Ken Burnside said it best.

Friends Don't Let Friends Use Reactionless Drives In Their Universes.

Yeah, I know that the blasted Tyranny of the Rocket Equation ruins science fiction writer's fun by making every gram count. But a Reactionless Drive is a solution that makes even worse problems. Kind of like removing lice by setting your hair on fire.

Sure you'll be giving Tyranny Of The Rocket Equation concrete overshoes and dumping it into the ocean to sleep with the fishies. But you will also be giving every space fleet, astromilitary, corrupt corporation, James Bond Villain and little Jimmy in his garage lab access to civilization-destroying relativistic weapons. Are you sure you wanna do that?

And besides, there's the iron-clad Law of Conservation of Momentum which says You Can't Do That. Sure, a future scientific breakthrough might let you have your way, but that's not the way to bet.

It came up in response to a reoccuring discussion on SFCONSIM-L, a mailing list I moderate (and participated actively in at the time as I was developing Attack Vector: Tactical).

New List Member: "Hi, I'm writing about X, with spaceships that do multiple G thrusts, just like in the works of author Y!"

Ken (and other list members): "How do you keep someone from sterilizing planets as a result of putting that multiple G thrust on a cruise missile, launching it from the orbit of Saturn and letting it hit at fractions of c? The only way to really avoid this is using delta-v limited thrust and the rocket equation."

New List Member: "You big meany! I'm just trying to tell stories of rip-roaring adventure! If it's good enough for author Y, it's HARD SF!"

Ken: "Author Y made their reputation {30|40|50} years ago, and standards have changed. Besides, reaction drive calculations can be done fairly simply with a spreadsheet. You will end up with multi-month travel times, going onwards of two years, which may impact the story you want to tell."

New List Member: "AAARGH! You're impossible!"

Ken: "Here's my advice: Friends don't let friends use reactionless drives in their universes."

This happened multiple times over four years, and Burnside's Advice became the shorthand form of the discussion.

I'm still amused that this gets quoted more than 15 years later!

• 

      ‘That leaves the southern end of Rama, which Commander Norton has been unable to reach, owing to that ten-kilometre-wide band of water. There are all sorts of curious mechanisms and structures up on the South Pole—you’ve seen the photographs. What they are is anybody’s guess.
     ‘But I’m reasonably sure of this. If Rama does have a propulsion system, it’s something completely outside our present knowledge. In fact, it would have to be the fabulous “space drive” people have been talking about for two hundred years.
     ‘You wouldn’t rule that out?’
     ‘Certainly not. If we can prove that Rama has a space drive—even if we learn nothing about its mode of operation—that would be a major discovery. At least we’d know that such a thing is possible.’

     ‘What is a space drive?’ asked the Ambassador from Earth, rather plaintively.
     ‘Any kind of propulsion system, Sir Robert, that doesn’t work on the rocket principle. Antigravity—if it is possible—would do very nicely. At present, we don’t know where to look for such a drive, and most scientists doubt if it exists.’
     ‘It doesn’t,’ Professor Davidson interjected. ‘Newton settled that. You can’t have action without reaction. Space drives are nonsense. Take it from me.’
     ‘You may be right,’ Perera replied with unusual blandness. ‘But if Rama doesn’t have a space drive, it has no drive at all. There’s simply no room for a conventional propulsion system, with its enormous fuel tanks.’

---

     ‘I’d like to comment on that,’ said the science historian. ‘Rama seems to have made a change of spin without using any jets or reaction devices. This leaves only two possibilities, it seems to me.

     ‘The first one is that it has internal gyroscopes, or their equivalent. They must be enormous; where are they?
     ‘The second possibility—which would turn all our physics upside down—is that it has a reactionless propulsion system. The so-called space drive, which Professor Davidson doesn’t believe in. If this is the case, Rama may be able to do almost anything. We will be quite unable to anticipate its behaviour, even on the gross physical level.’

     The diplomats were obviously somewhat baffled by this exchange, and the astronomer refused to be drawn. He had gone out on enough limbs for one day.
     ‘I’ll stick to the laws of physics, if you don’t mind, until I’m forced to give them up. If we’ve not found any gyroscopes in Rama, we may not have looked hard enough, or in the right place.’

---

     That was strange. The star field was shifting, almost as if he had actuated the roll thrusters. But he had touched no controls, and if there had been any real movement, he would have sensed it at once.
     ‘Skipper!’ said Calvert urgently from the nav position, ‘we’re rolling—look at the stars! But I’m getting no instrument readings!’
     ‘Rate gyros operating?’
     ‘Perfectly normal, I can see the zero jitter. But we’re rolling several degrees a second!’
     ‘That’s impossible!’
     ‘Of course it is—but look for yourself.’

     When all else failed, a man had to rely on eyeball instrumentation. Norton could not doubt that the star field was indeed slowly rotating—there went Sirius, across the rim of the port. Either the universe, in a reversion of pre-Copernican cosmology, had suddenly decided to revolve around Endeavour; or the stars were standing still, and the ship was turning.
     The second explanation seemed rather more likely, yet it involved apparently insoluble paradoxes. If the ship was really turning at this rate, he would have felt it—literally by the seat of his pants, as the old saying went. And the gyros could not all have failed, simultaneously and independently.
     Only one answer remained. Every atom of Endeavour must be in the grip of some force—and only a powerful gravitational field could produce this effect. At least, no other known field.

     Suddenly, the stars vanished. The blazing disc of the sun had emerged from behind the shield of Rama, and its glare had driven them from the sky.
     ‘Can you get a radar reading? What’s the doppler?’
     Norton was fully prepared to find that this too was inoperative, but he was wrong.
     Rama was under way at last, accelerating at the modest rate of 0.015 gravities. Dr Perera, Norton told himself, would be pleased; he had predicted a maximum of 0.02. And Endeavour was somehow caught in its wake like a piece of flotsam, whirling round and round behind a speeding ship.
     Hour after hour, that acceleration held constant; Rama was falling away from Endeavour at steadily increasing speed. As its distance grew, the anomalous behaviour of the ship slowly ceased; the normal laws of inertia started to operate again. They could only guess at the energies in whose backlash they had been briefly caught, and Norton was thankful that he had stationed Endeavour at a safe distance before Rama had switched on its drive.
     As to the nature of that drive, one thing was now certain, even though all else was mystery. There were no jets of gas, no beams of ions or plasma thrusting Rama into its new orbit. No one put it better than Sergeant Professor Myron when he said, in shocked disbelief: ‘There goes Newton’s Third Law.’

Oh, the Dean Machine, the Dean Machine,
You put it right in a submarine,
And it flies so high that it can't be seen —
The wonderful, wonderful Dean Machine!

1. First, Find Something to Push On.

As a method of sending a missile to the higher, and even to the “highest parts of the earth’s atmospheric envelope, Professor Goddard’s rocket is a practicable and therefore promising device…It is when one considers the multiple-charge rocket as a traveler to the moon that one begins to doubt…for after the rocket quits our air and really starts on its longer journey, its flight would be neither accelerated nor maintained by the explosion of the charges it then might have left. That Professor Goddard, with his "chair” in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react—to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools…

(New York Times,January 13, 1920, Editorial Page.)

This quotation, one of my favorites, exhibits clearly the grave dangers of a little knowledge. It makes plain the fact that the “knowledge ladled out daily in high schools” did not give that particular editorial writer a very good understanding of the mechanics of space flight. He knew that if you want to go some place you have to push against something, but he didn’t know enough to realize that a rocket simply pushes against its own exhaust—or that the escaping exhaust pushes the ship away, which amounts to the same thing.

