Negative Mass and its Implications

[Swapnil]

I was thinking the other day about how mass creates valleys in fabric of space-time and how objects follow that path. Then I came to think, isn't it theoretically possible that there could be a negative mass that creates hills in the fabric of space-time?

What do you guys think about this? Is it plausible? What would be the implications of this?

 

[JesseM]

I was thinking the other day about how mass creates valleys in fabric of space-time and how objects follow that path. Then I came to think, isn't it theoretically possible that there could be a negative mass that creates hills in the fabric of space-time?

What do you guys think about this? Is it plausible? What would be the implications of this?

In the rubber-sheet analogy, all that's important is the curvature of the surface, not its orientation. In the absence of non-gravitational forces, general relativity says that all objects should follow "geodesics" in curved spacetime. On a curved 2D surface like a rubber sheet, a geodesic would be the shortest path along the surface between the two points--for example, on a globe geodesics would always be segments of a great circle, like the equator or a line of longitude. The shortest path doesn't depend on how you orient the curved 2D surface in 3D space--if you imagine a metal sheet with dimples on it, the shortest paths between points will be the same even if you flip it over so the dimples become bumps.

In general relativity, the geodesics are in curved spacetime rather than just curved space as in the rubber-sheet analogy--usually they are the worldlines with the largest value of the "proper time" (the time as measured by a clock that moves along that worldline), although technically a geodesic has an "extremal" value of the proper time which could in some cases be a minimum (I'm not sure what kind of curved spacetime you'd need for the extremal path to be a minimal path, though). For example, in the flat spacetime of special relativity inertial paths are geodesics, and you may remember from the twin paradox that the inertial twin always experiences more time between the departure and return of his non-inertial twin who accelerates during the journey.

edit: that said, you can discuss the possibility of negative mass and negative energy in physics, it just doesn't have anything to do with creating "hills" rather than "valleys"--see pervect's post below.

 

[pervect]

see https://www.physicsforums.com/showpost.php?p=1129928&postcount=7

One annoying theoreitical problem with negative mass is its unstable thermodynamic properties. A collection of particles of negataive mass forming a gas would have a negtative temperature. This assumes the equivalence principle holds, and that a negative gravitational mass implies a negative inertial mass. See

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg_temperature.html

It might not be obvious at first glance, but thermodynamically the negative temeprature of a negative mass gas would result in the negative mass gas losing an unbounded amount of energy (i.e. gaining negative energy) to its surroundings. So a container of negative mass gas would tend to heat up its surroudnings, losing energy, until the container ultimately imploded under the unbounded negative pressure, assuming you can come up with a way to contain negative mass particles in the first place. (Not necessarily easy, when you start to think about the way negative mass particles move _towards_ repelling forces).

Of course nobody has actually seen such a thing.

 

[JesseM]

see https://www.physicsforums.com/showpost.php?p=1129928&postcount=7

One annoying theoreitical problem with negative mass is its unstable thermodynamic properties. A collection of particles of negataive mass forming a gas would have a negtative temperature. This assumes the equivalence principle holds, and that a negative gravitational mass implies a negative inertial mass. See

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg_temperature.html

It might not be obvious at first glance, but thermodynamically the negative temeprature of a negative mass gas would result in the negative mass gas losing an unbounded amount of energy (i.e. gaining negative energy) to its surroundings. So a container of negative mass gas would tend to heat up its surroudnings, losing energy, until the container ultimately imploded under the unbounded negative pressure, assuming you can come up with a way to contain negative mass particles in the first place. (Not necessarily easy, when you start to think about the way negative mass particles move _towards_ repelling forces).

Of course nobody has actually seen such a thing.

These problems with negative energy are also discussed here:

http://www.physics.hku.hk/~tboyce/sf/topics/wormhole/wormhole.html

As I understand it, the authors believe that various "quantum inequalities" put restrictions on negative energy in such a way that some of the more troubling behaviors, like the unstable thermodynamic properties mentioned above, could be avoided.