Everything you need to know about the Theory of Everything

One of the great ambitions of modern physics is to construct a theory that unites all four fundamental forces under one banner. Currently, two separate theories make the magic happen: general relativity describes gravity, while quantum field theory (the Standard Model) accounts for the weak force, strong force, and electromagnetism.

Individually, each theory is incredibly accurate, experimentally verified, and used in everyday technology like MRIs and GPS. The problem? They’re incompatible.

A potential “Theory of Everything” (or ToE), however, would bring it all together and help physicists better describe the universe at every level.

But what would a ToE look like? Why isn’t everything already under one theory? And why is gravity the odd one out?

Today, we go toe-to-toe with the ToE.

What is a Theory of Everything?

“The quickest and oldest definition of a ToE is a unification of the four fundamental forces,” says Luca Ciambelli, postdoctoral researcher in quantum gravity at Perimeter. Ciambelli’s research focuses on finding a description of gravity that fits into quantum field theory, sometimes called quantizing gravity.

A Theory of Everything differs from a Grand Unified Theory (GUT), a theory that would unite the three forces already under the Standard Model in a similar way to how electricity and magnetism were unified by James Clerk Maxwell in 1865. Currently, electromagnetism plus the strong and weak nuclear forces are well described, but physicists wonder why they are separate, especially at high energy levels.

“If you ask me, solving the Theory of Everything is understanding quantum gravity. Gravity as a classical theory is amazingly well described,” says Ciambelli, “Put it together with the Standard Model and that, for me, would be a good definition of what the ToE should be. A unified theory of the fundamental forces that requires quantizing gravity.”

Gravity, however, has been remarkably resistant to any attempt to quantize it.

Why general relativity and quantum field theory are incompatible

There are three major reasons why quantum field theory and gravity don’t get along: scale, approach, and ‘renormalization’ (a mathematical process in quantum field theory).

The scale problem

While the effects of quantum mechanics are most apparent at the smallest scales, general relativity has the greatest effect at the largest. In the boring middle of our every day, both are overkill. The effects of general relativity are so minute, for example, that NASA scientists were able to ignore it to send rockets to the Moon using Isaac Newton’s centuries old equations for gravity instead. Meanwhile, most of us go about our day without worrying about quantum effects like teleportation or entanglement – we’re too big for these processes to show up.

“The problem is that general relativity and quantum mechanics have a big zone where neither of them are really important. That’s where we live, which is why it took humans so long to figure them out,” says Geoffrey Ryan, research scientist at Perimeter who studies strong gravity, specifically how binary black holes evolve in the centres of galaxies. "You need something that's both incredibly heavy, so gravity is appreciable, and incredibly small, so that quantum mechanics applies. This is why black holes are so interesting for many physicists working on quantum gravity.”

Different approaches

Quantum field theory and general relativity approach their descriptions differently. General relativity is deterministic, meaning you can determine an output based on the input. No randomness is involved. Quantum, by contrast, is probabilistic. It uses probability distributions to make predictions based on those distributions. It also comes with a host of other questions.

“With general relativity, there's no quantum. There's no uncertainty principle,” says Ciambelli. “In quantum mechanics, you have to ask questions like: What is a measurement? How do I construct my apparatus? Do I change the state of the system by making a measurement? All these are very beautiful, important quantum processes.”

The math doesn’t add up

Finally, there is the mathematical issue of renormalization. When you describe interactions between particles in quantum field theory, the calculations generate infinities that need to be controlled by creating different parameters. Renormalization is the process of accounting for these infinities.

Gravity, it turns out, is non-renormalizable. That is, the infinities become a problem that the usual processes can’t correct.

“When you generate infinities in gravity, it generates more new infinities than can be absorbed into the parameters you have. Then you have to introduce new parameters absorbing those infinites,” says Ryan. “Eventually, you need an infinite number of parameters to absorb all these infinities. The results are completely unworkable. It’s like trying to fix a car with a piece of spaghetti.”

The math just doesn’t work, which is why researchers are taking such pains to make the math, and quantum gravity, make sense.

So how do we get a Theory of Everything?

Very broadly, a ToE could emerge from either quantizing gravity (making it fit into a probabilistic model that’s renormalizable and works in quantum field theory) or upending our understanding of general relativity and quantum mechanics altogether.

Quantizing gravity, in some ways, could be the most straightforward approach. If researchers discover a description of gravity that is compatible with quantum field theory and the Standard Model, then we would be closer to a ToE.

Today, there are a few leading theories for quantum gravity, many of which are being actively researched at Perimeter Institute. These include loop quantum gravity, which reconsiders the geometry of spacetime, and string theory, which posits particles are strings vibrating at multiple dimensions.

Upending our understanding of both quantum mechanics and general relativity is also a potential route. Since both have known limitations, either theory may need corrections, or a new theory altogether might replace them. That would require an approach that’s very different from our current understandings of both theories.

Of course, there’s also a third option. Maybe a ToE doesn’t exist. Nature continually defies our attempts to categorize it. Viruses, for example, exist somewhere between our definitions of animate and inanimate. Light acts as a wave and a particle at the same time. Perhaps a ToE is an attempt to conform nature to our thinking rather than a rigorous description of reality.

Ryan has his doubts about this final possibility, however. “The universe doesn’t operate on the whims of a mad god,” he says. “It does appear that there’s some structure here, some regularity, some order.”

“It feels like this is an answerable question. It’s workable. Hard, but workable.”

Whatever the path to a ToE, whether it’s quantizing gravity, upending our baseline theories, or accepting it’s not possible, the result will need to be something we can use and demonstrate. 

“Even if a ToE does exist, we won’t learn a lot of science if we can’t connect it to real life,” says Ciambelli. “Real-life implications will only happen if our ToE can help us take a step forward.”