End of reductionism
0:00 – Does reductionism end?
2:24 – Why there is probably a final theory
7h00 – Theory of quantum holonomy
12:53 – Surprising implications of QHT
Is there a final theory that can put an end to our reductionist research over ever shorter distances? Or is there no end to reductionism? There should be an end point because as the object of our measurement becomes small enough, the high energies required to measure it will create a black hole. And no information can come out of a black hole. So there is a limit to measurable reality.
We have united seemingly different forces in the past. For example, the unification of electricity and magnetism, and weak and electromagnetic forces. To continue this reductionism, we want a theory that unifies all known forces. Today we have two global theories for forces: Einstein’s theory of general relativity for gravity and the Standard Model for electromagnetic force, weak and strong.
The problem is, the Standard Model is a quantum field theory, but General Relativity is a classical field theory. The two are not compatible.
Past attempts for a theory of everything include string theory and looping quantum gravity. But string theory does not produce any falsifiable results. His math is too flexible. Looping quantum gravity is only about gravity and not about other forces.
The theory of quantum holonomy or QHT was pioneered by two Danish scientists, physicist Jesper Grimstrup and mathematician Johannes Aastrup. He begins by asking the question, how can a theory be immune to further scientific reductions, so that reductionism stops?
The presumed idea is that the easiest way to describe the universe is to move objects in three-dimensional space. The theory is based on the mathematics of empty three-dimensional space, just space, not even time. The starting point of QHT is therefore the mathematics of moving objects. There are endless ways to move an arbitrary object between points in space.
Each of these combinations of movements from point A to point B is called a recipe. A recipe for a combination of moves in physics is called a gauge field. A gauge field is the recipe for moving a particle from point A to point B. Gauge fields are what make up forces in the Standard Model. Since these are recipes for moving objects around in space, they represent how things interact with each other or how forces work.
The sum of all math recipes is called the “Config Space” of these recipes. The key point of QHT is that this space has geometry and stores a lot of information. Geometry means that two different recipes for moving objects can be considered to have a relation to each other. This is complicated but can be proved mathematically.
Grimstrup and Aastrup discovered that this geometry results in mathematics that looks almost identical to the mathematics we already know from quantum field theory – this includes Standard Model mathematics.
From the geometry you can get a Bott-Dirac operator. The square of this operator gives us the Hamiltonian for particles of matter and particles carrying force. The Hamiltonian represents the formula for all the energy in a system.
# Theory of everything
Once you have a description of the energies of all matter and the forces in the universe, that’s all you need to understand how matter interacts in the universe, and that’s basically all we need to do. would need to describe the universe, once all the calculations are worked out. Just considering the motions of objects in empty space, all that rich math that seems