The Quantum Mechanics Of A Singularity Through Systemic Functional Linguistics

Hawking (1988: 60-1):

Einstein’s general theory of relativity seems to govern the large-scale structure of the universe. It is what is called a classical theory; that is, it does not take account of the uncertainty principle of quantum mechanics, as it should for consistency with other theories. The reason that this does not lead to any discrepancy with observation is that all the gravitational fields that we normally experience are very weak. However, the singularity theorems discussed earlier indicate that the gravitational field should get very strong in at least two situations, black holes and the big bang. In such strong fields the effects of quantum mechanics should be important.

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From the perspective of Systemic Functional Linguistic Theory, general relativity is concerned with the relation between space-time and matter-energy, and construes it geometrically: in terms of contracted and expanded space-time dimensions and curved trajectories of matter-energy along those dimensions.  A gravitational field demarcates the extent of space-time altered by the presence of matter-energy: the contraction of space-intervals, inversely proportional to the expansion of time intervals.

Quantum mechanics, on the other hand, is concerned with the instantiation of matter-energy properties, with quantum fields demarcating the extent of space-time in which quantum instantiations potentially occur.

On this basis, the strong gravitational field around a black hole contracts the spatial intervals of a quantum field, thereby reducing the relative spatial extent of potential instantiations of matter-energy, while expanding its time intervals, such that quantum processes unfold relatively more slowly along spatial dimensions.

At the singularity itself, then, where spatial intervals contract to 0, the field of potential quantum instantiations contracts to 0.  As a consequence, there are no processes to unfold, and so: there are no processes by which to measure time, and so: there is no time dimension (time intervals expand to ∞).