100 Years of General Relativity

[This feature-length article was originally written for Popular Astronomy and appears in their November/December 2015 issue.]

The early twentieth century was something of a golden age for physics. It was a time of upheaval, of bold new ideas overturning long-established concepts and the beginning of the quantum revolution. For many, one particular breakthrough from that era stands above the rest as the crowning glory of modern physics: Albert Einstein’s development of the General Theory of Relativity in 1915.

Ten years earlier, the young Einstein had published an audacious theory that changed the way we saw our universe. Starting from the assumption that the speed of light is fixed and absolute, and further assuming that the laws of physics have to be the same no matter what speed you travel at, Einstein went on to derive what we now know as the Special Theory of Relativity. Along with the famous equation E=mc^2 which tells us that mass and energy are two sides of the same coin, special relativity tells us two important things about moving objects. As seen by a stationary observer:

  • The faster an object moves in space, the slower it moves in time (time dilation).
  • The faster an object moves in space, the shorter it will appear to be (length contraction).

Neither is obvious in everyday life because for these effects to become noticeable, an object would have to be moving at a sizeable fraction of the speed of light. These incredible properties tell us that neither time nor space is absolute. Our perception of both depends on how we are moving. Space and time are inextricably linked together, part of a larger concept called spacetime.

Spacetime is what we call our three dimensions of space (up-down, left-right and forward-backward) plus our one dimension of time. We are free to move in space however we like, but we are always moving forward in time.

The theory was called ‘special’ relativity because it dealt with a very particular type of motion: objects moving at constant speed. To be specific, the mathematics depended only on the relative speed of two objects, hence the name ‘relativity’. It couldn’t say anything about objects changing in speed. This was a much tougher problem to solve, and Einstein spent the next ten years attempting to generalise this theory and extend it to describe accelerating objects.

The story goes that, while sitting at his desk in the Swiss Patent Office, Einstein saw a workman fall off a roof and began to think about the problem of gravity. A person in free-fall in a gravitational field, such as the falling workman, would feel weightless. This led Einstein to wonder about the relation between gravity and acceleration. As with most such stories, however, this one is almost certainly apocryphal. By Einstein’s own account, he was simply sitting in his office thinking when his “happiest thought” occurred to him.

By realising that the pull of gravity was really just the same as any other type of acceleration, Einstein used the mathematics of relativity to predict that time flows at different rates depending on where you are in a gravitational field. The stronger gravity is, the slower time seems to move. (Believe it or not, this effect is crucial to the workings of our modern satellite navigation systems.)

Gravity was linked to time. Time was linked to space. Gravity had to be linked to space too. But how?

By spotting the connection between acceleration and gravity, Einstein had opened the door to a strange new world of unexpected, fantastic physics. Working for years on the fiendishly difficult mathematics – so difficult even he sometimes needed help with it – Einstein eventually generalised his previous Special Theory of Relativity to describe the motion of accelerating bodies and forever changed the way we look at the universe.

The General Theory of Relativity tells us not only that space and time are intertwined, but that the gravity we feel pulling us down to Earth is actually a property of this mysterious spacetime curving and bending beneath us. We don’t notice it because we are three-dimensional beings living in four-dimensional spacetime. Confused? You’re not alone. When asked if he was one of the only three people alive at the time who understood general relativity, astronomer Arthur Eddington reportedly thought hard for a moment and replied: “I’m trying to think of who the third person might be.

Since we find it hard to visualise the warping of four-dimensional spacetime, we usually picture general relativity in a simpler way. Imagine sitting in the centre of a large bed. The weight of your body will cause the mattress to bend beneath you in much the same way as a massive object causes spacetime to bend. If you then imagine rolling a marble across the bed, it will be pulled towards you by the curvature of the mattress. The mattress plays the role of spacetime here; this bending of spacetime is the origin of gravity, and is why massive objects are gravitationally pulled towards one another.


But before general relativity could be accepted, confirmation of its predictions was required. One observation in particular played a crucial role in establishing general relativity’s place in the pantheon of mainstream scientific theories: gravitational deflection of light beams. Einstein’s hypothesis predicted the precise amount that the trajectory of light would bend as it passed a massive object, such as a star. If you could somehow block out the light from the Sun and look at the stars very close to it in the sky, they would appear to be in the wrong place. The total solar eclipse in 1919 provided the perfect opportunity to test this prediction.

On May 29th 1919, astronomers led by Eddington on Principe Island, Africa measured the deflection of starlight during a solar eclipse and found that it perfectly matched the prediction made by Einstein’s theory. Instantly, Einstein was catapulted to scientific superstardom the likes of which has never been seen since. Here was a man who had revolutionised our concepts of space, time and gravity – and not only that, but he was a media-friendly, lovably eccentric scientist who was comfortable in the spotlight in a way that few of his peers were.

