The rubber-sheet picture

This optional article compares the familiar rubber-sheet demonstration with the spacetime description. Continue to Clocks at different heights for the next main lesson.

In the familiar demonstration, a heavy ball makes a dip in a stretched sheet. A marble rolled nearby curves around the dip and eventually spirals inward.

It is easy to picture a planet moving around the Sun this way. The similarity is useful, although the marble and planet follow their paths for different reasons.

What moves the marble?

Earth’s gravity pulls the marble down the sloping sheet, while the sheet supports it. The apparatus therefore uses an existing gravitational field to produce its motion.

The demonstration therefore borrows gravity from outside the picture. In general relativity, a planet follows a free path through spacetime. There is no additional downward pull making it roll into a dip.

Where is time in the picture?

The sheet shows a shape in space, but has no way to show clocks running at different rates. Near Earth, those rate differences give us most of what we need to calculate a slow fall. An important part of the explanation is missing from the sheet.

Curved-surface diagrams can still help explain spatial geometry. They need to be constructed for the particular geometry being shown; the shape of a stretched sheet is not automatically the right one.

Does space bend into another dimension?

A sheet bends into the room around it. That can make it seem that curved space must also have somewhere outside it to bend into.

We can describe and measure curvature from within. The walkers in How free-fall paths reveal curvature could measure the changing distance between their paths without leaving the globe. Likewise, measurements of neighbouring free-fall paths reveal spacetime curvature. General relativity does not require an extra surrounding space to make those measurements meaningful.

Why does the marble spiral inward?

The marble loses energy through friction and by deforming the sheet. An ideal orbit around a planet has no such resistance, so it can continue without spiralling inward.

Real orbits can change through atmospheric drag, tides, gravitational radiation or interactions with other objects. Those processes need their own explanation.

The falling objects and clock comparisons in this series give us more direct ways to explore gravity. Each shows something we can measure, without needing to imagine an extra downward pull outside the picture.