主题：几何直观地介绍广义相对论的时空以及大爆炸模型 （0） -- changshou

1. 愛因斯坦的廣義相對論=the highest IQ of humanity as of today

"时空本身是不嵌入某个欧式空间的流形"

that is the beauty of 愛因斯坦的廣義相對論

"爱因斯坦场方程的解是个场" , very often it is in a "local (or 特定)" 时空 situation such as 史瓦西时空, but most of time, when we really jump out of "local" into real 时空, our model can't figure out any 解 for 爱因斯坦场方程, with one of reasons as you said, "real"时空 cannot be 嵌入某个欧式空间的流形

2. witten1's comment is right as a physicist

because all the known physics model's have assumptions about model's "local" 时空, and we don't really have a "global" model anyway, and by the way, all the "global model" are basically "art"/philosophy, religion, "隱參數" based social science model, etc

2.1

"局部范围等效原理：引力=局部惯性系加速，and if you want to be more "robust", 狭义相对论 Poincare group always works, and other than that, most of the time newton/classical physics is good enough (we can explain 引力 as 局部惯性系(伽利略慣性系)加速) ", or locally, 引力 has "same" impact on all of us

2.2 actual physics modeling

廣義相對論 in a way is also 一個

局域的理論, 等效原理,

"量子力学第一性原理 )、“绝热近似”(由于原子核质量比电子大得多，而把原子核当成静止的点处理)和“轨道近似”(用一个独立函数来描述一个独立电子的运动"

here we can argue that 原子核 as a background /时空

for 电子=欧式空间, relative to all those moving 电子 around原子核: 原子核's impact on 电子 are too small/slow/same to all the 电子, or 原子核's impact on 电子="平直" to all 电子, and therefore we can further assume that 电子的运动=独立电子的运动, "no full interaction evil" in the model, model is safe.

by the same logic, we also have QFT's 电子穿衣服 model, with 重整化（Renormalization） as 量子场论中解决紫外发散的一种方法, originally "copied" from 朗道(did he say only 愛因斯坦 is "above: him in physics?) 元激發 model, and "leveraged" all the way to standard model.

by the same logic, we deal with "heat bath" using almost the same trick, so we have 正则系综, etc

3. the most important and fundamentally

there is no 欧式空间的流形 for gr's 时空, or in more GR-fitting 洛伦兹流形, we don't have 解 for 爱因斯坦场方程 anyway, most of time

so most of time we live and work in a 爱因斯坦场 where we don't have a clue about what kind of 场 that is, living in the dark, particularly socially

and partially because of that, our brain 熱消耗 everyday, 下意识trying to figure out "where we are", wasting a lot of energy

4 still, we have to model GR

廣義相對論基本上有一個無窮大的規範對

稱(gauge symmetry)，

http://phy.ntnu.edu.tw/~linfengli/articles/holography.pdf

周光召:共形场引力场没有质量，应考虑无质量场最大的时空对称群

kind of

"pure" gr 引力/时空=full interaction evil

and to gauge it:

we have 最大的时空对称群 "front running" everybody and every where, trying to figure out "隱參數/隱logic" before everybody else

5. SR, GR's "limitations" to social 爱因斯坦场

human being as a 靈性 animal, when there is a significant change in 时空, not everybody gets 靈性 and can figure out the change in 时空, our society in general is not a 某个欧式空间的流形

so, when Ricci曲率 "pops", not everybody can put on 衣服 to deal with change in 时空, and actually most of us are always out there naked, with a lot of risk exposure, and without putting on "宇航服" , we 太空失重, and eventually becoming part of 太空

good writings, thanks

and I hope witten1, you and others can comment on Verlinde's 全息屏 model, which I have made a lot of "wild" comments in my past posts