DC pole | Wartość | Język |
dc.contributor.author | Heller, Michael | - |
dc.contributor.author | Król, Jerzy | - |
dc.date.accessioned | 2019-03-27T11:24:31Z | - |
dc.date.available | 2019-03-27T11:24:31Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Universe (Basel), Vol. 13, iss. 1, art. no 16 (2017) | pl_PL |
dc.identifier.issn | 2218-1997 | - |
dc.identifier.uri | http://hdl.handle.net/20.500.12128/8681 | - |
dc.description.abstract | Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales. The so-called synthetic differential geometry—a categorical counterpart of the standard differential geometry—provides a tool to penetrate infinitesimally small portions of space-time. We use this tool to show that on any “infinitesimal neighbourhood” the components of the curvature tensor are themselves infinitesimal, and construct a simplified model in which the curvature singularity disappears, owing to this effect. However, one pays a price for this result. Using topoi as a generalisation of spaces requires a weakening of arithmetic (the existence of infinitesimals) and of logic (to the intuitionistic logic). Is this too high a price to pay for acquiring a new method of solving unsolved problems in physics? Without trying, we shall never know the answer. | pl_PL |
dc.language.iso | en | pl_PL |
dc.rights | Uznanie autorstwa 3.0 Polska | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/pl/ | * |
dc.subject | general relativity | pl_PL |
dc.subject | category theory | pl_PL |
dc.subject | synthetic differential geometry | pl_PL |
dc.subject | infinitesimal formal manifold | pl_PL |
dc.subject | curvature | pl_PL |
dc.subject | space-time singularity | pl_PL |
dc.title | Infinitesimal structure of singularities | pl_PL |
dc.type | info:eu-repo/semantics/article | pl_PL |
dc.identifier.doi | 10.3390/universe3010016 | - |
Pojawia się w kolekcji: | Artykuły (WNŚiT)
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