NEGATIVE matter is a hypothetical form of matter whose mass is opposite in sign to normal positive matter. It is not antimatter, which is ‘anti-‘ in its elementary particle properties, not its mass. Negative matter could exist somewhere in the Universe: modern theories of matter and energy do not forbid its existence, but if negative matter were to exist, its behaviour would be very strange.
Just how strange would it be? Detailed analyses according to the known laws of physics show that the gravitational field of an object made of negative matter would cause all other objects, including those made of negative matter, to move away from it, while the gravitational field of an object made of positive matter would cause all other objects, including those made of negative matter, to move towards it.
This leads to the unbelievable result shown in Figure 1. If we take a ball of negative matter with a negative mass -M and place it near a rocket ship with a positive mass +M of equal magnitude, then the negative mass will repel the positive mass, while the positive mass will attract the negative mass. According to Newton’s laws of motion, the rocket ship and the ball of negative matter will go off in the same direction with an acceleration equal to the force of gravity between them. This truly miraculous ‘negmatter’ reactionless space-drive provides an unlimited amount of unidirectional acceleration without requiring either an energy source or a reaction mass. It is also easy to imagine machines that could use negative matter to provide unlimited amounts of free energy.
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At first glance, these results seem to prove that negative matter cannot exist. The system starts out with two objects standing still. After a while, the two objects move off in one direction with nothing going in the opposite direction. This should obviously violate the laws of conservation of linear momentum and energy.
Amazingly enough, it doesn’t.
When the two objects are at zero velocity, the total momentum of the system is zero. After the two objects have reached some velocity, the momentum of the rocket ship is its mass +M, times its velocity v, or +Mv; while the momentum of the ball is its mass -M, times its velocity v, or -Mv. Their combined momentum is zero, just as it was when they were not moving, because while the rocket ship has gained positive momentum, the ball made of negative matter has gained an equal amount of negative momentum.
There is also no violation of the law of conservation of energy. When the two objects are at zero velocity, the total energy of the system is zero, because while the rocket ship made of positive matter has gained positive kinetic energy, the ball of negative matter has gained an equal amount of negative kinetic energy.
Hermann Bondi, now Master of Churchill College, Cambridge, was the first scientist to discuss negative matter. In 1957, in Reviews of Modern Physics, Bondi discussed negative mass in relation to Einstein’s theory of gravity – the general theory of relativity. He showed that the concept of a negative mass chasing a positive mass with a constantly increasing velocity was consistent with general relativity. William Bonner of Queen Mary and Westfield College and Navin Swaminarayan of King’s College, London later expanded Bondi’s ideas. They found an exact solution to the full relativity field equations that describe accurately how bodies with opposite masses accelerate uniformly under the effects of their gravitational fields, as shown in Figure 1. The only difference between the Newtonian solution and the general relativity solution is that, in the latter, the two masses are not quite equal and opposite because they are being measured in an accelerating reference frame. For the two masses to keep a constant separation in the accelerated reference frame, the negative mass should be slightly larger than the positive mass.
The paradoxical result of a ball of negative matter chasing a rocket ship off into space at a constantly increasing speed is so bizarre that there must be some logical reason why negative matter cannot exist. Recently, I took a thorough look at the concept of negative matter, and tried to find some law of physics or some rule of logic that would forbid the existence of negative matter. I found none.
I explored the cases where the magnitudes of the masses of the positive and negative objects were different from each other, and where the objects were coupled by forces other than gravity. I started by examining the behaviour of two objects made of opposite types of matter that were coupled by gravity, but did not have the same magnitude of mass.
We all know that if the two objects are made of positive matter, they will attract each other and fall toward each other. If one of the objects is much heavier than the other, the heavier one will not move much, while the lighter one will fall rapidly toward the more massive object. In reality, of course, both move together toward their common centre of mass.
Suppose we have two objects, one made of negative matter and one made of positive matter. The negative-matter object will create a repulsive gravitational field at the position of the positive-matter object. The positive object then responds to that repulsive gravitational field by producing a gravitational force in the direction away from the negative object. The positive mass then accelerates in the same direction as the applied force – away from the negative mass.
