Home Page  Overview  Site Map  Index  Appendix  Illustration  About  Contact  Update  FAQ 
Soon after Max Planck introduced the Planck constant h in 1899 to account for the spectrum of blackbody radiation, he realized that the only way to construct a unit of length out of h = 6.625x10^{27} ergsec, the velocity of light c = 3x10^{10} cm/sec, and the gravitational constant G = 6.67x10^{8} cm^{3}/sec^{2}gm, is L_{PL} = (Gh/c^{3})^{1/2}. This is the now famous Planck length. Since h is related to Quantum Theory, c and G emerge from the Special and General Relativity respectively, it implies that any length scale in a Quantum Gravity Theory would involve L_{PL}, which fittingly is extremely short at 4x10^{33} cm. 
 
Figure 1532 Realm of Planck Scale [view large image] 

define the length scale of the quantum process. In the present context, it can be interpreted as the appearance of paircreation with large quantum fluctuation in momentum (~ mc) resulting in position uncertainty (x/p) about the order of a Compton wavelength. Individual object does not exist in region below that line as the single particle description is no longer applicable. The straight line on the right is a plot of mass against the Schwarzschild radius r_{s}=2Gm/c^{2}. Objects cannot be accessed in region below that line as it would be wrapped inside the event horizon (since r < r_{s}). All objects exist only within the region bound by these two lines. Table 1503 lists some of the objects within or at the border. The two lines converge at a point where both quantum effect and gravity become important.  
Figure 1533 Quantum Gravity Convergence [view large image] 
Figure 1533 also shows some characteristic scales of the universe. 
Object  Mass (gm)  Compton Wavelength (cm)  Size (cm) 

Photon (Red Light)  3.4x10^{33}=E/c^{2}  6.65x10^{5}  Elementary Particle, Boson 
Electron  9.1x10^{28}  2.4x10^{10}  Elementary Particle, Fermion 
Proton  1.67x10^{24}  1.3x10^{13}  Composite Particle 
Buckyball (C_{60})  1.2x10^{21}  1.8x10^{16}  ~ 10^{7} 
Protein  ~ 10^{19}  2x10^{18}  ~ 10^{6} 
Virus  ~ 10^{8}  2.2x10^{29}  ~ 10^{5} 
Object  Mass (gm)  Schwarzschild Radius (cm)  Size (cm) 
Earth  6x10^{27}  0.9  6x10^{8} 
Neutron Star  10^{34}  2x10^{5}  10^{6} 
Cygnus X1  2x10^{34}  4x10^{5}  Stellar Black Hole 
SgrA*  8x10^{39}  1.2x10^{12}  Galactic Black Hole 
3C273  4x10^{42}  6x10^{14}  Quasar Black Hole 
Observable Universe  4x10^{55}  6x10^{27}  10^{28} (very close to form a Black Hole) 
 
Figure 1534 White Hole _{} 
Figure 1535 Evolution of Cosmic Entropy _{} 

Derivation of black hole entropy shows that the absolute value of information  I  = 1.2x10^{66} R^{2} bits, where R is the Schwarzschild radius (note that the entropy S = (k_{B}ln2)  I , with the Boltzmann constant k_{B} = 1.38x10^{16} erg/K^{o}). If the radius of the black hole R = L_{PL}, then  I  = 3, which agrees with the no hair theorem  only three number of parameters or three degrees of freedom (mass, angular momentum, and electric charge) is required to describe a black hole completely. So the entropy was at its minimum with S = 3x(k_{B}ln2) in Big Bang. It increases upward forever since then as expected by the 2nd law of thermodynamics.  
Figure 1536 Quantum Gravity _{} 
Figure 1536 shows the relationship between quantum gravity and the other branches of physics at the limit of the various universal constants. In other word, the various theories at the perimeter are just the special cases of the more general theory of quantum gravity  hence it is often referred to as the Theory of Everything. 