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Elegant Universe, The: Einstein's Dream

Classroom Activities


A New Building Block?

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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.

Materials for each team
  • copy of the "A New Building Block?" student handout (PDF or HTML)
  • 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
Procedure
  1. 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.

  2. Organize students into groups of four and distribute the "A New Building Block?" student handout and set of materials to each group.

  3. 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.

  4. 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.

  5. 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).

  6. 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.

Activity Answer

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.

Rope resonance chart: sample results table
Links and Books

See the full set of String Theory Resources


Standards

"The Elegant Universe" activities align with the following National Science Education Standards.

Grades 9-12

Physical Science

Science Standard B:
Physical Science

Structure of Atoms:

  • 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.

  • 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:

  • Atoms interact with one another by transferring or sharing electrons that are furthest from the nucleus. These outer electrons govern the chemical properties of the element.

Teacher's Guide
Elegant Universe, The: Einstein's Dream
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