General Relativity

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What’s the big idea?
Newton’s theory of gravity was good—it lasted for two and a half centuries—but it was not good enough. 
It took 10 years, but Einstein finally figured out a better theory of gravity called general relativity. Einstein 
realized that gravity is not a force, as Newton had imagined, but a warping of spacetime. This changed 
everything. Einstein’s ideas reveal a strange and fascinating universe of black holes, worm holes, and 
time machines, and form the foundations of our understanding of the big bang theory, the accelerating 
expansion of the universe, and much more. Explore the mind-warping ideas of general relativity!
Newton’s law of universal gravitation accounts 
very well for the motions of the planets, but not 
perfectly. For instance, by the late 1800s, it was 
clear that Mercury doesn’t quite follow the orbit 
predicted by newtonian gravity. Something was 
wrong. Moreover, Einstein’s special relativity 
ideas say that there is a universal speed limit—
the speed of light, which newtonian gravity is 
in clear violation of. According to Newton’s 
ideas, if you wave a rock in your hand, then the 
gravitational effects of this will travel with infinite 
speed to all masses in the universe. Something 
was really wrong. 
Einstein knew that a new theory of gravity was 
required. Perhaps the most crucial step he 
took was to realize that it is possible to create 
artificial gravity using acceleration. As a 
modern example, astronauts in a rotating space 
station will feel artificial gravity because of 
their acceleration towards the axis of rotation. 
Einstein wondered if such artificial gravity could 
tell him something about real gravity. So he 
carefully analysed the motion of accelerated 
observers using his special relativity ideas, 
and discovered that the artificial gravity they 
would experience is linked to a “warping” of 
their space or time. He wondered if a real 
gravitational field—the kind produced by mass, 
might be linked to a warping of spacetime.
In special relativity, spacetime is flat, like a 
four-dimensional version of a flat surface. In 
general relativity, Einstein allowed spacetime 
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What’s it good for?
Space and Time
What time is it? And where am I? Gazing to your 
right, you see nothing but the last remnants of 
the sun dipping below the barren landscape. 
To your left, darkness envelops the eerie 
silhouette of a lonely cactus. You turn on your 
GPS unit. Microwave signals from satellites 
are received that carry time stamps accurate 
to a billionth of a second, and your position is 
pinned down to within a single step. To know 
where cannot be answered without knowing 
when, and knowing when requires knowing that 
time moves more slowly on earth than it does 
high up where the GPS satellites orbit. The 
Global Positioning System would not work were 
it not for this profound understanding achieved 
by Einstein’s general theory of relativity—the 
unification of space, time, and gravity. 
to warp, or curve, and showed that if this 
warping is slight it can exactly reproduce 
the effects of newtonian gravity. This stroke 
of genius seamlessly unified spacetime and 
gravity. But it went far beyond newtonian 
gravity, including entirely new phenomena like 
gravitational waves, black holes, and the big 
bang. 
As an example of Einstein’s gravity in action, 
imagine two stars orbiting about each other. 
They will create gravitational waves—ripples 
in the geometry of spacetime, radiating 
outwards. If you and I were floating in space 
nearby, these waves would cause the distance 
between us to fluctuate, and yet we would 
feel no forces and experience no acceleration. 
How so? Suppose you are cross-country 
skiing, and moving in a straight line by 
doing a “parallel shuffle” (i.e., each time you 
push a ski forward, you slide it parallel to 
the other ski). I’m nearby, doing the same. 
We encounter a hill. Continuing our parallel 
shuffles, our paths might be as shown in the 
General Relativity animation: if they diverged 
before the hill, they might converge after. 
With a saddle-shaped terrain, the effect 
would be opposite: converging before, and 
diverging after (see animation). We’re both 
moving on straight lines (parallel shuffle), but 
due to the curved landscape, the distance 
between us is fluctuating. 
A gravitational wave is similar, except with 
our curved landscape now representing 
warped spacetime. One dimension of the 
blue grid represents space, and the other, 
time. The spacetime alternates back and 
forth between the hill and saddle shapes 
as the gravitational wave passes by us. 
We’re both moving on straight lines in 
this spacetime, and thus experiencing no 
forces or acceleration, and yet the distance 
between us is fluctuating! Gravity is not a 
force, as Newton imagined, but a warping 
of spacetime.
Today, general relativity underlies our 
understanding of everything from planetary 
orbits to the expansion of the universe. 
Ever higher precision tests of it are driving 
ever more astounding technological 
developments, with multiple spin off 
technologies. For example, the power of 
these ideas has enabled us to construct the 
Global Positioning System (GPS).
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High Tech
Two neutron stars circle each other, 
moving closer and closer together with 
each revolution, until finally they collide 
in a violent explosion. This cataclysmic 
event shakes the very fabric of spacetime, 
sending gravity waves outward like ripples 
on a pond—at least according to Einstein. 
But was he right? Attempting to answer 
this question has, and will continue to 
push a variety of technologies, both 
earth—and space-based, to entirely new 
levels, prompting the construction of 
ultra accurate atomic clocks, extremely 
sensitive vibration dampening systems, 
and position measurement technologies 
with unprecedented precision. All of 
which will surely see a wide variety of spin 
off applications in the years to come. 
Some of the most advanced technologies 
in the world are first created in physics 
laboratories, where precision tests of our 
understanding of nature’s laws are being 
pushed to new heights.
Science Begets Science
Ninety-six percent. That is the amount of 
stuff in the universe about which we know 
absolutely nothing. Atoms—the stuff we 
do know a lot about—make up only four 
percent. People, planets and stars are just 
the tip of the iceberg. How do we know 
this? We just looked out into the cosmos. 
And, of course, made sense of what we were 
seeing. That’s where general relativity comes 
in. It is the very framework that has enabled 
us to construct our entire understanding of 13 
billion years of cosmic evolution since the big 
bang. It’s also the lens through which we then 
view the universe, both figuratively and literally. 
For example, Einstein discovered that mass 
warps spacetime, and warped spacetime bends 
light, just like a lens. The simple fact is there’s 
a lot more bending of light going on than can 
be accounted for by people, planets and stars. 
There’s a lot of something else out there, but we 
don’t know what it is. Powerful ideas often bring 
into focus new and deeper mysteries, which in 
turn lead to ever more powerful ideas.