In a similar manner, the positive object creates an attractive gravitational field toward the positive mass. The negative object responds to that gravitational field by producing a force in the negative direction – away from the positive object. The force applied to the negative object produces an acceleration. The acceleration, however, is towards the positive object, because the applied force was away from the positive object and the negative mass acts perversely to the applied force. We thus have the expected but paradoxical result that both the positive and negative masses move off in the same direction at a constantly increasing velocity.
If I assumed the positive matter object was larger, then the larger mass of the positive object attracted the smaller negative object more than the smaller mass of the negative-matter object repelled the positive object, so the distance between the two objects decreased with time. On top of the motion closing the gap between the two objects, I found there was superimposed a unidirectional acceleration of both objects, the positive-matter object leading the way. The velocity of the negative-mass object was faster than the velocity of the positive-mass object and it was catching up to the positive-mass object, closing the distance between them. As the gap closed, the gravitational fields became stronger and the accelerations increased, until the two objects collided.
If I assumed the positive-matter object was smaller than the negative-matter object, then the distance between the two objects increased with time because the larger mass of the negative-matter object was repelling the smaller positive-matter object away. This motion was also accompanied by a unidirectional motion of both objects. In this case, however, the mutual gravitational fields and the acceleration levels decreased with time.
In all cases, when I calculated the net linear momentum of the system, it never changed from the initial value. Any increase in the positive linear momentum of the positive-matter object was always balanced by the increase in negative linear momentum of the negative-matter object. When it came to conservation of energy, however, there was a difference. The positive kinetic energy gained by the positive-matter object was different from the negative kinetic energy gained by the negative-matter object. But when I included the mutual gravitational potential energy of the two objects, I found that the change in gravitational potential energy was exactly equal and opposite to the change in the kinetic energy. Thus, even when two gravitating objects of opposite mass have different masses, I found there was no violation of the laws of conservation of linear momentum and energy.
Suppose, however, that we used a massless, ideal stiff rod to connect the two masses so they had the same velocity. Then, because the velocities of the two objects would be forced to remain the same, but their masses would be different, their momenta and energies would be different and would not add up to zero. My investigation of the stiff rod led me to study in detail how two objects coupled by elastic forces behave.
I next studied two point objects coupled by an ideal, massless spring. I first calculated the behaviour when the two objects had positive masses. As expected, the two objects oscillated sinusoidally back and forth. If one of the objects was very massive, then the heavier object stood still while the other object bounced back and forth with a frequency determined by the square root of the spring constant divided by the mass of the smaller object.
For the case where I assumed two objects that were made of opposite types of matter, the force of the spring on the positive-matter object caused the positive object to move towards the spring. In contrast, the force of the spring on the negative-matter object caused the negative object to move away from the spring because of the perverse reaction of the negative inertial mass to the spring’s force.
If I assumed that the positive and negative masses were equal, then the accelerations of both objects were the same. This produced the expected, but bizarre, result that both the positive-mass object and the negative-mass object moved off at a constant acceleration that was proportional to the strength of the spring, the initial extension of the spring, and inversely proportional to the magnitudes (equal) of the two masses. As in the case of gravity coupling, the total linear momentum and energy of the combined system remained zero.
If I assumed that the negative mass was larger than the positive mass, then the equation of motion for the length of the spring changed. Instead of the spring staying at a constant length, the length of the spring oscillated sinusoidally. This is similar to the case of the two positive masses, except that the frequency of oscillation of the spring now depended upon the difference of the masses instead of their sum. On top of the sinusoidal motion of the spacing between the two objects was superimposed a sinusoidal motion of the combined system, first off to one side, then the other side.
Then I calculated the total linear momentum and the total energy of the system for any point in time during the oscillation. As long as I included the energy stored in the stretched spring, the laws of conservation of energy and momentum remained inviolate.
If I assumed that the positive mass was larger than the negative mass, I found the behaviour was exponential instead of sinusoidal. After an initial transient moment, which involved both an exponential growth and an exponential decay, the exponential growth took over. Both objects moved off in one direction, with the negative mass leading and the positive mass following. Because the less massive negative-matter object moved faster than positive-matter object, the spring stretched. As the spring lengthened, its force increased and the system accelerated at an exponential rate. Again, I found no violation of the conservation laws.
Although real particles of negative matter, if they exist, may not have convenient ‘handles’ to hook springs to, and may not be dense enough to produce significant gravitational forces, they may be massive enough to be useful and also have an electrical charge. The electrical charge would give us a ‘handle’ on the negative-matter particle that could be used to ‘push’ and ‘pull’ the particle at a distance using electrostatic forces. Electric, magnetic and radio fields could also be used to build a computer-controlled active ‘trap’ that could capture and collect large numbers of negative-matter particles.
