Negative Mass

Basic Information

It is allowable within the laws of physics for there to be matter with negative mass, which would have interesting properties.

If you use negative mass as some sort of phlebotinum in a science-fiction game, you may want to use the term exotic matter instead and only go into the details when someone asks. Exotic matter sounds suitably scientific, while at the same time being just mysterious enough to let the GM not sweat the details.

Negative Gravitational Mass

It is worth distinguishing between inertial mass (which affects how matter responds to forces exerted on it) and gravitational mass (how it affects and is affected by gravity) in this context.

For story purposes it is usually convenient to assume that even though a material's gravitational mass is negative, its inertial mass is still positive (or equivalently, that inertial laws turn out to actually be based on the absolute value of mass). This technically violates current science, but this can be handwaved since current scientists have never encountered any matter with negative mass.

Negative-mass objects of this kind attract each other normally but repel positive-mass objects and vice versa. On regular planets, negative-mass objects fall upwards at the same rate positive-mass objects fall down. Such negative mass objects essentially have natural antigravity properties.

Effectively, negative mass (let's call it "natter") would mean that mass is working like electric charge - there are positive and negative charges, but a positive and negative ones repel and two positive or two negative ones attract. That would mean natter can form stars, planets and life, just like matter, anti-matter or even anti-natter.

Negative Inertial Mass

A bit more mind-boggling would be matter with negative inertial mass as well as negative gravitational mass. Technically this is more in line with current scientific understanding than natter would be, but it's got some bizarre implications for physics and is kinda hard to wrap your brain around. This may be more accurate than natter, but it might be less playable.

In theory, matter with negative inertial mass matter would respond to physical force in the opposite fashion of what you would expect. If you push it left, the object instead goes right. What happens to the hand you used to push it is probably left to the GM's most sadistic impulses… it just might rip your hand off and send it into orbit, but a kinder GM might have you just get bruised and lose your grip on the thing you were pushing.

Exotic matter with negative inertial mass starts to do some really crazy stuff anytime it interacts with normal matter. It gets most impressive when considered on a grander scale such as planets and gravity. When a really large exotic matter object gets close enough to large normal object, the normal object gets pushed away by gravity. The exotic object, instead of being pushed away as well, actually gets pushed in the same direction that the normal object did. One races off, but the other effectively chases after it. It's even possible that if the absolute value of the masses of the objects are equal, they will continue to accelerate as they move, until they eventually reach the speed of light. Getting anywhere near that fast will take a very long time, and it might not ever happen because the negative mass implies negative energy as you enter into some of the equations… which means again that it's all up to the GM.

This form of negative mass matter is unlikely to be organized into planetary bodies, because every atom repels other negative mass atoms. The larger the body of negative mass, the greater the forces tearing it apart.

Small negative inertial mass life-forms may or may not be possible at the GM's discretion, as the gravity repulsion affects wouldn't be strong enough to literally rip them apart unless the organism grew to extreme proportions. However, the constant acceleration effects their body parts would experience when colliding with anything would be quite the challenge. Depending on your take it might make them very fragile, require them to be quick healers or heavily armored, or restrict them to only simple unicellular life.

Summary of Reactions by Negative Mass type

This chart is to help illustrate the differences between the two types:

Object A	Object B	Gravitational Reaction	Collision Reaction
Normal	Normal	Attract	Standard
Normal	Natter	Repel	Standard
Natter	Natter	Attract	Standard
Normal	Negative Inertial	Normal is Repelled, Negative Inertial is Attracted	Normal matter behaves as standard, but Negative Inertial object goes faster instead of slowing down or bouncing.
Negative Inertial	Negative Inertial	Repel	Both objects try to accelerate through each other, possibly resulting in immobilization or destruction?
Natter	Negative Inertial	Natter is Attracted, Negative Inertial is Repelled	Natter behaves as standard, but Negative Inertial object goes faster instead of slowing down or bouncing

In this context, "Natter" is matter with negative Gravitational Mass, but positive Inertial Mass. "Negative Inertial" designates matter with negative values for both Gravitational and Inertial Mass.

