Will Two Identical Spherical Cavities in Free Space Attract or Repel Each Other?

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Discussion Overview

The discussion revolves around the interaction between two identical spherical cavities in free space filled with evenly distributed dust particles. Participants explore whether these cavities will attract, repel, or remain unaffected by each other, considering various physical principles and assumptions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the cavities will repel each other due to the gravitational forces acting on the surrounding dust particles.
  • Others argue that the cavities may attract each other because the mass around them would create a gravitational pull towards the voids.
  • A participant suggests using the principle of superposition to analyze the situation but finds it challenging to reach a conclusion.
  • One participant mentions that if one cavity is held fixed, the gravitational force on the second cavity would point away from the first, suggesting that the void moves towards the first cavity.
  • Another perspective introduced is treating the dust as massless and the cavities as having negative mass, leading to an attraction between the cavities.
  • Questions arise regarding the nature of the cavities and whether they can be treated as objects, with some asserting that they are simply voids in the dust distribution.
  • Concerns are raised about the initial conditions of the dust particles, including their thermal energy and how this might affect their behavior in relation to the cavities.
  • Participants discuss the potential for dust particles to aggregate into larger voids and the dynamics of multiple voids interacting in a three-dimensional space.
  • Surface tension is briefly mentioned as a potential factor in the discussion.
  • One participant notes that the problem is reminiscent of a physics olympiad question, suggesting that the configuration of dust remains constant and can be analyzed using potential energy concepts.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the interaction between the cavities, with no consensus reached on whether they will attract, repel, or remain unchanged.

Contextual Notes

The discussion includes various assumptions about the nature of the dust particles, the initial conditions of the system, and the treatment of the cavities, which may affect the conclusions drawn by participants.

zd1899
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Suppose that in free space , dust particles are evenly distributed all around.
Amidst the dust particles , there are two identical spherical cavities at some distance from each other. Do you think they will attract each other or repel or just be as they were??
 
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They repel. (Wrong...see below)
 
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And may i know how? I always think that they would attract each other as the mass around the spheres would try and close on in , i was thinking of going about this by using the principle of superposition but still couldn't get a conclusion.
 
Oops...sign error.

Hold one bubble fixed. Consider the force on the second bubble. If the first bubble didn't exist, there would be no force on the second. Since there is a gap, the gravitational force points away from the bubble. So the dust moves in that direction, away from the bubble, which means that the void moves towards it.
 
Hey thanks that cleared a lot up.
 
Another way you can think of it is to treat the dust as massless, and the bubbles as having negative mass. The force points in the opposite direction, so the acceleration points in the same direction: the bubbles attract.
 
zd1899 said:
Amidst the dust particles , there are two identical spherical cavities at some distance from each other. Do you think they will attract each other or repel or just be as they were??
What are these cavities composed of? Are they simply voids in the distribution of the particles? Is there anything holding them rigid? Is there anything holding the particles from filling them?
 
DaveC426913 said:
What are these cavities composed of? Are they simply voids in the distribution of the particles? Is there anything holding them rigid? Is there anything holding the particles from filling them?

Yes , they are simply voids. The Dust particles are distributed uniformly and there are two nearby spherical voids.
 
  • #10
zd1899 said:
Yes , they are simply voids. The Dust particles are distributed uniformly and there are two nearby spherical voids.
Then it is folly to pretend they act as an object. The particles will uniformaly distribute themselves within them.
 
  • #11
DaveC426913 said:
Then it is folly to pretend they act as an object. The particles will uniformaly distribute themselves within them.
Even if all particles are initially at rest?
 
  • #12
Won't all of the dust particles attract each other into a assemblage, thus merging the voids into one huge one that surrounds the object? (No offense, Vanadium, but the original question didn't assume the dust to be massless.)
 
  • #13
Yeah, I guess dust particles with empty space between are quite different from a fluid, which cannot be compressed or vaporize. How would they behave with only one spherical cavity, when initially all are at rest?
 
  • #14
A.T. said:
Even if all particles are initially at rest?
They cannot be at rest; they must have some thermal energy.
 
  • #15
DaveC426913 said:
They cannot be at rest; they must have some thermal energy.
Why?
 
  • #16
A.T. said:
Why?

Because if they lacked thermal energy, and they were at rest, you would pretty much know everything about them with certainty (position, velocity, energy) which violates the uncertainty principle
 
  • #17
theneedtoknow said:
Because if they lacked thermal energy, and they were at rest, you would pretty much know everything about them with certainty (position, velocity, energy) which violates the uncertainty principle
I was thinking more in terms of larger particles so I omitted this. How would they behave classically without quantum effects, just gravity.
 
  • #18
A.T. said:
I was thinking more in terms of larger particles so I omitted this. How would they behave classically without quantum effects, just gravity.
OK, I see where you're going.

The particles adjacent to the voids feel an imbalanced gravitational pull. The net effect is that they are pulled away from the voids, causing the voids to grow. The particles between the two voids have this imbalance ... uh ... balanced. They feel no pull towards or ways from the two voids, but they do feel a very small pull outward, as if being squeezed out from between the two voids.

The net effect is that the voids will grow until they are separated by a thin filament of particles.


If we expanded the model to include multiple voids in a 3D volume, we would see all voids grow until they were separated only by thin, dense filaments. Ultimately, the volume would be less "voids in a sea of particles" and more "empty space shot through with filaments", like a cobweb in a box.

Interestingly, this is exactly what is http://images.google.com/images?q=g...oe=utf8&rlz=&um=1&ie=UTF-8&sa=N&hl=en&tab=wi".
 
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  • #19
Surface tension has a role?
 
  • #20
Hey! I just found out that its an ex Physics olympiad problem.
The dust configuration remains constant , won't move in. So we can do this using the potential energy concept for the sphere's i.e. they would try and reduce their respective energies.
 

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