Immovable object [vs] unstoppable object

[zman9000]

It has been thought of by many people over time. two objects collide one cannot be stopped the other cannot be moved. what would this epicly impossible showdown be like in the real world.

Well my thoughts on this is I believe they would both win, and this is why:
[spoiler]for both objects do act the same in the real world they would have to have infinite mass.

so stop an object with infinite mass you have to have the same amount of energy and force. the same goes for moving a stationary object with infinite mass.
both have the same mass and energy. though it is infinite they are both the type of object, one is just moving the other is not.

when the collide the energy of motion transfers from the moving object to the unmovable one. being infinitally dense means that the energy transfers perfectly and completely. In the end you would still have an Immovable object and an unstoppable object, they would have just switched roles.[/spoiler]

So lastly if you are wondering why i made this topic when i think i have all the answers, well i don't, this is just my theory on how it would work.
I'd like to get some activity back to the site so, post what your take is on this impossible scenario.

[Misery]

If both objects have infinite mass, wouldn't they have to be the same object?
Logically, one or both objects would have to cease to exist. It's the only thing I can think of that doesn't contradict their unstoppable/immovable states.

[Atrius (He/They)]

For such objects to exist there would have to be zero transfer of energy when they collide with other objects.  Based on this fact there are two possible scenarios:

1)  After the collision both objects retain the same momentum, but it's direction is changed.  The unstoppable object bounces off the unmovable object without slowing down at all.

2) They are intangible, and do not interact with each other.  The unstoppable object passes through the unmovable object as though it does not exist.

[Rockisftw]

For such objects to exist there would have to be zero transfer of energy when they collide with other objects.  Based on this fact there are two possible scenarios:

1)  After the collision both objects retain the same momentum, but it's direction is changed.  The unstoppable object bounces off the unmovable object without slowing down at all.

I think he means that the first object cannot be stopped period, and a change in direction requires some give in the object. So the point is, between something that will knock everything away in its path vs something that cannot be moved no matter what.. whats going on.

[Aile~♥]

Yeah, they'd just go through each other, I think. Or the universe would cease to exist. DIVIDE BY ZERO ERROR.

[zman9000]

Yeah, they'd just go through each other, I think. Or the universe would cease to exist. DIVIDE BY ZERO ERROR.

And you see there is where the problem comes when people think about this. when you run a computer program on this, it comes up with an error.
And i wasn't talking about the question in general. I was saying: OK say these objects, like the size of... a bowling ball, were to collide in the real world how would they react.
since for an object to be unmovable or unstoppable in the real world, it would need infinite mass, and be infinitely dense.

technically this would make them act the same as the question. as for colliding the = the same mass/density as each other. And speaking about transfer of energy, something infinite hitting some infinite would have instant transfer of energy as there is no space for energy to move other then the other target.

And another thing i realized when reading back over your comments. say we take infinite density out of it, and just have infinite mass. there is a way for this to still be possible due to the very description of this event.
[spoiler]
Infinite means goes on forever.
now something we should have all learned in math using graffing and/or number lines as an example.
say you have two lines, the first starts at one point and goes in one direction forever. The second also starts at one point but goes in opposite directions forever.

it would look like this written visually
L1:                       |--------------->
L2: <--------------|-------------->

They are both the same length. because (infinite * infinite) = infinite.

so think two objects with infinite mass like this
<=====|       |=====>

they just go on forever in one direction. this proves you can have more then one object with with infinite mass interact with each other.
[/spoiler]
[spoiler]

If both objects have infinite mass, wouldn't they have to be the same object?

no they wouldn't, there are ways that it still works with out it taking up all space in this given event area. since half of infinite is still infinite. you can have an infinite number of infinite mass objects in an infinite space.

Logically, one or both objects would have to cease to exist. It's the only thing I can think of that doesn't contradict their unstoppable/immovable states.

this is half true, as it is, the most logical thing would be to say one goes away. but what would happen if you also said not only can they not move/be stopped but they were also indestructible?

the weird thing would be this, no the universe wouldn't go away. yes the objects could collide, the moving one would keep moving, the one that doesn't move wouldn't move, they wouldn't be destroyed, pass through each other, or anything else.
if you take it out of a real world setting and go for the literal "Immovable object", unstoppable object", this creates a paradox, yet just because of the paradox doesn't mean said universe goes away. you can't even comprehend this.[/spoiler]

finally there are three types of settings for this that people tend to lean to as their example.
universal shutdown since something happens that can't happen, the universe goes away. (this is in line if you think about it like a computer would)
real world example using what we know about how matter interacts. (this is in line if you think about how things that aren't real would work with our rules)
Cop-out example by ignoring the rules of how things work completely. (this is in line if you understand its impossible but feel there must be a right answer)

[leaf]

Hey zed, you actually made an interesting thread. Congrats.

Now, for a serious reply:
You're taking several assumptions that are not stated in the problem outline that renders the problem as overdefined. Who said the objects were the same size, for example? What if you had a very tiny particle, capable of fitting between the gaps in a much larger solid? The very tiny particle passes through the solid without stopping or slowing down, while the solid remains stationary. This satisfies the initial conditions, does it not? While not technically a "collision," one object has intersected with the surface plane of the other object.

