a while back I was teaching physics in
California I got to class and I was all
like hey class you want to hear a
physics joke yeah okay totally does
light hold mass I don't know it does it
no it's not even Catholic oh man she
went to the beach it is really totally
lame but wait doesn't light really have
mass it should
it's called momentum so it's gotta have
mass it adds momentum so it must have
mass whoa hey everyone just calm the
heck down you see the worst part of all
this wasn't that my joke bombed it was
that I actually managed to confuse
people by telling it my students had
read that light has momentum and they
were right light really does have
momentum but then I come to class and
I'm all like hey guess what light has no
mass now my students are thinking to
themselves dude but P equals MV in other
words if momentum equals mass times
velocity how could light which has no
mass ever have momentum well I had to
break it to my students that P equals MV
isn't really accurate for things that
travel close to the speed of life for
things going that fast you have to use
special relativity I don't want to waste
a lot of time talking about special
relativity in this video so you're just
gonna have to take my word for it that
the rules of special relativity allow
for a loophole this loophole provides a
way for massless objects to have
momentum all right so the bad news is
that we cannot use P equals mV
to find the momentum of a photon the
good news is that the formula for the
momentum of a photon is simple the
momentum of a photon equals H over
lambda H is Planck's constant 6.6 to 6
times 10 to the negative 34
joule-seconds lambda is the wavelength
of the light in meters be careful don't
use nanometers you have to convert to
meters
the momentum of a single photon is going
to be extremely small that's why it
doesn't feel like we're getting pushed
on very much when light shines on us
but theoretically if you had a big
enough solar sail the light bouncing off
of that solar sail could propel it
forward due to the impulse imparted by
the momentum of the light okay so very
long story short you should never ever
use P equals MV to find the momentum of
a photon to find the momentum of a
photon you should always use momentum
equals H over lambda