Einstein\u2019s theory of general relativity, which Newton\u2019s theory of gravity is a part of, is fraught with the problem of singularity that has been established as a theorem by Hawking and Penrose, the latter being awarded the Nobel Prize in recent years. The crucial hypothesis that forms the basis of both Einstein’s and Newton\u2019s theories of gravity is that bodies with unequal magnitudes of mass fall with the same acceleration under the gravity of a source object. Since, the validity of Einstein\u2019s equations is one of the assumptions based on which Hawking and Penrose have proved the theorem, therefore, the above hypothesis is implicitly one of the founding pillars of the singularity theorem. In this work, I demonstrate how one can possibly write a non-singular theory of gravity which manifests that the above mentioned hypothesis is only valid in an approximate sense in the \u201clarge distance\u201d scenario. To mention a specific instance, under the gravity of the earth, a 5 kg and a 500 kg fall with accelerations which differ by approximately 113.148*10-32 meter\/sec2 and the more massive object falls with less acceleration. Further, I demonstrate why the concept of gravitational field is not definable in the \u201csmall distance\u201d regime which automatically justifies why the Einstein\u2019s and Newton\u2019s theories fail to provide any \u201csmall distance\u201d analysis. In the course of writing down this theory, I demonstrate why the continuum hypothesis, as spelled out by Goedel, is undecidable. The theory has several aspects which provide the following realizations: (i) Descartes\u2019 self-skepticism concerning exact representation of numbers by drawing lines (ii) Born\u2019s wish of taking into account \u201cnatural uncertainty in all observations\u201d while describing \u201ca physical situation\u201d by means of \u201creal numbers\u201d (iii) Klein’s vision of having \u201ca fusion of arithmetic and geometry\u201d where \u201ca point is replaced by a small spot\u201d (iv) Goedel’s assertion about \u201cnon-standard analysis, in some version\u201d being \u201cthe analysis of the future\u201d. To further justify Goedel’s assertion, I provide a glimpse of what I may call \u2018non-standard physics\u2019.<\/p>\n","protected":false},"excerpt":{"rendered":"
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