Principles of Physical Cosmology最新文献_第3页

4. Einstein's World Model 4. 爱因斯坦的世界模型

Principles of Physical Cosmology Pub Date : 2020-12-31 DOI: 10.1515/9780691206721-006

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1. The Standard Cosmological Model 1. 标准宇宙学模型

Principles of Physical Cosmology Pub Date : 2020-12-31 DOI: 10.1515/9780691206721-003

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11. Wall, String, and Spherical Solutions 11. 管壁、管柱和球面解决方案

Principles of Physical Cosmology Pub Date : 2020-12-31 DOI: 10.1515/9780691206721-013

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10. Field Equations 10. 场方程

Principles of Physical Cosmology Pub Date : 2020-12-31 DOI: 10.1515/9780691206721-012

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19. Measures of the Galaxy Distribution 19. 星系分布的测量

Principles of Physical Cosmology Pub Date : 2020-12-31 DOI: 10.1515/9780691206721-021

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13. Neoclassical Cosmological Tests 13. 新古典宇宙学测试

Principles of Physical Cosmology Pub Date : 2020-12-31 DOI: 10.1515/9780691206721-015

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24. Diffuse Matter and the Cosmic Radiation Backgrounds 24. 漫射物质和宇宙辐射背景

Principles of Physical Cosmology Pub Date : 2020-12-31 DOI: 10.1515/9780691206721-026

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Field Equations 场方程

Principles of Physical Cosmology Pub Date : 2020-09-15 DOI: 10.2307/j.ctvxrpxvb.14

J. V. Leunen

{"title":"Field Equations","authors":"J. V. Leunen","doi":"10.2307/j.ctvxrpxvb.14","DOIUrl":"https://doi.org/10.2307/j.ctvxrpxvb.14","url":null,"abstract":"Field equations occur in many physical theories. Most dynamic fields share a set of first and second order partial differential equations and differ in the kinds of artifacts that cause discontinuities. The paper restricts to first and second order partial differential equations. These equations can describe the interaction between the field and pointlike artifacts. The paper treats periodic and one-shot triggers in maximally three spatial dimensions. The paper applies quaternionic differential calculus. It uses the quaternionic nabla operator. This configuration implements the storage of dynamic geometric data as a combination of a proper timestamp and a three-dimensional spatial location in a quaternionic storage container. The storage format is Euclidean. The paper introduces warps and clamps as new types of super-tiny objects that constitute higher order objects. Introduction Maxwell equations apply the three-dimensional nabla operator in combination with a time derirative that applies coordinate time. The Maxwell equations derive from results of experiments. For that reason, those equations contain physical units. In this paper, the quaternionic partial differential equations apply the quaternionic nabla. The equations do not derive from the results of experiments. Instead, the formulas apply the fact that the quaternionic nabla behaves as a quaternionic multiplying operator. The corresponding formulas do not contain physical units. This approach generates essential differences between Maxwell field equations and quaternionic partial differential equations. The quaternionic partial differential equations do not change the data format. The format of the information that the field transmits to observers, which the field embeds is affected by the information transfer. Instead of the Euclidean storage format, which governs at the location of the observed event, the observers perceive a spacetime format, which features a Minkowski signature. The Lorentz transform describes the format conversion. Generalized field equations Generalized field equations hold for all basic fields. Generalized field equations fit best in a quaternionic setting. Quaternions consist of a real number valued scalar part and a three-dimensional spatial vector that represents the imaginary part. The multiplication rule of quaternions indicates that several independent parts constitute the product. In this comment, we use a suffix r to indicate the scalar real part of a quaternion, and we use bold face to indicate the imaginary vector part. c = cr + c = a b = (ar + a) (br + b) = ar br − 〈 a, b 〉 + ar b + a br ± a × b The ± indicates that quaternions exist in right-handed and left-handed versions. The formula can be used to check the completeness of a set of equations that follow from the application of the product rule. The quaternionic conjugate of a is a* = (ar − a) From the product, rule follows the formula for the norm |a| of quaternion a. |a|2 = a a* = (ar + a) (ar − a)","PeriodicalId":390001,"journal":{"name":"Principles of Physical Cosmology","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132018983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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Robertson-Walker Geometry 罗伯森沃克几何

Principles of Physical Cosmology Pub Date : 2020-09-15 DOI: 10.2307/j.ctvxrpxvb.16

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The Standard Cosmological Model 标准宇宙学模型

Principles of Physical Cosmology Pub Date : 2020-09-15 DOI: 10.2307/j.ctvxrpxvb.5

V. Lukash

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