Though there was some controversy over the accuracy of Eddington’s measurements, the experiment has been repeated in other solar eclipses and been verified many times over. During the most recent solar eclipse in March 2015, PhD student Richard Middlemiss from the University of Glasgow led an expedition to the Faroe Islands in an attempt to replicate Eddington’s measurements using more modern equipment.

The luck of the 1919 expedition was not with them, however, and their attempt was foiled by clouds. How must Eddington have felt on his historic journey, knowing that the same could have happened to him? Richard told Popular Astronomy: “Eddington was one of the few people who understood the principle [of relativity], and he had a lot of pressure on him to prove it. The world was watching him. You get a sense that there’s not just foresight or knowledge, which of course are involved with Eddington’s experiment, but he also had a lot of luck on his side.”

After its verification, General Relativity was given the golden status of a scientific theory, having passed all mathematical and physical tests thrown at it. But it took until after Einstein’s death for it to become the subject of active mainstream research, mainly as a result one of its most extraordinary predictions.

A few months after Einstein’s 1915 reveal of general relativity, astronomer Karl Schwarzchild found an unexpected solution to Einstein’s equations. It turned out that a sufficiently massive object could have a gravitational pull so strong that even light would be unable to escape it. Today, we call these objects black holes.

Initially controversial, the idea of black holes was finally accepted by the scientific community in the late 1930s. Even so, it wasn’t until the 1960s that black holes became the subject of active research, following some trailblazing theoretical work and helped along by the discovery of pulsars (rapidly rotating neutron stars). Nowadays, astronomers believe there is a black hole at the heart of almost every galaxy, including our own.

An illustration of a massive object (in this case a galaxy) bending the light from a distant object and focusing it down onto a foreground object. [Image: NASA/ESA]
An illustration of a massive object (in this case a galaxy cluster) bending the light from a distant object and focusing it down onto a foreground object. [Image: NASA/ESA]
Much more recently, general relativity has been put to use in discovering planets orbiting other stars using a technique known as gravitational microlensing. We already know that massive objects can bend light, but if things line up just right, it turns out that light from far-off objects can actually be bent right around foreground objects and focused down onto Earth. The gravity of the foreground objects acts like a lens.

If a planet passes directly between its star and the Earth, some of the starlight gets bent around the planet and focused towards Earth. Our telescopes see a characteristic spike in the brightness of the star, a distinct sign of a planet passing in front of it. Not only has general relativity told us about the structure of space and time, but it’s also given us the means to look for new worlds in the night sky.

But is the story over for general relativity? Not by a long shot – there are still some predictions the theory makes that don’t match up with observations.

Pioneering work by Vera Rubin in the 1970s showed that most stars don’t orbit the centres of galaxies in the way that relativity predicts. The stars far from the galactic centres move too quickly. The orbital speed of the stars is related to the total mass of the galaxy: for general relativity to be correct, there must be some invisible mass in most galaxies that we can’t see. We call this missing mass ‘dark matter’, and no one knows what it is. In recent years, more and more evidence for this invisible matter has emerged in other observations, such as gravitational lensing of galaxy clusters.

The alternative is that there is no mysterious missing mass but that Einstein’s theory is simply not correct. The search is on: either find dark matter, or figure out a new theory of gravity that matches the observations without the need for dark matter at all. But that’s not the only problem faced by general relativity.

As a final twist, Einstein’s equations predict that the universe is expanding around us. Space itself is stretching out and observations confirm that almost every galaxy in the sky is slowly moving away from our own. Not only that, but the rate of expansion is accelerating and no one knows why. For now the cause of this acceleration – the elusive and evocatively named ‘dark energy’ – is nothing more than a term in an equation.

Attempts to use quantum mechanics to determine the physical origin of dark energy have led to a catastrophic mismatch between the two theories. General relativity, it turns out, is incompatible with quantum mechanics, the other great twentieth century revolution. With its problems multiplying, could it be time up for general relativity?

Professor Keith Horne of the University of St Andrews told Popular Astronomy: “We seem to need two miracles, dark matter and dark energy, to save general relativity on galaxy to cosmological scales. One miracle might be okay, but two is stretching it. While many possibilities are being investigated, no clear successor to general relativity has emerged. The observational constraints are quite tight, and most of the alternatives are more complicated and lacking the beauty and elegance of general relativity.

Even now, one hundred years after its inception, Einstein’s general theory of relativity continues to intrigue. But will general relativity ultimately have to be replaced with something new? Only time will tell. But ever since Einstein had his ‘happiest thought’ one hundred years ago, time and space haven’t quite been what they used to be.


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