# Would immovable rods have infinite mass? [closed]

Everyone's heard of immovable rods. They're a staple of fantasy tabletop rpgs. But recently, I started thinking as to how one would actually work. Theoretically, it would just be an object able to absorb whatever forces get thrown at it without budging. I haven't taken a physics class since high school, but I vaguely remember something about how the more mass an object has, the less it moves around when something else punches into it. So would an object with infinite mass not move at all when a force is exerted upon it?

Details:

• It is rod shaped. I don't think this matters but let's say it's a foot long and an inch in diameter.
• It has infinite mass.
• Obviously something with infinite mass would be so deep in a gravity well that it would collapse into a black hole and probably suck up the entire planet and destroy everything, so let's say that doesn't happen, because magic.
• Let's assume that the rod is localized, so that when you turn it on, it doesn't fly off into the distance as the planet moves away from it while it remains at the same static point in the planet's orbit. The rod moves with the planet as it rotates and orbits around the sun. Same with the rotation of the galaxy the planet is in, and other things of that nature.
• Youve created a paradox at the end there, since you are now moving the immovable rod. May 28 '18 at 4:10
• NB: The D&D version of the silly thing will 'snap off' when subjected to more than 8000lbf or 35.5kN. Of course, an 'immovable-until-someone-drops-the-world's-largest-lollipop-on-it rod' isn't nearly as interesting as a properly immovable one May 28 '18 at 4:55
• if it follows the planet orbit then it is for sure movable.
– L.Dutch
May 28 '18 at 5:29
• Everyone's heard of immovable rods. - I am deeply sorry but no. I have no clue about what immovable rods should/would/could be. Please provide such information, especially when it is the core of your question May 28 '18 at 7:14
• Infinite mass rod would end the universe as we know it — everything would fall on it with infinite acceleration. May 28 '18 at 7:32

What is unmovable? The Earth is spinning while orbiting the sun which in turn is in a spinning galaxy inside an expanding universe.

Mass isn't the solution and changing the mass will only create more problems.

The best you can do is that it locks itself relative to the largest closest gravitational mass.

Think of Thor's hammer in the movies.

• No mass in the Universe is standing still, else we would have a privileged reference frame.
– L.Dutch
May 28 '18 at 6:12
• Thor's hammer is a classic example, but it locks to reference frame not large mass. It doesn't break elevators or aircraft for example. May 28 '18 at 7:34
• Not quite. When Thor puts it in that dragon creature's mouth, it locks to the planet, not the dragon despite being inside the dragon. We never actually see it getting put down in an elevator or an aircraft. May 30 '18 at 2:20
• @Thorne, in the first avenger movie Thor left it on the helicarrier which was still flying and the hulk tried to lift it unsuccessfully. Jun 1 '18 at 10:33

The object would behave as if it had infinite inertial mass, but this would not change its gravitational mass; it would not become a black hole.

Actually, to be "truly" immovable, the object would also probably need to have no gravitational mass at all... unless it "dumped" gravitational force the same way it did electromagnetic interactions.

You could achieve something similar with a very precise inertial navigation system, plus an attitude control system of infinite (okay: much greater than anything you could throw at it) power and no visible external effect. Then you would try to move the object, the object would calculate where it should be according to its internal schedule, and apply whatever force it needed to neutralize your attempts. In this case you probably would notice some oscillations; the more reactive and powerful the system, the smaller the oscillations.

There was something similar in some novel (but now I'm conflating it with the uni-propulsion at the end of The Gods Themselves): the object generated a portal inside itself, and through that portal it reached for and grabbed a really large nickel-iron asteroid. At that point, the object - about a meter or so in size - behaved as if it had the inertia of the whole asteroid, and became immobile with respect to same. An attempt to move the object thus resulted in an attempt to move an asteroid weighing several billion tons.

It all depends on how you want to look at it. Infinite Mass means Infinite inertia (Inertia depends on mass) which means it won't be moving. But your also going to have a black hole the size of infinity and made out of infinite particles because infinity isn't really a number but more of a concept.

You might as well have the unmovable object be magical and have it reflect all forces applied to it, hence it won't move.

As a fun note, not all infinities are the same size and some infinities are larger than others.

