In 1915, Berlin was at the centre of an empire locked into a global war. But at least one resident of that city had his mind elsewhere: Albert Einstein was working to reconcile gravity with the theory of relativity he had invented a decade earlier. Einstein solved the problem by year's end, and in doing so he changed our understanding of space and time forever.

For Newton, space and time are the stage upon which the play-of-the-world takes place. The actors – planets, stars, people, atoms, and even light itself – move in space, but space itself is fixed and unchanging. In Newton's universe, space tells us where things happen and time tells us when things happen but nothing happens to space or time; gravity reaches across space, but does not change space itself.

In Einstein's universe, space is shaped by matter and that shape changes when matter changes its position. Einstein brings the wooden stage of Newtonian physics to life; space now responds as the actors move about. For a physicist, Einstein's understanding is as shocking and wonderful as a play in which the theatre springs to life and takes a speaking role in the drama.

Einstein welded space and time together into spacetime and showed that mass curves spacetime, and that gravity is encoded in this curvature. In Newton's universe, gravity drags the earth around the sun. In Einstein's universe the sun bends spacetime and the earth circles the sun by following the simplest path it can find though spacetime.

This year marks the centenary of Einstein's breakthrough, his General Theory of Relativity. The mathematical expression of the theory, the Einstein field equations, would fit on a postcard:

But the Einstein equations are a magic bag: far bigger on the inside than they appear on the outside. One hundred years later physicists and mathematicians are still working to unpack this expression and to fit it to the rest of our knowledge about the universe. Einstein's new theory immediately solved a 100 year old riddle, explaining why Mercury's orbit around the sun did not quite match Newton's predictions. Within 10 years, the underpinnings of the Big Bang and the expanding universe tumbled out of the magic bag of General Relativity: the universe is not expanding because distant galaxies move through space; the galaxies move because space itself is expanding. "Expanding space" is an idea you can have only after General Relativity tells you that spacetime is *dynamical*, rather than fixed and static.

Beyond clearing up the niggling behaviour of Mercury, Einstein made two *predictions*, each of which is a test that General Relativity must pass. First, gravity bends the passage of light itself; second, clocks run more slowly in strong gravitational fields. The bending of starlight was detected in 1919, via the changing positions of stars near the sun during a total solar eclipse; the slowing of time was inferred from observations in the 1920s and spectacularly confirmed in 1959. (And understanding this phenomenon is key to getting the GPS system to work, believe it or not.)

And there is much, much more. In 1915, also Einstein showed that as large objects accelerate they generate waves in spacetime. One hundred years later these "gravitational waves" have never been directly observed, but Advanced LIGO, the first observatory that should be sensitive enough to find them, is being commissioned just in time for the theory's 100th birthday.

Likewise, a fully unified theory, a self-consistent quantum mechanical description of gravity alongside the other forces in nature is as elusive today as it was for Einstein, who searched in vain for such a model during the last two decades of his life.

So 100 years on, physicists are still unpacking the magic bag Einstein that discovered in 1915...

Coda: Watch the World Science Festival programme Reality Since Einstein recorded in May this year...