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We have described the two great theories of the 20th century: the gently curving world of general relativity and the bubbling sea of quantum mechanics. They enable us to study the physics of huge, heavy galaxies, and tiny, energetic atoms. But what about the boundaries? Can we model the beginning of the universe or the inside of a black hole? There, matter is squashed into a space so small that our physics breaks down. Is it even possible to write down one equation that describes reality?

So far, no.

There are four fundamental forces in the Universe – gravity, electromagnetism, the weak force and the strong force. At present, general relativity describes gravity, while QFT accounts for the other three. Physicists expect that at high energies all these forces will fit into a single theoretical framework, sometimes called a Theory of Everything. This isn’t a very good name though – it might explain how things fit together on the smallest scales, but wouldn’t be much use for fixing your plumbing!

The electromagnetic and weak interactions are linked at high energies into a single framework called electroweak theory, for which Sheldon Glashow, Abdus Salam and Steven Weinberg received the 1979 Nobel Prize. This theory predicted the particles which carry the weak force, which were discovered in 1983.

There are candidate proposals to unify the strong, weak and electromagnetic interactions into a single force at high enough energies. Such ideas are called Grand Unified Theories. They have a reasonable amount of theoretical appeal but attempts to find experimental evidence – in particular through searches for decay of the atomic particle, the proton – have failed.

But when it comes to adding gravity into the mix, physicists are stumped. If we try to reconcile gravity and the other forces in the most obvious way, we get infinities. Infinity is a physicist’s brick wall – it is impossible for real things to have an infinite value! Where infinities appear there must be a problem with the theory.

General relativity gives infinite answers for regions of space that are very heavy but extremely small, like the inside of a black hole. Meanwhile our assumption that QFT works on arbitrarily small scales leads to infinite results.

Some of the problems may lie in the mismatch between the fundamental principles that govern general relativity and quantum mechanics. General relativity tells us that space and time are no longer absolute: they themselves become dynamical objects. On the contrary, in quantum field theories space and time are the fixed background against which fields are defined: variables depend precisely on where they are.

Furthermore, our interpretation of quantum mechanics is inseparably entwined with the role we play as observers. But in general relativity the observer makes no difference to the theory.

Finally, general relativity requires a smooth fabric of space, warped by mass. But the uncertainty principle in quantum mechanics tells us that nothing is really smooth: even empty space must be foaming with quantum fluctuations. It seems the most essential elements of the theories are incompatible.

We need a new theory allowing general relativity and quantum mechanics to coexist peacefully.  This theory could attempt to solve the problems of each to bring them together. Or it might start afresh and establish completely new ideas of reality.

String theory is an example of such a theory.

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