The idea that a spaceship sets itself in motion by pushing against its exhaust is usually related to Newton’s Third Law of Motion. This law states that whentwo objects interact with each other, the force acting on one object is equal and opposite to the force acting on the other. So if a rocket pushes on its exhaust gases, then the exhaust gases push the rocket in the oppositeidirection with equal force. It is an intriguing fact that Newton’s Third Law of Motion is not a universal law. That is, it does not apply to all situations. I would not blame you if you responded to this statement with disbelief. It was with a good deal of shock that I myself learned about the loop-holes in the Third Law. These holes represented serious lapses in my education, because I learned the Truth about the Third Law less than 10 years ago, and i’ve held a doctorate in physics for nearly 30 years. The experience demonstrates that it’s best to keep a sense of modesty about one’s knowledge.

It also demonstrates that real physics has gotten so far ahead of what is taught in an elementary physics course (or even in a course in engineering mechanics) that the average semi-educated person can very easily get himself sunk in deep and murky waters when venturing into the simplest topics. I make a point of this because there is still a certain amount of nonsense being bruited about concerning space drives, and the authors get away with it only because it requires more than an elementary knowledge of physics to demonstrate the fallacies in their ideas.

These fallacies arise because of misunderstandings concerning Newton’s Laws of Motion and some of the other fundamental laws of physics. (Yes, 60 years after that infamous editorial quoted above, there are those who not only misunderstand Newton’s Third Law, but make a determined effort to misunderstand it.)

What I want to do in this article is to take a hard look at the fundamental laws of nature, and to see what these laws tell us about the necessities of designing an interstellar spaceship. Along the way I want to separate some of the facts from the great gobs of fiction that have been thrown in our direction over the years. (And, I might add, fiction that very often comes to us labeled “Science Fact.” I sometimes wonder if we should lay the Federal Truth in Labelling Act on these people.)

First, what about those exceptions to Newton’s Third Law? You must be dying of curiosity about that. How can there be loopholes in such a fundamental law of nature? Well, these exceptions occur mainly in connection with magnetic forces, but they also occur with gravitational forces acting between objects moving very rapidly. A simple example shows what happens with magnetic forces. We know that between two electrically charged objects there is an electric force. This electric force is either an attraction or repulsion, and acts along the straight line between the two objects. If the objects are moving (relative to the observer), then an additional force—the magnetic force—makes itself felt. (Or, to put it more precisely, the magnetic force is a component of the electromagnetic interaction that depends on the velocities of the charges.)

• 

Look at the two charges in Fig. 1. They are moving with velocities v₁ and v₂. Velocity v₁ is in the x direction, and v₂ is in the y direction. Charge 1 produces a magnetic field (B₁) whose lines of force point in the z direction at the location of charge 2. The magnetic force acting on charge 2 is at right angles to both its velocity and the direction of the magnetic field. So that magnetic force is in the x direction.

On the other hand, charge 2 produces zero magnetic field at the location of charge 1 (because charge 1 is on the line of motion of charge 2). Therefore there is no magnetic force at all acting on charge 1! So if We add up the electric and magnetic forces (vectorially) we find that the total force acting on charge 1 is neither equal in magnitude nor opposite in direction to the force acting on charge 2.

It’s a shocker, isn’t it?

Well now, what are we to make of Newton’s Third Law, and how can we discard it so blithely? The Third Law was originally intended to deal with actions and reactions between pairs of objects. It works for ordinary mechanical forces (contact forces), and for gravitational forces under usual conditions, so it’s an adequate law for classical mechanics.

But it’s a law with two serious limitations. First, it assumes that only two objects are interacting. But the electromagnetic field cannot be ignored; it is part of the system. So in the case of two moving charged objects we do not have a simple two-body system. Second, the law assumes that when two objects interact, the force between them travels instantaneously. But this is not true. Even gravitational forces travel with the speed of light. So if we have a spaceship traveling very fast, the force acting on the ship depends on where the ship is located now, but the force acting on the planet depends on Where the ship was located a little While ago, because the planet doesn’t know yet that the ship has moved. So even with gravitational forces the Third Law is not strictly obeyed.

It doesn’t matter. Newton’s Third Law of Motion is not a fundamental law of nature. It just happens to be true in a number of useful situations. It does work for rockets, but if we are going to be looking for more novel means of propulsion, then we need a more general law.

The fundamental and general law that applies to our search is the law of conservation of momentum. Momentum is a rather abstract property of moving objects, but its definition is simple. The momentum of a moving body is simply its mass multiplied by its velocity. So, for example, a rocket with a mass of 1000 kilograms traveling 100 meters/second has a momentum of 100,000 kg m/sec. (Curiously, despite the supreme importance of momentum in physics, there is no single name for a unit of momentum.)

The law of conservation of momentum states that in a closed system—a system on which no force is acting from the outside—the total quantity of momentum must remain unchanged. It is important to remember that momentum is a vector quantity—that is, it has direction. Two objects may have the same amount of momentum, but if they are traveling in opposite directions, then their momenta are opposite in direction. Keeping this in mind, we can state the law this way: when a number of objects are moving about in a closed system, the sunvrof all their momenta is a constant. (And here we must understand that electromagnetic and gravitational fields carry momentum, so they are part of the system.)

What does this mean for a rocket? Think of a spaceship hanging out in space all alone. Suppose it is far from the sun so that there is no external force acting on it. If nothing happens, its momentum cannot change. Therefore it can only continue to move with constant speed in a straight line. (Hey—Newton’s First Law of Motion!)

If We want the ship to change its speed (and momentum) the only way it can be done is for the ship to push something away from itself. Then if the ejected material has a certain amount of momentum in one direction, the ship will have an equal amount of momentum in the opposite direction. If we continue to eject material away from the ship, the ship will continue to increase its speed: thus we have a reaction motor, or rocket.

Conservation of momentum requires that any kind of workable space drive must be a reaction motor. There are two exceptions: the mass-driver (or catapult) and the solar sail. In both of these exceptions the vehicle is not a closed system-.—it is being pushed by an external force originating on a more massive body. (Conservation of momentum still applies.) I am not going to consider catapults or solar sails in this article, because I’m talking about interstellar travel. Catapults are obviously out of the question. Solar sails won’t do you much good when you are trying to accelerate out of the solar system to very high speeds. They won’t do you any good at all in interstellar space, with radiation coming at you equally in all directions.

I’ve made a pretty dogmatic statement up above—and let me repeat it: If conservation of momentum is a valid law, then every interstellar space drive must be a reaction drive.

Now, I’ve stuck an if in there. But that’s the way we do logic. Well now, how valid is conservation of momentum? How sure am I that what I am saying is the truth, the whole truth, and always the truth?

Pretty damn sure. Conservation of momentum, together with conservation of energy, is one of the most fundamental of all ournatural laws. It has been verified experimentally to an exceedingly high degree of accuracy, and no exception to it has ever been found. The most important verifications are in reactions with elementary particles—for if the elementary particles obey these laws, then all the objects built out of them have to obey these laws. And we see in all kinds of experiments that when two particles collide with each other they recoil in accordance with our expectations. When an atom emits a photon of light, it recoils just like a rocket. For, let’s not forget that electromagnetic radiation carries momentum; this is why light exerts radiation pressure, why solar sails work.

Incidentally, it is important to be aware that modern physics considers momentum and energy to be parts of a single whole. Just as the 3 dimensions of space together with time make up a 4-dimensional spacetime, the 3 components of momentum together with energy make up a 4-dimensional momentum-energy tensor. Thus, conservation of momentum and energy are not separate laws. Conservation of momentum-energy is one law—represented by a single equation in 4-dimensional spacetime. The latest experiments have verified this law to within one part out of 10¹⁵.

So when I say this law is known exceedingly well, I’m not just dogmatically beating my chops. I’m talking about the results of very good experiments.

