Changes between Version 6 and Version 7 of u/JCFeb0713

Timestamp:

02/07/13 15:58:44 (13 years ago)

Author:

Jonathan

Comment:

—

u/JCFeb0713

@@ -51 +51 @@
 [[latex(T_H=\frac{\hbar c^3}{8 \pi GMk_B})]]
 
-If we assume that the Bekenstein-Hawking entropy times the Hawking temperature must equal the work done by gravity, then we have
+If we assume that the work done by gravity must equal the increase in the Bekenstein-Hawking entropy, then we have
 
 [[latex(F=T_H\frac{\partial S_{BH}}{\partial x})]]
 
 
+== Temperature of accelerated objects ==
+
 [[Image(JC3.png, width=600)]]
 
-What about 
+Assume that 
+[[latex(\Delta S = 2\pi k_B)]]
 
- * Space has one emergent holographic direction.  
- * There is a change of entropy in the emergent direction
- * The number of degrees of freedom are proportional to the area of the screen
- * The energy is evenly distributed over these degrees of freedom.
+when 
+
+[[latex(\Delta x = \frac{\hbar}{mc})]]
+
+then
+
+[[latex(\Delta S = 2 \pi k_B \frac{mc}{\hbar}\Delta x)]]
+
+and as Unruh showed, an observer in an accelerated frame experiences a temperature 
+
+[[latex(k_BT = \frac{1}{2\pi} \frac{\hbar a}{c})]]
+
+If we take this temperature and our entropy formula, and calculate the entropic force we recover 
+
+[[latex(F=ma)]]
+
+
+== What about gravitational force ==
+
+[[Image(JC2.png, width=600)]]
+
+If we assume that the number of degrees of freedom is proportional to the area of the enclosed space
+
+[[latex(N=\frac{Ac^3}{G\hbar})]]
+
+and that the temperature is determined by the equipartition rule
+
+
+[[latex(E=\frac{1}{2}Nk_BT)]]
+
+and that the total energy is just the enclosed rest mass
+
+[[latex(E=Mc^2)]]
+
+we recover 
+[[latex(F=G\frac{Mm}{R^2})]]
 
 
 
+