Einstein's elevator

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.

In 1907, Albert Einstein had what he later called the happiest thought of his life: a person falling freely feels no gravity. This insight, born from a simple thought experiment about an elevator in free fall, became the cornerstone of general relativity, one of the most profound theories in all of physics. Einstein realized that inside a closed cabin, no experiment could distinguish between being at rest in a gravitational field and being uniformly accelerated in empty space. This equivalence principle has far-reaching consequences: it implies that gravity is not a force in the traditional sense but rather a manifestation of curved spacetime. The smartphone in your pocket contains an accelerometer that directly illustrates this principle. When stationary, it reads 9.81 m/s² (the gravitational acceleration) not because it is accelerating but because the table pushes it upward against gravity. If you drop it, the reading drops to zero during free fall. This experiment allows students to explore the equivalence principle firsthand using nothing more than a smartphone.

Learning objectives:

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.

Level:

High school

FizziQ

Author:

Duration (minutes) :

30

What students will do :

- Compare accelerometer readings in three scenarios: stationary, uniform motion, and vertical acceleration
- Observe that the accelerometer cannot distinguish between gravitational acceleration and inertial acceleration
- Understand Einstein's equivalence principle through direct measurement
- Analyze accelerometer data to identify different states of motion
- Connect the experimental observations to the conceptual foundations of general relativity

Scientific concepts:

- Equivalence principle
- General relativity
- Gravitational field
- Inertial and non-inertial frames of reference
- Thought experiment

Sensors:

- Accelerometer (absolute acceleration or Z-axis component)

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

Experimental procedure:

Open FizziQ and select the Accelerometer sensor. Choose absolute acceleration for the clearest demonstration.
Scenario 1 (At rest): Place the smartphone flat on a stable table. Start recording for 10 seconds. Observe that the reading is approximately 9.81 m/s² (1g), even though the phone is not moving.
Save this recording and note the average value. Discuss: why does a stationary object register an acceleration?
Scenario 2 (Uniform motion): Hold the smartphone steadily and walk at a constant pace in a straight line. Record for 10 seconds. The reading should remain close to 9.81 m/s², just as in the stationary case.
Save this recording. Note that uniform rectilinear motion and rest are indistinguishable to the accelerometer, consistent with Galilean relativity.
Scenario 3 (Brief free fall): Place the smartphone in a protective padded box. Hold it at waist height over a thick pillow or cushion.
Start the recording, wait 2 seconds, then release the box so it falls onto the cushion. Let it record for 2 more seconds after impact.
Retrieve the smartphone and examine the graph. During the fall, the acceleration should drop to approximately 0 m/s² (weightlessness), then spike sharply upon impact.
Measure the duration of the free fall from the graph (the time interval where acceleration ≈ 0).
Calculate the expected fall duration from the height: t = √(2h/g). Compare with the measured duration.
Scenario 4 (Elevator or car): If possible, record the accelerometer in an elevator. Note the increased reading during upward acceleration (>1g) and decreased reading during downward acceleration (<1g).
Summarize your observations: the accelerometer measures g + a_inertial, and cannot distinguish the gravitational contribution from the inertial one. This is the essence of the equivalence principle.

Expected results:

In the stationary and uniform motion scenarios, the accelerometer should read approximately 9.81 m/s² (±0.05 m/s²), demonstrating that these two states are indistinguishable to the sensor. During free fall, the reading should drop to near 0 m/s² (typically 0.1-0.5 m/s² due to air resistance and rotation). The free-fall duration for a 1-meter drop should be approximately 0.45 seconds. Upon impact with the pillow, a brief acceleration spike of 20-50 m/s² (2-5g) is typical. In an elevator, students should observe readings of approximately 10.5-11 m/s² during upward acceleration and 9.0-9.5 m/s² during downward acceleration, with 9.81 m/s² during constant-speed travel.

Scientific questions:

- Why does a stationary smartphone read 9.81 m/s² on its accelerometer even though it is not accelerating?
- What would the accelerometer read inside a freely orbiting spacecraft? Why?
- Einstein said his happiest thought was about a person in free fall. What did he realize?
- How does the equivalence principle lead to the prediction that light bends near massive objects?
- Can you design an experiment inside a closed box that distinguishes between gravitational acceleration and uniform acceleration?
- What is the connection between weightlessness and free fall?

Scientific explanations:

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.

Extension activities:

Frequently asked questions:

Q: My smartphone reads 9.83 m/s² instead of 9.81 m/s² when stationary. Is it broken?
R: No. Small deviations of ±0.05 m/s² are normal due to sensor calibration differences and local variations in the actual value of g (which varies from about 9.78 to 9.83 m/s² depending on latitude and altitude). The important observation is that the reading is constant and close to g.

Q: During free fall, the reading does not reach exactly zero. Why?
R: Air resistance on the falling box and any residual rotation of the smartphone contribute a small acceleration even during the fall. Additionally, the fall duration is very short (under 0.5 seconds), so the sensor may not have enough time to settle completely.

Q: Is it safe to drop my smartphone?
R: Always use a thick pillow or cushion to cushion the landing, and place the phone in a padded box or case. Drop from a moderate height (0.5-1.0 m). Modern smartphones can withstand accelerations of 100g or more during brief impacts, far more than a cushioned drop produces.

Q: Why does the equivalence principle say gravity and acceleration are the same thing?
R: The equivalence principle states that locally (in a small enough region of space and time), no experiment can distinguish between being in a gravitational field and being uniformly accelerated. This is exactly what the accelerometer demonstrates: it cannot tell whether its reading comes from gravity or from acceleration.