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Familiar Axioms versus Paradigm Shift

General Relativity precisely describes the motion of stars and galaxies at large scale. Quantum Mechanics on the other hand, accurately predicts and describes the strange world that we encounter while experimenting in micro scales. Ideally, they would have to work hand in hand to account for the entire reality as a whole. Unfortunately, we have not been able to find a feasible relationship between these two major domains of physics. In fact, they are currently considered incompatible. If we use the mathematics of general relativity in quantum mechanical calculations many times we encounter infinity. Since infinity is not defined in our present model of the universe, these calculations are discarded and incompatibility is declared.

The fact is within the current axioms, appearance of zero and infinity in the equations shatters the calculations. Therefore, Physicists decided to avoid paying heed to road signs that are erected in every step of the way. This is all done by clinging to objectivity (Tangibility). The problem is that we are using traditional judgment and logic to define this objectivity. Existing physical theories constantly circumvent singularities and infinities that frequently present themselves in experiments and calculations.

Maybe the time has come to discard the traditional thinking and revise our definition of logic. During 15th Century mathematicians frequently found that positive numbers could not explain all of the functions that existed in the mathematical domain. They realized that they had to expand the field to include and reach to new horizons. The new domain would be different than the one that they had been acquainted with. Eventually, they extended the field to accommodate negative numbers. By doing so, many unexplained calculations would then be accounted for and subsequently understood.

Then once again, when faced with the square root of negative numbers (√-n), mathematicians realized that their understanding of math is not complete. So they added yet another arena. They opened themselves to the concept of the so-called imaginary numbers, although the concept was still mysterious and obscure at the time.
It seems that in the field of physics, we have to explore and adapt to new horizons. Recently many new ideas have been presented in theoretical physics but almost all of them are within a kind of space-time arena. Despite the fact that known physics tells us that space, time and matter are not concrete and that most paradoxes arise when we get close to the boundaries of objective elements, we still hesitate to go over the cliff.

We avoid delving into a field beyond that of the familiar, space-time realm. The majority of attempts to find explanations for the unexplained, such as the super string theories, loop quantum gravity, etc. have been constructed within framework of the “known” arena.
Inside a space-time setting, our contemporary science only deals with computable elements. The physical meaning of zero is not defined in the objective realm. In addition, because quantities in space-time are numbered and ultimately finite, we cannot define infinities either. Thus in these kind of models, we regularly eliminate and ignore them and as we call it (normalize these entities) in our equations. But a sure signal of direction is the fact that calculus has been the mathematics of choice to explain the fundamentals of theoretical physics. Differential calculus, derivatives, tangents, and Zeno problems and such all point to” point zero”. However we introduce artificial limits and ran away from facing what calculus leads us to. Instead of avoiding it maybe its better to shift our perspective and take a look from other possible angles to find a solution.

Many mechanisms have been adopted to bypass zeros and infinities. Even Schrodinger’s equation, which helps us to understand and calculate quantum mechanical functions, has been formulated to help cliff settlers remain on their safe spot (familiar space-time) and continue their calculations in a secure and familiar environment. Theoretical physicists call these run away mechanisms “re-normalization”. Although for practical purposes such normalization is necessary to develop intermediate theories, but the ultimate theory cannot include it. Gordon Kane from university of Michigan in Ann Arbor believes,
“As we go to smaller distances or higher energies, we expect each effective theory to need re-normalization this is not a problem or an unexpected failure of the theory. However, the primary theory (Theory of everything) had better not need such inputs or re-normalizations."
It is understandable if a midway theory, which is not able to go deep enough, requires re-normalization in order to present its mandate. However, as Gordon Kane states, the ultimate theory cannot ignore any portion of evidence and would have to explain every aspect of reality. Regrettably, he further argues: “It has to be a finite theory (One that never gives an infinite prediction for a physical quantity).”

   
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