摘要
最近, 埃里克·韋爾蘭德提議一些重力及慣性來自熵交換的猜想。 在這篇論文中, 我們試著重組這些建議。一開始,我們以歷史上的角度來介紹穩態黑洞視界上的熵正比面積定律, 及靜態黑洞上的能量均分法則。 將熵正比面積定律推廣到任意穩態的視界上, 或將能量均分法則推廣到任意靜態的類空屏上,人們可以此二定律為出發點推出重力方程式。 我們主要的工作為韋爾蘭德對慣性的猜想。 一開始,我們研究在加速座標系上一顆粒子造成的重力效應。 當粒子在某屏幕附近移動, 我們發現屏幕的面積會隨之改變。 利用面積熵定律或靜態時空的能量均分法則, 我們發現全息屏上的熵變化正比於粒子質量乘上位移。這個關係式在韋爾蘭德的建議中是一個關於慣性概念的猜想, 我們於此推導出此關係式。其中, 韋爾蘭德需要透過與牛頓第二定律比較而得其係數, 不過我們在這邊不需要與牛頓第二定律比較就可以得出所要的正比係數。 與牛頓第二定律比較後,我們可以解釋重力場源的慣性質量及重力質量間的等價關係 (雖然愛因斯坦於發展廣義相對論時以重力場及重力加速度間的等價關係來解釋“被重力作用粒子＂的慣性質量及重力質量間的等價關係, 但“重力場源＂及其所帶之慣性間的關係依然為難以理解的事物)。 我們將在最後討論此領域未解決的問題及待開發的領域。
並列摘要
Recently, Erik Verlinde proposed some conjectures about the origins of inertia and gravity. In this thesis, we will try to reconstruct these proposals. First, we introduce the entropy-area law for a stationary black hole horizon and the equipartition rule for a static black hole horizon. By generalizing the entropy-area law to any stationary horizon, people may get the equation for gravity. We may also do so by generalize the equipartition rule for any static, space-like screen. Our work is mainly related to the Verlinde’s conjecture for inertia. First, we study in details the gravity effect by a particle in an accelerating frame. When we shift the particle near a screen, we find that the area of the screen will be changed. Using the entropy-area law or equipartition rule for the static spacetime, we get a linear relation between the entropy on the holographic screen and the particle’s displacement times it’s mass. This relation related to the concept of inertia is a conjecture in Verlinde’s original proposal. However, we derive this relation here. Compared to the Newton’s second law of motion, Verlinde got the coefficient we wanted. However, we can get the coefficient directly. By studying the thermo equilibrium between the screen and environment, we get the Newton’s second law of motion. Then we may also explain the equivalence between inertia mass and gravitational mass for a gravitational source theoretically (Although Einstein used the equivalence between gravitational acceleration and gravitational field as a starting point to establish the equivalence between the inertia mass and gravitational mass, the role of “gravitational source” related to inertia still remains as a mystery). At the end of the thesis, we will discuss unsolved problems and unexplored areas in this frontier of entropic gravity.