Equivalence principle

The equivalence principle is an important idea about gravity. It says that all objects fall the same way, no matter what they are made of, because of a special link between two types of mass: gravitational mass and inertial mass.

People have noticed for a long time that if you drop different objects, they hit the ground at the same time if you ignore things like air. This is called the weak form of the equivalence principle.

Later, Albert Einstein expanded this idea. He said this link should also work when things are moving very fast or in ways described by special relativity. His idea helped create a new theory called general relativity, which explains more about how gravity works. There are even stronger versions of this principle that test if it works for very big objects like stars. Tests show that any differences are extremely small, which helps scientists learn more about the universe.

Concept

In classical mechanics, Newton’s equation shows that the mass that resists motion and the mass that feels gravity are the same. Experiments prove these two kinds of mass are always equal, no matter what the material is. This idea is called the equivalence principle.

Imagine you’re in a room with no windows. You can’t tell the difference between being on Earth where gravity pulls you down and being in a spaceship far from any planet that’s speeding up to mimic Earth’s gravity. In both cases, everything would feel and act the same.

History

By experimenting with how different materials move, Galileo Galilei found that gravity affects all objects the same way, no matter their mass.

Isaac Newton later tested if gravity and motion worked the same on different objects. He used pendulums made of different materials and saw they swung at the same rate. This showed that gravity and motion act the same, which is called the "weak equivalence."

Albert Einstein took this idea further in 1907. He noticed that the rules of physics look the same whether you are in a place with steady gravity or in a rocket moving steadily far from any gravity. Because of this, he believed gravity and steady movement were "physically equivalent."

In 1911, Einstein used this idea to predict that clocks tick slower in stronger gravity and that light bends when it passes through a gravitational field. Later, he remembered that a simple thought — imagining what it would feel like to fall freely — helped him develop his theory of gravity, known as general relativity.

Definitions

There are three main forms of the equivalence principle: weak, Einsteinian, and strong.

The weak equivalence principle states that all objects fall at the same rate in a gravitational field, no matter what they are made of. This means that if you drop different objects from the same height, they will land at the same time if there is no air resistance.

The Einstein equivalence principle builds on this idea. It says that the weak equivalence principle is true and also that the rules of physics are the same no matter how fast you are moving or where you are in a gravitational field, as long as the area you are looking at is small. This helped Einstein predict things like the gravitational redshift, where light changes color when it moves away from a massive object.

The strong equivalence principle is even more strict. It says that very massive objects, like stars or planets, also follow the same rules as small objects when they are falling freely. This principle is important in Einstein's theory of general relativity.

Experimental tests

Tests of the weak equivalence principle

Scientists test the weak equivalence principle by checking if different objects fall at the same speed. A famous example is when David Scott dropped a feather and a hammer on the Moon in 1971, and they landed together. Today, experiments at the University of Washington continue to test this idea with great precision.

There are also ideas for new experiments in space to test this principle even better. Scientists are also exploring whether antimatter falls the same way as normal objects.

Tests of the Einstein equivalence principle

Beyond the weak equivalence principle, the Einstein equivalence principle also needs testing. This includes checking if the speed of light stays the same in all directions and if basic physical rules stay constant over time and space. Experiments on Earth and in space help scientists understand these important ideas.

Tests of the strong equivalence principle

The strong equivalence principle can be tested by looking at how objects orbit each other, like the Earth around the Sun. Scientists use tools like Lunar Laser Ranging experiments to check these orbits very carefully. So far, they have found no surprising changes, which helps us understand gravity better.

Chronology of weak equivalence principles tests
Year	Investigator	Sensitivity	Method
500?	John Philoponus	"small"	Drop tower
1585	Simon Stevin	5×10⁻²	Drop tower
1590?	Galileo Galilei^: 91	2×10⁻³	Pendulum, drop tower
1686	Isaac Newton^: 91	10⁻³	Pendulum
1832	Friedrich Wilhelm Bessel^: 91	2×10⁻⁵	Pendulum
1908 (1922)	Loránd Eötvös^: 92	2×10⁻⁹	Torsion balance
1910	Southerns^: 91	5×10⁻⁶	Pendulum
1918	Zeeman^: 91	3×10⁻⁸	Torsion balance
1923	Potter^: 91	3×10⁻⁶	Pendulum
1935	Renner^: 92	2×10⁻⁹	Torsion balance
1964	Roll, Krotkov, Dicke	3×10⁻¹¹	Torsion balance
1972	Braginsky, Panov^: 92	10⁻¹²	Torsion balance
1976	Shapiro, et al.^: 92	10⁻¹²	Lunar laser ranging
1979	Keiser, Faller^: 93	4×10⁻¹¹	Fluid support
1987	Niebauer, et al.^: 95	10⁻¹⁰	Drop tower
1989	Stubbs, et al.^: 93	10⁻¹¹	Torsion balance
1990	Adelberger, Eric G.; et al.^: 95	10⁻¹²	Torsion balance
1999	Baessler, et al.	5×10⁻¹⁴	Torsion balance
2008	Schlamminger, et al.	10⁻¹³	Torsion balance
2017	MICROSCOPE	10⁻¹⁵	Earth orbit

Tests of changes in fundamental constants^: 19
Constant	Year	Method	Limit on fractional change per year
weak interaction constant	1976	Oklo	10⁻¹¹
fine-structure constant	1976	Oklo	10⁻¹⁶
electron–proton mass ratio	2002	quasars	10⁻¹⁵