Einstein's elevator
Exploring Einstein's Equivalence Principle with a Smartphone
Autor:
Título 4
Learning objectives :
This activity allows students to intuitively understand Einstein's equivalence principle, the basis of general relativity. She uses the smartphone's accelerometer to illustrate how gravity and acceleration produce locally indistinguishable effects.
Concepts covered
Equivalence principle; General relativity; Gravitational field; Inertial and non-inertial frames of reference; Thought experiment
What students will do :
The student uses the FizziQ accelerometer to compare three situations: smartphone stationary on a table, smartphone in uniform rectilinear movement and smartphone in vertical acceleration. By analyzing the values measured in each case the student understands that the accelerometer cannot distinguish between the effect of Earth's gravity and an acceleration in empty space, thus illustrating the thought experiment of Einstein's elevator.
What is required :
Smartphone with the FizziQ application; A flat surface for static measurements; A rigid box or pocket to hold the smartphone; FizziQ experience notebook
Scientific background :
The equivalence principle, the cornerstone of Einstein's general relativity (1915), states that it is impossible to locally distinguish between the effects of a gravitational field and those of an acceleration. Einstein illustrated this principle with the elevator thought experiment: an observer locked in a cabin cannot determine whether he is subject to Earth's gravity or whether the cabin is accelerating in empty space. The smartphone's accelerometer demonstrates this principle perfectly. When resting on a table, it measures approximately 9.81 m/s² (the acceleration of gravity g), because it detects the reaction force of the support which opposes gravity. In uniform rectilinear motion, it continues to display g, in accordance with Galileo's principle of inertia. During an upward vertical acceleration, the measured value increases: if the natural acceleration is a, the accelerometer indicates g+a. This increase is exactly what an observer would experience as an apparent increase in weight. Conversely, during free fall (where the natural acceleration is -g), the accelerometer would theoretically display zero, reproducing the state of weightlessness. This local equivalence between gravity and acceleration led Einstein to his revolutionary vision: gravity is not a conventional force but a manifestation of the curvature of space-time. Massive bodies distort the space-time fabric, and this altered geometry determines the movement of objects. This conception has been confirmed by various observations, notably the deflection of light by the Sun and the advance of Mercury's perihelion.