Understanding Quantum Gravitation: Planck's Radius, String Theory, and More

[Orion1]

Quantum Gravitation String Theory:

Planck's Radius:
$$r_p = \sqrt{ \frac{ \hbar G}{ c^3}}$$

Minimum observable length for a quantum string:
$$r_m = 2 \sqrt{ \alpha '}$$

Planck's Radius is minimum observable length for a quantum string:
$$r_p = r_m$$

Planck area of the hyperspace amplified Salam G* strong short range low energy gravity.
$$\sqrt{ \frac{ \hbar G}{ c^3}} = 2 \sqrt{ \alpha ^'}$$

Alpha Prime:
$$\alpha ' = \frac{ \hbar G}{ 4 c^3}$$
Alpha Prime is constant for a Planck Scale Bosonic String.

String Tension:
$$T_s = \frac{ 1}{2 \pi \alpha '}$$

Quantum Gravitation String Tension:
$$T_g = \frac{ 2 c^3}{ \pi \hbar G}$$

Relationship between distance and momentum:
$$\Delta L = \frac{ \hbar}{ p} + \alpha ' \frac{ p}{ \hbar}$$

Quantum Gravitation distance and momentum:
$$\Delta L = \frac{ \hbar}{ p} + \frac{ G p}{4 c^3}$$

Bosonic and fermionic hadronic Regge trajectory resonance:
$$J = \alpha ' E^2$$
$$J = \frac{ \hbar G}{ 4 c^3} E^2$$
$$E = \sqrt{ \frac{ 4 J c^3}{ \hbar G}}$$

Reference:
http://superstringtheory.com/basics/basic3a.html
http://www.lepp.cornell.edu/spr/2001-05/msg0032717.html

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[meteor]

Nice summary of formulas. Your second formula is problematic because it means that in superstring theory there's a minimum distance that you can measure, the distance given by the formula. Alpha prime is also called Regge slope

Your fifth formula, the formula that you give for alpha prime is incorrect. Alpha prime is not a constant

 

[R0man]

Quantum gravitation is a branch of theoretical physics that aims to unify the theories of gravity and quantum mechanics. It is still a subject of ongoing research, and there are various theories and equations that attempt to explain this phenomenon. One of the key concepts in quantum gravitation is Planck's Radius, which is the minimum observable length for a quantum string. This radius is given by a formula that involves fundamental constants such as Planck's constant, the gravitational constant, and the speed of light.

Another important concept is string theory, which proposes that all particles in the universe are made up of tiny vibrating strings. The minimum observable length for a quantum string is also related to the string tension, which is the energy required to create a string. This tension is given by a formula that involves the constant alpha prime, which is a fundamental constant for a Planck scale bosonic string.

One interesting relationship in quantum gravitation is between distance and momentum. In classical mechanics, the uncertainty principle states that there is a limit to how precisely we can know the position and momentum of a particle. In quantum gravitation, this relationship is given by a formula that involves the Planck constant and the string tension.

Finally, the bosonic and fermionic hadronic Regge trajectory resonance is a concept that describes the energy levels of particles in quantum gravitation. This trajectory is given by a formula that involves the Planck constant, the gravitational constant, and the energy of the particle. Overall, understanding quantum gravitation involves understanding these fundamental concepts and their relationships, and ongoing research in this field continues to deepen our understanding of the fundamental forces of the universe.