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The Higgs particle: a useful analogy for physics classrooms
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2010 Phys. Educ. 45 73
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2. FE A T U R E S
The Higgs particle: a useful
analogy for physics classrooms
and Ramon Cid2
Particle Physics Departament USC, 15706 Santiago de Compostela, A Coru˜na, Spain
IES de SAR, 15702 Santiago, A Coru˜na, Spain
E-mail: email@example.com and firstname.lastname@example.org
In November 2009, the largest experiment in history was restarted. Its prime
target is the Higgs particle—the last remaining undiscovered piece of our
current theory of matter. We present a very simple way to introduce this topic
to senior secondary school students, using a comparison with the refractive
index of light.
The standard model
The standard model of particle physics is the best
theory that physicists currently have to describe
the building blocks of the Universe. It is one of
the biggest scientiﬁc achievements in twentieth-
The standard model describes the Universe
using six quarks and six leptons. There are
four known interactions, each mediated by a
fundamental particle, known as a carrier particle.
In the 1970s physicists realized that there are
very close ties between two of the four fundamen-
tal interactions—namely, the weak interaction and
the electromagnetic interaction.
The two interactions can be described within
the same theory, which forms the basis of the
standard model. This ‘uniﬁcation’ implies that the
interaction-carrying particles have no mass.
We know from experiments that this is not
true. To solve this problem several physicists
proposed the existence of a new ﬁeld with its
corresponding quantum particle, the Higgs ﬁeld
and the Higgs particle.
The Higgs particle has been nicknamed (by
Nobel Prize-winning physicist Leon Lederman)
the ‘God particle’ because of its importance to
the standard model. Detecting this particle is
one of the Large Hadron Collider’s (LHC’s) main
purposes. The LHC is the world’s largest and
highest-energy particle accelerator, intending to
collide opposing particle beams of either protons
at an energy of 7 TeV per particle or lead nuclei
at an energy of 574 TeV per nucleus. It lies in a
tunnel 27 km in circumference, as much as 100 m
beneath the Franco–Swiss border near Geneva,
The mass of the particles
Why do particles have mass? Why are the masses
what they are? Why are the ratios of masses what
In the early 1970s, Peter Higgs, Franc¸ois
Englert, Robert Brout, Gerald Guralnik, Dick
Hagen and Tom Kibble independently proposed
that the Universe is full of a ﬁeld later called the
Higgs ﬁeld. Disturbances in this ﬁeld, as particles
move through it, cause objects to have mass. It is
important to say that the original basis of Higgs’
work came from the Japanese-born theorist and
2008 Nobel Prize winner Yoichiro Nambu.
Different ways of explaining this mechanism
to a general audience have been proposed. For
example, the discrete units which stir up the ﬁeld,
Higgs particles, act like a kind of cosmic molasses
0031-9120/10/010073+03$30.00 © 2010 IOP Publishing Ltd PH Y S I C S ED U C AT I O N 45 (1) 73
3. X Cid and R Cid
which ﬁlls all of space. As objects move through
space they have to ‘wade’ through these Higgs
particles that ‘cling’ to them, causing a drag that
shows up as mass.
Another analogy often cited describes it well:
imagine you are at a party. The crowd is rather
thick, and evenly distributed around the room,
chatting. When a big star arrives, the people
near the door gather around him. By gathering
a fawning cluster of people around him, he has
gained momentum, an indication of mass. He is
harder to slow down than he would be without the
crowd. Once he has stopped, it is harder to get him
Further analogies have been presented, but we
prefer one that is closer to physics.
Comparing refractive index and mass
When light, composed of photons, passes through
a transparent material such as water or glass, its
velocity changes according to the refractive index
of the material. If a beam of light enters the
material at an angle, it is bent or refracted as a
result of this decrease in velocity.
The reason why photons are slower when
passing through a transparent material is the effect
of electrical ﬁelds surrounding the electrons and
nuclei of atoms in the material.
The photons are slowed down by interacting
with these electrical ﬁelds. The effect is greater in
materials such as water and glass than it is in air, a
result of their greater relative densities.
The ﬁelds almost act like ‘friction’ on the
photons, decreasing their transmission velocity. It
is like trying to walk through a muddy ﬁeld.
A measure of how much photon speeds are
reduced is given by the refractive index of the
material. The refractive index (i) of a material
equals the speed of light in a vacuum (c) divided
by the speed of light in the material (v):
i = c/v.
