# Controlling Inertia

Disclaimer: I feel I know enough about Physics to be dangerous.

There have been a number of questions about overly large swords and changing mass, and the common theme in all the answers to these sorts of questions seems to have been inertia. So, what if you could control the inertia of the sword?

Inertia is basically the resistance to movement, right? Which can be considered "acceleration". If you could negate the effects of inertia while starting to swing a sword, would it reach the max speed you can swing a sword at nearly instantly? Would there be some sort of forces problem between the inertia-less sword and the hand swinging it? I also believe that if someone were to swing a forever-inertia-less sword, it would be pretty useless when it hits something, as it would not have any deceleration, and would instead immediately stop before it would have the time to cut anything. So you would need to be able to control the inertia, not just negate it all the time- is there any problem with no inertia during the swing but 'turning it back on' right before it hits the target?

• Some baseball bats are filled with water. Essentialy allowing less intertia at the start of the swing – Ewan Jul 23 '16 at 16:45
• Reminds me of Asimov's Billiard Ball. I seem to remember he apologized in a later preface for handwaving the physics. Nice little story, though. – IMSoP Jul 24 '16 at 1:00
• @Ewan how does inertia vary and why would water be different than another substance? – JDługosz Jul 25 '16 at 0:38
• The inside is hollow and not totally filled. So the water flows to the handle when you hold the bat at the ready and to the end as you swing. – Ewan Jul 25 '16 at 5:13
• Yet another person trying to make implausibly useless weapons using implausibly advanced technology. It is unclear what you are asking but ask your self two questions. Is it a better weapon than (gun, laser drone, weaponised nanotech...) and is it easier to make? – Donald Hobson Oct 14 '16 at 21:43

These are actually issues that the Star Wars crowd has to discuss when dealing with lightsabers. It's not immediately apparent whether the lightsaber has any mass at all besides the hilt itself.

As stated in a few comments, the best way to think of inertia is not resistance to movement, but resistance to changes in movement (or resistance to accelerations). An object without inertia would happily be accelerated in any way desired, without any force at all.

The interesting question would be what happens when you come in contact with something. This inertia-less object could have rigidity. In such a case, it would permit you to use your hand to apply force to the object you hit -- transferring the force to another object, even though its own acceleration did not call for any force.

The effect could be similar to a Darth Vader style force choke. An invisible, ephemeral, rigid connection between Vader's fingers and the throat of the officer being choked.* The connection is there, and it's massless, but it can still be used to transmit force.

Don't try to mess with turning inertia back on, though. If you change the velocity at any point in the path, you will fail to conserve momentum. Conservation of momentum is a natural consequence of Noether's theorem and the fact that the laws of physics work the same at all points in space. Theoretically you could play games to get around this, but realistically the games you play are so far from the way we currently believe physics works that you're better of just chalking up the inertia control to magic.

* It's not clear whether this is actually what happens in the movies when there is a force choke, but I like to think Darth Vader would choose to do this, just so he can feel the other guy's windpipe in his fingers.

• Good point about the problems with violating conservation of momentum given Noether's theorem, but it might be possible to think of ways around this--maybe changing the momentum of the sword causes a compensatory change in the momentum of some fluid filling space that we ordinarily don't notice because it doesn't interact with ordinary matter via the electromagnetic force, like neutrinos or the most popular candidates for dark matter, WIMPs. – Hypnosifl Jul 23 '16 at 20:30
• @Hypnosifl You could certainly play that game. The Chinese had an ancient bamboo staff weapon where each chamber of the bamboo was half filled with mercury. You could transfer quite a bit of momentum into such a hidden space, only to release it later on the foe – Cort Ammon Jul 23 '16 at 20:37
• Well, the Star Wars universe has different laws of physics than ours does – Xandar The Zenon Aug 9 '16 at 22:30
• It's Noether's theorem, not Nother's. – celtschk Oct 15 '16 at 10:18

I’m amased at how many answers get the meaning of inertia wrong, even while claiming others are wrong.

To be clear, inertia is a mass’s property that makes it require some effort to accelerate. For straight-line motion that is equivalent to mass and is the meaning of m in F=ma. For rotation, it depends on the distribution of mass around the center of rotation, and this moment of rotational inertia is noted as I. The equivilent of force = m × acceleration becomes torque = I × angular acceleration. In a swing, the rotation version might be important.

