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My teacher wanted to test our understanding before starting a new topic. The question he gave goes something like this

“There are 2 vacuums present here about which there is an abundance of mass of any material (i.e. solid or fluid) surrounding it everywhere. Describe the nature of the movement of the vacuums. Would it be attractive (would they come closer)? Would it be repulsive (would they move farther apart)? or would it be stationary?”

My thoughts: I knew this was a special case and enquired if it were the case of an ‘absolute vacuum’ to which he said “No. Fluctuations in a permeating field do exist but I don't think that would affect the solution.” This led me to think that absence of any material with the presence of the exact opposite of that would mean something similar to the notion of ‘negative mass’ or rather more similar to ‘relativistic mass’. My conclusion was repulsive(I thought about a little sci-fi G.R with negative mass involved). The vacuums would move apart. He told me that I may have gotten 1 or 2 things wrong but the idea basically stays the same. Anybody can confirm this solution in a better manner? Or perhaps suggest counter-intuitive questions such as this which suggest 'other-wise' solutions? Or perhaps is this question right( I have a feeling this might be wrong due to some missing information)?

A drawing to illustrate the problem

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  • $\begingroup$ Welcome to physics SE, this is not a homework automation solution. For me - the question is why the bubles should survive. They have no mass, and it reminds a bit Archimedes. $\endgroup$ – jaromrax Jan 28 at 17:26
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I think the two vacuums will be effectively attractive.

Due to the attractive nature of the gravitation, there will be a pressure on both vacuums to force them merge. (there will be a net force pointing to the right for the left vacuum, and a net force pointing to the left for the right vacuum).

I would rather say "effectively", since the force is actually exerted on the masses surrounding the vacuums.

For some different view points,

  1. you may imagine this is entropic, making them attractive.

  2. you may consider the surface tension, merging the two bubbles help to reduce the surface free energy.

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  • $\begingroup$ "there will be a net force pointing to the right for the left vacuum, and a net force pointing to the left for the right vacuum"- Well, I don't think such a net force exists since the mass is of infinite expanse so it effectually cancels each other. Moreover, we are talking about the forces between 2 vacuums, thus any question of gravity as a force is challenged. $\endgroup$ – user220704 Jan 29 at 2:23
  • $\begingroup$ "you may consider the surface tension, merging the two bubbles help to reduce the surface free energy." I think one of the conditions is that energy is utilized in maintaining the vacuums since vacuums can't be maintained in such a manner. But the energy is used only to the extent that the vacuums exist without needing to control the directions they expand or move in. However this might be a made-up condition and can possibly be ignored. "you may imagine this is entropic, making them attractive." I don't follow. Can you elaborate? $\endgroup$ – user220704 Jan 29 at 2:27
  • $\begingroup$ For the force, I would rather say, the gravitational force is exerted on the masses around the vacuum, instead of on the vacuum. Though the mass is infinitely large, but due to to the existence of two vacuums, they will not exactly cancel each other, unless the point is very far away from the vacuum. And since the mass will move, effectively the vacuum will move also. However, deciding in which directing the vacuum will move, if you want to make sure, it might be better to do a numerical calculation, i.e., obtain the gravitational force field in space. $\endgroup$ – Zecheng Gan Jan 29 at 2:43
  • $\begingroup$ The problem about surface tension is that, some clear physical model for the surface free energy is needed; and you may have different assumptions, such as whether the vacuum can change volume (i.e., the outside mass can be compressible, etc)... $\endgroup$ – Zecheng Gan Jan 29 at 2:46
  • $\begingroup$ The entropic argument, I just want to qualitatively use it, since calculation using the entropy concept again requires detailed definitions and setups... if you check the wiki "en.wikipedia.org/wiki/Entropy", you will see a sentence "pressure, density, and temperature tend to become uniform over time because the equilibrium state has higher probability than any other state". As a result, combining the two vacuums will be favored by entropy maximum principle. $\endgroup$ – Zecheng Gan Jan 29 at 2:55
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There will be no atraction or repulsion between the vacuums. Vacuum is the absence of matter which translates into absence of gravitational force (positive or negative).

If you had some type of antimatter (which I don't know what it is or if there is such a thing) then your theory might apply

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