Principles of Physical Cosmology最新文献

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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

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)

场方程出现在许多物理理论中。大多数动态场共享一阶和二阶偏微分方程，不同之处在于导致不连续的各种伪影。本文限制一阶和二阶偏微分方程。这些方程可以描述场与类点伪像之间的相互作用。本文在最大的三个空间维度上处理周期性和一次性触发器。本文应用四元数微分。它使用四元数的纳布拉运算符。这种配置将动态几何数据存储为四元数存储容器中适当的时间戳和三维空间位置的组合。存储格式为欧几里德格式。本文介绍了构成高阶物体的新型超微小物体翘曲和钳形。麦克斯韦方程组将三维纳布拉算子与应用坐标时间的时间导数相结合。麦克斯韦方程组是由实验结果推导出来的。因此，这些方程包含物理单位。在本文中，四元数偏微分方程应用了四元数符号。这些方程不是由实验结果推导出来的。相反，这些公式应用了这样一个事实，即四元数的nabla表现为四元数的乘法算子。相应的公式不包含物理单位。这种方法产生了麦克斯韦场方程和四元数偏微分方程之间的本质区别。四元数偏微分方程不会改变数据格式。场向观测者传输的信息的格式受到信息传输的影响，这些信息是场嵌入的。而不是欧几里得存储格式，它支配着观察到的事件的位置，观察者感知到一个时空格式，它具有闵可夫斯基签名。洛伦兹变换描述了格式转换。广义场方程广义场方程适用于所有基本场。广义场方程最适合于四元数设置。四元数由实数标量部分和表示虚部的三维空间向量组成。四元数的乘法规则表明乘积由几个独立的部分组成。在此注释中，我们使用后缀r来表示四元数的标量实部，并用粗体表示虚向量部分。c = cr + c = a b = (ar + a) (br + b) = ar br−< a, b > + ar b + a br±a × b±表示左右手四元数同时存在。这个公式可以用来检验由乘积法则推导出的一组方程的完备性。a的四元数共轭是a* = (ar−a)从乘积，规则遵循四元数a的范数|a|的公式。|a|2 = a a* = (ar + a) (ar−a) = ar ar +⟨a, a⟩四元数nabla∇的作用类似于乘法算子。(偏)微分∇ψ表示场ψ的全一阶变化。φ =∇ψ = φr + φ =(∇r +∇)(ψr + ψ) =∇r ψr -⟨∇，ψ⟩+∇r ψ +∇ψr±∇x ψ该方程是一个四元数一阶偏微分方程。右边的五项表示构成整个一阶变化的分量。它们表示域φ的子域，通常具有特殊的名称和符号。∇ψr是ψr⟨的梯度，ψ⟩是ψ的散度。∇x ψ是ψ φr的旋度=∇r ψr−⟨∇，ψ⟩(这不是麦克斯韦方程的一部分!)φ =∇r ψ +∇ψr±∇x ψ Ε = -∇r ψ−∇ψr Β =∇x ψ从上述公式得出，麦克斯韦方程不构成一个完备集。物理学家使用规范方程使麦克斯韦方程更完备。χ=∇*φ=∇*∇ψ=(∇r−∇)(∇r +∇)(ψr +ψ)=(∇∇r +⟨∇,∇⟩)ψ和ζ=(∇∇r−⟨∇,∇⟩)ψ是四元的二阶偏微分方程。第一个方程分为两个一阶偏微分方程。最后一个二阶偏微分方程不能分解为两个四元数一阶偏微分方程。这个方程提供了波作为其解集的一部分。因此，它也被称为波动方程。∇r∇r ψ =⟨∇，∇⟩ψ = ω ψ ÷ f = exp(2π ωxτ)在奇数参与维数中，两个二阶偏微分方程都提供激波前作为其解集的一部分。F (cτ+xi) + g F (cτ−xi);一维锋面f(cτ+ri)/r + g f(cτ−ri)/r;经过一段时间的积分后，球形激波锋面产生了球形条件下场的格林函数。Q =(∇r∇r -⟨∇，∇⟩)等价于d'Alembert算子。∇r∇r +⟨∇，∇⟩描述了主题的方差规范方程必须扩展麦克斯韦方程以导出二阶偏波方程。麦克斯韦方程使用坐标时间，而四元数微分方程使用固有时。对于四元数，四元数的范数起着坐标时间的作用。这些时间值并不适用于它们的绝对版本。因此，只适用于时间间隔。希尔伯特空间只能处理除法环的数字系统。在除法环中，所有非零成员都有唯一的逆。只有三个合适的除法环存在。这些是实数，复数和四元数。因此，以闵可夫斯基签名为特征的动态几何数据必须首先分解为实数，才能在希尔伯特空间中服务。四元数可以在不拆解的情况下使用。量子物理学家使用希尔伯特空间为他们的理论建模。四元量子力学似乎代表了一种自然选择。泊松方程Φ =⟨∇，∇⟩ψ = G°Φ描述场如何在一个点状触发器的分布Φ上与其格林函数G发生反应。

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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

.The progress and problems of standard cosmological model are considered. We analyze geometry and matter composition as well as the origin of initial conditions and dark components in the Universe.

讨论了标准宇宙学模型的研究进展和存在的问题。我们分析几何和物质组成，以及宇宙中初始条件和暗成分的起源。

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