Putting gravity together

This series has covered forces, scales, accelerometers, curvature, clocks and light. Taken together, they come down to four statements. These are the part worth remembering; each one links back to the lesson that explains it.

Questions that come up

Is the object looking for the most clock time? No. It carries on as it was already going. “Most clock time” is how we recognise the straight path, not something the object is after. It is also only ever a comparison between paths that start at the same event and end at the same event.

If higher clocks run faster, why does a held stone need holding? Fix two events: the stone at hand height now, and at the same height two seconds later. Staying still is not the path with the most clock time between them. Rising a little and coming back down is: the thrown ball from Free fall and elapsed time. Your hand holds the stone on a path with less time on its clock, and that is why holding it takes effort.

Does that not assume we already know where the stone ends up? The comparison also holds for every short piece of a free path. Take any two nearby moments on it, and the piece between them must have more clock time than any other route between the same two points. That is enough to rule out a path that bends upwards. Picture a stone at rest that starts to rise on its own, slowly at first and then faster. A steady climb between the same two points is higher at every moment in between, so its clock runs faster, and it never needs the fast finish, so it never has the extra slowing that speed brings. The steady climb has more clock time on both counts, so the upward bend cannot be free.

A downward bend is different: it is higher than the steady path but moves faster. Too little bend misses some of the height, too much brings too much speed, and the two balance at exactly one amount of bend. Near Earth’s surface, that is 9.8 metres per second squared. No destination is needed: a free path always bends downwards by that amount, and where it goes is set by where it starts and how it is moving.

So why does a released stone go down rather than up? Going up is allowed; bending upwards is not. A thrown ball rises, but it slows as it rises, so its path is bending downwards the whole time. A stone at rest has no upward speed, so rising would mean bending upwards. Its only free path is down. It is in the same state as a thrown ball at the top of its arc, at the instant it stops.

Where the explanation stops

Statements 2 and 4 follow from the other two. Statements 1 and 3 are starting points. No deeper theory says why an object left alone carries on as it was, or why mass slows the clocks near it. Einstein’s equations say exactly how strongly mass affects the clocks, just as Newton’s law said exactly how strongly masses attract, without saying why.

Statement 3 is also a simplification. More fully, mass shapes the geometry of spacetime, which includes distances as well as clock rates. For slow objects such as a dropped stone, the clock rates are the part that matters. Light moves fast enough that the geometry of space matters too, which is why How spatial geometry affects light needed more than the clock calculation.

One Earth, four objects

Imagine four objects near Earth: a stone held above the ground, a second stone just released, a ball thrown upwards and a satellite in orbit. They move differently, but the same four statements account for all of them.

The released stone, the thrown ball and the satellite are all going straight through the same spacetime. Their paths differ only because they started with different velocities. The released stone gains downward speed relative to the ground. The thrown ball rises, slows and returns. The satellite has enough sideways motion for its path to continue around Earth without reaching the surface.

All three are in free fall while other forces are negligible. Free fall includes the upward part of the ball’s flight and the satellite’s entire orbit. It describes the absence of support or propulsion, rather than a particular direction of travel.

Objects with different masses but the same starting position and velocity follow the same path in this approximation. Nothing about the path depends on what is following it, which is why heavy and light objects fall together.

Standing and feeling weight

The held stone is the odd one out. The hand keeps it at one height, off its straight path, and a scale beneath it would measure that support.

Your feet experience the same kind of support from the ground. Remove it and you begin to fall freely. An accelerometer falling with you reads zero, even while your speed relative to Earth changes.

That zero reading does not make gravity disappear. Compare two nearby freely falling objects and their separation can still change. These tidal effects reveal the curvature that a single small falling room cannot remove from the wider picture.

What we mean by gravity

In Newton’s account, gravity is an attractive force between masses. This remains an accurate and convenient description for many everyday and orbital calculations.

In Einstein’s account, nothing pulls. Mass changes how time runs nearby, an object left alone goes straight through spacetime, and near a mass the straight path bends towards it. The weight you feel is the ground holding you off that path.

The theory does not settle every deeper question, including how gravity should fit with quantum physics. Understanding a falling stone does not require those questions to have been answered.