Abandoning Lorentz Transformations

Nima Arkani-Hamed says we should find a reformulation of QFT which removes the fabric of spacetime. This is a novel idea, as it will unambiguously allow for information to be transferred between conformal infinity and the spacetime we live in.

Assume electric charge warps spacetime. But not very much. If this is true, then F=kqq/r^2 breaks down classically because we changed r. The typical calculational procedure says q is renormalized, which is an error in our philosophical framework. This error gets propagated from microsystems to macrosystems. Information is destroyed, due to the quantum mechanical nature of “superrotations”, the generators of quantum rotation. Once this happens, we have introduced bad infinities into our theory. If the fabric of spacetime is removed, then no ambiguities or infinities are ever brought into the system. If you do not remove spacetime, it almost seems that MOND ideas may be sensible or that energy conservation breaks down. BMS Symmetry preserves this classical notion of energy and momentum and proves it is well defined. However, it neglected the dynamical nature of rotations from it’s studies, which is inherently quantum mechanically driven fluctuations.

But wait! There should be a conservation of infinities. Where did this divergence go? We choose a path integral which has integrated over all of spacetime, leaving only the quantum mechanical Scri of Penrose. Now that we have integrated over all of spacetime, we must now integrate over an infinite number of particle collisions and include that in our path integral. With entanglement, quaternions, Chris Doran’s geometric algebra, and Nima’s passion, we can reformulate QFT sensibly for gravity, as we can have computer simulate gravitational scattering of a few particles. As long as we take the analytic structure of these few particles, rather than an infinite number of particles, we can transfer information without loss of anything. I conjecture that if you integrate over 4 dimensions of spacetime, then you can only be right if your theory uses gravitational scattering of 4 or less gravitons. If you are 100% certain that more than 4 gravitons would never interact, then you can pretend spacetime is always essentially flat and renormalize everything okay using dimensional regularization. The reality is that physicists are entities which exist in an infinite dimensional realm.

This motivates the study of BMS symmetry and extending it rigorously quantum mechanically. The difficulty is constructing the method for performing this path integral over spacetime. It is an integral that destroys all information about distances between objects and only leaves the information of conformal infinity.

I claim that non-standard analysis could be taught to a computer, and a double copy of bits could be used to simulate a quantum computer. This could then be tested against experimental evidence, and we could simulate simple quantum gravity systems. In order to remove spacetime, we must throw away our current notion of a Lorentz transformation. I define a new type of transformation, which is a new type of fundamentally quantum mechanical and special relativistic theory.

Spacetime is ill-defined at short distances, so it makes most sense to integrate out the fabric of spacetime to actually know what we are talking about. It seems that the methods of Doran may help with rigorously defining this new method for solving the path integral. Think of it as integrating out spacetime, but still having momentum space around because life is complex. Now you can integrate over momentum space and not get infinities, because there is no longer any reference to the fabric of spacetime, no distance is ever referred to.

It seems that in order for the BMS symmetry to be real, we might need to make the assumption that humans exist in an infinite dimensional realm, which is difficult to precisely define mathematically. Energy can be transferred through people by emotions. This illogical type of statement is actually logical, yet does not exist in a 4 dimensional universe. It only exists in infinite dimensional universes. Essentially, humans have the ability to control which dimension they are in. This changes our perception of reality in ways we cannot fully comprehend… yet!


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