I also know that when I say: “It is impossible for an interstellar space drive to operate without using a reaction principle,” somebody is going to throw Clarke’s Law up in my face.

Our good friend Arthur C. Clarke, in a weak moment, made the statement: "When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.” (In Profiles of the Future.)

Of course, this law does not apply to me, since I am not particularly distinguished, although moderately elderly. Nevertheless, such a statement cannot go unchallenged, since it would belittle any distinguished, elderly scientist who said that perpetual motion was impossible. And a space drive that purports to operate Without pushing against anything is in precisely the same category as perpetual motion. (Remember, conservation of momentum cannot be separated from conservation of energy.)

In a situation where a proposed invention violates a well-established law of nature, the burden of proof is on the inventor. If he can build a space drive that does not push against anything, then he proves that the law does not apply. But first he has to build the drive.

---

2. The Dean Drive.

And now we come to the Dean Drive. The Dean Drive is a gadget, first hurled into notice through a series of articles in the 1960 Astoundings of John W. Campbell. It was a device supposed to be capable of accelerating itself through space without pushing against anything, and thus free of the limitations of rockets. In the original article the Dean Drive was described as a small box filled with rotating weights, driven by an electric motor. Photographs showed this box mounted on a bathroom scale, demonstrating a distinct loss of weight when the motor was turned on and the weights were spinning around.

The implication was that if the motor had only been more powerful the device would have lifted itself by its own bootstraps and taken right off into the air. Nobody said What the device did on a beam balance instead of a bathroom scale, or whether the thing felt lighter if you just held it in your hands.

Campbell’s main beef, as always, was that the scientists of the world simply ignored this wonderful invention, the greatest thing since the invention of the wheel, and refused to look at it. I wrote to Campbell, saying, well I’m a Working scientist and I would like to look at the Dean Drive. I’ll even bring my own bathroom scale. Perhaps he was offended by my apparent sarcasm. For unknown reasons he never took me up on the offer.

However, never let it be said that all scientists gave the Dean Drive the silent treatment. I may be a science fiction nut, but—at that time, at least, I was a real scientist, working at the Princeton Plasma Physics Laboratory, and I was seriously interested in looking at the device. (Perhaps Campbell thought that the machine was one of those sensitive things that just can’t work in the presence of a skeptic. Or am I being sarcastic again?)

Naturally publication of the Dean Drive article raised a great furor. There were the usual letters to the editor, and more than one person dutifully raised the proper technical objections to the whole idea. The effect of the mysterious box on the bathroom scale was explained as a result of an impulsive kind of force acting on a frictional system. Like hunching your bottom across a reasonably smooth floor. (But not a completely frictionless floor.)

And while we all waited for a working model to lift itself off the ground, somehow the whole thing just faded away into the background. More interesting things were going on in the 1960s.

Now, I find to my amazement, the matter has never been dead. Just submerged temporarily, now surfacing in an article by G. Harry Stine (Destinies, Oct—Dec, 1979). Since my purpose in this article is to explore options for interstellar travel, I really can’t avoid discussing this remarkable device—an invention that would do away with the fuss and bother of rockets if only somebody would take the trouble to build one and make it work.

The Dean Drive is purportedly based on an invention by Norman L. Dean. Its patent (U.S. Patent 2,886,976) is entitled: “System for Converting Rotary Motion into Unidirectional Motion.” Back in 1960 I studied this patent very carefully and discovered a very interesting thing about it. The device does convert rotary motion into unidirectional motion, but its method of performing this feat is no more mysterious than the operation of an electric motor pulling a vehicle along a track. It is nothing more or less than a very elaborate ratchet.

Left out of every previous discussion of the Dean Drive is the following interesting fact: In the Dean patent, the heart of the system is a metal tape that passes through the center of the machine. All that the device does is to climb up the tape. That’s all it does. No antigravity. No action without reaction.

It’s as though you took my Spinwriter (the printer for the computer on which I am composing), fastened one end of its paper strip to the ceiling, and then had the machine climb up the paper by means of the sprocket drive. Except the Dean machine did it in a much more complicated way.

Now none of the articles on the Dean Drive mention this fact. Even when they refer to the patent they don’t mention it. All they talk about is a box that is supposed to lift itself up off the floor without pushing or pulling on anything. Consequently, all of the claims made for the Dean Drive are based on an out-and-out falsehood. The whole business is fraudulent.

The theoretical arguments given, trying to prove that a non-reaction space drive is possible, are equallyphony, and are based on very elementary misunderstandings of physics. For example, there is supposed to be something very mysterious about the relationship between force and acceleration. We know that acceleration is the rate of change of velocity. And we also know that according to Newton’s Second Law of Motion the force acting on an object is proportional to its acceleration. But now suppose you have an object whose acceleration is changing. That means, according to this argument, that there must be a component of force proportional to the rate of change of the acceleration.

Which is nonsense, of course. By definition the force acting on an object is proportional to its acceleration. So if the acceleration has a rate of change, this means the force has a corresponding rate of change. It is not necessary (and in fact is incorrect) to invoke a special component of force proportional to the rate of change of the acceleration. (Strictly speaking, the force acting on an object is equal to the rate of change of the object’s momentum. When the mass is changing, this distinction is important, as we shall see.)

The point is, there’s nothing mysterious at all about varying accelerations. Physicists continually deal with systems in which the acceleration varies with time. (Plasma waves with oscillating electrons, for example.) The argument made by the Dean Drive enthusiasts is the kind of thing that would be dreamed up by somebody who has never gone beyond Physics I, where constant acceleration is the only topic treated. So as soon as he encounters a situation where the acceleration changes with time, he thinks this is a very unusual situation. But it’s actually the usual situation. Very rarely are we fortunate enough to encounter a real physical situation where objects undergo constant acceleration for any great period of time.

I have tried to convince you that reactionless space drives will not work. The fundamental argument is based on the deepest law of physics: the law of conservation of energy-momentum.

The complaints that “science” is ignoring an important discovery are false. The truth is that the advocates of reactionless space drives don’t know enough physics to convince a real physicist that he should stop whatever he’s doing to invest his heart and soul and money in building such a drive. Not understanding Why they are studiously ignored, these advocates sit on the sidelines and grumble about the unimaginative habits of the establishment.

I imagine that my arguments will not change the minds of any true space drive enthusiasts. They will persevere. By the same token, I imagine that there are still people out there busily building perpetual motion machines, trisecting angles, and squaring circles. (However, I imagine there may be fewer people engaging in such activities nowadays, since the current fad is to pursue telekinesis and other psi phenomena by electronic means.)

The screen which he was watching at the moment, however, was not connected with an underground pickup.

It was linked with a pickup in the bottom of a basketball-sized sphere driven by a small inertial engine that held the sphere hovering in the air above the game sanctuary on the northern tip of Manhattan Island.

In the screen, he had an aerial view of the grassy, rocky mounds where the earth hid the shattered and partially melted ruins of long-collapsed buildings.

YOU GO FASTER IF YOU HOLD YOUR FARTS IN —

Near-infinite specific thrust from drive that ignores physics

Conservation of momentum is for a different universe, apparently.

NASA is renowned for doing really difficult stuff. You want to drop a Mini-sized lander on Mars using a sky crane? Well, NASA will do that for you. There is a view of NASA as staid and conservative but, on the whole, I think the agency is full of innovative problem solvers, albeit sometimes crippled by political oversight.

The side-effect of being innovative is that some rather strange and unphysical ideas sometimes escape from NASA. This probably explains the Helical Drive.

Twisting the laws of physics

The basic idea of the Helical Drive, according to the author of that link, is simple. Imagine that you have a mass in a cylinder that is oscillating back and forth. Every time the mass hits the end of the cylinder, it will impart some momentum, accelerating it. Because the mass sequentially collides with each end of the cylinder, the net force is zero, and the only outcome is that the cylinder gets a massive headache.

