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Re: [Phys-L] Higgs in a HS physics class

On 07/26/2012 02:47 PM, wrote:
I'm considering addressing the Higgs discovery in my HS Intro Physics class this
year. I don't want to take a huge chunk of time, but the news coverage makes it
an interesting opportunity.

One possibility is to have the students work through a newspaper or popular
science article.

Any alternatives or other suggestions?

Here's my take on this:

1) All the youtube videos I've seen fall into the category of
"being outside looking in". That is, the student gets to
/talk/ about physics without actually _doing_ any physics.
I suppose this is better than nothing ... but I find it quite
unsatisfying. Talking about food is not the same as actually

2) As a related point, an analogy about skiers who sink into
the snow, or don't sink in, is not broadly useful. It's not
an idea that you can use again and again.

The same two criticism apply to all the newspaper articles and
"popular" magazine articles I've seen.



In the introductory course, I would start by saying "There are
about 12 things you need to understand before you can have any
clue what the Higgs field is or why it is important. Some of
those things are within the scope of this course, although some
of them are not. You wouldn't want me to explain everything all
at once, but we can pick one idea -- one piece of the puzzle --
and figure that out. Even better, let's pick an idea that is
useful /in general/ ... useful for solving lots of problems, not
just for explaining the Higgs field. This illustrates yet again
the power and elegance of physics.

Ideas on the list include:
*) Symmetries in general.
-- The connection between symmetries and conservation laws.
Noether's theorem.

Example: Gauge symmetry. Here is a DC voltmeter. We want
to measure one voltage, so why does this thing have two wires,
not just one?

-- It's only a symmetry if you pick the gauge once and use it
consistently. If you pick a different gauge in different
places, that's not necessarily wrong, but you need to be
careful. Weird and interesting things are going to happen,
and you need to do some work to account for them.

*) Spontaneous symmetry breaking.

Example: Consider an empty roulette wheel with no markings.
It has an N-fold radial symmetry. N=37 in Monte Carlo and
N=38 in the United States. Similarly the ball is as symmetrical
as it possibly could be. However, there is no symmetrical way
of putting the ball into the wheel. The ball lands in *one*
of the pockets, breaking the symmetry. The key idea here is
that the statement of the question is completely symmetrical,
but the answer is not symmetrical.

Less-good example: A simple coin toss raises the same issues,
but in a less obvious way, so this is not such a good pedagogical

Example: Suppose there are 1001 students. Somebody has
divided them into three categories, A, B, and C. You are
told that 33% of them are in each category. You would like
to know the actual number of students in each category,
rather than the percentages. You quickly discover that the
33% number suffers from roundoff error, but 33% is all the
information you have.
a) There are surprisingly many ways of assigning integer
numbers of students to each category, consistent with
rounding off to 33% in each category.
b) There is no symmetrical assignment. Putting 333 in
each category is not viable. Putting 334 in each category
is not viable.

Once again the key idea is that the statement of the
problem is completely symmetrical, but the solution is
not symmetrical.

Example: Ferromagnetism. An iron needle above the Curie
point is completely symmetrical end-to-end. Below the
Curie point it will become spontaneously magnetized. The
symmetry will be broken.

*) Goldstone bosons.

In the aforementioned ferromagnet, there are a lot of spins
all lined up. This explains the magnetic field. Now if you
disturb some of those spins, they will precess around the local
magnetic field created by the neighbors. Conversely the neighbors
will precess around the field created by the disturbed spins.
If you work through all the details, you find there will be a
/spin wave/. If you quantize this, the quanta are called magnons.
These are an example of /Goldstone bosons/. Note that if there
were no symmetry breaking, there would be no local magnetic
field, and therefore no spin waves. This is the hallmark of
a Goldstone boson: It existence depends on a broken symmetry.

The Higgs boson is in this category: It is a Goldstone boson.

*) The origin of mass.

This is beyond the scope of the typical high-school physics,
course, or even the typical first-year college physics course,
but it well within the scope of the second-year course. In
any case, it's interesting.

Consider an electromagnetic wave in an ordinary rectangular
waveguide. There is a cutoff frequency. More generally,
there is a nontrivial dispersion relation, i.e. a nontrivial
relationship for ω as a function of k. As Feynman was fond
of saying, the same equations have the same solutions ...
and the dispersion relation for a waveguide is exactly the
same as for a massive scalar particle. The cutoff frequency
corresponds to the mass, i.e. the energy is nonzero when the
momentum is zero.

So ... even though a photon in empty space is a massless
particle (moving in three dimensions), a photon in a waveguide
is for all practical purposes a _massive_ particle (moving in
one dimension).

Quite generally, you can give particles mass by postulating
the existence of some extra dimension(s) and doing something
funny with the wavenumber in the extra direction(s). String
theory makes heavy use of this, but the idea is not limited
to string theory.

Things get even more interesting if the waveguide cross-section
is rectangular, not square. Then the "a" polarization has a
different mass from the "b" polarization.

In the limit where we have two parallel conducting plates, the
wave can propagate in two dimensions. It has two polarizations,
one of which has a mass while the other is massless.

This explains -- roughly -- how the Higgs field can couple in
such a way that some pieces of the other fields acquire mass
while other pieces (such as the photon) remain massless. It's
just an analogy, but it's a lot more meaningful and useful than
the skier analogy.

Also ... you can create a nontrivial dispersion relation (i.e.
mass, in effect) by postulating that the particles are hopping
along a lattice, rather than moving through free space. This
has tremendously great relevance to solid state physics, with
all that implies for modern technology.


There's a lot more that could be said about this.

I like this because rather than letting the Higgs discussion take
time away from useful physics, it becomes an additional motivation
for doing physics that we were going to do anyway.