Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model
In physics, we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands of years ago, and I discuss some challen...
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MDPI AG
2024-11-01
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| Series: | Entropy |
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| author | Marian Kupczynski |
| author_facet | Marian Kupczynski |
| author_sort | Marian Kupczynski |
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| description | In physics, we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands of years ago, and I discuss some challenges and open questions in quantum foundations and in the Standard Model. We liberated nuclear energy, landed on the Moon and built ‘quantum computers’. Encouraged by these successes, many believe that when we reconcile general relativity with quantum theory we will have the correct theory of everything. Perhaps we should be much humbler. Our perceptions of reality are biased by our senses and by our brain, bending them to meet our priors and expectations. Our abstract mathematical models describe only in an approximate way different layers of physical reality. To describe the motion of a meteorite, we can use a concept of a material point, but the point-like approximation breaks completely when the meteorite hits the Earth. Similarly, thermodynamic, chemical, molecular, atomic, nuclear and elementary particle layers of physical reality are described using specific abstract mathematical models and approximations. In my opinion, the theory of everything does not exist. |
| format | Article |
| id | doaj-art-8885dd3424fa4e3f9469b39b2e73624d |
| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-8885dd3424fa4e3f9469b39b2e73624d2025-08-20T02:08:00ZengMDPI AGEntropy1099-43002024-11-01261199110.3390/e26110991Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard ModelMarian Kupczynski0Département de l’Informatique et d’Ingénierie, Université du Québec en Outaouais (UQO), Case Postale 1250, Succursale Hull, Gatineau, QC J8X 3X7, CanadaIn physics, we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands of years ago, and I discuss some challenges and open questions in quantum foundations and in the Standard Model. We liberated nuclear energy, landed on the Moon and built ‘quantum computers’. Encouraged by these successes, many believe that when we reconcile general relativity with quantum theory we will have the correct theory of everything. Perhaps we should be much humbler. Our perceptions of reality are biased by our senses and by our brain, bending them to meet our priors and expectations. Our abstract mathematical models describe only in an approximate way different layers of physical reality. To describe the motion of a meteorite, we can use a concept of a material point, but the point-like approximation breaks completely when the meteorite hits the Earth. Similarly, thermodynamic, chemical, molecular, atomic, nuclear and elementary particle layers of physical reality are described using specific abstract mathematical models and approximations. In my opinion, the theory of everything does not exist.https://www.mdpi.com/1099-4300/26/11/991physical realityperceptions and neuroscienceBild conceptioncausalitymathematical modelingclassical mechanics |
| spellingShingle | Marian Kupczynski Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model Entropy physical reality perceptions and neuroscience Bild conception causality mathematical modeling classical mechanics |
| title | Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model |
| title_full | Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model |
| title_fullStr | Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model |
| title_full_unstemmed | Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model |
| title_short | Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model |
| title_sort | mathematical modeling of physical reality from numbers to fractals quantum mechanics and the standard model |
| topic | physical reality perceptions and neuroscience Bild conception causality mathematical modeling classical mechanics |
| url | https://www.mdpi.com/1099-4300/26/11/991 |
| work_keys_str_mv | AT mariankupczynski mathematicalmodelingofphysicalrealityfromnumberstofractalsquantummechanicsandthestandardmodel |