Besides the problems with the answers, it promps me to wonder just what did the OP mean? From his prose it is clear that the word was used correctly: he wants the sword to be easy to swing, yet still deliver blows like a weighty object.

Let’s start with angular inertia and torque, since that’s something that can in fact be altered. When you open a door you push at the edge as far from the hinge as you can, and push at 90° to the current position of the door. If you pushed an inch from the hinge it would require a lot more force to push it the same amount. An object’s I works the same way: imagine a wheel. If the mass is at the rim it will be harder to get moving than if the mass were concentrated at the hub.

So you can change the effort required to swing something by changing the shape and points of leverage.

Imagine the mass concentrated at the far end, more of a war hammer. If the weight could be retracted to the handle then swinging would be easy! You just lowered the value of I. Now you have this lightweight stick moving in an arc at some considerable speed, and you release the weight and send it back to the far end. What happens? The rotation slows to nearly nothing! You can’t deliver a hard blow after all.

Now for straight-line inertia (mass). If you had some way of turning the inertia off and on again it would play havoc with the laws of physics. Conservation of energy, conservation of momentum, and if you patch that up by delivering energy and recoil from a magical source in a simple way, you break relativity.

But the angular form shows how it can be made to work without breaking physics. Imagine this real-world implementation: the sword is hollow and filled with dense fluid. You swing it empty (light), and then the fluid is replaced. In the physical example you need hoses and pumps, and in principle you see that the fluid needs to catch up with the object and match velocity. This requires an engine (pump) to do so.

Now rather than physical fluid you can imagine the momentum being drained and refilled somehow, using more convienient wires (like electrical conductivity) and at higher speed. But the end result is the same: you will either lose the speed when you fill it back up with non-moving weight, or some external engine matches the speed and this takes as much energy (and picks up recoil) as it would have taken to accelerate the mass normally.

You can’t instantly turn the mass back on: it is a process which delivers the mass back to the state (position and velocity) you wanted in the first place.

So the real (useful) point is that the force is supplied by an external engine, not your muscles. This is what we do in the real world with hydrolics! You can turn your car’s steering wheel with no effort—the weight you feel is left on purpose for better control—and the tires follow your command, powered elsewhere.

Imagine a lightweight stick that you swing and point, and a hydrolic system moves the heavy sword to match. If the motion keeps up exactly, the stick could be hidden inside a small hollow in the sword which protrudes as a handle. It would feel like a weightless sword.

Now in the real world this would be an exoskelliton, or (as with construction machinery) not co-located with the control. You can imagine the magic making what’s essentially an invisible exoskelliton, using magic-provided energy to move the weight. And there you have it.

But why not the equivalent of magic-implemented buldozers, cranes, and end loaders instead? Why a sword when the technology could be used to make a projectile weapon, or simply toss the enemies aside?

Inertia is basically the resistance to movement, right?

Yes, physicists commonly define inertia using similar phrases, for example this page defines inertia as "the tendency of an object to resist changes in its state of motion." They probably wouldn't phrase it as "resistance to movement" though since it would be ambiguous whether "movement" refers to acceleration or velocity, and inertia is specifically about resisting acceleration. This resistance is quantified by the value of an object's inertial mass, which is conceptually distinct from its gravitational mass, though the equivalence principle in Einstein's theory of general relativity implies that they must be equal (but this wasn't obvious in Newton's time).

Which can be considered "acceleration".

Not exactly, although the larger the inertial mass, the smaller an acceleration you will get when a given amount of total force is applied to an object. The key here is Newton's second law, which says that the net force on an object is equal to its inertial mass times its acceleration, or $F=ma$; if you divide both sides of the equation by $m$ you get the equivalent equation $a = F/m$, which tells you that the amount an object will accelerate is equal to the applied force divided by its inertial mass. So, the larger the inertial mass, the smaller the acceleration, given a fixed amount of force--that's the sense in which the inertial mass is quantifying resistance to acceleration.

