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Elegant Universe, The: Einstein's Dream
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Classroom Activities
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Background
Some physicists think there is a unit of matter more fundamental
than what has been experimentally confirmed to date. They think that
everything in the universe is made of tiny vibrating strands of
energy called strings. One feature of strings is that each one
vibrates in a unique way, representing the mass, charge, and spin of
known elementary particles. In this activity, students will use a
rope to simulate a string's vibrational pattern and deduce the
relationship between the mass of an elementary particle and the
vibrational energy of its representative string.
Objective
To learn about a new theoretical fundamental unit—a
string—and explore how its vibrational pattern indicates the
particle it is.
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copy of the "A New Building Block?" student handout (PDF
or
HTML)
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15-foot-long rope (4.6 meters), 1/4- to 3/8-inch in diameter (6.3-
to 9.5-millimeters)
- measuring tape, at least 15 feet (4.6 meters)
- clock or watch with a second hand
- calculator
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Share with students the idea that there may exist a subdivision
of matter more fundamental than the currently confirmed quarks
and leptons. This unit is called a string, and is thought by
some to be the single building block of nature. Tell students
that in this activity they will be exploring one feature of
strings—that different patterns of string vibration
correspond to the different matter and force particles that make
up the universe they see around them.
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Organize students into groups of four and distribute the "A New
Building Block?" student handout and set of materials to each
group.
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Illustrate the process outlined on the student handout for
finding the fundamental frequency. For the fundamental
frequency, the rope twirler's arm motion will be circular, as if
the twirler were playing jump rope. For the first overtone, a
very small, rapid rotary hand motion will need to be applied,
using just the wrist while keeping the twirling loop moving
smoothly. It takes a bit of practice to achieve this.
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Demonstrate the fundamental frequency using the circular motion.
Then demonstrate the first overtone by speeding up the rotation.
Do this by shifting to a rapid small hand motion, until the
twisting loop splits into two twirling loops with a pinch point
in the middle. (This pinch point is known as a node.) Explain
that by using ever-faster hand motions, additional overtones of
the fundamental frequency can be formed.
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Have students do the trials and record their results through the
second overtone. After this point it will be likely that
students will not be able to twirl the rope fast enough to
create a third overtone (up to a point, creating a third
overtone is somewhat easier with a longer rope).
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To close, point out that Einstein's famous equation,
E=mc2, indicates that mass can be viewed as a form of
energy. Have students report which overtone required the most
energy. Ask them to suggest which "strings,"or overtones, might
be more massive.
Choosing a Rope
When choosing a rope for this activity, look for one that will drape
over your hand, not stick out stiffly. Thick, soft ropes like nylon
tend to be easier to twirl than thin, stiff ropes like cotton
clothesline.
In Conclusion
Although string vibration patterns give rise to the distinct
elementary particles, strings are different from point particles in
many ways. One of the most important differences is that strings are
one-dimensional (unlike point particles, which have zero
dimensions), which allows strings to behave in a way that permits
the unification of the four forces. In addition, string theory
offers a conceptual framework for answering questions such as why
matter and force particles exhibit their observed properties.
Present theories currently do not provide this information.
As students twirl the rope faster and faster, the original loop
breaks into first two, then three, smaller loops. These loops are
separated by steady nodes.
Students may notice that as the loop length decreases, the frequency
increases. As students twirl the rope faster, the frequency
increases roughly proportionally to the overtone number. You may
wish to have students pursue the reciprocal relationship between
loop length and frequency.
Explain to students that the frequencies they produce in their
trials are based on several factors—the length of the rope,
the tension of the rope during the trial, and the mass per unit
length of the rope. Different ropes will have different mass per
unit length. Therefore, student results will most likely differ from
the sample results in the chart on the right.
Students will find that it takes increasing effort to twirl the rope
to higher overtones and from this they may surmise that rapidly
vibrating strings are more energetic than more slowly vibrating
strings. Einstein's famous equation E=mc2 shows that mass
is a form of energy. A more massive particle has more energy when
sitting still than a less massive particle. This relationship
explains how a single unit—a string—can account for
particles of very different masses. A more massive top quark would
correspond to a more energetic string (a higher overtone) than a
less massive electron.
See the full set of
String Theory Resources
"The Elegant Universe" activities align with the following National
Science Education Standards.
Grades 9-12
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Science Standard B:
Physical Science
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Structure of Atoms:
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Matter is made of minute particles called atoms, and atoms are
composed of even smaller components. These components have
measurable properties, such as mass and electrical charge. Each
atom has a positively charged nucleus surrounded by negatively
charged electrons. The electric force between the nucleus and
electrons holds the atom together.
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The nuclear forces that hold the nucleus of an atom together, at
nuclear distances, are usually stronger than the electric forces
that would make it fly apart.
Structure and Properties of Matter:
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