Cristinel Stoica's essay is very relevant to points I have made above, so I show comments I made on his thread:
Cristi gets off to a great start showing the isomorphism between 'number scrabble' and 'tic-tac-toe'. He notes that "in mathematics, isomorphism's are ubiquitous", mentioning that Euclidian geometry ~ axiomatics ~ symmetries ~ numbers/equations, for example.
This supports very nicely my thesis that physicists project mathematical structure onto physical reality, and then come to believe that physical reality has that structure. While it is relatively simple for competent mathematicians to 'switch' from one formulation to another isomorphic formulation, the physicist who "freezes" the projected mathematical structure onto physical reality has a tendency to "see" reality is having that structure.
For example, spins tend to align in fields such that statistically they are aligned or anti-aligned with each other in neighborhood/domains. Based on an over-simplistic interpretation of Stern-Gerlach data, Pauli projected a 'qubit' structure, O|+> = +|+>, O|-> = -|-> onto spin, despite that the SG data is distributed almost exactly as predicted by calculations of 3D spin traversing an inhomogeneous magnetic field. Based on Pauli's 'qubit'-based Hamiltonian, Bell 'believed' the qubit to be real and thus required qubit results: A = +/-1, B = +/-1 rather than variable deflection as seen in the data. The variable data satisfies Bell's relation which he claims is impossible to satisfy.
In another comment Cristi states: "Because Bell's theorem is a theorem. Trying to refute it is like trying to find in Euclidean geometry a right triangle which violates Pythagoras's theorem. It is simply impossible." Of course Bell's theorem is a foregone conclusion, from his very first equation, in which he forces the only allowed data to be +1 or -1. There is no physics involved in this, simply an initial condition that is 'projected' onto the reality of spin.
Thus Bell's 'belief' in Pauli's mathematical projection, causes him to reject 3D spin, which does satisfy ABcos(A,B), and to claim this impossible, leading to "entanglement" as a new mystery, on which thousands of papers can be written. This is compounded by "proofs" of Bell's theorem being conducted with valid two-state experiments, where the states are detection or not of photons.
Finally, as Bell was forcing 'qubits' on spin, Feynman, who was in love with the two-slit photon experiments, realized that he could apply Pauli's 'qubit wave function' for spin in a manner analogous to the two-slit experiments and he applied this to SG, thus projecting 'superposition' onto spin. Although Feynman's gedanken experiments have never been tested, several QM texts now begin with Feynman's two-slit-spin analogy. Thus Feynman and Bell forced a 'mystical' view on spin and Aspect "confirmed" it with photon analogs.
Once these giants froze the qubit projection onto reality, other isomorphisms go to hell. Isomorphisms are formalisms, qubit spin is (believed to be) physical reality! To seriously question this "reality" can be dangerous to one's career.
I discuss qubits because the genealogy is so clear cut. I could've discussed iso-spin, in which Heisenberg replaced two real fundamental particles with an imagined particle with 'qubit-like' projections onto reality, etc.
In my essay I treat another projection onto reality. Einstein, while basing his treatment on Hertz, projected a 4D-coordinate system with a new universal time dimension onto each moving object. The addition of new time dimensions (the physical 'reality' corresponding to the math structure) of course demolished time as universal symmetry and replaced it with "the relativity of simultaneity". This 'freezing' of the 4D-projection on the moving objects has lasted 100 years, despite the fact that the 'energy-time' conjugation in one inertial frame is isomorphic to Einstein's 'space-time symmetry' in two inertial frames, and agrees with all relativistic particle physics data.
In similar fashion, one can derive Bekenstein's "holographic principle" in terms of energy alone, without ever conceiving of information. But the 'information' projection is now 'believed' by physicists, and the door is closed to isomorphisms.
In summary, as long as the isomorphisms are mathematical, they are easily seen to morph into one another. But as soon as a mathematical structure is projected onto physical reality, it becomes "frozen" in the mind of the (consensus) physicist, and the fact that other isomorphic interpretations (such as 'classical' versus 'quantum') are equally possible are dismissed or rejected with almost religious fervor.
Cristi wrote on Jan. 27, 2018 @ 11:32 GMT, that while it is natural to question non-intuitive physics, one has to move on in his career. Nevertheless, he says:
"But I still think it is necessary to start by questioning everything, and you should never stop."
I believe that if one projection that leads to non-intuitive 'nonsense' can be replaced by another isomorphism that is compatible with the real data, and yet makes intuitive sense, this change of isomorphisms should be made.
So thank you, Cristi, for focusing on 'isomorphism' and 'fundamentality' as you have done. Your essay is well written and enlightening. Of course I agree with your proposition that geometric algebra is the tool we should be using. I hope my essay is read in terms of such isomorphisms.
Edwin Eugene Klingman