G is Newton's gravitational constant, c is the speed of light, m, and [r.sub.*] are the Planck mass
and length respectively [4, p.
where the relations ch/[l.sub.p] = [M.sub.p][c.sup.2] and [M.sub.p] = [c.sup.2][l.sub.p]/G ([M.sub.p] being the Planck mass
) have been used.
Various calculations based on theory dictate that the Higgs mass should be comparable to a figure called the Planck mass
, which is about 17 orders of magnitude higher than the boson's measured heft (SN Online: 10/22/13).
where [[xi].sub.0] = [(2[pi]/ln 2).sup.1/2] [approximately equal to] 3.010 and [m.sub.Pl] [([??]c/G)1.sup./2] is the Planck mass
; therefore we see that [m.sub.gr] [varies] 1/[square root of (N)[.
Here [beta] = [[beta].sub.0][l.sup.2.sub.p]/[h.sup.2] = [[beta].sub.0]/[M.sup.2.sub.p][c.sup.2], [[beta].sub.0] ([less than or equal to] [10.sup.34]) is a dimensionless constant and [l.sub.P] and [M.sub.P] are Planck length and Planck mass
. Adopting rational approximation, according to the line element and the modified Hamilton-Jacobian equation, we can get the following motion equation of a scalar particle:
The interpretation of the Planck mass
as eigenstate in a chain system of oscillating protons has allowed us to derive the proton rest mass from fundamental physical constants .
The D-dimensional Planck mass
[m.sub.D] is considered as the maximal energy scale in the rest of the article.
Furthermore, the interpretation of the Planck mass
as an eigenstate in a chain system of oscillating protons has allowed us to derive the proton rest mass from fundamental physical constants .
Assuming that (1) is not just a coincidence implies that it is valid at any epoch; then using (4) since the FLRW metric describes a simple 4-ball, we can slice it with 4-spheres centered at the origin, of radius r and thickness 2 [l.sub.p] (both along the light cone), and each slice adds an identical energy increment [M.sub.p], the non-reduced Planck mass
, and it looks like the universe is a Planck power space-time generator.
where -[pi] [less than or equal to] [phi] [less than or equal to] [pi] is the extra dimension coordinate, the coefficient [r.sub.c] is the compactification radius, and the parameter k is related to the 5-D Planck mass
The existence of the Planck mass
[+ or -] [M.sub.Pl] = [+ or -] [([??]c/G).sup.1/2] opens a unique opportunity to represent a macroscopic space-like structure.
At the Planck mass
the slope is infinite, corresponding to the zero heat capacity of the black hole.