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Problems of gravity

Albert Einstein is an icon and for good reason. His general theory of relativity, which describes the force of gravity, was an intellectual tour de force. Not only were his ideas entirely new, they have also stood the test of time. Despite this success, some physicists are doing what many would consider sacrilege: they are tinkering with the theory, producing modified versions of it. But why?

What's wrong with general relativity?

Einstein's theory of relativity, which describes the force of gravity, was an intellectual tour de force.

"General relativity correctly describes what we observe at the scale of the solar system," reassures Constantinos Skordis, of The Universities of Nottingham and Cyprus. "It all works beautifully at this scale and it has been tested." The problems arise when you look at the Universe at very small or at very large scales.

At the turn of the twentieth century people realised that at very small scales, in the realm of atomic and sub-atomic particles, the world looked very different from what they had expected. The theory of quantum mechanics grew out of that realisation and posed a new challenge: the descriptions of the fundamental forces of nature now had to be adapted to the new quantum mechanical insights — they had to quantised (see Schrödinger's equation — what is it? and Let me take you down cos we're going to .. quantum fields).

The problem is that general relativity stubbornly refuses to comply in this undertaking. "Einstein's theory cannot be easily quantised; we can't find a quantum counterpart in the same way as we found one for electromagnetism," explains Thomas Sotiriou of the University of Nottingham. In fact, the problem of finding a quantum theory of gravity is so challenging, and so important, many consider it the holy grail of modern physics.

Another mystery arises when you look at the Universe as a whole. Since 1929 physicists have known that the Universe is expanding, a fact that came as a shock even to Einstein: stars and galaxies are moving away from each other. Nearly 70 years later, in the 1990s, observations of far away objects also showed that this expansion is speeding up. General relativity cannot explain what causes this acceleration. If we believe the theory, then we must concede that there is something else out there, a mysterious form of energy which drives the acceleration. That something has been dubbed dark energy.

"Dark energy is bizarre," says Skordis. "It's not a particle, you can't detect it in the lab. It's just a missing form of energy which must have some peculiar properties. For example, it must exert negative pressure, which is what drives accelerated expansion. We just don't know what causes it." (See here for more on dark energy.)

Quantum physics offers one explanation for dark energy. According to this theory, the vacuum does not really exist in the sense we usually understand it, as empty space. Instead, particles constantly pop in and out of existence, resulting in a vacuum energy, an energy of space itself, which might be driving the accelerated expansion. There's a number which measures that vacuum energy, called the cosmological constant, whose value particle physicists can estimate. The trouble is that this estimated value is bigger than what observations suggest. And not just a bit: the two values, observed and theoretical, differ by at least 60 orders of magnitude (see this article for more). Although the estimate stemming from quantum physics is rough and perhaps naive, the difference is so big that something is clearly, very wrong.

These problems, dark energy and the need to quantise gravity, provide some of the motivations for meddling with general relativity. And perhaps they are even connected. "The very large and the very small [scale problems] are not necessarily distinct," says Sotiriou. "It is technically very challenging, but not inconceivable that one could have an extension of general relativity that deals with the large scale problems, which would at the same time have a better behaviour when it comes to quantisation. Maybe we can hit two birds with one stone."

But how does one go about finding such an extension of general relativity?

Violating symmetry

One place to start is a fundamental principle underlying Einstein's physics. The word "relativity" refers to the fact that when you observe an object in motion, what you see depends on how you are moving yourself. We're all familiar with this. When you observe a moving train from the platform, you see it rushing past, but if you are travelling alongside it at the same speed it looks stationary. Motion is relative: it depends on what you measure it against.

If you throw a ball up in the air in a moving train, you will see it behaving in exactly the same way as if you were standing on the platform, as long as the train is not slowing down, speeding up, or swerving.

Some things, however, do look the same whether you are moving or not. If you throw a ball up in the air in a moving train, you will see it behaving in exactly the same way as if you were standing on the platform, as long as the train is not slowing down, speeding up, or swerving. Einstein thought that this was a fundamental feature of nature: that two observers performing the same experiment should see the same result even if they are moving at different speeds, as long as their relative velocity is constant. (That is, if one were to look across to the other, they wouldn't perceive him or her to be slowing down, speeding up, or swerving.) The results they see should also be independent of the direction in which their laboratory is oriented in space.

This principle is known as Lorentz invariance or Lorentz symmetry, after the Dutch physicists Hendrik Antoon Lorentz who played a major role in developing the underlying ideas. Einstein's special theory of relativity, which came before the general one, is built on the principle of Lorentz symmetry and the additional principle that the speed of light should appear the same to all observers. Squeezing the two principles into the same theory came at a price: things we would normally think of as absolute, such as time or the lengths of objects, in special relativity also become relative, depending on the observer's state of motion (see this article for more).

