Physics Crisis: Faith in Gravity Clarified

  • Context: Undergrad 
  • Thread starter Thread starter T@P
  • Start date Start date
  • Tags Tags
    Physics
Click For Summary

Discussion Overview

The discussion revolves around the nature of gravitational attraction between point masses, particularly the implications of the formula Gm1m2/r^2 as the distance r approaches zero. Participants explore theoretical scenarios, limitations of classical mechanics, and the relationship between gravity and other forces, such as electromagnetic interactions.

Discussion Character

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

Main Points Raised

  • One participant expresses doubt about the validity of gravitational attraction as r approaches zero, questioning if the force becomes infinite.
  • Another participant suggests that in practical terms, r will never reach zero, implying that the formula is not applicable in such scenarios.
  • Some participants mention the uncertainty principle, stating that knowing particles have zero separation would require infinite momentum.
  • A participant notes that the gravitational formula applies only when the distance is large compared to the dimensions of the masses involved, indicating the need for different methods at small separations.
  • Discussion includes the Pauli exclusion principle and its relevance to the concept of superposition of masses.
  • One participant introduces the concept of the Schwarzschild radius, explaining that extreme densities lead to black holes, where gravitational attraction could be considered infinite.
  • Another participant discusses the analogy of light bending in a gravitational field, clarifying that light follows a straight path in curved spacetime.
  • Some participants draw parallels between gravitational and Coulomb forces, noting both exhibit singularities at zero distance but are treated differently in quantum mechanics.
  • Concerns are raised about the implications of gravitational force not reaching infinity, suggesting it may relate to the debate over the continuity of space.
  • One participant calculates the Schwarzschild radius for an electron, discussing the limitations of bringing two masses arbitrarily close together.

Areas of Agreement / Disagreement

Participants express a range of views on the implications of gravitational attraction as distance approaches zero, with no consensus on the nature of gravitational force at such limits. Multiple competing perspectives on the relationship between gravity, quantum mechanics, and the structure of space are present.

Contextual Notes

Participants highlight limitations in applying classical mechanics to scenarios involving very small distances and the need for quantum mechanical considerations. The discussion also touches on unresolved mathematical steps and assumptions regarding the nature of mass and point particles.

T@P
Messages
274
Reaction score
0
i kinda lost 'faith' in gravity. can you clear this up?

supposedin you take two point masses, m1 and m2. the attraction between them is Gm1m2/r^2, right?

now what happens when r goes to 0? does the attraction really go to 0? that would mean that when two anythings get really close, you can't pull them apart because the *gravitational* force is almost infinite. where did i go wrong? (oh and same with point charges, the other similar law)

thanks
 
Physics news on Phys.org
Theoretically, yes. But for all practical purposes, r will never reach zero.
 
Uncertainty principle would forbid this from happening. If you had some way of knowing the particles had 0 separation, they would then need infinite momentum.
 
That formula can only be applied when the 2 objects are a good approximations to a point. This means that r must be large with respect to any dimension of either of the bodies. If this is not the case you must use other methods to compute the gravitational force.
 
Gravity is measured from the centres of the masses involved. For the separation to be '0', they would have to be superposed. The Pauli exclusion principle would have something to say about that.
 
My classical mechanics teacher put it this way: "The r is an arbitrary unit and must have a length of a minimum of one." In essence it is only valid if r is larger than one in any unit. That means that it is possible to be as small as anything, because you can choose your unit freely, but it can't be zero.
 
T@P said:
supposedin you take two point masses, m1 and m2. the attraction between them is Gm1m2/r^2, right?

now what happens when r goes to 0? does the attraction really go to 0? that would mean that when two anythings get really close, you can't pull them apart because the *gravitational* force is almost infinite. where did i go wrong? (oh and same with point charges, the other similar law)
What you describe would occur if the mass were concentrated in a volume smaller than the Schwarzschild radius:

[tex]R_{Schwarzschild} = \frac{2GM}{c^2}[/tex]

This would be a black hole, and the gravitational attraction would indeed be almost infinite. But for normal matter, you just can't get those kinds of densities so you never have that much matter that close together.

