### Testing the equivalence principle

This exercise is a part of Educator Guide: Galileo Experiment Re-created in Space / View Guide

Directions: Read the article Galileo experiment re-created in space” and then answer these questions.

1. Summarize the article by making brief statements defining “who,” “what,” “where,” “when” and “why.”

Possible student response:

Who: Manuel Rodrigues and other scientists working on the MICROSCOPE project.

What: Rodrigues and colleagues showed that two cylinders composed of different materials free-falling in space accelerated at rates matching within two trillionths of a percent.

Where: A satellite in orbit around Earth.

When: Scientists published their results on December 4, 2017.

Why: The MICROSCOPE experiment was testing the equivalence principle without certain pitfalls of land-based equivalence principle tests. The equivalence principle is a foundation of Einstein’s theory of gravity, which is known as the general theory of relativity. To test if that theory is correct, scientists need to test the equivalence principle.

2. In what primary research journal did MICROSCOPE scientists report their findings?

Possible student response: Physical Review Letters

3. What was the experiment that inspired this space test, and who is sometimes said to have performed the experiment?

Possible student response: Galileo supposedly dropped two balls of different densities from the Leaning Tower of Pisa, showing that the balls accelerated at the same rate.

4. How did scientists determine if the two cylinders accelerated at the same rate during the experiment?

Possible student response: Electrical forces were used to keep the two cylinders aligned during free fall, with one cylinder centered inside the other. If the cylinders had different accelerations, their relative positions would change and adjustments would be made to correct their alignment. Any change in relative positions would vary with a regular frequency, tied to the rate at which the satellite rotated and orbited Earth.

5. How long were the cylinders in the experiment accelerating at the same rate?

Possible student response: The cylinders accelerated at the same rate for 120 orbits, or about eight days.

6. How precise were the results of this experiment? How much precision do the scientists hope to achieve in future experiments?

Possible student response: The cylinders’ acceleration rates match within two-trillionths of a percent for this experiment, which is about 10 times more precise than previous tests. In future experiments, scientists hope to measure whether the cylinders’ acceleration rates match within a tenth of a trillionth of a percent, or about 100 times more precise than previous tests.

7. Why are the results important?

Possible student response: A key element of Einstein’s general theory of relativity is the equivalence principle, which states that an object’s inertial mass (which sets the amount of force needed to accelerate the object) is equal to its gravitational mass (which determines how the object responds to a gravitational field). So free-falling objects accelerate at the same rate (at least in a vacuum, where air resistance is eliminated), regardless of their mass or composition. The results of this experiment give an even more precise measurement of the equivalence principle. Theoretical physicists are attempting to combine general relativity with quantum mechanics (the physics of the very small). Some theories of how to combine the two predict that there might be small differences between an object’s inertial mass and its gravitational mass — a violation of the equivalence principle. But those differences have not been detected yet. If a violation of the equivalence principle were found, it could help scientists understand how to combine general relativity and quantum mechanics. So scientists want to test the equivalence principle with even greater precision.

8. What other questions do you still have after reading the article?

Possible student response: How could similar experiments be performed under more extreme conditions that might show where current theories start to break down and new theories are needed? Could scientists make astronomical observations of objects falling into a black hole, or conduct experiments in which the falling objects are particles with quantum behavior?