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What happens if an immovable object meets an unstoppable force? Is a popular
question on the internet.
Of course, relativity clearly tells us that there is no such thing as an immovable object
- here's why: If you pick any supposedly immovable object, or just something like your house
or the earth, I can make it move. All I need to do is start to move relative to it, for
example I might ride a rocket, and suddenly from my perspective, I'm not moving and the
earth sails by outside. The laws of physics make no preference for inertial frame of reference,
so from my perspective here, I do not stir, and yet it's clear: the immovable object moves!
So because of relativity, "immovable objects" cannot be. But what I think people normally
MEAN by "immovable object" is something that if it's not moving, you can't make it start
moving by Pushing on it. So, not an immovable object, but an "un-acceleratable" one.
Using Newton's second law, we know that an
object's acceleration is equal to the total force on it divided by its mass (though you've
probably seen this as F=ma). So an "un-acceleratable" object would be an object with infinite mass;
an object so massive that no matter how big the total force F is, when you divide F by
m you always get zero.
Of course, as we've said, not being able to accelerate an object doesn't necessarily mean
that the object isn't moving - it just means that you can't directly change its speed - if
it's not moving, then it'll stay not moving. And if it's moving at 100 miles an hour, then
it'll stay moving at 100 miles per hour.
So, what about an unstoppable force? Well, all the fundamental forces in nature are actually
caused by particles (like photons or gluons or gravitons) that interact with an object
and change its momentum - the only way to NOT be affected by a force is to not interact
with it at all (like how electrons don't interact with gluons so they aren't subject to the
strong nuclear force). Even light itself is an unstoppable force - every photon that hits
your body changes your momentum a tiny little bit, and there's nothing you can do about
it other than avoid light altogether or become transparent.
So all forces are already unstoppable
but my impression is that the phrase "unstoppable force" isn't really meant to imply anything
about "forces" like electromagnetism or gravity, but rather, something that you cannot stop
from barreling down on you. That is, an object whose velocity cannot be changed by pushing
on it.
So, IF by an unstoppable force we mean an object moving at a speed that can never be
changed, then that means the object cannot accelerate - but wait a second, this sounds
familiar! Recalling what we learned earlier, an unstoppable force must be an un-acceleratable
object! And that means that an "unstoppable force" and an "immovable object" are really
just the same, viewed from different reference frames!
Now, since infinite mass requires infinite
energy, we don't know of anything in the universe that behaves like this, not the least because
it would automatically be a black hole so big that everything in the universe would
already be inside of it. But what if we ignored gravity and imagined there WERE an
un-acceleratable object? Well, first it would be a source of infinite free power and would
allow us to live in a 100% happy utopian society and break the second law of thermodynamics
and probably create portals and time travel, too (you can do a lot with infinite energy).
But more importantly, if two of these infinitely massive un-acceleratable objects were moving
towards each other and collided, then since by definition it's not possible for the velocity
of either of them to change, the only possibility is that they must pass right through each
other with no effect on each other at all.