AM
 
oh so it does go to infinity but it can't happen because its not an ideal 'point mass'... i see
I suppose nothing like this can happen with two opposite charges, because once they touch they neutralize...
also, is there anything that gravity can't affect? like i heard somewhere that even light bends near the sun (massive object). is there anything it won't touch?
 
T@P said:
is there anything it won't touch?
Gravity doesn't exactly bend light. The light is going in what is to itself a straight line. The space that it's moving through is distorted, though, so an outside observer sees it as bending. It's roughly equivalent to you walking 'straight' home from school. To you it's straight; to someone in orbit you're following the curvature of the Earth.
 
  • #10
The answers to the question posted in this thread still do not tell us how classical mechanics solves this problem. Newton knew nothing of Heisenberg, Pauli or black holes.
He did make a remark on this, but I can't remember . :frown:
 
  • #11
Coulomb force and gravity force have the same mathematical structure and both have a singularity at zero distance.While for the Coulomb potential this matter is dealt with by QED and its renormalization,unfortunately/fortunately this thing has not been done with gravity (namely graviton loops (unlike gluon ones) are not renormalizable).

Daniel.
 
  • #12
dextercioby said:
Coulomb force and gravity force have the same mathematical structure and both have a singularity at zero distance.While for the Coulomb potential this matter is dealt with by QED and its renormalization,unfortunately/fortunately this thing has not been done with gravity (namely graviton loops (unlike gluon ones) are not renormalizable).
Classically it can be done with electric charges because the electron is treated as a point charge. The issue arises with an electron and a positron. The energy released (or work done by) by a positron and electron moving closer to each other keeps increasing - but only to a point. One can never get an electron and a positron arbitrarily close to each other. They both annihilate due to weak interaction at a finite distance.

But mass is a different story. There is no such thing as a point mass, so you cannot put one mass arbitrarily close to another. So the energy is limited - they don't have to destroy each other in order to avoid infinite energy being released.

AM
 
  • #13
seems a pity that the gravitational force can't go to infinity, it would be so much easier for things to stay in place :)

actually, doesn't this have any influence in the 'debate' over wether space is continuous or just made up of a bunch of little pieces? it seems that since you can't have two object be with distance 0 from their center of masses, then maybe space is not continuous? just a thought.
 
  • #14
T@P said:
seems a pity that the gravitational force can't go to infinity, it would be so much easier for things to stay in place :)

actually, doesn't this have any influence in the 'debate' over wether space is continuous or just made up of a bunch of little pieces? it seems that since you can't have two object be with distance 0 from their center of masses, then maybe space is not continuous? just a thought.
The smallest particle with rest mass (apart, perhaps, from a neutrino) is the electron. The smallest meaningful size would be its Schwartzschild radius, which is [itex]2Gm_e/c^2[/itex]. That works out to:

[tex]2Gm_e/c^2 = 2*6.67 \times 10^{-11}9.1\times 10^{-31}/9\times 10^16 = 1.35\times 10^{-56}[/tex]m.

Unfortunately, you can't get two electron masses that close (eg. positron and electron) so we can't tell what would happen if you could.

AM
 
  • #15
:( i feel sad now. oh well, i guess lunch will cheer me up
 

Similar threads

Undergrad Question about geometrical engineering (placeholder name)
  • · Replies 32 ·
2
Replies
32
Views
3K
Undergrad Looking closely at the descent into a black hole
  • · Replies 51 ·
2
Replies
51
Views
3K
Undergrad GR vs Newtonian Physics: Mass Curving Spacetime & Gravity Effects
  • · Replies 9 ·
Replies
9
Views
2K
High School Linking Quantum Physics and Relativity: Theory of Everything?
  • · Replies 16 ·
Replies
16
Views
2K
Undergrad Is Newton's Equation for Gravity Accurate for All Situations?
  • · Replies 7 ·
Replies
7
Views
2K
High School Mechanics behind curved time causing gravitation/geodesics
  • · Replies 27 ·
Replies
27
Views
8K
Undergrad Principle of relativity and Galileo's group
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Black Hole: Knock on the horizon
  • · Replies 34 ·
2
Replies
34
Views
3K
Undergrad Myths of Modern Popular Physics
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Does Relativistic Mass Influence Gravity and Energy in High-Velocity Objects?
  • · Replies 32 ·
2
Replies
32
Views
10K