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

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Discussion Overview

The discussion revolves around the relationship between Planck scale mass and the strength of gravity, exploring theoretical implications, definitions, and potential conjectures related to gravitational interactions at the Planck scale. Participants examine the inverse relationship between Planck mass and gravitational strength, questioning the foundations and proofs of these concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants reference Lisa Randall's assertion that the Planck scale energy determines gravitational strength, noting that a large Planck mass correlates with weak gravity.
  • One participant presents the definition of Planck mass and speculates that if gravity were stronger, the gravitational constant would increase, leading to a smaller Planck mass, suggesting a "running coupling constant" for gravity.
  • Another participant questions the proof of gravity's inverse proportionality to mass and the derivation of related formulas, raising concerns about the speculative nature of these relationships, particularly regarding Planck black holes.
  • Some participants discuss Newton's law of gravitation, indicating that if Planck mass were to increase, the gravitational force would decrease, which they argue does not rely on speculative concepts.
  • Questions arise about the reality of Planck scale mass as a physical entity and its implications for virtual particles, with one participant expressing confusion about its existence and relevance.
  • A layman proposes a speculative idea regarding the relationship between mass and energy at the Planck scale, suggesting a unique connection that could open new avenues for understanding particle physics.

Areas of Agreement / Disagreement

The discussion contains multiple competing views and remains unresolved regarding the nature of Planck scale mass, its implications for gravity, and the validity of the relationships presented. Participants express uncertainty about the foundational aspects of these concepts.

Contextual Notes

Participants highlight limitations in understanding the derivations and proofs of the relationships discussed, indicating a reliance on speculative ideas and the need for further clarification on the nature of Planck mass and its implications.

rogerl
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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?
 
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The Planck mass is defined as [tex]M_p=\sqrt{\frac{\hbar c}{G}[/tex]. If gravity would be stronger [tex]G[/tex] gets larger which in turn makes [tex]M_p[/tex] 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).
 
kloptok said:
The Planck mass is defined as [tex]M_p=\sqrt{\frac{\hbar c}{G}[/tex]. If gravity would be stronger [tex]G[/tex] gets larger which in turn makes [tex]M_p[/tex] 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?
 
rogerl said:
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 [tex]M_p[/tex], we can write the force between two masses as

[tex]F(r) = \frac{\hbar c}{r^2} \frac{m_1m_2}{M_p^2}.[/tex]

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

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

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