Gravity SeriesLesson 5 of 11
Free fall and acceleration
A falling object accelerates relative to the ground, yet an accelerometer falling with it reads zero. These measurements describe different aspects of its motion.
Watch a ball fall past a window. Its speed relative to the building increases. Attach an ideal accelerometer to the ball, however, and it records zero while the ball falls freely.
An accelerometer at rest on a table records about 9.8 metres per second squared upwards. It measures the support preventing it from falling.
A zero reading does not mean the object is outside Earth’s gravity. It tells us that the instrument is falling freely, with no support pushing it away from that motion.
Two meanings of acceleration
The ball’s changing speed relative to the building is a coordinate acceleration: it depends on the reference frame used to describe the motion.
An accelerometer measures something different: how strongly the object is being pushed away from free fall. This is called proper acceleration. The table produces that reading by supporting the instrument; once the support is removed, the reading falls to zero.
Newton’s description assigns a gravitational force to the falling ball. General relativity instead treats free fall as unforced motion through spacetime, the combined description of where and when events occur. The table’s supporting force prevents that free motion and produces the accelerometer reading.
For an ordinary drop near Earth, both descriptions predict essentially the same falling speed. Einstein’s account helps explain why the falling instrument reads zero.
Looking from the falling room
Imagine a small room falling freely alongside the ball. A loose object released gently inside stays close to where it was let go, because both object and room are falling together. Looking out from that room, you would see the building’s floor accelerate upwards towards you.
The rocket example gives a similar picture. A released ball continues freely while the accelerating rocket floor catches up with it.
Why Earth does not expand
Saying that the ground has upward proper acceleration does not mean its radius is increasing. It means support continually prevents objects on the surface from following their free-fall paths.
Imagine another falling room on the opposite side of Earth. Its direction of fall differs from yours. Each room gives a useful local viewpoint, but we cannot extend either one around the whole planet and make every falling object appear to drift freely alongside it.
To understand how those local descriptions fit together, we need to look at the changing separation between neighbouring falling objects. That leads to spacetime curvature.