Combined, general relativity and quantum mechanics can explain virtually all of observable reality and every fundamental phenomenon we have discovered. However, they cannot both be correct, there must be a deeper theory that unites them – a theory of quantum gravity. Yet even science’s greatest minds have thus far fallen short in the hunt for a theory of everything, and it remains possibly the greatest challenge in modern physics. In this article, we discuss why quantum gravity is so essential and why it continues to elude us.

According to Einstein’s theory of general relativity, the fabric of space and time is distorted by the presence of mass and energy which in turn disturbs the motion of other objects, an effect we perceive as gravity. Conversely, quantum theory describes how the universe works at a subatomic level where particles also exist as waves of infinite possibility that, while strange, can be predicted with extreme accuracy. Furthermore, although earlier versions of quantum theory treated space and time separately in a somewhat Newtonian fashion, modern spacetime is fully incorporated as general and special relativity.

However, quantum field theory falls short of predicting the warping of space and time which is described in general relativity. This can cause conflicts between the two theories. For example, quantum theory states that quantum information cannot be destroyed, whereas according to general relativity, black holes can completely delete it from the universe. This is known as the black hole information paradox. It is worth noting that Stephen Hawking was able to show that the information is in fact preserved through Hawking radiation, but the union he devised was incomplete and did not equate to a universal theory of quantum gravity. Along the same lines, general relativity can be squeezed into quantum theory, yet this method does not hold up when trying to make predictions about strong gravitational effects on small scales of space and time, with a black hole for example.

The issue is that the warping of spacetime at a subatomic level is an exceptionally challenging concept. This is primarily because you need to measure a particle in order to define its location. However, according to the Heisenberg uncertainty principle, the more precisely a position is measured, the higher the energy required. Defining a location within a Planck length would require so much energy that it would create a black hole, which is also true if you try to measure a period shorter than the Planck time. Furthermore, the greater the accuracy in measuring locations, the more uncertain a particle’s momentum becomes.

On a more theoretical level, quantum theory utilises spacetime as the arena in which quantum behaviour occurs, defining it in mathematics as a smooth and continuous grid. There isn’t an issue when quantising other forces of nature such as electromagnetism, which can be developed into quantum electrodynamics because they are background-independent. However, the same cannot be said for gravity because it doesn’t occur in spacetime, it is spacetime. Trying to quantise spacetime itself leaves no coordinate system on which to ground the theory.

While it is an undoubtedly tough challenge, there has been progress in the search for a theory of quantum gravity. Presently, there are two main approaches. The first is to attempt to quantise general relativity in a way that maintains background independence whilst also removing the infinities which currently appear in mathematics. The foremost example of this is loop quantum gravity. Loop quantum gravity utilises connections which are mathematical functions that tell you how something such as a vector changes as it moves between two points in space. It tries to describe spacetime using connections instead of regular coordinates, evaluating them over closed loops so that each point connects back to itself, which creates a sort of closed circuit of the gravitational field. If the individual loops are ‘laced’ together then they can define any geometry of space, which can subsequently be quantised relatively easily. However, this theory is not without its problems. Although this method does create background independence in relation to space, it is not yet clear whether this extends to full spacetime. It also hasn’t been determined whether it is able to produce the mathematics of general relativity when applied to large, non-quantum scales.

The second approach is to consider general relativity as a phenomenon which emerges from a deeper, more universal quantum theory. The most prominent candidate for this is string theory. It describes the characteristics of many different elementary particles as different modes of vibration of a one-dimensional string, and most importantly, it integrates gravity very well. If it can be developed further, string theory promises to unify all the fundamental forces of the universe, but nevertheless, it also has its issues. In order to describe the necessary characteristics, the strings need to vibrate in more than three dimensions, specifically, it uses ten ‘curled up’ tiny dimensions which may not exist. Furthermore, no prediction of string theory has thus far been proved in an experiment which has led some physicists to declare it simply a dead end.

Gravity was the first fundamental force to be discovered but it nevertheless remains the least understood, the only one of the four that we have been unable to quantise. The hunt for a theory of quantum gravity has been driven by a belief that the same rules of gravity should apply at all scales, throughout the universe. Yet progress towards this goal has been beset by difficulties. The scales at which the empirical testing of potential theories of quantum gravity must be conducted are far beyond our current capabilities, and the apparent lack of background independence has proved a tough obstacle to overcome. However, while they undoubtedly have their issues, physicists have nonetheless continued to put forward innovative new ideas such as string theory or loop quantum gravity which may eventually provide an answer. These or something entirely new might be the key to finally unlocking a theory of everything.