時空的熱力學面向｜國立中央大學博碩士論文系統

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研究生：	江書賢 Shu-Sian Jiang
論文名稱：	時空的熱力學面向 Thermodynamic Aspects of Spacetime
指導教授：	陳江梅 Chiang-Mei Chen
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
畢業學年度：	99
語文別：	英文
論文頁數：	88
中文關鍵詞：	時空、重力、黑洞、黑洞力學、貝肯斯坦、黑洞熱力學、霍金輻射、廣義熱力學第二定律、熵界、昂魯溫度、昂魯輻射、昂魯效應、全像原理、全像屏、熵力、熵重力、賈寇柏森、愛因斯坦方程、韋爾蘭德、李淼、廣義相對論、3+1 分解、準局域能量、粗粒化、突現、能量均分
外文關鍵詞：	Spacetime, Gravity, Black Hole, Black Hole Mechanics, Black Hole Thermodynamics, Bekenstein, Hawking Radiation, Generalized Second Law of Thermodynamics, Entropy Bound, Unruh Temperature, Unruh Radiation, Unruh Effect, Holographic Principle, Holographic Screen, Entropic Force, Entropic Gravity, Jacobson, Einstein equation, Verlinde, Miao Li, General Relativity, 3+1 Decomposition, Quasilocal Energy, Coarse-graining, Emergent, Equipartition of Energy
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　　從黑洞力學四定律與熱力學四大定律的相似性出發，物理學家發現黑洞是一個熱力學系統。除此之外，黑洞的熵值正比於其表面積而非體積，此一事實導致了重力的全像原理(猜想)。Ted　Jacobson的研究工作強烈暗示：不只是黑洞，時空本身可能便是一個熱力學系統。Erik P. Verlinde以全像原理及某些時空的熱力學特性為假設，在去年提出了一個革命性但備受爭議的想法：我們所認知的(3+1)維時空是由一個(2+1)維的時空突現(emergent)而來，除此之外，重力是一種熵力。在本論文中，我們將對把時空視為一個熱力學系統的概念作回顧(第一、二章)、試著把Verlinde的想法敘述清楚(第三章)、並討論某些可能實現他的突現性時空圖像的線索(第三至五章)。

　　Starting from the resemblance between the four laws of black hole mechanics and those of thermodynamics, physicists find that the black hole is a thermal system. In addition, the entropy of a black hole is proportional to its surface area instead of its volume. This fact leads to the holographic principle (conjecture) of gravity. Ted Jacobson''s work strongly suggests that not just black holes, but the spacetime itself may be a thermal system. Taking the holographic principle and some thermodynamic properties of spacetime as assumptions, Erik P. Verlinde proposed a revolutionary but highly controversial idea last year: our (3+1)-dimensional spacetime is emergent from a (2+1)-dimensional spacetime, in addition, gravity is an entropic force. In this thesis, we would make a review on the ideas of treating spacetime as a thermal system (Chapter 1 and Chapter 2), try to clarify Verlinde''s ideas (Chapter 3) and discuss about some possible hints for the realization of his emergent picture of spacetime (Chapter 3 to Chapter 5).

Abstract(Chinese Version) {i}
Abstract {ii}
Acknowledgements {iii}
Table of Contents {v}
List of Figures {vii}
List of Tables {viii}
Units and Notations {ix}
Chapter 1 Introduction {1}
1.1 From Black Hole Thermodynamics to the Holographic Principle {1}
1.1.1The Four Laws of Black Hole Mechanics {1}
1.1.2 Black Hole Entropy and Generalized Second Law {3}
1.1.3 Hawking Radiation {5}
1.1.4 Unruh Effect {6}
1.1.5 Entropy Bound {7}
1.1.6 From Entropy Bound to Holographic Principle {8}
1.2 The Emergent Idea of Spacetime {12}
1.2.1 The Revolution of the Concept of Spacetime
From Newton to Einstein General Relativity {12}
1.2.2 Is Spacetime An Emergent Phenomenon? {16}
1.3 Thermodynamic Aspects of Spacetime:
From T. Jacobson, T. Padmanabhan to E. Verlinde {19}
Chapter 2 Gravity from Thermodynamics {21}
2.1 Einstein''s Equations from Thermodynamics {21}
2.2 Thermodynamic Aspects of Gravity:
Entropy, Microscopic Degrees of Freedom & Equipartition of Energy {25}
2.3 Holography in Action {29}
Chapter 3 Entropic Gravity {34}
3.1 Verlinde: ``On The Origin of Gravity and the Laws of Newton'' {34}
3.1.1 Entropic Force {34}
3.1.2 Verlinde''s Proposal {36}
3.1.3 Emergence of Newton''s Second Law {38}
3.1.4 Newton''s Law of Gravity in Spherical Space {40}
3.1.5 Newton Potential, Screens & Emergence of Space {41}
3.1.6 Newtonian Gravity for General Matter Distribution {42}
3.1.7 Relativistic Generalization{43}
3.2 Miao Li: ``New Entropic Force Scenario''{48}
3.2.1 Li''s Procedure {48}
3.2.2 Discussion {50}
3.3 Brown & York''s Quasi-local Energy {53}
3.3.1 Introduction to the formulation {53}
3.3.2 Energy and the Generator of Time Evolution {56}
3.3.3 Discussion {56}
Chapter 4 The Emergence of a Spatial Dimension? {59}
4.1 Motivation {59}
4.2 The (3+1) Decomposition of Gravitational Action {60}
4.2.1 The Formalism {60}
4.2.2 Our Trials {62}
4.2.3 Discussion {63}
4.3 Turning the (3+1) constrained gravitational system to a (2+1) unconstrained system {64}
Chapter 5 Conclusion {67}
Bibliography {69}
Appendix A Spatial (3+1) Decomposition of Spherically Symmetric Spacetime {72}
Appendix B Spatial (3+1) Decomposition of the Kerr Spacetime {77}

                                

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