But, what if—you're going to love this—you could magically increase the size of the mass when it was traveling in one direction and decrease the mass when it was traveling in the other direction? If the velocity of the mass is kept the same, the force imparted at one end would be greater than at the other. You would have a net force: the cylinder would continuously accelerate in one direction.

Now we just have to fill in the magic part: how do we magically change the mass? The answer here is special relativity. If something is moving at close to the speed of light, its mass will increase. Indeed, the closer the object is to the speed of light, the larger its mass.

So, the answer, apparently, is simple. If we use a very strong magnetic field along the length of the cylinder, then alpha particles (helium atoms with the electrons stripped off) will start to corkscrew around the field. An accelerator in one section can accelerate the ions to as close to the speed of light as possible, while in a different section a countering accelerator will slow them back down. At each end, the ions reflect, imparting momentum to the cylinder.

Even better, the energy lost in accelerating the ions can be recovered when you slow them down, so it's nearly free acceleration (it is not a perpetual-motion machine in that sense, anyway). To put this in perspective, the author modeled this using magnetic fields of about 13T. The accelerator requires 160MW of power, which the author hopes to recover from the particles when they slow.

Conservation of momentum should not be ignored

Now, the author argues that because the inertial mass grows nonlinearly with speed, there is an average acceleration in one direction. Even better, this difference increases as the peak particle speed gets closer to the speed of light. Unfortunately, the Universe just doesn't quite work like that.

So, let's just state up front: this drive won't work. The problem is that, even though the author does a very nice simulation, he has left out the fields that do the accelerating. When we accelerate ions using a magnetic or electric field, the ions push back on the field. There is an equal and opposite force exerted on the electrodes and coils that produce the fields, and those just happen to be in the spaceship, too.

In the first step, where we accelerate the mass to a high relativistic speed, we also accelerate the cylinder in the opposite direction. Now, in special relativity, we don't conserve energy and momentum separately. Instead, they are conserved together. If you only consider momentum (and not energy), then you will find net forces everywhere due to inertial mass changes—things get heavier as they approach the speed of light. This is exactly what the author has found. If you consider energy and momentum simultaneously, those forces will suddenly disappear.

This is where the increase in inertial mass comes from in the first place: energy is sucked out of the field and turned into mass. When the particles are slowed, that mass is given up as photons in the field, which slow the cylinder as they are absorbed. What is the net force? Zero, 0N of force.

Now, my issue with this idea is not that it doesn't work. And my issue is not that NASA has people who spend time wondering about ideas like this—the author's job title includes the word "manager," so the more time he spends on this, the less damage he can do managing. My issue is that the last set of bullet points in the last slide tell the entire story.

• Basic concept is unproven
• Has not been reviewed by subject-matter experts
• Math errors may exist!

Yes, and the author works at an organization full of physicists who are subject-matter experts. I can't decide whether the moral of the story is that you should talk to people who know things before publishing anything or that, if you can't figure out where the momentum has gone, you don't understand what you are modeling.

• 

ABSTRACT

All existing methods of space propulsion are based on expelling a reaction mass (propellant) to induce motion. Alternatively, "space coupling propulsion" refers to speculations about reacting with space-time itself to generate propulsive forces. Conceivably, the resulting increases in payload, range, and velocity would constitute a breakthrough in space propulsion.

Such speculations are still considered science fiction for a number of reasons: (1) It appears to violate conservation of momentum. (2) No reactive media appear to exist in space. And (3) No "Grand Unification Theories" exist to link gravity, an acceleration field, to other phenomena of nature such as electrodynamics.

This paper focuses on the rationale behind these objections. Various methods to either satisfy or explore these issues are presented along with secondary considerations. It is found that it may be useful to consider alternative conventions of science to further explore speculations of space coupling propulsion.

---

CONSERVATION OF MOMENTUM

The primary reflexive response to the notion of space coupling propulsion is concern over conservation of momentum. Newtonian mechanics requires that momentum be conserved, and propulsion without propellant appears to violate this law. In the case of conventional propulsion, conservation is satisfied because the expelled propellants possess equal and opposite momentum to the vehicle. Space coupling propulsion appears to violate this law because the reaction mass is not readily apparent. Conservation of momentum can be satisfied in various ways that do not require having an on-board supply of reaction mass. These include: conservation by using the contents of space as the reaction mass, conservation by expelling non-mass momentum, conservation by negative mass, and conservation by coupling to distant masses via the intervening space. Several of these treatments, most notably interacting with the contents of space and coupling to distant masses, evoke secondary issues.

Conservation Using the Contents of Space:

Rather than using an on-board reaction mass, momentum can be conserved by using the matter that is available in space in much the same way that aircraft propellers react against the medium of air. Space, however, is commonly thought to be empty which is another major barrier to the notion of space coupling propulsion. Space is not empty, however. Space contains interstellar matter, magnetic fields, star light, Cosmic Microwave Background radiation, and subtle substructures of space like Zero Point Energy and the virtual sea of pair creation/annihilation. And, underlying all of these media, is the "structure" of inertial frames which may also constitute a reactive medium.

The more familiar contents of space, matter, light, and magnetic fields, are probably too feeble to be an adequate reactive media. Methods have been proposed that use these media for propulsion, namely solar sails and an "Interstellar Ramjet", but these methods do not constitute genuine space coupling propulsion.

A less obvious candidate for a reactive media in space, which was discovered in 1964 and is being studied today by the COBE space craft, is the Cosmic Microwave Background radiation. Presumed to be a remnant from the Big Bang, this background radiation permeates all space and appears to be coincident with the mean rest frame of the galaxies surrounding earth, and provides a phenomena by which velocities relative to that frame can be measured (directional doppler shifts). Such features invite using this background as a medium to possibly react against, but, like interstellar matter, it is very feeble (4×10^-34 g/cm³). Although not promising as a direct reactive medium, it may one day provide a useful reference for deep space navigation.

A more fundamental category space coupling media is the substructures of space. These include Zero Point Energy (also known as the vacuum fluctuations of the electromagnetic field) and the sea of virtual pair creation/ annihilation. Zero Point Energy is the absolute minimum energy of a harmonic oscillator at its ground state. This means that even in the vacuum of space, there is a non-zero energy of electromagnetic oscillations. The sea of virtual pairs refers to the quantum mechanical possibility that particle pairs (matter-antimatter) are spontaneously produced and reconverged throughout space. Usually they are low energy photons, but could occasionally be electron/ positron pairs (reference 1). Some concepts for reacting against these medium have been speculated and may be candidates for Space Coupling Propulsion.

Perhaps the most likely media for genuine space coupling propulsion are inertial frames themselves. Inertial frames are the fundamental frameworks against which the laws of motion are described, and as such, have some physical significance beyond just mathematical entities. The nature of this physical significance and the correlation to other phenomena is not fully understood. Imagining inertial frames as a candidate reactive media is difficult because inertial frames are used as a reference for observing interactions, rather than as a participant of interactions. The utility of inertial frames will be discussed later in this paper under the heading; "Conservation Using Coupling to Distant Masses".

Perhaps one way to consider interacting with inertial frames is to use the previously described contents of space, in particular, the Cosmic Microwave Background radiation and Zero Point Energy. Both of these phenomena are coincident with inertial frames, and perhaps are fundamentally linked to some "structural" property that may some-day provide an indirect means to reactively couple to inertial frames themselves.

Conservation Using Non-Mass Momentum:

Another way to satisfy conservation of momentum is to consider that some non-mass momentum is expelled from the vehicle, such as photons, gravitons, or hypothetical "space waves" (figure 1).

