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Quantum Gravitation String Theory:

Planck's Radius:

[tex]r_p = \sqrt{ \frac{ \hbar G}{ c^3}}[/tex]

Minimum observable length for a quantum string:

[tex]r_m = 2 \sqrt{ \alpha '}[/tex]

Planck's Radius is minimum observable length for a quantum string:

[tex]r_p = r_m[/tex]

Planck area of the hyperspace amplified Salam G* strong short range low energy gravity.

[tex]\sqrt{ \frac{ \hbar G}{ c^3}} = 2 \sqrt{ \alpha ^'}[/tex]

Alpha Prime:

[tex]\alpha ' = \frac{ \hbar G}{ 4 c^3}[/tex]

Alpha Prime is constant for a Planck Scale Bosonic String.

String Tension:

[tex]T_s = \frac{ 1}{2 \pi \alpha '}[/tex]

Quantum Gravitation String Tension:

[tex]T_g = \frac{ 2 c^3}{ \pi \hbar G}[/tex]

Relationship between distance and momentum:

[tex]\Delta L = \frac{ \hbar}{ p} + \alpha ' \frac{ p}{ \hbar}[/tex]

Quantum Gravitation distance and momentum:

[tex]\Delta L = \frac{ \hbar}{ p} + \frac{ G p}{4 c^3}[/tex]

Bosonic and fermionic hadronic Regge trajectory resonance:

[tex]J = \alpha ' E^2[/tex]

[tex]J = \frac{ \hbar G}{ 4 c^3} E^2[/tex]

[tex]E = \sqrt{ \frac{ 4 J c^3}{ \hbar G}}[/tex]

Reference:

http://superstringtheory.com/basics/basic3a.html

http://www.lepp.cornell.edu/spr/2001-05/msg0032717.html

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