Uncertainty principle 2

Uncertainty principle and observer effect

Today, logical positivism has become unfashionable in many cases, so the explanation of the uncertainty principle in terms of observer effect can be misleading. For one, this explanation makes it seem to the non-positivist that the disturbances are not a property of the particle, but a property of the measurement process — the particle secretly does have a definite position and a definite momentum, but the experimental devices we have are not good enough to find out what these are. This interpretation is not compatible with standard quantum mechanics. In quantum mechanics, states which have both definite position and definite momentum at the same time just don’t exist.

This explanation is misleading in another way, because sometimes it is a failure to measure the particle that produces the disturbance. For example, if a perfect photographic film contains a small hole, and an incident photon is not observed, then its momentum becomes uncertain by a large amount. By not observing the photon, we discover indirectly that it went through the hole, revealing the photon’s position.

— Wikipedia on Uncertainty principle

2011.01.06 Thursday ACHK

驗算校對 1.2

這段改篇自 2010 年 4 月 23 日的對話。

每題立刻驗算的話,可能令你只能完成八成的題目,但是,那八成都是運算準確的。不每題立刻驗算的話,可能令你可以完成十成的題目,但是,那十成之中,有多少成是運算準確的,你也不敢估計。

其實,哪一個「害」比較大,要有上文下理:視乎是哪一個考生、哪一份試卷。所以,我並沒有說定,哪一個方法,比較適合你。要知道哪一個方法,在什麼時候,比較適合你的話,你要在平時練習,做 past papers(歷屆試題)時,事先測試好。例如,你剛才說你會在真正考試前,「限時間」和「計分數」做三份 past papers。你應該在第一份試用「每題立刻驗算」的方法;在第二份試用「做完整份才驗算」的方法。然後,看看哪一個方法令你得到高些分數。那樣,你就可以根據這個客觀數據,決定在真正考試時,用兩個方法中的哪一個。

要留意,「每題立刻驗算」並不如想像中那麼花時間。一題數要運算三分鐘,不代表要驗算三分鐘。例如,解一題方程用了三分鐘,才得到答案。驗算時,你只需把你計到的答案,代落原本方程的左手邊,看看數值是否和右手邊的相等。這個過程,一定會在三十秒以內。

— Me@2011.01.06

2011.01.06 Thursday (c) All rights reserved by ACHK