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Assuming that it were possible to focus all this expelled radiation along a single direction, the general equation relating power (P), force (F), and velocity (v), P = F × v could be used to indicate the potential force per radiated power. The velocity term refers to the radiation velocity, and in the case of photons and gravitons, this is the speed of light. Entering the speed of light into this equation translates to a rather feeble force per radiated power: 3.3×10^-9 Newtons/Watt (I thought it was 3.3×10^-8 but I must have been wrong).

This force/power equation assumes, however, that the radiation has zero rest mass. Gravitons have been speculated as being a more promising candidate of energy expellant because they might not have zero rest mass and because they are related to mass/acceleration phenomena. Gravitons are quantized gravitational waves analogous to the way that photons are quantized electromagnetic waves. Unfortunately, gravitons are still just theoretical entities, and no methods have yet been proposed for using gravitons for propulsion.

Another avenue for exploring this non-mass momentum theme would be to look for alternative forms of "space waves" that either have a non-zero rest mass, or have much lower propagation velocities than light. Perhaps oscillations in the "structure" of inertial frames may constitute these hypothetical space waves.

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Conservation Using Negative Mass:

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An imaginative means of conserving momentum is to create a condition where the total mass, and hence momentum, is always zero. This treatment uses hypothetical "negative mass". If equal amounts of positive and negative mass were placed side by side, they would both accelerate along the vector pointing from negative toward positive matter because of the interactive properties of negative and positive mass (figure 2). This negative matter propulsion concept does indeed. satisfy the laws of motion. The weakness of this negative matter scheme, aside from the problem of obtaining and handling negative matter, is whether or not the laws of motion would still be satisfied if unequal proportions of negative and normal mass were used. Conservation may still hold with unequal masses if the concept of coupling to distant masses is considered. This concept is discussed next.

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Conservation Using Coupling To Distant Masses:

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Perhaps the most fundamental and broad-sweeping concept for space coupling propulsion is the concept where a vehicle produces its own acceleration field to push against some "structure" of space. To satisfy conservation of momentum with this concept, it is necessary to speculate that the reaction force is imparted onto distant masses via this space structure in much the same way that gravity attracts distant masses. Momentum is conserved by the equal and opposite momentum imparted to the space/matter system (Figure 3). This requires the perspective that matter is somehow connected to space, and that space has a degree of "stiffness" to transmit force to distant niatter. This perspective is difficult to conceptualize, and evokes secondary issues that are discussed next.

Mass is known to "connect" to space in two ways; gravity and Mach's Principle. Gravity is the field phenomena related to the presence of mass, where this field causes an attraction with other distant masses. Mach's Principle relates the presence of matter to the definition of inertial frames. Mach theorized that inertial frames exist only because of the presence of matter. Additionally, as indicated by inertial drag, a given point in space may actually be a composite of inertial frames, each of which is somehow "connected" to its source mass. Another interesting point is that gravity and inertial frames are related. Gravitational fields are, in essence, accelerated inertial frames, and alternatively, unaccelerated inertial frames are gravitationally flat (the gravitational potential across the space is constant).

To further consider reacting against distant masses, it is useful to indulge some alternative perspectives of these known phenomena. For example, it is useful to consider that inertial frames and their "connection" to their source masses provide the structures for reactive coupling. This implies that inertial frames would have a property for referencing position, in addition to referencing acceleration, to allow position relative to the frame’s source mass to be uniquely defined. This is unconventional because inertial frames are thought to provide only a reference for measuring accelerations, not velocity or position. Additionally, it is useful to assume that this position property has some characteristic "stiffness" that allows forces to be imparted across space to the source masses. Such considerations evoke the notions of the proverbial "aether" and the theoretically defunct "absolute reference frame". The similarity between these views and those unpopular notions is not exact, and hence, should not prejudice indulgence in these perspectives.

Continuing with these speculative perspectives, forces could be induced relative to inertial frames if it were possible for a vehicle to alter its gravitational field distribution or its connectivity to its own inertial frame. By redistributing its own gravitational field, it could, in effect, create a local asymmetric acceleration field. The reaction forces would be imparted to the "stiff" inertial frames and subsequently to their source matter (figure 3). This is similar to the special case in the concept of negative mass propulsion where there is more normal mass than negative mass. In this case the non-zero momentum of the vehicle would be balanced by the equal and opposite momentum of the inertial space and its associated matter.

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An issue related to these speculations, whose investigation may provide clues to the "structure" of inertial frames, is the proportionality of the imparted forces. If inertial spaces are pushed against, do the frames' source matter move in unison (Case A, figure 4), or do they move proportionally (Case B, figure 4)? What is this proportionality based on; the distance from that point and/or the magnitude of the source mass? One speculation to quantitatively explore this proportionality is to assume that the proportionality coefficient at a given point in space is simply the gravitational potential of the source mass at that point in space. These speculations and questions have yet to be fully explored.

The concept of coupling to distant masses requires some unconventional perspectives on the structure of space, particularly with respect to the definition of inertial frames and their relation to matter. Further investigations of this coupling possibility would likely require further indulgence and refinement of these unconventional perspectives, including exploration of the proportionality issue and the relation to Mach’s Principle.

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SEARCHING FOR A FORCE INDUCING TOOL PHENOMENA

Having addressed the issues of conserving momentum and the contents of space, and having identified the desirability of inducing a localized acceleration field onto an inertial frame, the next issue is to identify candidate mechanisms to create this acceleration effect. Acceleration fields imply gravity, and hence, the target mechanism is to discover some means to alter gravity. This evokes the last major reflexive response to the notion of space coupling propulsion: There are no known ways to practically manipulate the phenomena of gravity. There are two avenues to respond to this issue. The first avenue is direct manipulation of gravity by the motion of masses. The second avenue is to induce gravitational forces via an intermediary phenomena, such as electrodynamics, which evokes the need for a "Grand Unification Theory". Although science has not yet provided such a theoretical mechanism, there are several different approaches toward discovering a useful connection between gravity and other phenomena. All these approaches offer different applicability or viability for space coupling propulsion and are described next.

Inducing Accelerations by Motion of Masses:

Several concepts exist that consider inducing force or local accelerations by the motion of nearby masses. In general, these concepts are either impractical because of the enormous mass densities and speeds required, or are of doubtful viability because of uncertain physics.

1. General Relativity Based Gravity Devices: An impractical, but theoretically sound method to create acceleration forces is based on "magnetic gravity". General relativity provides the possibility of an analogous phenomena to gravity that magnetism is to electricity. Unfortunately, in order to produce appreciable forces with these conceptual devices, ultra-dense masses (densities approximately that of a white dwarf) must be moved at relativistic speeds along strictly defined paths.
2. Gyroscopic Antigravity Machines: On a more speculative side, devices have been designed and patented (reference ll), that claim to produce gravity negating forces by gyroscopic motion. These devices are variations on a theme of converting angular momentum into linear force; a scheme which violates conservation of linear momentum. One example of this is a "Laithwaite Engine" which gives the appearance of providing upward forces by the upward swing of its gyroscopes once the device begins to rotate. This motion, however, is not a propulsive force, but rather a torque that makes the gyros change orientation in order to conserve angular momentum. This device and others like it do not hold much promise as propulsion devices, but are excellent instructional tools for understanding conservation of angular momentum.
3. Anomalous Gyroscopic Measurements: Recently, another gyroscopic device has been reported to produce reductions in weight proportional to rotational motion. This report is not a proposed antigravity device, but rather an observation of an unexplained result. A gyroscope weighing on the order of 150 grams and with a vertical spin axis, was found to have weight reductions on the order of milligrams when rotated in the right-hand direction, and no weight change when rotated in the left hand direction. This is probably just an experiential error, but being such a peculiar observation, it is worthy of note.

