在愛因斯坦的特殊相對論中，提出了光速為恆定的一個假設。在特殊相對論提出之後，有許多的理論及實驗有了不同的看法。因光速約為3×10^8 m/sec，在地球上物體的運動速度遠小於光速，意即不易找到第二個參考座標以驗證勞倫茲轉換及恆定光速的假設，然而我們可以利用地球公轉的速度及恆星對太陽的相對運動，以星球為第一參考座標，地球為第二參考座標，以實驗驗證恆定光速的假設及勞倫茲轉換。
我們設計一個系統，可以直接量測及比較各個星體的光速。目前量測目標為：五車二、參宿四、大角星、織女星等，皆為亮度強、距離地球遠並且與地球之相對速度較大的星體。本研究提出的系統架構包含一個發射端與一個接收端，在發射端我們將星光、635 nm紅光以及1550 nm紅外光訊號調制為脈衝訊號，分別當作此量測系統當中的訊號源、參考光源以及觸發訊號。在行經4,302公尺的傳輸距離之後，進入到接收端，我們更利用一個本地白光訊號作為校正系統與追蹤穩定度之用。在此研究中，我們期望可以量測到各個星光到達接收端的時間，相互之間以及與白光之間將會有所不同。
在量測期間與資料處理過程中，我們仔細的評估實驗誤差，並且在這幾年當中得到了一些結果。由結果顯示，五車二所發出的星光光速，於2010年三月份的量測中，在接收端與地球本地光經過4,302公尺的傳輸有著2.28 nsec的平均延遲時間差，而在2011年三月份的量測中，則有著3.02 nsec的平均延遲時間差。由此可看出，星光之光速與地球本地光之光速應有差異。

The constancy of the speed of light is the second fundamental hypothesis of Einstein’s special relativity, but there are also some hypotheses and observations against the constancy of light speed hypothesis. We design a system to directly measure the speeds of starlights of Capella, Betelgeuse, Acturus, and Vega which are far away and have various relative radial velocities to the Earth. The system consists of two parts: a transmitter and a receiver. At the transmitter, we modulate the starlights, the terrestrial 635 nm red 1ight and 1550 nm infrared into pulses in which we take the red light and 1550 nm infrared pulses as the reference and the trigger signals. After travelling a distance, these pulses are detected by the receiver. We employ a terrestrial white light to calibrate the system and track stability. We expect to find that the starlight pulses arrive at the receiver with various delays comparing with the white light or the starlight pulses each other.
We carefully eliminate the errors during the measurement and the data processing, and get some reliable results in these years. The measured average time delays of the starlights pulses from Capella with respect to the terrestrial white light pulses were 2.28 nsec in March 2010 measurement and 3.02 nsec in 2011 measurement. The result indicates that the speeds of starlights might be different from the speed of terrestrial light.

摘要 -----------------------------------------------------------------------------------------------I
Abstract -------------------------------------------------------------------------------------------II
誌謝 ---------------------------------------------------------------------------------------------III
Outline -------------------------------------------------------------------------------------------V
Index of Symbols -----------------------------------------------------------------------------VII
Index of Figures and Tables ------------------------------------------------------------------IX


Chapter 1. Introduction -----------------------------------------------------------------------1
1.1 Prologue -----------------------------------------------------------------------------------1
1.2 Some hypotheses and observations ----------------------------------------------------2
1.3 Organization of the thesis ---------------------------------------------------------------3

Chapter 2. System Design --------------------------------------------------------------------4
2.1 System description -----------------------------------------------------------------------5
2.2 Design of components -------------------------------------------------------------------9
2.3 System set up and alignment ----------------------------------------------------------23

Chapter 3. System Analysis ----------------------------------------------------------------25
3.1 The concepts of system design -------------------------------------------------------25
3.2 Speckles in light spots -----------------------------------------------------------------28
3.3 Fitting function analysis ---------------------------------------------------------------31
3.4 The analysis of stability ----------------------------------------------------------------32
3.5 Thermal expansion effects -------------------------------------------------------------33
3.6 Rotation speed of spindle --------------------------------------------------------------36
3.7 Air dispersion ---------------------------------------------------------------------------37
3.8 Thermal effect of the fiber delay line ------------------------------------------------38

Chapter 4. Data Processing and Results --------------------------------------------------40
4.1 Data processing step --------------------------------------------------------------------40
4.2 Data measured in March 2010 --------------------------------------------------------43
4.3 Data measured in March 2011 --------------------------------------------------------50
4.4 Data measured in February 2012 -----------------------------------------------------52
4.5 System errors measured in November 2009 ----------------------------------------54

Chapter 5. Future Works --------------------------------------------------------------------56
5.1 One-way transmission -----------------------------------------------------------------56
5.2 More reference light --------------------------------------------------------------------58
5.3 Optical chopper modulation -----------------------------------------------------------60

Chapter 6. Conclusions ---------------------------------------------------------------------66

References --------------------------------------------------------------------------------------68
Appendix ----------------------------------------------------------------------------------------71
作者簡介 ---------------------------------------------------------------------------------------74

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