it most definitely can,
although not nearly as much as an object with rest mass.
There is a force on the face of paper from the light in this room.
It’s on the order of nano-newtons.
If you’ve got a really big reflector though like a solar sail, the force can add up.
The light hits the back of the sail and pushes it forward.
If we use Newton’s second law again... wait a minute!
Light doesn’t have rest mass.
This isn’t going to work.
If I’m being completely honest though, that isn’t even Newton’s second law.
Sure, this is the first version students ever see,
but it’s not actually about mass and acceleration.
This is the real Newton’s second law.
Any change in momentum for a single object tells us the force experienced by that object.
So you can think of momentum as the oomph something has.
Light hits the sail and reflects.
The change in momentum results in a force.
Light can exert forces.
Therefore, light has momentum.
No mass required!
Anyway, what was that third thing?
I think it was velocity.
Yeah yeah yeah, that was it.
Misconception number three!
Momentum doesn’t even require velocity.
Light is just an electromagnetic wave, so if light has momentum,
then it stands to reason the electromagnetic field does too.
Hmm.
Remember that weird Poynting vector?
It described the flow of energy in the electromagnetic field?
Well, we’ve already seen that momentum is related to energy for light,
which means this energy flow vector should also give us a momentum.
That doesn’t even require the fields to be changing.
Say we’ve got two big metal plates above and below carrying some charge.
That gives us an electric field.
Now let’s say we’ve got two strong magnetic poles on either side.
That gives us a magnetic field.
The Poynting vector tells us that, as long as we’ve got both fields, we’ve got an energy flow
and so we’ve got a momentum.
That momentum points into your screen in this example.
There’s no moving matter here and the fields are static.
Yet there is a momentum.
And that momentum must be accounted for
at least if we expect conservation of momentum to hold true.
So how can light have momentum if it doesn’t have mass?
Momentum does not require mass.
It doesn’t even require velocity.
This equation is not a fundamental definition.
For fast moving objects, it’s this.
For light, it’s this.
All that really matters is that a change in momentum results in a force.
Light can exert a force.
Therefore, light has momentum.
End of story.
If you’ve got any other questions about momentum, please ask in the comments.
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And until next time, remember, it’s OK to be a little crazy.
The featured comment comes from Arjan Marku who asked:
Can we generate electricity if we pass light through a coil?
Well, yeah.
That’s how a receiving antenna works.
Long straight conductors for the electric field and a circular coil for the magnetic field.
It just isn’t enough current to do much other than receive a signal though.
Anyway, thanks for watching!