Inducing Acceleration Effects via Intermediary Phenomena:

In addition to the perspective of inducing forces from the simple motion of matter, there is the perspective of using some intermediary phenomena to induce effects. This means finding some controllable phenomena that is related with the phenomena of gravity, and using this control phenomena to indirectly kduce gravitational effects. An example of this intermediary principle is the way that microwaves (electrodynamics) are used to induce molecular vibrations (heat). With respect to space coupling propulsion, the prime intermediary phenomena is electrodynamics. Various approaches to correlate gravity to other phenomena are briefly reviewed below and include: (1) General Relativity's connection between inertial frames and gravity as referenced by electrodynamics, (2) Gravity as an index of refraction for electrodynamics, (3) Gravity as a Zero Point Energy effect, and (4) The hypercharge force.

1. General Relativity, Conventional Correlations: Although gravity is known to effect electrodynamics (gravitational fields bend the path of light), General Relativity has not provided a gravity/electrodynamic tool applicable for space coupling propulsion. Instead, General Relativity uses electrodynamics (specifically the speed of light) as the reference for describing how gravity relates to inertial frames. For example, in the basic equation governing the relation between distance (d), time (t), and the phenomena of light, d = t × c , the speed of light (c) is the reference constant, and space and time are the variables that "warp" relative to gravity (reference 3). Although this perspective has proven its usefulness, it may not be optimum for the perspective of space coupling propulsion.
2. Index of Refraction and Gravity: An alternative approach to describe the same natural observations is to treat the speed of light as the variable that gets "warped" in the presence of gravity. Basically, this perspective takes the form of relating the index of refraction of light to gravitational potential (references 14, 15). In the case of space coupling propulsion, it may be more useful to consider distance as "stiff" and the speed of light as the variable with respect to gravity. This approach allows considering electrodynamics as the intermediary mechanism rather than as the reference. To date, no proposed mechanism based on such perspectives have been reported, but this may be an interesting avenue for further exploration.
3. Gravity and Zero Point Energy: An interesting alternative approach to relating gravity and electrodynamics is the theory that gravity is an induced effect associated with Zero Point Energy fluctuations of space. Various methods that use Zero Point Energy for propulsion have been proposed, but no concept has been proposed that takes advantage of these correlations to induce asymmetric gravity fields. This approach also merits additional consideration.
4. Fifth Force, Hypercharge Force: Another interesting perspective linking gravity to some other more manageable phenomena, is the "hypercharge force" concept. In a reanalysis of the experiment that demonstrated that all masses, independent of composition, accelerate uniformly in a gravitational field, it was found that there may be a correlation between gravitational acceleration and a sub-atomic characteristic called hypercharge or baryon number. This correlation has yet to be fully proven or disproven, but either way, it does not hold much promise as a candidate mechanism for space coupling propulsion. The differences in gravitational attraction by hypercharge are negligible (delta-g/g approximately 10^-7).

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Negative Matter

As unbelievable as these machines for controlling gravity might seem, they at least use a form of matter which we know exists, even if it is presently found only in the interiors of far distant stars. There are speculations that there might exist another type of matter. It has very strange properties. If it ever could be found or made, then a whole new era of gravity control would open up.

All the matter that we know of is the type called regular (positive) matter. Yet both the Newton and the Einstein Theories of Gravity allow the existence of an opposite form of matter, called negative matter. According to the theories of gravity and mechanics, an atom of negative matter would repel all other matter (including other atoms of negative matter).

Now, the first thing you should realize is that negative matter is not "antimatter". Antimatter is different from regular matter in its quantum mechanical properties, not its gravitational properties. Although it has yet to be proven experimentally, we are fairly sure that antimatter attracts other forms of matter, just like normal matter. Negative matter, however, would repel other forms of matter.

We do not know how to make negative matter. But when we do, we will discover that it will not cost us any energy to make that negative matter. Because the rest mass energy of a particle is proportional to its mass (E=mc²), the rest mass energy of a negative mass particle is negative! That means that if we always create equal amounts of positive and negative matter at the same time, it will cost us no net energy to do so! One can imagine a future scene in some huge laboratory, where great machines apply intense electric, magnetic, and gravitational forces to some microscopic point in empty space. The energy levels of the fields are raised higher and higher until the "nothing" itself is ripped apart into a ball of regular matter and an equal sized ball of negative matter, the whole process using no net energy except for the losses in the generating machines.

Once we have our negative matter, we can start using it to make antigravity machines. But we must be very careful how we handle the negative matter. Unlike a chunk of regular matter, which responds to your push by moving away, if you push on a chunk of negative mater, it will come toward you! (If by mistake, you pushed on some negative matter, and it started to move toward you, you must quickly run around behind it and give it a slap on the rear to bring it to a halt!)

Now that we have learned how to control our working material, the simplest antigravity machine that we can make is to form the negative matter into a dense disc and lay it on a good strong floor. If the disc is dense enough and thick enough, then the repulsive gravity field on both sides of the disc will be one Earth gravity. That negative gravity field from the disc would then cancel the gravity field of the Earth. In the region above the disc, the gravity attraction would be zero and you could float there in free fall. (and in a space ship in free fall, such a disc in the ceiling would provide Terra normal gravity by repelling you downward)

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The negative gravitational field of negative matter can also be used for gravity propulsion. If you place a ball of very dense negative matter near a similar dense ball of regular matter (which is incidentally attached to your spaceship), you will find that the negative matter ball will repel the regular matter ball, which in turn will attract the negative matter ball. The two dense balls will start to move off in a straight line at a constantly increasing speed. The acceleration will be the strength of the gravitational attraction of one ball for the other, with the negative matter ball chasing after the positive matter ball and the positive matter ball carrying your spaceship along with it. (Question: how do you stop this when you've reached your destination?)

You might at first worry that I'm getting something for nothing. First there were two balls of matter, both standing still, with no kinetic energy. Then, after a while they are both moving off together at high speed with no propulsion energy being expended. You might think that would prove that negative matter is impossible, since it looks like the law of conservation of energy is being violated.

But if you look very closely, you will find that negative mass propulsion does not violate any laws of physics. It is true that the ball of regular mass gains speed and increases its kinetic energy [E=1/2(+m)v²], so it looks like it is getting energy out of nowhere. But while it is doing so, the ball of negative matter is gaining negative energy [E=1/2(-m)v²] and the total energy of the two masses is zero, just as it was when they were standing still. Thus, negative mass propulsion does not violate the law of conservation of energy.

By the same type of argument, you can also show that negative mass propulsion does not violate that other important law of physics, the law of conservation of momentum. For while the momentum of the positive ball of mass is increasing, the momentum of the negative ball of mass is decreasing, resulting in zero net momentum, even though the two balls started out standing still and now are moving off at high speeds.

So far as we know, negative matter doesn't exist. We don't know why it doesn't. After all, both the positive and negative forms of electricity exist, so why not the positive and negative forms of mass? Perhaps there is some yet unknown law of physics that prevents it from forming. But even if we can never obtain this indistinguishable from magic material, we can still devise ways to control gravity with just regular matter, if just work hard and use enough energy and intelligence.

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• 

(ed note: Randy's asteroid prospectors discovered an alien creature, which they named the Silverhair. It is apparently composed of negative matter. And so it the "ball", which is basically Silverhair poop.)