So, if you could change an object's inertial mass at will, then in the limit as the inertial mass approached zero, the acceleration in response to a given amount of force would approach infinity--in Newtonian physics, this means the slightest force would cause the object to zoom off in the direction of the force vector at infinite speed. In relativity things would be a little different, since the equation $a=F/m$ gets replaced by the more complicated $\mathbf{a} = \frac{1}{m_0 \gamma(\mathbf{v})} \left( \mathbf{F} - \frac{ ( \mathbf{v} \cdot \mathbf{F} ) \mathbf{v} }{c^2} \right) \,.$ It's still true here that as the mass $m_0$ approaches zero, the acceleration in response to a given force approaches infinity. The difference is that in Newtonian physics, as the acceleration approaches infinity, the increase in velocity over some fixed finite time interval (say, one microsecond) approaches infinity too, whereas in relativity, as four-acceleration (whose magnitude is equal to the proper acceleration, the g-force that will be felt by the accelerated object) approaches infinity, the increase in velocity over some fixed finite time interval approaches the speed of light. So here, the slightest touch would cause your sword to zoom off at the speed of light (or very close to it, if you just reduced the inertia to some very small value without making it exactly zero).

As for stopping an already-moving object, if the inertia was very small, there would be a corresponding very small force needed to bring it to rest, the force would just have to be applied in the direction opposite to the direction it was moving. In the Newtonian case where the math is simpler, the change in velocity $\Delta v$ of an object subjected to a given acceleration $a$ for time interval $\Delta t$ is just $\Delta v = a * \Delta t$, and from before we had $a = F/m$ so this is equivalent to $\Delta v = (F * \Delta t) / m$. So even if the force $F$ you can apply is small as is the time $\Delta t$ in which you want to bring it to rest, you can always find a sufficiently small value of $m$ so that you do get the desired $\Delta v$ for that force and time.

• So far I think this most directly addresses my question(s). I may be biased against the others, though. However, what about stopping? – FinAndTonic Jul 23 '16 at 19:44
• Added a paragraph on stopping. – Hypnosifl Jul 23 '16 at 19:50
• Stopping: it would be a Nerf sword, which you can do in the more obvious way of making it have a very low mass. – JDługosz Jul 25 '16 at 1:20
• @JDługosz - As I said, I interpret lowering the inertia to be just another way of saying lowering the (inertial) mass, since there isn't any other measure of inertia in physics. A permanently low-mass nerf sword wouldn't be able to do much damage, I think that's why the last two sentences of the original question talked about lowering the inertia when you're swinging it, but selectively raising it back up "right before it hits the target". – Hypnosifl Jul 25 '16 at 22:49
• @Hypnosifl we’re in agreement. See my answer on analysis of adding the inertia back in without breaking physics? – JDługosz Jul 26 '16 at 0:08

Inertia is thought to be controlled by the Higgs field, so manipulation of the field is what would be needed to manipulate inertia.

The best way to think of this is the "Higgs Party" A room is filled with party goers (the Higgs field at rest). When a famous person enters the room, the party goers rush to surround the famous person, hindering movement. This is analogous to the field resisting the movement of a particle. The Higgs field also works on energy. If you imagine a rumour is started in the party room and all the people rush to the middle to gossip, this is the same as the field resisting the movement of energy or information. So you would have to somehow "mask" the appearance of the famous person so the party goers don't congregate around the person to allow for free movement.

Edit to add pictures. For whatever reason I was having difficulty finding the "Higgs Party illustrations and posting them. Corrected now.

• I really like the final analogy. – FinAndTonic Jul 23 '16 at 23:47
• The Higgs field determines the rest mass of particles, but inertial mass is a consequence of total energy obeying $E=mc^2$, so even if you could cause rest mass of particles to become zero it wouldn't make inertial mass of composite systems zero. For example, the binding energy between particles contributes to mass, see the discussion here, and even unbound massless photons in a box would still contribute to the box's inertial mass due to their kinetic energy. – Hypnosifl Jul 23 '16 at 23:54
• And (adding to @Hypnosifl) the mass of atoms is mostly due to the energy in the protons and neutrons. If you somehow turned off Higgs mass, you would only affect it by less than 1%, as the electrons are parts per thousand and quarks mass are complicated. – JDługosz Jul 24 '16 at 23:21
• Turning off the Higgs mass would make your electrons fly off at the speed of light and the weak force to become long range, so all your atom’s neuclei would collapse into one big one. I hesitate to think what happens when you turn it back on again. – JDługosz Jul 24 '16 at 23:24
• Those illustrations are from Scientific American: you may want to site the issue so those with subscriptions can look it up (and cite the source. And some articles are free access.). – JDługosz Jul 25 '16 at 9:56

Your definition of inertia is wrong. From Wikipedia:

Inertia is the resistance of any physical object to any change in its state of motion (this includes changes to its speed, direction or state of rest). It is the tendency of objects to keep moving in a straight line at constant velocity. The principle of inertia is one of the fundamental principles of classical physics that are used to describe the motion of objects and how they are affected by applied forces.

