The Quantum Nature of Lorentz Invariance
If the reality underlying classical physics is quantum in nature, then it is reasonable to assume that the transformations of fields, currents, energy, and momentum observed macroscopically are the result of averaging of symmetry groups acting in the Hilbert space of quantum states of elementary con...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-12-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/5/1/1 |
| _version_ | 1811297650309332992 |
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| author | Richard Kerner |
| author_facet | Richard Kerner |
| author_sort | Richard Kerner |
| collection | DOAJ |
| description | If the reality underlying classical physics is quantum in nature, then it is reasonable to assume that the transformations of fields, currents, energy, and momentum observed macroscopically are the result of averaging of symmetry groups acting in the Hilbert space of quantum states of elementary constituents of which classical material bodies are formed. We show how Pauli’s exclusion principle based on the discrete <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula> symmetry group generates the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="bold">C</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> symmetry of the space of states of an electron endowed with spin. Then, we generalize this reasoning in the case of quark colors and the corresponding <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mn>3</mn> </msub> </semantics> </math> </inline-formula> symmetry. A ternary generalization of Dirac’s equation is proposed, leading to self-confined quarks states. It is shown how certain cubic or quadratic combinations can form freely-propagating entangled states. The entire symmetry of the standard model, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mi>U</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, is naturally derived, as well. |
| first_indexed | 2024-04-13T06:08:18Z |
| format | Article |
| id | doaj.art-de1b320054544448bdc52a5819f1807d |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-04-13T06:08:18Z |
| publishDate | 2018-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-de1b320054544448bdc52a5819f1807d2022-12-22T02:59:11ZengMDPI AGUniverse2218-19972018-12-0151110.3390/universe5010001universe5010001The Quantum Nature of Lorentz InvarianceRichard Kerner0Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne-Université, 4 Place Jussieu, 75005 Paris, FranceIf the reality underlying classical physics is quantum in nature, then it is reasonable to assume that the transformations of fields, currents, energy, and momentum observed macroscopically are the result of averaging of symmetry groups acting in the Hilbert space of quantum states of elementary constituents of which classical material bodies are formed. We show how Pauli’s exclusion principle based on the discrete <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula> symmetry group generates the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="bold">C</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> symmetry of the space of states of an electron endowed with spin. Then, we generalize this reasoning in the case of quark colors and the corresponding <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mn>3</mn> </msub> </semantics> </math> </inline-formula> symmetry. A ternary generalization of Dirac’s equation is proposed, leading to self-confined quarks states. It is shown how certain cubic or quadratic combinations can form freely-propagating entangled states. The entire symmetry of the standard model, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mi>U</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, is naturally derived, as well.https://www.mdpi.com/2218-1997/5/1/1quark modelZ3-graded algebrascolor dynamicsDirac’s equationLoretnz invariance |
| spellingShingle | Richard Kerner The Quantum Nature of Lorentz Invariance Universe quark model Z3-graded algebras color dynamics Dirac’s equation Loretnz invariance |
| title | The Quantum Nature of Lorentz Invariance |
| title_full | The Quantum Nature of Lorentz Invariance |
| title_fullStr | The Quantum Nature of Lorentz Invariance |
| title_full_unstemmed | The Quantum Nature of Lorentz Invariance |
| title_short | The Quantum Nature of Lorentz Invariance |
| title_sort | quantum nature of lorentz invariance |
| topic | quark model Z3-graded algebras color dynamics Dirac’s equation Loretnz invariance |
| url | https://www.mdpi.com/2218-1997/5/1/1 |
| work_keys_str_mv | AT richardkerner thequantumnatureoflorentzinvariance AT richardkerner quantumnatureoflorentzinvariance |