What is the relationship between Planck scale mass and the strength of gravity?

[rogerl]

Lisa Randall's states in the book "Warped Passages" dealing with the Hierarchy Problem:

"The Plank scale energy determines the strength of gravitational interactions...the strength is inversely proportional to the second power of that energy...A huge Plank scale mass is equivalent to extremely feeble gravity."

What's the connection between Planck scale mass and gravity? Why is that when the former is huge, the latter should be extremely feeble?? They are inversely proportional. Is this a definite connection or just a conjecture or speculation?

 

[kloptok]

The Planck mass is defined as $$M_p=\sqrt{\frac{\hbar c}{G}$$. If gravity would be stronger $$G$$ gets larger which in turn makes $$M_p$$ smaller. I'm not sure how the gravitational constant would vary more exact, but I would guess that this would be seen as some kind of "running couling constant" of gravity, similar to other forces (where the coupling is not constant).

 

[rogerl]

The Planck mass is defined as $$M_p=\sqrt{\frac{\hbar c}{G}$$. If gravity would be stronger $$G$$ gets larger which in turn makes $$M_p$$ smaller. I'm not sure how the gravitational constant would vary more exact, but I would guess that this would be seen as some kind of "running couling constant" of gravity, similar to other forces (where the coupling is not constant).

But what's the proof that gravity is inversely proportional to mass. How is the formula derived. Couldn't it be just an speculation or conjecture like how a Planck black hole behave? meaning if there is no Planck black hole, then the formula is wrong?

 

[fzero]

But what's the proof that gravity is inversely proportional to mass. How is the formula derived. Couldn't it be just an speculation or conjecture like how a Planck black hole behave? meaning if there is no Planck black hole, then the formula is wrong?

At long distances, gravity is well described by Newton's law. Using the relationship between the gravitational constant and $$M_p$$, we can write the force between two masses as

$$F(r) = \frac{\hbar c}{r^2} \frac{m_1m_2}{M_p^2}.$$

If we were somehow able to vary $$M_p$$, it's easy to see that as $$M_p$$ gets larger, the force gets smaller.

This argument does not depend on any sort of speculation about black holes or quantum gravity.

 

[rogerl]

I'm rereading Lisa Randall Warped Passage. So is the Planck scale mass real? Is there really a particle that is Planck scale mass? How come she worried that it may contribute to virtual particles that is Planck scale mass in the Higgs if there is no such thing as Planck scale mass in the first place?

 

[mquirce]

I would like to tell a speculation from a layman about Plank mass.
The energy of plank mass after Newton is it E = G Mp^2 / Rp, but strange enough that the
mass in this case is E / C^2 =Mp = G*Mp^2 / Rp*C^2. This is unique only for Plank mass, and open the door for speculation. If we supose that "mass" and "mater" are two different notions, that have common the unity of measure(gr,Kg.) but that occupy different posts in physics, we my speculate that the "Plank mater" stay in the base of all common particles via:
mx. = G*Mp^2 / Rxcompton* C^2 . Am i wrong?