If your theory of everything has tensors set equal to scalars then it is wrong. Simply put, a scalar is a single number that is widely recognized. A vector consists of 3-4 numbers arranged in a specific sequence, typically representing coordinates and time. A tensor is an array of these numbers in a 3x3 or 4x4 matrix. There are nuanced details to this; for instance, in certain complex scenarios, a set of numbers can be defined where scalars are represented as pairs of numbers, like complex numbers in the form of a+bi. However, to maintain simplicity, we will not delve into those complexities. To summarize, the initial statement of this post can be rephrased to say that a 4x4 matrix of numbers is not equivalent to a single number.

In the video, Sabine Hossenfelder effectively critiques a published 'theory of everything' paper. My brief impression of this paper is as follows: Upon reading the abstract, its meaning is unclear to me. This is not because I lack expertise in the subject matter and require further study, but rather because the abstract fails to convey its intent. Additionally, I noticed numerous instances where equations equate scalars to rank-2 tensors, and where scalars, vectors, and rank-2 tensors are added and subtracted.

In simple terms an object with two Greek indices is a tensor. You can multiply a tensor by a scalar but not add a scalar to one. Likewise an object with one index is a vector. These things cannot be added and subtracted. Am I totally insane or did no human being read this?

Mathematically, this is not possible. This is not a subtle thing either I mean. Think about it. If I tell you to walk 5 miles west. Then add 5 miles per hour to that (not specifying a direction). I have just told you to take a vector and add a scalar to it that has totally different units. It is like adding $5 to 5 square feet.

Problems that are fundamentally tensorial can be formulated in terms of invariant scalar quantities by contracting indices (multiplying one tensor by another in a specific manner). This method solves many problems. However, these rules are not applied in this paper. While attempting to create a theory of everything is commendable, this paper appears to be either very confusing or fundamentally flawed.

Indeed, considering the paper and my knowledge as a part-time AI trainer, it wouldn't surprise me if it were AI-generated to demonstrate that such a paper could bypass peer review. I'm not referring to a paper written by a person and then copy-edited with AI assistance. That would constitute using AI as a tool. An LLM with limited physics expertise might produce equations that erroneously equate a vector with a scalar.  IF this is AI generated it is wholly AI generated. 

That said I could somehow be wrong, I don't think so though. 

References.

Chavis Srichan, Pobporn Danvirutai, Adrian David Cheok, Jun Cai, Ying Yan, “On the same origin of quantum physics and general relativity from Riemannian geometry and Planck scale formalism”, Astroparticle Physics, Volume 164, 2025, 103036, ISSN 0927-6505, https://doi.org/10.1016/j.astropartphys.2024.103036. (https://www.sciencedirect.com/science/article/pii/S0927650524001130)

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