     “ After I gave him all the facts and showed him some video segments, he conceded that maybe negative matter could exist after all. What really convinced him was the description of my injury, where the cut edges looked like a thin sliver of material had been evaporated.”
     “Why is that?” asked Randy.
     “Well, as Steve explains it, according to one theory, when negative matter touches normal matter, equal amounts vanish—nothing is left, not even energy. The process is called nullification. It’s like the annihilation of matter by antimatter, but in the nullification process, since the normal matter has positive rest mass and the negmatter has negative rest mass, the net rest mass is zero, so zero energy is released. That’s why we didn’t notice any radiation when the Silverhair and I collided.”
     “What else did Steve have to say?” asked Randy.
     “He told us to look for electric or magnetic fields around the Silverhair and the ball,” said Jim. “Negative-matter particles repel each other gravitationally, so they would normally tend to spread far apart from each other. But since the negative-matter particles in the Silverhair and the ball are jammed together at high density, there must be some other force field involved that holds them together.”
     Philippe spoke up. “Hiroshi found a very strong positive electric field associated with both the ball and the Silverhair. It’s as if the material were all made of particles with the same charge.”
     “Normally, particles of the same charge would repel each other and be pushed apart,” said Jim. “But according to Steve, when you attempt to repel a negative-matter particle, it responds in a perverse manner and comes toward you.”
     “That explains one thing,” said Randy. “Siritha noticed some static-cling effects of space dust on her helmet. But there was nothing large—no lightning bolts.”
     “Both the Silverhair and the ball rapidly develop a cloud of orbiting electrons around them,” said Philippe. “They must attract the negative electrons from the plasma in space while repelling the positive ions. The negative electric charge of the electron cloud cancels out the positive electric charge of the negative matter, unless, of course, you get inside the orbiting cloud of electrons and very close to the surface of the negative matter. Hiroshi got some good measurements of the electric field around the ball by enclosing it in a plastic container, sweeping up all the electrons near the ball with a grounded metallic plate, then making measurements inside the container while all the interfering electrons were forced to stay outside the container. We then did some experiments on the ball.”
     “What kind of experiments?” asked Randy, looking intently at Philippe.
     “Since the ball is charged,” Philippe answered, “it’s easy to push it by charging up a metal plate placed near it. Of course, being negative matter, when you push it, it comes toward you.”
     “That can get dangerous, said Jim, holding up his cast. “If it gets too close, you get nullified.”
     “In the experiment Hiroshi did,” Philippe went on, “he used a metal plate with a negative electric charge so it would attract the positive electric charge of the ball. The ball pulled away in the opposite direction, pulling the test apparatus, the power supply, and Hiroshi along with it. When Hiroshi saw what was happening, he quickly turned the field off. He then had to reverse the field and push on the ball for a while to bring it to a halt again.”
     “It was just as Steve predicted,” said Jim in awe. “A true reactionless space drive.”
     “A space drive?” exclaimed Randy in amazement.
     “That is correct,” said Philippe, his voice deepening as his face turned deadly serious. “When that ball of negative matter was pulling Hiroshi and his test apparatus along, there was nothing going in the opposite direction. There was no reaction mass and no energy source involved, but they moved nevertheless. That means a large enough negative-matter ball electrostatically coupled to a positive-matter spacecraft can propel the spacecraft at any acceleration the crew can stand for as long as you want. Flight to the stars at near light speed is no longer a dream . . .”
     When the enormity of the finding hit Randy, a broad smile spread across his face. An interstellar space drive! He had dreamed of exploring the stars and now his dream, could come true! He leaned forward over the table, eyes on Philippe.
     “What are the limitations?” he asked, knowing there must be some.
     “The mass of the negative matter must be exactly equal and opposite to the positive mass of the spacecraft,” said Philippe. “If it isn’t, then the separation distance between the mass and the spacecraft will change with time. If it gets too close, you risk nullification. If it gets too far away, you risk losing it.”
     “You have to control the mass of one or the other, then,” mused Randy. “Not easy.” He thought some more. “Didn’t you say the silver ball has a mass of ten tons?”
     “Yes,” said Philippe. “A negative ten tons.”
     “Then that one ball can drive a ten-ton spacecraft. Do you think you could arrange for a demonstration using one of the prospector flitters? They mass around ten tons.”
     “Perhaps,” said Philippe, thinking. His finger rose to feel the mustache under his nose, then followed it across his face and up over his ear as he thought further about the idea. “Yes,” he said finally.
     “Do it!” said Randy. “I’m going to get some breakfast and then go hack out to see the Silverhair. I wonder if Bob can get it to lay more of those silver eggs.”
     “Careful,” warned Philippe. “Don’t kill the goose ...”

(ed note: since the "eggs" are Silverhair poop, Randy now has access to a steady supply of negative matter)

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     A week later, Philippe took Randy to the hangar cavity on the other side of Hygiea.
     “We’ve installed the negmatter drive in the hold,” said Philippe, leading the way as he and Randy floated in through the cargo, door in their space suits. “Right at the center-of-mass of the ship.”
     In the center of the cargo bay was a large, cubical metal box nearly twice as tall as Randy. Surrounding the box were some large power supplies. A technician was tying up some stray wires.
     “Is the negmatter ball in there?” asked Randy.
     “Ready to go,” said Philippe. “All six high-voltage supplies are operating and pushing on the ball equally from all directions. In the control room is a three-axis maglev joyball just like the ones that are used in the drop capsules on the rotovators. You push the ball forward, the fore and aft power supplies change their voltages, the negmatter ball gets pushed in the backward direction, and it responds by moving in the forward direction, pushing the spacecraft ahead of it. If you want to go sideways or vertically, just move the ball in that direction and the power supplies for those axes will respond.”

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     “Don’t want to get out of sight of the base,” said Randy, he pulled the joyball to one side to bring them around in a large circle.
     “We’re going sideways!” he complained.
     “With only one ball of negmatter, I was unable to obtain any torque control,” said Hiroshi.
     “l’ll fix that,” said Bob, firing some attitude rockets and tuming the ship around so that it faced in the direction it was traveling. “You just do what you want with the drive controls; boy-boss, and granddaddy Bob will follow your every move and keep us lined up with the straight and narrow.”
     After Randy and Bob had completed a few more practice turns, a warning chime carne from the engineering console in front of Hiroshi. Randy instinctively pulled back on the joyball until they were once again in free-fall.
     “ls there a problem?” he asked apprehensively.
     “The ball of negative matter is starting to drift away from the center of the drive control box,” reported Hiroshi. “As Bob uses fuel to control our orientation, the mass of the spacecraft slowly decreases.”
     “Too bad we can’t control the mass of the ship” said Randy.
     “There is a way to do that,” said Hiroshi. “But I didn’t include that feature in this first design.”
     “In that case,” said Randy, pushing forward on the controls again, “let’s head for base and rework the drive. I want to go back to Earth in style!”

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     “Hiroshi’s new six-degree-of-freedom negmatter drive is pretty complicated,” said Philippe. “It has linear drive and torque control in all three axes. For control of the ship’s mass, the hull is covered with activated metal foam that absorbs and holds on to any gas or dust that strikes it. With a constant flow of positive matter coming in, we can afford to shoot propellant out from ion engines to provide mass trim and drag makeup.”
     “lt’s amazing how fast Hiroshi and the rest of your techs solved the engineering problems of coping with negmatter,” said Randy.
     “Since the negmatter is electrically charged, it turned out to be easy,” said Philippe. “You use radio fields to make the balls vibrate. If you vibrate them at just the right frequency, you can make them break into two, three, or four pieces, or even spit out little droplets.”
     “Glop those small pieces together and you can make any-sized ball you want,” said Randy. “I still think it’s amazing. ”...
     “You sure are a lucky bastard, Randy,” started Steve. “One little find, and you end up owning a spacewarp, a reactionless space drive, and a nearly infinite source of free energy.”
     “Free energy?” Randy repeated, a little taken aback.
     “Yep,” said Steve. “When negative matter and positive matter interact through long-distance forces, the negative matter gains negative kinetic energy, while the positive matter gains positive kinetic energy. Take a drop of highly charged negative matter, push on it with electric fields until it is going at nearly the speed of light, and in return you get electrical energy back. The only limit on the amount of energy you can get is how close to the speed of light you can push the negative matter before losing control of it.”
     “That could cause a serious hazard,” said Randy. “The whole solar system contaminated with high-speed negative-matter particles.”
     “Simple solution,” replied Steve. “Just direct the high-speed negative matter into a beam stop. Generic dirt will do. The negmatter with all its negative kinetic energy will just disappear when it hits the dirt and nullifies.”
     “Hmmm,” said Randy. “Looks like I had better start an energy production division.”

