Editing Gravitational singularity (section)

==Interpretation==

Many theories in physics have [[mathematical singularities]] of one kind or another. Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory, as in the [[ultraviolet catastrophe]], [[renormalization|re-normalization]], and instability of a hydrogen atom predicted by the [[Larmor formula]].

In classical field theories, including special relativity but not general relativity, one can say that a solution has a singularity at a particular point in spacetime where certain physical properties become ill-defined, with spacetime serving as a background field to locate the singularity. A singularity in general relativity, on the other hand, is more complex because spacetime itself becomes ill-defined, and the singularity is no longer part of the regular spacetime manifold. In general relativity, a singularity cannot be defined by "where" or "when".<ref>{{Cite book |last=Ashtekar |first=Abhay |title=100 years of relativity: space-time structure, Einstein and beyond |date=2005 |publisher=World Scientific |isbn=978-981-256-394-1 |editor-last=Ashtekar |editor-first=Abhay |location=Singapore |chapter=3: "The nature of spacetime singularities" by Alan D. Randall}}</ref>

Some theories, such as the theory of [[loop quantum gravity]], suggest that singularities may not exist.<ref>{{Cite journal |last1=Gambini |first1=Rodolfo |last2=Olmedo |first2=Javier |last3=Pullin |first3=Jorge |date=2014-05-07 |title=Quantum black holes in loop quantum gravity |journal=Classical and Quantum Gravity |volume=31 |issue=9 |pages=095009 |arxiv=1310.5996 |bibcode=2014CQGra..31i5009G |doi=10.1088/0264-9381/31/9/095009 |issn=0264-9381 |s2cid=119247455}}</ref> This is also true for such classical unified field theories as the Einstein–Maxwell–Dirac equations. The idea can be stated in the form that, due to [[quantum gravity]] effects, there is a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses becomes shorter, or alternatively that interpenetrating particle waves mask gravitational effects that would be felt at a distance. 

Motivated by such philosophy of loop quantum gravity, recently it has been shown<ref>{{Cite journal |last=Majhi |first=Abhishek |year=2022 |title=Resolving the Singularity by Looking at the Dot and Demonstrating the Undecidability of the Continuum Hypothesis |journal=Foundations of Science |language=en |volume=29 |issue=2 |pages=405–440 |doi=10.1007/s10699-022-09875-9 |issn=1233-1821 |s2cid=246942045|url=https://hal.science/hal-03528767v2/file/RSLAD.pdf }}</ref> that such conceptions can be realized through some elementary constructions based on the refinement of the first axiom of geometry, namely, the concept of a point<ref>{{Cite book |last1=Euclides |url=https://farside.ph.utexas.edu/Books/Euclid/Elements.pdf |title=Euclid's elements of geometry: the Greek text of J. L. Heiberg (1883–1885): from Euclidis Elementa, edidit et Latine interpretatus est I. L. Heiberg, in aedibus B. G. Teubneri, 1883–1885 |last2=Heiberg |first2=J. L. |last3=Fitzpatrick |first3=R. |date=2008 |publisher=s.n |isbn=978-0-615-17984-1 |editor-last=Fitzpatrick |editor-first=Richard |edition=Revised and corrected |translator-last=Fitzpatrick |translator-first=Richard}}</ref> by considering Klein's prescription of accounting for the extension of a small spot that represents or demonstrates a point,<ref>{{Cite book |last=Klein |first=Felix |title=Elementary Mathematics From A Higher Standpoint |date=2016 |publisher=Springer Berlin Heidelberg |isbn=978-3662495155}}</ref> which was a programmatic call that he called as a fusion of arithmetic and geometry.<ref>{{cite book |last=Klein |first=Felix |url=https://www.gutenberg.org/files/36154/36154-pdf.pdf |title=The Evanston Colloquium Lectures on Mathematics Delivered From August 28 to September 9, 1893 Before Members of the Congress of Mathematics Held in Connection with the World's Fair in Chicago, Illinois |date=2011 |publisher=The Project Gutenberg}}</ref> Klein's program, according to Born, was actually a mathematical route to consider 'natural uncertainty in all observations' while describing 'a physical situation' by means of 'real numbers'.<ref>{{cite book |last=Born |first=Max |date=1968 |title=Physics in My Generation |publisher=Springer New York}}</ref>