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    Ettin in the Playground
     
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    Default Would an object with negative mass levitate on the moon?

    A thought popped into my head recently about theoretical objects with negative mass...

    Ok, so as I understand it, although a theoretical object with negative mass would technically gravitationally repel other objects, the gravity from objects with positive mass would still attract it, and thus overall gravity would pull it towards a planet or other celestial body since its own repulsion would be negligible in comparison.

    HOWEVER, in an atmosphere I would expect it to still rise due to bouyancy, since it would necessarily be of very low density, negative in fact (assuming that the absolute value of its mass was more than the mass of its containment vessel). On the moon, however, there is no atmosphere, but having negative density the object would still be less dense than the vacuum surrounding it, so would it still float? I'm thinking it probably wouldn't because vacuum probably doesn't act like a fluid, but I'm not at all sure.

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    Orc in the Playground
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    Default Re: Would an object with negative mass levitate on the moon?

    Positive and negative mass interactions are weird. In general: positive masses attract each other; negative masses repel each other; and for mixed systems, the negative mass is accelerated towards the positive mass, while the positive mass is accelerated away from the negative mass.

    Thus, for masses of the same value (but opposite sign) this leads to infinite acceleration (termed "runaway motion".) For a (relatively) small object of negative mass placed above the surface of the moon, I believe the smaller object will experience a larger acceleration than the larger object and end up colliding. After the collision, I'm not exactly sure what would happen. The larger object would still want to accelerate away, while the smaller object will still want to accelerate towards the larger object, so maybe the smaller object burrows to the center of the moon and eventually pushes the moon apart? (Not to mention the fact that the negative mass object would try to rip itself apart due to the repulsive force.)
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    Ettin in the Playground
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    Default Re: Would an object with negative mass levitate on the moon?

    Probably for any kind of realistic theory with a negative mass, you need inertial and gravitational masses to be different in that theory. A negative inertial mass means that kinetic energy is unbounded below in a classical theory, so everything explodes. In a relativistic theory, I think it means that the energy can be a complex number, which is arguably worse.

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    BlackDragon

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    Default Re: Would an object with negative mass levitate on the moon?

    Quote Originally Posted by Battleship789 View Post
    Positive and negative mass interactions are weird. In general: positive masses attract each other; negative masses repel each other; and for mixed systems, the negative mass is accelerated towards the positive mass, while the positive mass is accelerated away from the negative mass.
    Curious as to how that falls out of the equations? As far as I recall, the gravitational attraction between two bodies is proportional to both masses (and this is equal and opposite per Newton), so if one mass were negative and one positive then they ought to repel, while if both were negative I would expect them to attract. This is assuming that anything like a negative mass can exist in the first place, of course, but I'm pretty sure we're supposed to just go with that assumption given the question being asked.

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    Default Re: Would an object with negative mass levitate on the moon?

    Quote Originally Posted by factotum View Post
    Curious as to how that falls out of the equations? As far as I recall, the gravitational attraction between two bodies is proportional to both masses (and this is equal and opposite per Newton), so if one mass were negative and one positive then they ought to repel, while if both were negative I would expect them to attract. This is assuming that anything like a negative mass can exist in the first place, of course, but I'm pretty sure we're supposed to just go with that assumption given the question being asked.
    You are correct about the directions of the gravitational forces, but an object with negative inertial mass (which, as NichG points out, leads to huge problems) accelerates in the opposite direction of any force exerted on it. So a negative and positive mass experience gravitational repulsion, but the negative mass responds to that repulsion by moving towards the positive mass, so if they start at rest and their masses are equal except for sign, the negative mass will just chase after the positive mass forever, with both of their speeds approaching infinity. Similarly, if you have two negative masses, they will be attracted, but respond to that by accelerating away from each other.

    This also means that a negative mass won't actually float in an atmosphere. The air pressure on the bottom will be slightly higher than on the top, so the net force from the air will be upwards, and thus it will accelerate downwards faster than in a vacuum. On the moon, there is no air to push on it, so the only force with be gravity, pushing it up and causing it to fall down. Once it hits the ground, the ground pushing it up will cause it to go down even faster, with effects roughly like Battleship789 described.

    An object with positive inertial mass but negative gravitational mass, in contrast, would be repelled by positive masses (both in terms of forces and accelerations) and so would float with or without an atmosphere (slightly more with one).
    Last edited by PirateMonk; 2019-08-20 at 03:12 PM.
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    BlackDragon

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    Default Re: Would an object with negative mass levitate on the moon?

    Quote Originally Posted by PirateMonk View Post
    You are correct about the directions of the gravitational forces, but an object with negative inertial mass (which, as NichG points out, leads to huge problems) accelerate in the opposite direction of any force exerted on it.
    Ah, that was the crucial detail I missed--thanks!

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