Understanding Planck Mass and Gravity Formula for the Hierarchy Problem

[cube137]

from the formula

M_p=\sqrt{\frac{\hbar c}{G}

If gravity is weak.. Planck mass is huge.
Does the formula assumes whether general relativity is classical limit of some quantum theory or whether general relativity needs quantization?

Because the problem with the Hierarchy problem in the electroweak sector is the Higgs have to coupled to the Planck mass virtual particles.. so what kind of gravity details would make it decouple so there would be no Planck mass in the first place to produce any Hierarchy Problem (let's assume also for now there was no GUT mass)?

 

[mfb]

If gravity is weak.. Planck mass is huge.

That is exactly what happens.

Does the formula assumes whether general relativity is classical limit of some quantum theory or whether general relativity needs quantization?

Where is the difference between the two cases? But it does not matter, any quantum theory would also use G as parameter.

There is always a Planck mass, as unique way to get a mass from physical constants.

 

[cube137]

That is exactly what happens.Where is the difference between the two cases? But it does not matter, any quantum theory would also use G as parameter.

There is always a Planck mass, as unique way to get a mass from physical constants.

If gravity is coarse graining of some degrees of freedom and not even a force... would there still be Planck mass? And what's this quantum theory would use G as parameter stuff?

 

[mfb]

There is a Planck mass simply because there are the constants of nature. This is a purely mathematical statement, and true in every theory.

And what's this quantum theory would use G as parameter stuff?

This also does not matter. It has to have GR and Newtonian physics as classical / nonrelativistic limit, so it has to have a parameter that correspond to G.

 

[cube137]

There is a Planck mass simply because there are the constants of nature. This is a purely mathematical statement, and true in every theory.This also does not matter. It has to have GR and Newtonian physics as classical / nonrelativistic limit, so it has to have a parameter that correspond to G.

Without using any formula.. but just using visualizing.. how come weak gravity produce huge Planck mass.. is it because you can only create microscopic black hole by focusing energy in so small a space (HUP).. and when gravity is stronger, the black hole is bigger or Planck scale bigger.. but intuitively.. why is Planck scale bigger when gravity is stronger (without using any formula) maybe it's because the HUP is lesser because Planck scale or black hole bigger (and black hole bigger because gravity is stronger)?

 

[mfb]

For an object with the Plack mass, gravitational forces and other forces would be of similar magnitude. As the gravitational force is weak but proportional to mass, this object must have a huge mass.

 

[cube137]

For an object with the Plack mass, gravitational forces and other forces would be of similar magnitude. As the gravitational force is weak but proportional to mass, this object must have a huge mass.

I read that the Planck mass is the mass required to form a black hole with an event horizon of a Planck length. So is it correct to tell laymen that the reason the Planck mass is big when gravity is weak is because you need a lot of mass in the Planck length for more gravitational attraction to form Planck black hole.. whereas if gravity is strong.. you need less mass in the Planck length?

 

[mfb]

Right.

Note that "mass required for a Planck length black hole" and "mass where the interactions have similar strength" lead to same result (apart from numerical prefactors that won't be too far away from 1, but as we don't have a theory of quantum gravity we don't know those precise numbers yet).

 

[ohwilleke]

from the formula

M_p=\sqrt{\frac{\hbar c}{G}

If gravity is weak.. Planck mass is huge.
Does the formula assumes whether general relativity is classical limit of some quantum theory or whether general relativity needs quantization?

The Planck mass is purely a result of combining fundamental physical constants in a manner that produces a dimension of mass. Likewise, Planck time is a result of combining fundamental physical constants in a manner that produces dimensions of time, and Planck length is a result of combining fundamental physical constants in a manner that produces dimensions of length. There is no underlying theory behind the formula other than to combine physical constants in a manner that produces a combination with the desired units.

These are natural units that would be universal without regard to historical baggage. (Although one could debate over whether h or hbar should be used as they have the same units). But, the powerful role we attribute to Planck units as fundamental to the laws of the universe or thresholds of new phenomena is more a function of beauty and a lack of other candidates to fill that role than any rigorous logic.

Because the problem with the Hierarchy problem in the electroweak sector is the Higgs have to coupled to the Planck mass virtual particles.. so what kind of gravity details would make it decouple so there would be no Planck mass in the first place to produce any Hierarchy Problem (let's assume also for now there was no GUT mass)?

This question seems to me to be nonsensical. Any kind of gravity that has an analog to Newton's constant with the same units would have a Planck mass. And, the Hierarchy Problem is in any case a problem of scientists being too presumptuous about what values physical constants should take rather than a genuine physical problem. No matter how "improbable" it may seem, the values of the relevant physical constants do balance out and always will because, being constants, they don't change.