Ask Ethan No. 91: Is string theory necessary for quantum gravity?

It seems to me that so many different interesting things have happened in string theory that it cannot be wrong. People do not understand it well, but I do not believe that there is a cosmic conspiracy that has created such a thing that has nothing to do with the real world.

Edward whitten

There is no doubt that from a mathematical point of view we have no shortcomings in all sorts of beautiful and elegant mathematical apparatuses. But not all of them make sense in the physical universe. For every brilliant idea that describes what we can see and measure, there is another brilliant idea that tries to describe the same thing, but it turns out to be wrong. Discussing questions regarding string theory alternatives last week, I found the following statement:

Hope you have time to do an article on quantum gravity. More precisely, I wonder if there is progress in this area over the past 5-10 years. From my unprofessional point of view, it seems that things got stuck since when string theory began to lose confidence due to problems with its checks and due to the presence of ^10,500 different solutions. Is this really so?

Firstly, there is a big difference between quantum gravity, a solution to string theory, and other alternatives.

Let's start with our dear universe. There is a general theory of relativity - our theory of gravity. She postulates that the whole system works somewhat more cunningly than the simple "long-range action" that Newton invented, in which all the masses in all places of the universe emitted forces acting on each other, inversely proportional to the square of the distance between them.

Mass, as Einstein explained using the equivalence principle E = mc ²in 1907, there is only one form of energy. This energy wraps the very fabric of space-time, changing the path along which the bodies move, and bending what the observer would see as a Cartesian lattice. Objects are not accelerated by an invisible force, but simply travel along a path curved by the various forms of energy present in the universe.

This is gravity.



On the other hand, we have the quantum laws of nature. Electromagnetism controlled by electrically charged particles and their motion. They are described by the carrier of interactions, the photon, which acts as an intermediary and due to which a phenomenon arises that we associate with electricity and magnetism. There are still two nuclear forces - the weak, responsible for radioactive decay, and the strong, which holds the nuclei of atoms together and generally allows protons and neutrons to exist.

Calculations of these forces are done in flat space-time - so every student begins to study quantum field theory. But in the presence of curved space-time, obeying the general theory of relativity, everything starts to behave incorrectly.



“Well, let’s do our quantum calculations against the background of a curved space!” - you suggest. This is called semi-classical gravity, and allows us to calculate things like Hawking radiation. But even then, these calculations occur only on the horizon of the events of the black hole, and not where gravity is even stronger. As the physicist Sabina Hossenfelder explained , we need the quantum theory of gravity in several places, and all of them are connected with the physics of gravity at microscopic distances.



For example, what happens in the center of a black hole? A singularity - but this is not so much a point of infinite density as a point at which the mathematics of GR gives meaningless answers for potentials and forces. What happens, for example, when an electron passes through two slots at the same time?



Does the gravitational field pass through both slots? Through one of them? There are no answers to this question in GR.

As if there should be a quantum theory of gravity for such and other similar problems associated with a “smooth” general relativity. To explain what happens at short distances in the presence of sources of gravity, or mass, we need a quantum, discrete, that is, particle-based theory of gravity.

Thanks to the properties of general relativity, we already know something.



Known quantum forces are transmitted by particles called bosons, or by particles with a whole spin. A photon transmits an electromagnetic interaction, W and Z bosons transmit a weak interaction, and the gluons transmit a strong one. For all these particles, the spin is equal to 1, that is, the spin of massive particles (W and Z) can take values ​​-1, 0 or +1, and massless (gluons and photons) - only -1 or +1.

The Higgs boson is a boson, although it does not transfer interaction and has spin 0. Our knowledge of gravity (GR is the tensor theory of gravity) says that it should be transmitted by a massless particle with spin 2, that is, one whose spin can take values -2 or +2.



That is, we already know something about the quantum theory of gravity, even before we formulate it! Whatever it may be, it must correspond to GR at large distances - just as GR must degenerate into the Newtonian theory of gravity in cases of weak fields.

But how? How can gravity be quantified so that the theory is correct in describing the world around it, compatible with GR and TKG, and, preferably, leads to calculated predictions of such phenomena that can be observed and measured?

You have heard of the leading candidate - this is string theory.