Note that the last option on the chart, probably isn't really an option. Whether or not the matter with Negative Gravitational Mass also has Negative Inertial Mass shouldn't really be a function of the properties of the matter itself, but rather a function of the laws of physics. Then again, this is all so hypothetical and out-there that you can't really say one take is more logical than the other. Do whatever sounds the most fun to you.

Sources

Bibliography

1. Wikipedia article on exotic matter

2. Far more detailed math and discussion on the talk page of the wikipedia article

3. Wikipedia on Newton's law of universal gravitation

Game and Story Use

• If available in large quantities, negative mass can allow for all kinds of otherwise preposterous engineering projects. You can make anything float if you add enough negative mass counterweights and fine-tune using lifting gas and ballast.
• An alloy of negative-mass and regular metals can be effectively weightless (or have whatever weight you choose) while offering the same protection and structural integrity as ordinary metal. This makes it a very useful material for air- and spacecraft.
  • It'll be useful for a lot of other things too.
  • Storing negative mass in such alloys makes the logistics easier as you don't have to worry about it falling off your planet.
• Negative-mass material can be a highly fought-over resource.
• When inertial mass is negative too, you get a highly bizarre substance that's impossible to use for mundane purposes but might do any of the following:
  • Serve as the key ingredient in the diametric drive, which allows for arbitrary acceleration without consuming anything. (See below)
  • Stabilize a wormhole.
  • Be used to create a Tipler Cylinder.
  • Generally serve as phlebotinum for the settings dimension-bending supertech.
• Negative inertial mass would probably open up some rather bizarre design space for weapons. You might use electrical fields to cause the weapon to move "normally" when swung or fired, but when the blade or projectile hits a target it actually speeds up and drives deeper through the flesh.
  • A railgun firing exotic matter negative mass bullets would be very interesting.
  • You know that exaggerated knockback you see in video games and movies where a big guy hit by a little piece of metal goes flying an insane distance in direct violation of the normal laws of physics? This could totally do that. Or rather, it could at least be the handwavium that explains such effects.
  • Such weapons would have to be kept constantly powered. If your army were hit by an EM pulse, you'd experience madcap comic chaos as their weapons broke apart and flew away.
  • Melee weapons of this style would be quite a challenge to use. With every hit, your weapon is pulled away from you, and tugging back might not be the right response. Using them properly is probably dependent on some sort of advanced skill beyond that used for mundane melee weaponry, sort of a zen "bend like a reed in the wind" combat style. This trade-off in skill points gets you increased damage, armor penetration, knockback, or whatever other cool benefit your game system can model. It's also possible that those not trained in this special way of fighting might not be able to effectively parry or respond to your weaponry.
• An exotic element with negative mass could be a key component in a very efficient stardrive. When at rest, carefully tuned electromagnetic fields isolate the normal and exotic matter in the drive system and prevent them from interacting. To accelerate, you reverse the polarity and the negative mass clunks against some armored bulkhead or engine structure, which it then pushes forward faster and faster, dragging the rest of the ship through the void.
  • I imagine this would result in space vessels that were huge heavy armored clunkers, with limited maneuverability and poor braking. In other words, perfect for steampunk settings.
  • They'd also be extremely fuel efficient, as the engine itself is essentially a perpetual motion machine. Baseline acceleration requires no outside energy, power is only used for braking and steering systems.
  • Perhaps the coolest notion about this is that if your ship had a power-outage, it would actually speed up. Starship combat and malfunction might carry with them the risk of being hurtled past the frontiers in an ever-accelerating race to the edge of the galaxy. That's got some great dramatic possibilities built into it.
• Creatures with negative mass may make for a good Monster of the Week, providing interesting challenges for the players.
  • Such a species would probably be a bad choice for a campaign-length threat, recurring NPC, or player-character race, as it would require the players to constantly have to second-guess their natural intuitions about how things work. It may break suspension of disbelief or be hard to visualize.