(ed note: and you know that eventually somebody is going to weaponize this)

There are basically two approaches you can use:

1. There is a special frame of reference. In this case, the "reactionless" drive is really pushing against an infinitely massive special frame of reference.

(ed note: which means you've just destroyed Einstein's Relativity, with all the collateral science damage that implies)

or

2. There is no special frame of reference. In this case, the only way to sort of preserve conservation of energy is to limit drive efficiency to that of a photon drive. This is not a very useful drive, though, since it has the same (low) performance as a photon drive.

(ed note: the photon drive, where one lousy Newton of thrust takes three hundred freaking megawatts!!)

There is the complication that "energy of the thrust" is as meaningless a phrase as, e.g., "mass of the time".

Thrust is a force, not an energy. Force, multiplied by distance, gives an energy. A force of one pound, applied as an object moves over a distance of one foot, equates to (unsurprisingly) one foot-pound of energy. The same force, over a greater or lesser distance, comes to proportionately more or less energy.

In MKS, by the way, that would be one Newton of force over one meter of distance equals one Joule of energy. If we assume constant force and motion, we can extend that to one Newton of force applied constantly at a velocity of one meter per second, equals a power of one watt.

The question is, velocity relative to what?

If it is a rocket, the relevant velocity is that of the rocket's own exhaust relative to the rocket itself. For an "intertialess thruster", the answer isn't clear and the power or energy associated with a given thrust will change widely depending on what reference frame you use to measure your velocity.

Which is one facet of the reason "inertialess thrusters" seem to be physically nonsensical. However, if you really need one for some SFnal purpose, you could try either

1. the one universally invariant velocity in real physics. That being the velocity of light, giving you a figure of three hundred megawatts of power per Newton of thrust. A tad high for most purposes, I think, and functionally equivalent to saying your thruster is a photon drive or a (nearly-)massless-neutrino drive or a Dark Energy Rocket or whatever.
2. the velocity of the spacecraft relative to some absolute reference frame. Either a cosmic absolute, or a local absolute tied e.g. to the nearest massive body or bodies in whatever manner is most convenient to the story. This is functionally equivalent to the old aetheric theories, and you can mine those for ideas.

Because an ordinary rocket has a "reaction". The amount of kinetic energy added to the rocket by a rocket thrust depends upon what frame of reference you look at it. Indeed, there are plenty of frames of reference where the rocket thrust subtracts kinetic energy from the rocket! So you can't meaningfully talk about THE amount of kinetic energy added to the rocket. However, you CAN meaningfully talk about how much kinetic energy the rocket adds to the system because kinetic energy is also added to (or subtracted from) the rocket exhaust. No matter what frame of reference you use, the total amount of kinetic energy in the rocket plus the exhaust is increased by the same amount.

In an ordinary rocket, both the kinetic energy of the rocket and the kinetic energy of the exhaust will change. Different observers will disagree about the absolute change of each, but will agree about the net change in kinetic energy, and so energy conservation can be enforced.

Example: A hundred-kilogram satellite ejects one gram of nitrogen through a cold-gas thruster at a velocity, relative to the spacecraft, of one hundred meters per second.

An observer at rest relative to the initial position of the spacecraft will see it accelerate to 0.001 meters per second, increasing its kinetic energy by 0.05 millijoules. The exhaust will be observed to accelerate to 99.9995 meters per second, with resulting kinetic energy of 4.99995 Joules. The total kinetic energy increase, provided by the expanding gas, comes to 5 Joules.

An observer zipping along in the opposite direction at 1,000,000 meters per second, will see both the spacecraft and the propellant as having had an initial velocity of 1,000,000 meters per second, and an initial kinetic energy of 50,000,000,000,000 Joules and 500,000,000 Joules, respectively. The spacecraft accelerates to 1,000,000.001 meters per second, giving it a new kinetic energy of 50,000,000,100,000 Joules - a gain of 100,000 Joules. Far cry from the .05 millijoules the stationary observer had thought the spacecraft acquired.

But the moving observer will have seen the slug of exhaust gas decelerate from 1,000,000 m/s to 999,900.0005 meters per second, with a new kinetic energy of 499,900,005 Joules. That's a loss of 99,995 Joules. So the net change in energy is, spacecraft +100,000.0, exhaust -99,995.0, or plus 5.0 Joules. Both observers agree on conservation of energy. And, for that matter, momentum.

If there were only the spacecraft involved, they'd be arguing about the missing hundred kilojoules.

If you're talking about a "true" reactionless drive, where energy is converted directly into momentum (or angular momentum), then there are lots of complications. Consider for instance that kinetic energy goes as the square of the speed:

K = (1/2) m v^2

So the power P you need to accelerate is dK/dt:

dK/dt = (1/2) m [2 v dv/dt] = m v a

As you can see, the power is a function of not only the acceleration that you want (which seems obvious), but also the speed at which you're currently traveling. The snag there is that your current speed is frame dependent. Consider that you're already doing your job and accelerating along nicely. At that point you pass someone who is already coasting at nearly the same speed you are. He sees you using much less power! Who's right?

The solution is that you either need to play by the rules of the game and use reaction drives (even if it's just reaction momentum, like a photon drive), or posit a special frame in violation of special relativity. With the special frame, now there's a "correct" frame where all the kinetic energy calculations are "official" and everyone agrees on them.

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Reactionless Drive: The important thing to remember about a reactionless drive is that it’s not reactionless.

A vector control drive is a member of the entire family of vector-control technologies, and like all the other members of said family, it obeys Newton’s Third Law. Vector control used for artificial gravity transfers the reaction to the action it’s applying to the stuff between the gravity rotors to the structural framework it’s bolted to. Vector control used in tractor/pressor beams pushes the party of the first part every bit as much as it pulls the party of the second part, and on the precisely opposite vector. And a vector control drive, while it utilizes extremely fancy ontotechnological trickery to spread the reaction to the action out across all the ambient mass in appropriately vast volumes (if not the entirety of, but that’s real hard to measure) of the local universe, is absolutely no different in this respect.

What you get from a vector control drive is not needing to haul all those vast quantities of reaction mass around with you. Note: only the remass. Vector control drives still need fuel, and since there are certain inevitable inefficiencies in coupling the action to the reaction quite so indirectly, they need significantly more fuel than an equivalent reaction drive. You aren’t getting away from having those huge spherical tanks of D and He3 strapped to the back of your starship that easily.

Another thing you might get is a degree of, um, stealth, inasmuch as you don’t have the huge bright drive flare that most reaction drives tend to produce. Of course, as we all know, there ain’t no Stealth In Space, because apart from your life support’s comfortable temperature alone making you stand out like a lighthouse against the 3K sky background, you’re also running a bloody great reactor (and radiating its heat) to power your vector control drive.

In short: the existence of vector control permits you to build something damned close to a classic SFnal reactionless drive. It provides you with rather fewer reasons as to why you might want to, outside a few highly specialized edge cases.

(Side note: the mad scientists out at Resplendent Exponential Vector have also been experimenting along the lines of the Alcubierre drive to get reactionlessness and a working fittler in one package. After their prototype vaporized a fortunately-spare dwarf planet and exploded first time out, their tort insurers have been reluctant to cover further development at a price they can afford.)