As the name suggests, special relativity only applies to special situations, which is why Einstein went on to formulate the more universal general theory of relativity. It ended up providing a complete description of the force of gravity, and it encodes Lorentz symmetry in a fundamental way.

Lorentz symmetry isn't just an idea: it has been tested experimentally and so far it seems that it does indeed hold. But still, there are people who suspect that it's where general relativity might be going wrong. "The name of the game is to say, can I actually have a violation of the symmetry; deviations from the standard picture that are small enough so that experiments will not detect them, but that would still lead to a better behaviour [of the theory]," says Sotiriou.

Physicists are in the process of formulating such Lorentz violating theories, and although their efforts are not yet complete, results are interesting. "It turns out that theories that don't satisfy Lorentz's principle tend to behave better when you go to smaller and smaller length scales," says Sotiriou. "There's a theory that fits the bill, initially proposed by Petr Hořava at UC Berkeley. It doesn't seem to contradict any experiments so far, and in principle it seems that it will have better quantisation properties than general relativity. But the theory is not yet completely worked out. It needs to be looked at more."

Massive gravity

Another approach that has seen recent progress also involves the attempt to quantise gravity. Quantum physics, which does well at describing fundamental forces other than gravity, holds that these forces are "mediated" by force-carrying particles. For example, when two electrons interact via the force of electromagnetism, they do so by exchanging photons. A quantum description of gravity would require such a force carrying particle for gravity too, called the graviton.

The force of gravity reaches all the way across the solar system. Image courtesy NASA.

The mass of a force carrying particle determines how far the corresponding force can reach. Photons, for example, have no mass at all. This turns them into swift travellers, giving the force of electromagnetism an infinite reach. The weak nuclear force, by contrast, is mediated by the relatively massive particles, and can only act across very short distances within atoms.

So what about gravity? Our existence on Earth confirms that its reach is very long. The gravitational pull of the Sun, nearly 150 million km away, is strong enough to keep the Earth in orbit. General relativity goes all the way, assuming the reach of gravity to be infinite, resulting in a massless graviton. There is no reason, however, why the graviton couldn't possess a tiny little bit of mass. Assuming that it does modifies the effects of gravity over very large distances and still fits in with observations. And interestingly, theory suggests that a massive graviton would lead to a Universe whose expansion self-accelerates – so no need to evoke the mysterious dark energy to explain the acceleration.

"[Massive gravity] is an old problem," says Skordis. "In the 1930s Markus Fierz and Wolfgang Pauli already tried to propose [such a theory]. Later in 1970s it was realised that if you try to do this, you run into problems. You get negative energy, which creates instabilities and pathologies. But [in 2010] new research showed that there is perhaps a way of getting rid of [these problems]; that perhaps there is a good way of creating a consistent theory of massive gravity. It's a very active field of research, although it remains to be seen whether it can provide an acceptable solution to the dark energy problem."

But not everyone agrees

After Fierz and Pauli's initial efforts, physicists turned away from trying to modify Einstein's original ideas, though in the last 20 years or so, the activity has gained in popularity — and acceptance. Finding a new and better theory that resolves some of the problems is one motivation, but another is simply to push general relativity to its boundary and rule out alternatives. "We should be testing general relativity regardless, because you should test any theory," says Skordis. "It's part of physics to test everything."

Wolfgang Pauli was one of the first people to think about massive gravity.

Many people are still skeptical, however. David Tong, a theoretical physicist at the University of Cambridge, believes that modified gravity doesn't really solve the problem with dark energy. Its models do explain why the expansion of the Universe accelerates, that is, why the cosmological constant is not zero, but they don't explain why its value is so much smaller than what particle physics predicts. This, according to Tong, is the interesting problem. "I've also been skeptical because it seems to me that whenever you mess with general relativity bad things happen — the resulting theories just don't make sense," he says. "I do think that [the recent breakthrough in massive gravity] is genuinely interesting. I suspect it's not good for what they want it to be good for, which is describing our Universe, but it does seem to be an interesting theoretical development at least."

Ultimately, to find out whether these modifications of general relativity are correct we need to test them in experiments. Such tests are on the horizon. The Euclid satellite, to be launched in 2020, will hopefully provide more insight into dark energy, and may therefore give information about whether massive gravity is viable. Lorentz-violating gravity makes predictions about the structure of those gravitational monstrosities called black holes. Once these predictions have been worked out in detail they can also be tested against observations. We will have to wait and see.

About this article

Constantinos Skordis has recently moved from the University of Nottingham to the University of Cyprus as an Assistant Professor, where he will be the Principal Investigator of the European Research Council (ERC) grant Theories and Models of the Dark Sector: Dark Matter, Dark Energy and Gravity.

Thomas Sotiriou

Thomas Sotiriou is Associate Professor & Reader at the University of Nottingham and the Principal Investigator of an ERC-funded research group that focusses on the limits of General Relativity as a theory of gravity.

Marianne Freiberger is Editor of Plus.

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