62 | | * Space has one emergent holographic direction. |

63 | | * There is a change of entropy in the emergent direction |

64 | | * The number of degrees of freedom are proportional to the area of the screen |

65 | | * The energy is evenly distributed over these degrees of freedom. |

| 65 | when |

| 66 | |

| 67 | [[latex(\Delta x = \frac{\hbar}{mc})]] |

| 68 | |

| 69 | then |

| 70 | |

| 71 | [[latex(\Delta S = 2 \pi k_B \frac{mc}{\hbar}\Delta x)]] |

| 72 | |

| 73 | and as Unruh showed, an observer in an accelerated frame experiences a temperature |

| 74 | |

| 75 | [[latex(k_BT = \frac{1}{2\pi} \frac{\hbar a}{c})]] |

| 76 | |

| 77 | If we take this temperature and our entropy formula, and calculate the entropic force we recover |

| 78 | |

| 79 | [[latex(F=ma)]] |

| 80 | |

| 81 | |

| 82 | == What about gravitational force == |

| 83 | |

| 84 | [[Image(JC2.png, width=600)]] |

| 85 | |

| 86 | If we assume that the number of degrees of freedom is proportional to the area of the enclosed space |

| 87 | |

| 88 | [[latex(N=\frac{Ac^3}{G\hbar})]] |

| 89 | |

| 90 | and that the temperature is determined by the equipartition rule |

| 91 | |

| 92 | |

| 93 | [[latex(E=\frac{1}{2}Nk_BT)]] |

| 94 | |

| 95 | and that the total energy is just the enclosed rest mass |

| 96 | |

| 97 | [[latex(E=Mc^2)]] |

| 98 | |

| 99 | we recover |

| 100 | [[latex(F=G\frac{Mm}{R^2})]] |