https://www.kitp.ucsb.edu/statement-by-the-yangmills-working-group
The proof is claimed to be "rigorous", which is strange, because in quantum mechanics, nothing seems to be rigorous.
We may have found a fatal problem in the proof.
What is the momentum of the energy of the vacuum? Any value given to the momentum introduces preferred coordinates and breaks Galilei covariance
The proof is based on a lattice model, in which we assume that "zero-point fluctuations" of the fields are allowed if the wavelength of the fluctuation is larger than the lattice spacing.
There is a lot of energy E in zero-point fluctuations. The momentum p of that energy is zero relative to the lattice. But this breaks Galilean covariance: all inertial frames should be equivalent in vacuum.
How to restore Galilean covariance: "renormalize" the energy density of the zero-point fluctuations to zero by subtracting some constant C from the density. If the energy density is zero, then we have no need to assign any velocity, or momentum, to that density.
We declare the lowest energy of the zero-point fluctuations as the "vacuum". An example from the real world: let us have a crystal. Even at zero kelvin, there is oscillation of atoms and groups of atoms in the crystal. They are the zero-point fluctuations in this system. We declare the state at 0 K as the "vacuum" in that system and define its energy density to be zero.
Let us then reduce the lattice spacing toward zero and take the limit. We keep the energy density of zero-point fluctuations renormalized to zero. This is what the OpenAI proof presumably does.
However, there is a problem in this. If we have interactions between fields, then matter can interact with zero-point fluctuations in the vacuum. Those interactions can extract some energy from the zero-point fluctuations, like they do if the Casimir effect is explained through zero-point fluctuations.
The problem: what is the momentum of the energy which we extract from the vacuum? We may assume that the momentum is zero relative to the lattice. But then we break Galilean invariance.
*** WORK IN PROGRESS ***