1) String Theory. This is an interesting apparatus - it can include all fields and particles known to the Standard Model, both fermions and bosons. It also includes a ten-dimensional tensor-scalar theory of gravity, where there are 9 spatial, one temporal dimension and a scalar field parameter. Removing six dimensions using compactification (an incompletely described process) and moving the parameter ω, which describes scalar integration, to infinity, we obtain GR.

But with TS there are many phenomenological problems. For example, she predicts the presence of a bunch of new particles, including all supersymmetric ones, none of which were found. She claims that she does not need “free parameters” as the Standard Model (particle mass), but she replaces this problem with an even worse one. Kent talks about ^10,500various solutions - and they refer to the vacuum expectations of the string field values, but there is no mechanism that would allow them to be established. If you need the TS to work, you discard the dynamics and say: "Well, it was chosen according to the anthropic principle."

But ST is far from the only option.



2) Loop quantum gravity. PCG, instead of quantifying particles, suggests considering the option of discrete space. Imagine a stretched sheet with a bowling ball in the middle. Only this fabric will not be smooth - the real sheet is actually quantified, it is made of molecules, and those of atoms, and those of nuclei and electrons.

So it is with space. It may work like a fabric, but it can also be made from finite entities. Maybe it is sewn and loops - where does the theory take its name. Sew the loops and you get a network representing the quantum state of the gravitational field. In this case, not only matter, but space will be quantized. How to arrive at realistic quantum computations from this idea is an open question, and his research, which made a breakthrough in 2007-2008, is still actively moving forward.



3) Asymptotically safe gravity. My favorite attempt to approach the CTG. Asymptotic freedomwas developed in the 70s to explain the unusual property of strong interactions - at short distances, the force is very weak, and as the color-charged particles are removed, it intensifies. Unlike electromagnetism, in which the interaction constant is small, in strong interaction it is large. Thanks to the interesting properties of quantum chromodynamics, if you build a system without colors, the strength of the interactions will decrease very quickly.

Asymptotic security seems to solve the main problem associated with this - you do not need the interaction constants small, or tending to zero. You need the constants to be finite. All interaction constants vary with energy, and asymptotic safety simply selects a value for the constant in high-energy cases, and everything else after that can be calculated for lower energies.

True, so far we have figured out how to cope with this only in two-dimensional space, where 1 dimension is in space and one is in time. But the process is going on. Christoph Wetterich published two breakthrough works in the 90s. And six years ago, he used this theory to predict the mass of the Higgs boson before it was discovered by the LHC.



And the result coincided with reality. This is such a wonderful prediction that when the bar of calculation errors drops even lower and the masses of the W-boson and Higgs boson are finalized, we don’t even need other elementary particles (like supersymmetric) for physics to behave stably all the way to Planck scales.

It is not only promising, it has the same positive properties as string theory: it quantifies gravity, degenerates to general relativity at low energies, and is UV-finite. And she, unlike strings, does not need a carriage of any additional junk for which there is no evidence.



4) Causal dynamic triangulation. This is a new product developed in 2000 by Rinate Loll.. It resembles the PCG in terms of the discreteness of space, but mainly deals with the evolution of space itself. One of the interesting properties of this theory is that time is also discrete. The theory implies 4-dimensional space-time (not postulated, but it follows), which at high energies turns into two-dimensional. It is based on the mathematical concept of a simplex, which is a multidimensional analogue of a triangle. 2-simplex is a triangle, 3-simplex is a tetrahedron, and so on. Interestingly, the principle of preservation of causality clearly follows from this theory. She may be able to describe gravity, but so far we are not 100% sure that the Standard Model of elementary particles can be pushed into it.



5) Induced gravity. The most speculative and recent theory that became known in 2009, when Eric Verlinde proposed the theory of entropy gravity - a model where gravity is not the main force, but follows from a phenomenon associated with entropy. The seeds of this theory go back to the discovery of conditions for the emergence of baryonic asymmetry of the universe, to the concept of Andrei Sakharov, proposed by him in 1967. The theory is too new to ask much from it.



Well, what do we have today regarding the issue of quantum gravity. We need it to make the universe work at particle levels, but we do not know how it looks and whether any of the theories described will play. String theory is the most studied of all, asymptotically safe gravity is my favorite, loop quantum gravity is the second most popular of the five, and causal dynamic triangulation and induced gravity are new theories that are now being actively developed.