By swinging the sword, you are changing its inertia. It is not traveling in a straight line, but in an arc due to your arm's motion. At every point of the arc, you are changing the sword's inertia. If you were to let go of the sword, inertia would take over and it would travel in a straight line. Well, it wouldnt, as gravity would pull it down.

If you could break the laws of physics, and the sword had zero inertia, then the sword could not be moved. Ever.

• Let me see if I can spell this out for myself, and hopefully you can yes/no it. No inertia means no change in velocity (acceleration). No change in velocity means you cannot go from 0 speed to 100mph. – FinAndTonic Jul 23 '16 at 17:37
• I agree with everything except the last line--the measure of an object's inertia is just the inertial mass which appears in Newton's second law F=ma, which can be rearranged as a = F/m, so as the inertial mass m approaches zero, the acceleration a in response to any given amount of force F would approach infinity--any amount of force would cause the object to zip off with infinite speed in the direction of the force, at least in Newtonian physics. – Hypnosifl Jul 23 '16 at 17:37
• @Hypnosifl but the sword has mass, therefore it cannot move or else inertia would be created. – Keltari Jul 23 '16 at 17:43
• Either way, it would not be conducive to a sword fight. – Keltari Jul 23 '16 at 17:48
• And so come to think of it, I also disagree with the part of your answer where you say "At every point of the arc, you are changing the sword's inertia"--I think you may be confusing inertia with momentum, an object's tendency to resist acceleration (i.e. its inertial mass) does not change when it is accelerated, and in physics there isn't any well-defined measure of an object's "inertia" distinct from its inertial mass. – Hypnosifl Jul 23 '16 at 19:04

Um, no.

Inertia is the concept that an object will maintain its state of motion unless some external force acts on it. That means an object at rest stays at rest, an object in motion continues to moves in a straight line. Inertia therefore occurs when net acceleration is zero.

What you described as resistance to movement is called friction. Inertia would mean you swing the sword and let it go, it disappears over the horizon. Friction means the sword eventually stops moving.

An inertia-less sword is inconceivable. And yes, the word means what I think it means. You are postulating an object changing its movement without any force acting on it. I certainly wouldn't trust a sword that moved when like it had a mind of its own.

A frictionless sword, on the other hand, is something people have been trying to achieve. Aerodynamics to reduce air resistance, a sharp blade and even edge to reduce the force needed to cut through flesh and bone; centuries of refinement has gone into blade design. You want to minimise friction all the time to make it easier on the user and to increase the durability of the blade. Every ounce of force spent overcoming friction is extra effort on the part of the wielder, and, inside solid or liquid objects, just that much extra wear on the blade.

• Comments are not for extended discussion; this conversation has been moved to chat. – HDE 226868 Jul 27 '16 at 12:07

I feel the answers here miss the point of the question. So under the assumption that Inertia is something that magic can alter (both linear and rotational), what would the consequences be?

Assuming all aspects of inertia can be altered, you can effectively move the center of mass to the grip of the weapon, making the weapon easier to swing, and than largely it is just a matter of strength to hold the weapon.

Well, F=m*a would effectively be F=a (since the m is basically just inertia) if you reduce it to zero. So this means that Swinging a 7 ton sword with 0 inertia would feel as light as air! And if you wanted to hit someone with it? F=a so... The opponent would need the same strength you used to swing it to stop it... pretty useless BUT if we change the inertia mid-swing? Than you could hit someone with a 1 pound sword like it weighed 5 tons (the breaking point of said sword will remain the same though so... go easy or use other peoples swords =3).

TL;DR: Altering an objects inertia is equivalent to altering the object's effective mass. (this is basically the 'Mass Effect' from the game Mass Effect!)

• F=a is setting m to 1, not eliminating it. One what? That’s a unit mismatch, and if you just mean F is proportional to a, that doesn’t say anything useful since m is just the constant of proportionality. If we change the inirta mid swing: an analysis of that is the subject of my answer. You’re just saying “do that” so how's that add anything beyond what was in the original question? – JDługosz Oct 15 '16 at 7:22