What happens when an unstoppable force meets an immovable object?
You may not like the answer. But here it is, this question doesn’t make sense. It stems from two contradicting axioms (statements taken to be true by definition) which nullify whatever result we derive from them.
These kinds of questions come in many forms:
- Can God create a stone so heavy that He cannot carry it?
- Impenetrable shields vs. irresistible spears
The latter actually has origins in ancient Chinese.
Spears and Shields
A certain man in ancient China sold spears and shields. He would praise his spears saying, “My spears are so sharp that among all things there’s nothing they can’t penetrate.” And he would praise his shields, “My shields are so solid nothing can penetrate them.” Someone asked, “What if somebody tries to penetrate your shields with your spears, what would happen then?” The man was speechless.
Moral of the story: don’t overplay your mouth!
This is the shield and spear paradox, others include, the irresistible force paradox, the unstoppable force paradox, and the one involving God and his Almighty powers, the omnipotence paradox.
But let’s try to solve one of these paradoxes and see what we’ll find.
The Unstoppable Force Paradox
So we have a question, what happens when an unstoppable force meets an immovable object?
First, we straighten up the terms:
- Unstoppable force: A push or a pull so strong that it will move any form of resistance in its path.
- Immovable object: An object that won’t budge no matter, no matter the force.
- And by meeting, we mean physical contact between the two.
One can already see the problem here: the two definitions are contradictory.
That can’t be right, at least they can’t co-exist in the same system.
When an unstoppable force meets an immovable object – a solution
We’ll keep things simple so you don’t lose track of the argument. Starting from basic definitions,
The relationship between force and energy
Force – an interaction between objects in the form of a pull or a push. It has the effect of making bodies speed up, slow down, change direction, or change shape. In all these cases, there is an energy transfer from one body to another – and the medium of that transfer is force.
For example, when a force compels an object to change shape, energy transfer is in the form of heat; the temperature of the deformed body rises. Likewise, when a force compels an object to accelerate, that relates to an energy transfer in the form of kinetic energy, and so on. So an unstoppable force means a medium capable of transferring infinite amounts of energy from one body to another.
Hold this thought for now as we turn our attention to the other mysterious term, “immovable object”.
Relationship between an immovable object and energy
An immovable object is any body with an infinite ability to resist motion. In physics, the ability of a body to resist motion is its inertia. Thus an immovable object has infinite inertia.
In classical physics, inertia relates to the mass of an object. In fact, we can think of mass as a measure of inertia of an object. In short, “the bigger the mass, the bigger the inertia”.
Therefore, when we say infinite inertia, we mean infinite mass.
$$Infinite\;Inertia\;=\;Infinite\;Mass$$
This implies that an immovable object has infinite mass. Still with me? I hope so!
Now you probably remember Einstein’s famous equation:
$$E\;=\;mc^2$$
This equation relates the mass of a particle to its energy at rest. So mass is some kind of energy.
So when we say infinite mass, we really mean infinite energy. Still with me? Now let’s get back to our argument.
Unstoppable Force Vs an Immovable Object
According to our argument so far: an unstoppable force would require infinite amounts of energy (i.e. all the energy available in the universe – ever) to move an immovable object. Yet, the immovable object represents an infinite amount of energy (all the energy available in the universe – ever) by virtue of its mass.
Since a single universe cannot have two separate infinite energies, the two terms cannot co-exist. They are mutually exclusive!
This is only one of the many ways to verify these kinds of paradoxical questions don’t have definitive answers. I am sure there are ways to arrive at the same conclusion with the other variations of this paradox.
Conclusion: Unintended consequences
In classical logic, we have the Principle of Explosion (P.O.E). It is a law that basically says: if you have contradicting statements that are taken to be true, then any other statement(s) can be deduced to be true. Using contradictory statements, one can prove that the Earth is flat, or unicorns are real, and 1+1=3.
To wind up, the question, “What happens when an unstoppable force meets an immovable object?” has no answer. It doesn’t even make sense.
Fun Facts:
- In the 2008 blockbuster superhero movie, The Dark Knight. The Joker tells Batman, “This is what happens when an unstoppable force meets an immovable object”. Seems like the Joker was this unstoppable force wreaking havoc across Gotham until he runs into Batman – who won’t budge (Immovable object).
- The term for “contradiction” or “paradox” in the Chinese language is a reference to the Shield and Spear paradox. “Paradox” is written as 矛盾 (mao dun). A combination of two words, 矛 (mao) which means “spear”, and 盾 (dun) which means, “shield”. So whenever you say “contradiction” or “paradox” in Chinese, you are figuratively referring to this paradox, and literally just saying “spear-shield”.
Acknowledgments
In writing this article, I had valuable input from ideas put forward by Alejandro Jenkins (Ph.D., California Institute of Technology), Jack Fraser (Masters of Physics, University of Oxford, 2018), and Yuan Gao.
