Let's cut to the chase: How does the Higgs
field "give" particles mass? (and to be clear,
we're talking about the Higgs field and NOT
the Higgs Boson, which is merely an excitation
leftover after the process we're about to
explain. But I digress…back to mass!)
To begin, we need to know what we even mean
by "mass" - so we'll head the other direction
and talk about what it means to be massless:
This may sound crazy, but the defining feature
of any particle without mass is that it travels
at the speed of light. In fact, if we're honest
it should really be called the "speed of massless
particles," but since the first massless particles
we knew about were photons of light, the name
has stuck.
Anyway, the point is that all massless particles
travel 300 million meters every second. The
details of this are explained by special relativity,
but simply put, it's physically impossible
for a massless particle to NOT travel at 300
million meters per second. They can travel
in a straight line or bounce off of things
and change direction, but the speed of a massless
particle never changes.
And so mass is just the property of NOT HAVING
TO always travel at the speed of light. As
a side effect, this also means not being ABLE
to travel at the speed of light, but the key
is that particles with mass are lucky enough
that they get to travel at ANY speed they
want – as long as it's slower than light.
The amount of mass something has just tells
how hard it is for it to change from one of
these speeds to another.
Now, in Part I we mentioned that if there
were no Higgs field in the Standard Model,
ALL particles should be massless and thus
travel at the speed of light. But you and
I and swiss cheese clearly have mass, because
we have the beautiful luxury of being able
to sit still.
So how does the Higgs field help us do that?
Well, while massless particles can only travel
at the speed of light, they ARE allowed to
bounce off of things. Things like particles,
which are really just excitations in a quantum
field. For example, the electron field is
more concentrated at certain places called
"electrons" - and everywhere else is "empty
space". But the Higgs field is unusual in
that it has a high value EVERYWHERE – and
to be clear, this high value is NOT the famous
Higgs Boson - that's an extra excitation in
addition to this already elevated field. But
because the Higgs field has this everywhere
non-zero value, any particle that CAN interact
with it is pretty much bouncing off of it
all the time.
And if a massless particle bounces back and
forth and back and forth (or, since it's quantum
mechanics, does both at the same time), then
even though in between bounces it travels
at the speed of light, when you add everything
up it LOOKS like the particle is going slower
than light. Even... like it's not moving!
And since only things with mass are allowed
to not move, our massless particle now looks
and acts like it has mass. Well done, Higgs!
What's more, the Higgs field can even interact
with its own excitations, which is to say,
it can give mass to the Higgs Boson, too.
Actually, the Higgs field likes to interact
with itself so much more than with the lowly
electrons and protons that make us up, that
the Higgs Boson has a great deal more mass
– and that's part of why it's been so hard
to find. But we shouldn't complain, because
even though the Higgs has given us a lot of
trouble and only a little bit of mass, at
least we have mass, which allows us the simple
pleasure of not moving.