The Bronstein Hypercube of Quantum Gravity

New Direction in the Foundations of Physics 2014

As advertised, I will stop the mathematical presentations for a little while and I will present interesting talks from New Direction in the Foundations of Physics 2014 conference in Washington DC.

The first talk was by Daniele Oriti and was entitled “The Bronstein Hypercube of Quantum Gravity”*. To introduce the topic I wave to say a bit about the Bronstein cube. Matvei Bronstein imagined a cube specified by the fundamental constants of nature and placed at the corners various limiting theories.

This was popularized by Sabine Hossenfelder at her blog:  and the point of Daniele Oriti’s talk is that we need an extra dimension added to this picture. First how can we visualize such an object (which is called a Tesseract)? The shadow on a 2-dimensional surface (the computer screen) looks like this:

and in each node all lines are suppose to make 90 degrees angles (impossible to build in 3D), but you get the picture.

The point is that in addition to gravitational constant, the speed of light, and Planck’s constant we need to consider N-the number of degrees of freedom- because the limits for large N is qualitatively different.

For example, it is evident that fluids represent an emergent behavior of a large number of molecules under certain conditions. Here is a picture from the talk illustrating emergence of new physics in case of a large number of degrees of freedom.

But what is the basis for this, particularly in the case of gravity? Is space-time intrinsically discrete and what we experience is only an emergent property?

In Quantum Gravity there are hints of the “disappearance of space-time”:

• In General relativity there is no absolute space
• Planck distance is very possibly a minimal length
• Existence of singularities
• Black hole thermodynamics shows that entropy is finite meaning discreetness may be present

Welcome to the world of quantum gravity where radical conceptual shifts are considered in the hope is to obtain the continuous space-time limit from discrete ingredients. Here are some examples:

• Loop Quantum Gravity: based on spin networks (graphs labeled by algebraic data). It has discrete spectra and uses path integral and Regge calculus.
• Group Field Theory (GFT): is using SU(2) and the building blocks are tetrahedrons (more precisely GFT is the second quantization version of LQG and is using spin networks dual to simplicial complexes labeled by data from the SU(2) group)
• Tensor models: removes algebraic data and keeps only the combinatorics.

But how is smooth spacetime and geometry emerge from many discrete building blocks? This is the key question in quantum gravity. In the original Bronstein cube, in the limit of large N, classical and quantum mechanics will generate solid state physics and condensed matter-fluids/hydrodynamics.

A crucial tool in the large N limit is the renormalization group. Then one can perform for example GFT renormalization in standard quantum field theory.

There are major conceptual and technical issues however. For example the fundamental degrees of freedom are ambiguous because they depend on the vacuum state (which corresponds in algebraic field theory to the representation of the algebra). Also you need to prove the emergence of robust novel properties.

As a standard example of emergence one can consider the Bose-Einstein condensate where you have a single collective wavefunction responsible for superfluidity.

The emergence problem for quantum gravity is a major open problem in physics and there are some tempting speculations that we can understand the Big Bang as a phase transition for example. In everyday life we experience phase transitions every Winter when liquid water tuns into snow and ice. Maybe the universe started its existence by condensing some primordial "quantum gravity atoms" into space-time. And maybe before the inflation period “geometrogenesis” occurred.

When we will have a good model for the emergence of space-time we can investigate if other phase transitions can be physically realized. So the prospects are exciting and amazing if we will be able to work out the problems.

Until all the puzzles of quantum gravity are solved, here are some interesting results showing the way for the emergence problem using GFT renormalization: arXiv:1303.3576 (PRL 111 (2013) 031301) and arXiv:1311.1238 Here (states of) macroscopic homogeneous universes are build as condensate states in group field theory. This is similar with coherent (condensate) states in Bose-Einstein condensates, and the effective dynamic is extracted directly from the underlying quantum theory.

For the benefit of the reader, let me make a few additional points not directly relevant to the talk but which help frame the general context: is it really necessary to quantize gravity? The answer is yes because it can be shown that there are no consistent mixed theories of quantum and classical physics. And with quantum mechanics we naturally encounter discrete spectra which give rise to quantized areas and volumes. String theory takes another route and presupposes a continuous space-time background, but the supporters of loop quantum gravity and related approaches counter that with the main lesson from general relativity that there is no such thing as an absolute background. String theorists reply by pointing out that a discrete space-time would have measurable consequences, like violations of Lorenz symmetry for light. Why? The same reason the sky is blue: light gets scattered by the molecules of air and different colors (wavelengths) scatter differently (in particular the blue color gets scattered the most). Similarly light can get scattered by the granular structure of space-time. The effect is small, but it can be amplified over galactic distances. This was tested with supernova explosion observations which checked the arrival time of various wavelengths and no delay was observed. So the background independent theories should also solve the Lorenz symmetry problem, but it is hoped that space-time emergence will take care of this issue.

* I thank Daniele Oriti for giving the permission to post his completye talk. Please use the link to view the document. I also thank him for suggestions to make this post better. I am not an expert in quantum gravity and I am the sole person responsible for any inaccuracies in this post.