I also analysed the interaction of a positive-matter object and a negative-matter object coupled by electrostatic forces. I obtained the same results of unidirectional motion of the combined system at an acceleration proportional to the electrostatic force. Again, there was no violation of the laws of conservation of momentum and energy.
The purpose of bringing up the subject of negative-matter again after 30 years is to remind people that the concept of negative matter is not logically forbidden. In physics, there is an unwritten law that if something is not forbidden, it is compulsory. So where is negative matter? There are some clues that may point to places where we might find negative matter. One clue that there may be large amounts of negative matter in the Universe can be found in research papers discussing the huge voids found in large-scale-three-dimensional ‘maps’ of the Universe. These ‘bubbles’ are 100 million light years across (our Milky Way is a mere 0.06 million light years across). The bubbles are sharply defined by large numbers of galaxies that seem to lie on the surface of the bubbles. There seem to be almost no galaxies in the voids, and those that are found there are unusual galaxies which are very bright and highly active.
One possible explanation for the ‘frothy’ structure of the Universe today is that it was formed with equal amounts of negative-matter particles and positive-matter particles. The ‘voids’ are full of the negative-matter particles trying to keep as far away from each other as possible, meanwhile pushing the positive-mass particles to the surface of the voids where they attract each other to form galaxies, stars, planets, and us. One way to test this hypothesis is to use some of the available computer models of the Universe to see if an equal mixture of positive and negative matter would separate out into regions similar in size and shape to those observed.
If there are large numbers of negative-matter particles in the Universe, then positive masses, like our Sun, will attract those negative-matter particles. Some Soviet scientists have calculated that when the negative-matter particles strike the positive-matter particles in the Sun, they do not slow down, but accelerate continuously. In the process, they gain negative kinetic energy and put positive kinetic energy into the particles in the Sun, so heating it up.
The Sun, however, is clearly not heating up catastrophically. So some researchers argue that either there are very few negative-matter particles, or that they do not interact easily.
There is another explanation: it could be, instead, that an influx of negative-matter particles heats the Sun. This may answer one of the long-running puzzles in cosmology: why the neutrinos astronomers have observed coming from the Sun amount to only one-third that calculated assuming that all the energy in the Sun is generated by thermonuclear fusion plus gravitational contraction.
It also may be that there are relatively large numbers of negative-matter particles streaking through the Solar System. But when they come into contact with normal positive matter, ‘nullification’ takes place. Nullification would be a physical process similar to the ‘annihilation’ process that takes place when antimatter comes into contact with normal matter. During matter-antimatter annihilation, the total rest mass of the two particles is converted into energy. In the case of matter-negmatter nullification, the net rest mass is zero because the negative-matter object has negative rest mass and the positive-matter object has positive rest mass. Nullification, therefore, releases no energy. As a result, our energy-sensitive instruments on Earth would not detect any events caused by negative-matter particles.
We could, however, design detectors that use electric, magnetic, gravitational, photon or other massless ‘force fields’ to look for negative matter without physically touching it and setting off nullification. Once we have detected negative matter, then we can use the same ‘force field’ techniques to gather the negative matter and harness its remarkable powers.
There is as yet no logical reason why negative matter cannot exist. If it were created during the formation of the Universe, there is good reason why most of it would be elsewhere. Even if there were any in the Solar System, there are also good reasons why it would not stay around very long, and it would be hard to detect unless you designed your detecting instruments specifically for the problem.
Realistically, it is very likely that one of these days someone will come up with a proof that negative matter is logically forbidden. In the process of discovering that proof, perhaps we will learn some new physics. But there is always the small, faint hope that negative matter is not forbidden, and that a properly designed search will lead to its discovery. Then, those ‘impossible dreams’ of countless back-yard inventors for ‘reactionless space drives’ and ‘free energy machines’ will finally come true.
Robert Forward writes about science fiction and science fact. He is also a consulting scientist specialising in exotic physical phenomena and advanced space propulsion.
Further reading Robert L. Forward, ‘Negative matter propulsion’, Journal of Propulsion and Power, vol 6, Jan-Feb 1990, p 28.