A very important detail is that the speed of light in
a transparent material depends on the wavelength
(i.e. momentum) of the photons. For instance,
consider visible light in water, the refractive
indices for the different colours are:
1.337 1.333 1.331
‘Yellow’ photons travel through water faster than
blue, and red photons are even faster. You
could say that blue photons have greater difﬁculty
moving in water than yellow and red photons. You
could say that blue photons behave as if they have
more ‘inertia’, i.e. more ‘mass’. Refractive index
gives a measure of the interaction between photons
and a material medium through which they travel;
it could also be considered an ‘index of mass’,
since the bigger its value the lower the photon
In a vacuum, all photons travel with identical
speed but, if the Universe were ﬁlled with water,
photons corresponding to different wavelengths
would travel with different speeds.
As has been said before, they would appear to
have ‘different masses’. So you would pass from
a symmetrical situation to a nonsymmetrical one.
This is what in particle physics is called symmetry
Now we are ready to establish our compari-
The standard model suggests that all particles
were massless just after the big bang but, as the
Universe cooled and the temperature fell below a
critical value, an invisible ﬁeld called the ‘Higgs
ﬁeld’ appeared, ﬁlling all space. You could
also say that the Higgs ﬁeld was created at the
beginning of the Universe, but it only showed its
inﬂuence once the Universe cooled down enough.
The massless symmetry of particles was broken.
Unlike magnetic or gravitational ﬁelds, which
vary from place to place, the Higgs ﬁeld is exactly
the same everywhere. What varies is how the
different fundamental particles interact with the
ﬁeld and are given mass. Of course, other kinds of
interaction, such as the electromagnetic, weak or
strong interaction may also contribute signiﬁcantly
to the resulting mass. Moreover, the degree of
resistance of the Higgs ﬁeld is different depending
on the fundamental particle, and this generates,
for example, the difference in mass between an
electron and a quark.
Now, suppose a quark or electron is moving
(making up composite particles such as protons,
neutrons or various atoms) in a uniform Higgs
ﬁeld. If these atoms (or molecules) change their
velocities, that is, if they accelerate, and if the
Higgs ﬁeld exerts a certain amount of resistance
or drag, then this is the origin of inertial mass.
74 PH Y S I C S ED U C A T I O N January 2010
4. The Higgs particle: a useful analogy for physics classrooms
The situation is similar to refraction, dis-
cussed above. The Higgs ﬁeld acts as a ‘transpar-
ent material’ with a speciﬁc ‘refractive index’ for
each kind of fundamental particle. In this way, the
Higgs ﬁeld gives each different particle its charac-
ter, what physics calls ‘mass’.
For instance, when a proton interacts with an
electron, it undergoes an effect almost 2000 times
smaller than the electron, because the ‘index’ in
the Higgs ﬁeld for protons is almost 2000 times
The analogy only works if you consider light
as particles, and not as waves. The refraction of
light happens only in a material medium, which
the Higgs ﬁeld is certainly not. Provided these
limitations are made explicit and clear, we think
the refraction analogy can help secondary students
to understand the Higgs ﬁeld.
From a quantum point of view, however,
you can only stir up the Higgs ﬁeld in discrete
units. The smallest possible disturbance is due
to a Higgs particle, or more precisely, a Higgs
boson. ATLAS and CMS are general-purpose
LHC detectors designed to see a wide range
of particles and phenomena produced in LHC
collisions. The Higgs boson, possibly hundreds of
times heavier than a proton, could be created in the
proton collisions in the centre of their detectors.
More than 4000 physicists from about 40
countries will be using the data collected from both
complex detectors to search for Higgs particles. It
is widely believed that they exist or at least some
sort of Higgs-like particle which plays that role.
But there is no real guarantee that the LHC will
ﬁnd it. It should ﬁnd it, at least in the simplest
models, but the simplest models are not always
Anyway, following Professor Hawking, even
a failure would be exciting, because that would
pose new questions about the laws of nature. So, if
it turns out that we cannot ﬁnd the Higgs particle,
this will leave the ﬁeld wide open for physicists
to develop a completely new theory to explain the
origin of particles’ mass.
The authors would like to thank Abraham Gallas
Torreira and Diego Mart´ınez Santos for their
helpful comments and corrections to this article.
Received 28 August 2009, in ﬁnal form 15 October 2009
Taking a closer look at LHC http://lhc-closer.es
High school teachers at CERN teachers.web.cern.ch/
Detector CMS cmsinfo.cern.ch/outreach/
Detector ATLAS atlas.ch
Xabier Cid Vidal graduated in physics in
2007. He is currently doing his PhD on
experimental particle physics, taking part
in the LHCb collaboration at CERN with
the University of Santiago’s group.
Ramon Cid graduated in physics and
chemistry and has taught physics at
secondary school since 1980. He
participated in the HST programme at
CERN in 2003. He has coordinated
various European teaching projects and
several annual ENCIGA (Association of
Science Teachers of Galicia) science
January 2010 PH Y S I C S ED U C A T I O N 75