Why are we searching for TOEs when we can't even see our GUT?
I should probably clarify what a TOE and a GUT is here:
TOE = Theory of Everything
GUT = Grand Unified Theory.
Now, the average physicist might begin to appreciate how clever the title is. It also brings to light some core issues currently surrounding high energy theory and the competing ideas what a GUT, or usually, a theory of quantum gravity (QG) may look like. Before I may state my issue with the current atmosphere in theoretical physics, lets review a few of the current programs for TOEs and GUTs (or QG).
Currently, the only TOE around is String Theory. This theory states that all particles and forces, are mediated by a singular, fundamental constitute of reality, a string. The string can be closed, or open. If open, the string must be connected to another object, that must be fundamental, called D-branes. Currently, string theory has made achievements mainly in mathematics, perhaps by giving a qualitative proof of the Holographic Principle (originally stated by 't Hooft then formulated by Susskind), and one could argue that string theory has shown on mathematically deep the final solution to a unified field theory will be (which also runs into philosophical, yet mathematically sound, issues such as Godel's Incompleteness Theorem). However, there are issues: practically infinite amount of vacua solutions, no solid predictions (unless and unrealistic amount of symmetry is used), no-singular formulation, and the one that kills me no positive cosmological constant.
As for GUTs and QG schemes, I categorize them as being almost identical, with regards to if you can formulate a theory of QG, then it should nicely fit in with the standard model as: (QG) x SU(3) x SU(2) x U(1), but it doesn't have to be a group (my reasoning stems from early universe arguments).
Anyways, a handful of QG formulations are: Loop Quantum Gravity (LQG), Twistor Theory, Group Field Theory (constructed as QFT but in curved spacetime), Wheeler-DeWitt (if you can solve it also based on canonical QG), and a lot more (more mathematically inclined). Of course, just like string theory, there are issues: consistency of the theory and mathematically, LQG can't be shown to reproduce GR (general relativity), LQG also hasn't been shown to unify with the other forces, and formulating GR as a gauge theory (in the QFT sense, since GR is a gauge theory in a broad sense) it seems there is not a basic group structure (like SU(2)) that can re-construct GR.
Now, for the statement of this post, we should first understand the quantum gravity theories currently formulated, then, find a grand unified theory, now finally, formulate out of this grand theory a theory of everything. Instead of "jumping the gun."
It is for this reason, that I would rather study more QG theories that stem from a relativist point of view, and not a gung-ho particle physics theory of paper after paper after paper after paper.... So, I implore one to adopt the point of view in solving research questions (at least try it once) to first draw a picture, or representation of what you are thinking and working on, and put mathematical structure around the diagram. Next, write down a plausible theory in abstract notation, that could dictate the image. Finally, take the abstract formulae, put them in a particular view-point (or reference frame), find their component notation and solve. If you can't get step one (draw), then this is where a nice walk takes place, to enjoy the surroundings (there are geometric structures in everything)!
For example, take a fishnet being thrown onto a lake or general body of water. The water is your manifold M, with properties or transforms that behave like waves, then the fishnet becomes your coordinate system where you can now compute local geometry and construct a 2 (or 3) index tensor T, that counts the fish-per square foot of net!