An immovable rod wouldnt rely on mass but on perfectly countering any force applied to it. You push on a wall and it pushes back exactly the same, otherwise one of you move. The rod can do the same just with any amount of force on any scale. And like a wall, it's doing the same to earth and that is why it moves with it.

• A wall is only as immobile as what it's anchored to. May 28 '18 at 6:32
• @Schwern: why do i get the impression that "A wall is only as immobile as what it's anchored to" is destined to become some form of great philosophical quote? May 28 '18 at 8:09
• @BladeWraith The Greeks got there first. May 31 '18 at 15:50
• @sneftel, Ah... fair enough, i did look it up but couldn't find it Jun 1 '18 at 6:22

I think you just invented the most fun physics toy of all time. What you are abusing is Sir Isaac Newton's second law of motion. Force equals mass times acceleration. You could also say: force divided by mass equals acceleration. That means if mass is infinite no amount of force is going to cause a net acceleration.

This has fun consequences. For one thing if it's moving when you turn it on it's going to keep moving. If you drop it, even slightly, before turning it on it's going to slowly plow through earths core for no better reason than it's not stoping for nothin no how. See Newton's first law. (And Thor's hammer).

If you don't move it before turning it on you can leave it hovering in the air. Gravity is still pulling on it but it isn't gonna budge. If it wasn't for your magic the earth would be moving toward it. It almost sounds like you've suspended the third law. Or maybe you just figured out how to have all the mass you like and not cause any gravity.

I know I want one. I'll spin it before turning it on. Perpetual motion! Energy crisis over!

Call it infinite Inertia. It's just as magic as the mass thing but does not carry as much baggage that would have to be handwaved.

But infinite Inertia is just another way of saying 'immovable', so...

On a different note: i do not know any immovable rods featuring outside of D&D, and those are limited to about 4t of weight.

You are touching on 2 subjects that have never been encountered in nature.

All matter moves! Even black holes, the largest masses of matter, are affected by gravitation. So in a large way, based on what I know, there is nothing that fits under your description!

SO! Let's assume that your object goes beyond that, not because of magic(that goes against what we do here..) but because it surpassed the normal limits of physics by exceeding the normal mass a space CAN have, and even gravity waves are sucked in!

The biggest problem you have now is that it will not be localized in the way you mean it! Although you have an object that is indestructible, it will most likely behave like it has no weight!

The only way you can achieve your goal is if you have an force field with a very powerful energy source on the inside! It is the only way you can have an object that is localized on a planet and does not allow for people to pass.

We can get around the "infinite mass" problem by saying this object has infinite "inertial mass" not "gravitational mass". It counts for inertia and momentum, but doesn't count for gravity... because we say so. Good enough for D&D.

It has infinite inertia, but exerts no gravity. It's also not affected by gravity, because then you could "move" it by undermining it. I'll explain why it doesn't float away in a moment.

Next problem is "immovable" in what reference frame?

The apparently "immovable" rod, and you and I, are revolving around the axis of the Earth at about 1200 kph, depending on the latitude. The Earth itself is revolving around the Sun at about 30km/s. The Sun is moving through the Milky Way, etc. Since these are all rotating, the objects inside are under acceleration, they're all non-inertial reference frames.

We can fix this by saying the immovable object maintains the non-inertial reference frame from when it was cast. It is the center of its universe. The Sun and stars revolve around it. The Earth below is stationary.

Take away the floor beneath it and it would serenely float in the air, unaffected by gravity. During an earthquake it would appear to wobble about and up and down crazily as the Earth bucked below it.

If you take this to the extreme, the "immovable" object would appear to move a few centimeters a year as the continents drift beneath it, to the rod it is standing still and the continents are moving beneath it. It would appear to move as Earth's rotation wobbles and slows down, to the rod, the Earth beneath it would begin to rotate. It would appear to sink as the continents rebound from glaciation, to it the surface of the Earth is rising.

It would be an amazing reference point for geophysical measurements.

Being locked in its reference frame, having infinite inertia, it would either destroy anything in its path, or be destroyed. If you also specify that the immovable rod is also indestructible, it will slowly gouge a path across the Earth. Or above it. Or through it.

An ancient immovable, indestructible rod created by a long forgotten sorcerer might be a great feature of a campaign as it slowly, unstoppably plows through the landscape.