SpaceTime
Spacetime as a combined word, is an idea to describe geometry with time as an extra dimension. This notion was probably proposed by Einstein, and later re-affirmed by Cheng-Ning Yang, who stated that Einstein re-interpreted Newton's physical description language into a language of geometry. To describe dynamical properties in geometry, time must be included as a measurable dimension.
The inclusion of time as a spatial or geometrical dimension is critical, because it allows all information content to be discussed to be treated equally in a consistent mathematical language. For example, one can include time dimension as an extra geometrical dimension in a tensor. This means that all interactive effects of spatial properties and temporal properties can be analyzed and composed in a consistent manner. This integrative framework puts both space and time in a coherent mathematical structure, and allowed mathematicians and physicists to work on many common problems without necessary interfering with each other. Cheng-Ning Yang explicitly stated that he later realized that his Gauge Field Theory work has many things in common with Fiber Bundle, and one mathematician, James Simons even explicitly stated that Fiber Bundle is mathematician's Gauge Field Theory.
References
- Yang's talk in Chinese Part I (普通話) 楊振寧教授主講 Part I 學習生活, At 22':15", he starts talking about Hermann Weyl's Gauge Invariance.
- Yang's talk in Chinese Part I (普通話) 楊振寧教授主講 Part I 學習生活, At 25':10", he starts talking about the relationships between symmetry and natural phenomenon. specifically, nuclear reaction related phenomenon.
- Yang's talk in Chinese Part III (普通話) 楊振寧教授主講 Part III 研究經歷, At 27':02", he starts talking about the J. Simmons telling him about the connections between Fiber Bundle and Gauge field theory.
- Yang's talk in Chinese Part III (普通話) 楊振寧教授主講 Part III 研究經歷, At 30':20", he starts talking about the 陳省身 Chern Shiin-Shen telling him about the natural relations between mathematical abstractions and physical reality.
- Yang's talk on The relations between Math and Physics in the 20th Century, spoken in Chinese in Taiwan 楊振寧院士-《20世紀數學與物理的分與合》, At 45':10", he starts talking about Gauge Field Terminology and Fiber Bundle and stated the Natural connection between mathematical abstractions and physical reality.
- Yang's talk on The relations between Math and Physics in the 20th Century, spoken in Chinese in Taiwan 楊振寧院士-《20世紀數學與物理的分與合》, Starting 49':45", Yang stated again, and pronounced in both English and Chinese, that mathematicians like Chern thought that mathematical ideas are real and natural .