V2EX minkowski metric

Minkowski Metric

定义 Definition

闵可夫斯基度量(Minkowski metric)是狭义相对论中用于描述平直时空几何结构的度量(内积形式),用来计算两事件之间的时空间隔(spacetime interval)。它的典型符号形式为对角矩阵,常见约定之一是
\(\eta_{\mu\nu}=\mathrm{diag}(-1,\,1,\,1,\,1)\)(也有人用相反号约定)。

发音 Pronunciation (IPA)

/mnkfski mtrk/

例句 Examples

The Minkowski metric is used in special relativity.
闵可夫斯基度量用于狭义相对论。

Using the Minkowski metric, we can compute the spacetime interval and show it remains invariant under Lorentz transformations.
利用闵可夫斯基度量,我们可以计算时空间隔,并证明它在洛伦兹变换下保持不变。

词源 Etymology

Minkowski来自德国数学家Hermann Minkowski(赫尔曼闵可夫斯基)的姓氏,他将“时间与空间统一为四维时空”的几何观点系统化;metric源自希腊语 metron(“测量”),在数学与物理中指“用来测量长度/间隔的规则或形式”。合起来即“闵夫斯基提出/使用的时空度量”。

相关词 Related Words

文学与经典著作中的用例 Literary Works

  • Relativity: The Special and the General Theory Albert Einstein(讨论狭义相对论背景下的时空观,常提及闵可夫斯基时空与相关度量思想)
  • Spacetime and Geometry: An Introduction to General Relativity Sean Carroll(以闵可夫斯基度量作为平直时空基准并引入曲率与广义相对论)
  • Gravitation Misner, Thorne & Wheeler(将闵可夫斯基度量作为局部惯性系与更一般度量的参照)
  • General Relativity Robert M. Wald(用闵可夫斯基度量对比一般洛伦兹度量并用于定义局部结构)
  • Introduction to Special Relativity Wolfgang Rindler(系统讲解洛伦兹变换与闵可夫斯基度量下的不变量)
  • A First Course in General Relativity Bernard Schutz(从闵可夫斯基度量过渡到一般时空度量与测地线)
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