每日彙整: 2015-10-06

樹莓派、樹莓派之學習、樹莓派之教育

勇闖新世界︰ W!o《卡夫卡村》變形祭︰感知自然‧極限‧終

什麼是『百分之一』的呢？假使活在『百分之九十九』的人都是『色盲』的社會裡，是否那 1% 就『不可能』代表『真實』的呢 ？？畢竟『費曼』是一位『物理大師』，他說的『不二過』教訓

那麼在湯姆森發現『電子』之後，『原子』的面紗也已經逐漸揭開以來，又要如何量測一個『電子』的電荷量的呢？這就是科學史上著名的『油滴實驗』Oil-drop experiment，是美國物理學家羅伯特‧密立根 Robert Millikan 與哈維‧福萊柴爾 Harvey Fletcher 在一九零九年所進行的一項物理學實驗。密立根並因此獲得一九二三年的諾貝爾物理學獎。

265px-Millikan's_setup_for_the_oil_drop_experiment

450px-Simplified_scheme_of_Millikan’s_oil-drop_experiment

羅 伯特‧密立根在諾貝爾獎頒獎典禮上，表示他的計算值為 4.774(5) \times {10}^{-10} 靜庫侖，約等於 1.5924(17) \times {10}^{-19}庫侖。現今已知的數值與密立根的結果差異小於百分之一，但是仍然比密立根測量結果的『標準誤差』 standard error 大了五倍，因此具有統計學上的顯著差異。在密立根油滴實驗六十年後，科學史學家發現，密立根一共向外公布了五十八次觀測數據，而他本人一共做過一百四十次觀測。他在實驗中先通過預先估測，去掉了那些他認為有偏差，以及誤差大的數據。

一九七四年美國大物理學家理查‧費曼 Richard Phillips Feynman 曾經在『加州理工學院』 California Institute of Technology 的一場畢業典禮演說當中述說『草包族科學』Cargo cult science，他其中有一段講：

從 過往的經驗，我們學到了如何應付一些自我欺騙的情況。舉個例子，密立根做了個油滴實驗，量出了電子的帶電量，得到一個今天我們知道是不大對的答案。他的資 料有點偏差，因爲他用了個不準確的空氣粘滯係數數值。於是，如果你把在密立根之後、進行測量電子帶電量所得到的資料整理一下，就會發現一些很有趣的現象： 把這些資料跟時間畫成座標圖，你會發現這個人得到的數值比密立根的數值大一點點，下一個人得到的資料又再大一點點，下一個又再大上一點點，最後，到了一個 更大的數值才穩定下來。

為 什麼他們沒有在一開始就發現新數值應該較高？── 這件事令許多相關的科學家慚愧臉紅 ── 因為顯然很多人的做事方式 是：當他們獲得一個比密立根數值更高的結果時，他們以為一定哪裡出了錯，他們會拚命尋找，並且找到了實驗有錯誤的原因。另一方面，當他們獲得的結果跟密立 根的相仿時，便不會那麼用心去檢討。因此，他們排除了所謂相差太大的資料，不予考慮。我們現在已經很清楚那些伎倆了，因此再也不會犯同樣的毛病。

─── 引自《【Sonic π】電聲學導引《三》》

 

不知到底敵過敵不過『心理詐術』的耶！！

然而『費曼』他打開了『古典力學』通達薛丁格之『波動方程式』之路逕，再一次的將『時‧空』的角色平等『對應定位』起來，

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Annemarie and Erwin Schrödinger’s gravesite; above the name plate Schrödinger’s quantum mechanical wave equation is inscribed:

i \hbar \frac{\partial}{\partial t}\Psi = \hat H \Psi

RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw

Richard Feynman at the Robert Treat Paine Estate in Waltham, MA, in 1984.

Three_paths_from_A_to_B

These are just three of the paths that contribute to the quantum amplitude for a particle moving from point A at some time t0 to point B at some other time t1.

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The diagram shows the contribution to the path integral of a free particle for a set of paths.

 

Path integral formulation
Feynman’s interpretation

Dirac’s work did not provide a precise prescription to calculate the sum over paths, and he did not show that one could recover the Schrödinger equation or the canonical commutation relations from this rule. This was done by Feynman.[4]

Feynman showed that Dirac’s quantum action was, for most cases of interest, simply equal to the classical action, appropriately discretized. This means that the classical action is the phase acquired by quantum evolution between two fixed endpoints. He proposed to recover all of quantum mechanics from the following postulates:

  1. The probability for an event is given by the modulus length squared of a complex number called the “probability amplitude”.
  2. The probability amplitude is given by adding together the contributions of all paths in configuration space.
  3. The contribution of a path is proportional to e^{i S/\hbar}, where S is the action given by the time integral of the Lagrangian along the path.

In order to find the overall probability amplitude for a given process, then, one adds up, or integrates, the amplitude of postulate 3 over the space of all possible paths of the system in between the initial and final states, including those that are absurd by classical standards. In calculating the amplitude for a single particle to go from one place to another in a given time, it is correct to include paths in which the particle describes elaborate curlicues, curves in which the particle shoots off into outer space and flies back again, and so forth. The path integral assigns to all these amplitudes equal weight but varying phase, or argument of the complex number. Contributions from paths wildly different from the classical trajectory may be suppressed by interference (see below).

Feynman showed that this formulation of quantum mechanics is equivalent to the canonical approach to quantum mechanics when the Hamiltonian is quadratic in the momentum. An amplitude computed according to Feynman’s principles will also obey the Schrödinger equation for the Hamiltonian corresponding to the given action.

The path integral formulation of quantum field theory represents the transition amplitude (corresponding to the classical correlation function) as a weighted sum of all possible histories of the system from the initial to the final state. And Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude.

也許『人性』最平凡的詮釋，就是從『眾』到唯『我』間，無窮之『可能性』的吧！？