Black hole information paradox

The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could permanently disappear in a black hole, allowing many physical states to evolve into the same state. This is controversial because it violates a commonly assumed tenet of science — that in principle complete information about a physical system at one point in time should determine its state at any other time. A fundamental postulate of quantum mechanics is that complete information about a system is encoded in its wave function. The evolution of the wave function is determined by a unitary operator, and unitarity implies that information is conserved in the quantum sense.

— Wikipedia on Black hole information paradox

2012.04.23 Monday ACHK

微積分驗算 1.1

這段改編自 2010 年 6 月 2 日的對話。

考試時,你怕做錯 differentiation 的話,就應該做驗算。驗算的方法有兩種。你選擇其中一種方法去用就可以。

第一種方法是,做了 differentiation 後,用計數機核對。現在,有一些計數機,有 differentiation 的功能。

第二種方法是,你用超過一種途徑,去運算同一題 differentiation,看看可不可以得到同一個答案。例如,如果要運算 d/dx ( sin x / x ),你既可以用 product rule,又可以用 quotient rule。

用 product rule 的話,你就要把「sin x 除以 x」看成「sin x 乘以 1/x」。

— Me@2012.04.23

2012.04.23 Monday (c) All rights reserved by ACHK