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# General Relativity

Joining space and time was half the job.

Einstein reconciled Maxwell's speed of light equations with Newton's laws of motion, by describing space and time as being two parts of a single entity—but there was still a problem fitting gravity into the picture. To solve this problem, Einstein not only had to join space and time, he had to bend them.

This description of gravity cleared up a small mystery about free-fall. Massive objects have a lot of momentum, and are difficult to stop or turn around. That is described by inertial mass.

Massive objects also create a strong gravitational force. That is described by by gravitational mass. Gravitational Mass measures how much gravity an object creates. Inertial Mass measures how an object reacts to a force.

Newton explained free-fall by equating these two types of mass, but it is not entirely clear why this should be the case. Einstein said that gravitational mass is the same as inertial mass, because gravity is the same as inertia.

One part of this problem was solved in 1908 when a painter fell off a roof. Einstein heard of the accident, and asked the painter what it felt like to fall. He found out that while falling freely, the painter felt weightless.

Einstein realised that a body that is freely falling along a path under the influence of gravity is behaving similarly to an object moving in a straight line under inertia.

To complete his theory, Einstein had to develop the mathematics for his four dimensional Universe and find a way of describing gravitational paths as straight. This proved to be possible—but only in a Universe with a curved geometry.

Planetary orbits look curved in three dimensions. But in four dimensions of space and time, these paths are straight—as straight as they can be in a space-time that is bent!

This theory of General Relativity says that space-time bends in the presence of mass, and that matter moves along straight lines in this curved space-time. It is sometimes summarised as "Matter tells space how to curve, and space tells matter how to move."

Albert Einstein

Gravitational and inertial mass

Einstein's equations of General Relativity

Diagram showing curved spacetime