How the old Theory of Everything gets a new life

For decades, physicists have tried to create a quantum theory of gravity. Now the approach dating back to the 1970s is beginning to draw attention to itself.

Twenty-five particles and four interactions. This description, the Standard Model of Particle Physics, is the best explanation available to physicists today for everything. It is neat and simple, but does not fully satisfy anyone. Most annoying to physicists is that one of the interactions, gravity, stands out from the general range. Gravity is different.



Unlike electromagnetic, strong and weak nuclear interactions, gravity is not a quantum theory. This is not only aesthetic, but also a mathematical headache. We know that particles have both quantum properties and gravitational fields, therefore gravitational fields must have quantum properties, like particles causing them. But the theory of quantum gravity is very difficult to find.



In the 1960s, Richard Feynman and Bryce Dewitt decided to quantize gravity using the same techniques that made it possible to transfer electromagnetism to quantum theory, quantum electrodynamics. Unfortunately, when applied to gravity, well-known technicians gave out a theory that, when extrapolated to high energies, began to produce an infinite amount of infinities. So this quantization of gravity was considered incurably sick, and it could only be used when gravity is very weak.

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Since then, physicists have made several other attempts to quantize gravity, hoping to find a theory that could work in strong gravity. String theory , loop quantum gravity , causal dynamic triangulation, and some other theories have sought this goal. So far, none of them have any experiments confirming it. Each has mathematical pros and cons, and there’s no end in sight. But while these approaches competed for attention, they were overtaken by an old competitor.



A theory called "asymptotically safe gravity" was proposed in 1978 by Stephen Weinberg . Weinberg, who only a year later shared the Nobel Prize with Sheldon Lee Glashow and Abdus Salam for combining electromagnetic and weak nuclear interactions, realized that problems with the naive quantization of gravity would not necessarily bury this theory. Although everything looks as if the theory fails to extrapolate to high energies, this failure may never occur. But in order to say what exactly is happening, the researchers had to wait for the emergence of new mathematical methods, which only recently came at their disposal.



In quantum theories, all interactions depend on the energy at which they occur, which means that the theory changes when some interactions turn out to be more significant and some less. This change can be quantized by counting as numbers included in the theory — parameters — depend on energy. For example, a strong nuclear interaction, becomes weak at high energies, when a parameter such as “interaction constant” approaches zero. This property is known as " asymptotic safety ", and it cost another Nobel Prize , in 2004, which was received by Frank Wilczek , David Gross and David Polyzer .



An asymptotically safe theory behaves well at high energies and does not cause trouble. Gravity quantization does not belong to this type of theory, but, as Weinberg noted, a weaker criterion would fit: for quantum gravity to work, researchers must be able to describe the theory at high energies only with the help of a finite number of parameters. This situation is the opposite of what they encounter in a naive extrapolation, requiring an infinite number of indeterminate parameters. Moreover, none of the parameters also tend to infinity. These two requirements — a finite number of parameters and a finite value of parameters — make the theory “asymptotically safe.”



In other words, gravity would be asymptotically safe if at high energies it behaved as well as at low energies. By itself, this idea is not particularly interesting. The most interesting thing begins after understanding that such good behavior does not necessarily contradict what we already know about this theory at low energies (from the early works of DeWitt and Feynman).



And although the idea that gravity could be asymptotically safe, has existed for four decades, it was not until the late 1990s that the studies conducted by Christoph Wetterich from the University of Heidelberg and Martin Reuter from the University of Mainz helped to reveal asymptotically safe gravity. Their work provided the mathematical formalism needed to calculate what happens to the quantum theory of gravity at high energies. Thus, the strategy of moving toward asymptotic safety is to begin with a theory at low energies and use new mathematical methods to learn how to arrive at asymptotic safety.



So is gravity asymptotically safe? No one has yet proved this, but researchers have several independent arguments in support of this idea. First, studies of gravitational theories in space-time of smaller dimensions, which are much easier to do, have found that in these cases gravity is asymptotically safe. Secondly, approximate calculations also support this feature. Third, the researchers applied general methods to the study of simpler theories that did not encompass gravity, and found them to be reliable.



The main problem with this approach is that calculations in full space (with an infinite number of measurements!) Are impossible. To make calculations valid, researchers study a small part of the space — but then the results provide only a limited level of knowledge. Therefore, although the existing calculations do not contradict asymptotic safety, the situation remained inconclusive. There is one more unanswered question. Even if the theory is asymptotically safe, at high energies it can become physically meaningless, since it can break down some necessary elements of quantum theory.



Nevertheless, physicists have already tested the ideas behind asymptotic safety. If gravity is asymptotically safe - that is, it behaves well at high energies - this imposes restrictions on the number of fundamental particles that may exist. This restriction puts asymptotically safe gravity in conflict with several attempts at great unification . For example, the simplest version of supersymmetry — an old popular theory that predicts the existence of partners for all particles — is not asymptotically safe. The simplest version of supersymmetry, meanwhile, was eliminated thanks to experiments at the Large Hadron Collider, as well as several other extensions proposed to the Standard Model. But if physicists had previously studied their asymptotic behavior, they would have concluded that these ideas would not have worked anyway.



Another recent study has shown that asymptotic safety limits particle masses. From this it follows that the mass difference between the upper and lower quarks should not be greater than a certain value. If by this time we had not measured the mass of the upper quark, this could be used as a prediction.



These calculations are based on estimates that may be unjustified, but the results demonstrate the power of this approach. The most important consequence is that physics on those energies where all interactions can unite — usually they are considered hopelessly unattainable — is complexly connected with low-energy physics; they are united by the requirement of asymptotic safety.



When I talk with colleagues who are not working on asymptotically safe gravity, they call this approach “disappointing.” I think this is because asymptotic safety means the absence of something new, which one could learn from quantum gravity, that it’s all the same story, just more quantum field theory, everything, as usual.



But asymptotic security not only provides a link between the low energies to be tested and the unattainable high ones — as the above examples show — it also does not have to contradict another way of quantizing gravity. This is because the extrapolation underlying asymptotic security does not exclude the appearance of a more fundamental description of spacetime at higher energies - for example, with strings or with networks. Asymptotic security does not just not disappoint, it can help us, finally, to combine the famous Universe with the quantum behavior of spacetime.