Suppose we strip away all classical and relativity physics and set up a topological space containing only the minimal entitities relevant to quantum phenomena together with their relations such as connectedness (of a kind), superposition/entanglement, etc. There might have to be some ongoing adjustments to the number of entities as well as to the functions defined on this space.

Might mathematicians recognise in the structure of this space deep patterns?

If so, it might then be possible of 'annex' bit by bit the objects of classical space, introducing the particles, forces, laws, etc., finding that this basic topology underlies and gives rise to a unification.

A thought experiment: assume that reality is described by the phenomena associated with experiments on quanta. Next, discard all results from classical physics and construct a topological space out of the objects solely of relevance to the quantum world together with functions defined in this space and describing non-locality, superposition, 'real' randomness and unpredictability, etc... if possible.

Conceivably, that space could have an internal structure or logical pattern alien to our notions of cause and effect, finite speed of light, action at a distance, etc.

Next, attempt to incorporate, by degrees, the entities (particles, forces, etc.) from conventional physics. Might a GUT emerge, vastly different in formulation (unrecognisably so) but more felicitous in accuracy of prediction of physical phenomena?

An address to anonymous
A great question is posed, not often examined deeply enough - neither by physicists or mathematicians. Presently “reality” is reflected in the stochastic, uncertain and probablistic analysis contained within the mathematics of QFT - Directly linked to the Copenhagen interpretation of QM.

It is fascinating to me that such small wave spaces can be examined – with only a cursory recognition of consciousness within its internal operations; Even in approaches where consciousness comes into play, as for example in the work of Bohm and perhaps that of Penrose, the significance of its projective presence is completely alien to the accepted constructs of mathematics. In this way an amazing factor has been overlooked within the thinking of this field: Consciousness itself is entangled within the deep non-local interior of the wave geometries that underlie its own dimensional experiential setting. This poses the real possibility of transforming - completely - our self-perspective as well as our view of the kind of science and technology we can develop and the way humans interact with each other.

A mathematical edifice, thus accepted as law, cannot transcend its own limitations through the assembly and disassembly of its constituent parts – tinkering is what a genius called it. GUT’s – which may be misnomers as a representative class - cannot be found upon such a base.

Internal transformations of the order that is aimed for with this thought exercise – which would create new architectures that may expose very different kind of geometric wave topologies (perhaps a new kind of projective (non-math) topology?) certainly lie within the provance of human conception – a decidedly non-mathematical notion.

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Have fun today!
Maarten Forsyth

In the paper he coauthored with Podolsky and Rosen in 1935, Albert Einstein argued that quantum mechanics was not a complete description of reality by demonstrating that two eigenstates could exist on the same quantum particle at the same time. He then predicted the existence of local hidden variables (LHV), which postulated that a quantum system had to have all the possible measurement outcomes recorded before a measurement.
In 1964, the Bell inequalities were developed by John Bell, stating that any system violating the inequalities could not follow the LHV theory. With a thought experiment, he proved with a probabilistic argument that two electrons in an entangled spin system violated the inequalities, proving that Einstein had been incorrect. Thus, quantum mechanics is a complete description of reality. In 1981-82, French researcher Aspect verified Bell's thought experiment experimentally in his lab.