If you must take the term "collision" literally, then atrius's solutions are the only possible ones. As it is now, the event of a strictly defined unmovable object and a strictly defined unstoppable object colliding is only a theoretical construct. It is not that the world would collapse if they existed in the real world, or that the objects themselves would cease to exist; they simply could not exist in the first place. If such objects ever did exist and entered such a collision, they would be redefined on the spot to fit within the bounds of the real world (which would result in one of the solutions atrius proposed).

[zman9000]

Ah yes, now you have explained it like that i see what you mean.
I was taking it as colliding and I suppose I was more talking about how it would work if i said. hey i have two objects here with infinite mass and density, one isn't moving, one is going to hit the other, what would happen?

technically the way i explained it is a little backwards. since it is technically using a stoppable, and movable object.
Wait... does mean we were kinda sorta almost on the same page?

[leaf]

Sorta. Your answer (using two objects of infinite mass) is probably fairly close to a real world equivalent. If you assume a perfectly elastic collision of equal masses (a highly erroneous assumption, but we'll go with it for now), their velocities will switch places and the "immovable" object will become "moving and unstoppable" while the "unstoppable" object will become "unmoving and immovable." The problem with this assumption is that "infinite" is not a defined quantity; both (infinity - infinity) and (infinity/infinity) are undefined. Furthermore, while some collisions in real life can approach perfect elasticity, afaik, there is no way to create a true perfectly elastic collision. The problem ultimately reduces to which object is "more infinite," which we have no way to measure, and as such, the problem is unsolvable.

The other problem is that this model neglects gravity. Two objects of infinite mass will create a very large gravitational force. F = G*m1*m2/r^2. If we assume the objects are an infinite distance apart, the equation reduces to infinity^2/infinity^2, which is undefined. If we make the assumption that the objects are infinitely large, it is possible to force a collision in this state. If this problem reduces to any finite non-zero answer (for example, if F = G), the "immovable" object will lose immediately, as it will be pulled by the "unstoppable" object. The "unstoppable" object would then lose on collision. In this case, the immovable object loses first, but in the end, they both lose.

Since the assumption of two objects of equal, infinite mass obviously creates unsolvable contradictions, let's explore some different models. These are the conditions that need to be fulfilled, both before and after the collision:
Immovable object: X = 0, v = 0, a = 0
Unstoppable object: X = v0*t, v = v0, a = 0

If you're using traditional Newtonian physics of two simple spherical objects of some given mass colliding, a solution using these boundary conditions is impossible. The only solution is the trivial solution where no collision takes place, which could be represented by one or both objects being intangible (and therefore passing through each other).

But, what if we expand the problem statement to encompass non-spherical objects in collision? The problem never specified what these objects looked like or how they collided. Non-homogeneous objects should be perfectly acceptable within the bounds of the problem statement.

The biggest problem is in how to model the "immovable" object. How literally should this be taken? If you take "unmoving" literally down to a micro scale, it would imply the object is held at absolute zero. This would imply that not even the atoms are moving. While this could be a legitimate model of an "immovable object," you would have the problem of how to prevent energy transfer to the system (neglecting the fact that true absolute zero is impossible to achieve, and that if it ever were, it may exhibit properties we have yet to see in systems that merely approach absolute zero). Therefore, I propose that the molecular motion be neglected. The "immovable object" can thus be modeled simply as a mass that does not exhibit any change in center of gravity during a collision.

By modeling the "immovable object" as an infinite spring of zero stiffness and zero mass attached to a small cube of some small finite mass, this condition is fulfilled. The spring can be compressed infinitely without ever exhibiting a change in the center of gravity of the object, since the spring itself contributes no mass; the center of gravity is always located at the center of the cube. However, since the spring has zero stiffness, any object that collides with the spring will transfer no force to the cube, causing the cube to remain immobile even from extremely high energy collisions.

The next problem is modeling the "unstoppable object." For this, we will use a sphere of infinite velocity and some small finite mass. Since a finite number times infinity is still infinity, the momentum of this object is infinite. Thus, by definition, an object with infinite momentum cannot be stopped by an object with finite momentum. Furthermore, since the mass is small and finite, gravity can be neglected.

Finally, we move on to the collision. The sphere collides with the spring which is compressed infinitely. The cube remains stationary throughout the process and the sphere never ceases movement. Both conditions of "immovable" and "unstoppable" are fulfilled simultaneously, leading to a possible solution to the problem.

Q.E.D.

[Misery]

I think I've found a conclusive answer to the question of "what happens when an unstoppable object collides with an immovable object"
and it's not the more realistic "they don't"

The unstoppable object keeps moving in the same direction, and the immovable object retains its exact same position and form.

Though technically, that only describes what happens after they collide... so what happens when they collide? That's still open for discussion.
This has gotten me thinking about some other things though.

Saying that an object is "immovable" assumes a static universe of finite space where everything has an exact position. What constitutes an immovable object? What is it immovable in relation to? Can such an object even exist?[spoiler]I believe the answer to the last question is "yes, if the object occupies an infinite space"[/spoiler]Can an object of infinite mass exist within a finite space?[spoiler]Again, I believe the answer is yes, but the space it occupies cannot be defined. I'd explain why I think that, but
1: I'd like to see if anyone else reaches the same conclusion in the same way, and
2: I'm lazy[/spoiler]
The other things I thought of mostly relate to infinity and these two questions...

In response to leaf's post: Is infinite velocity actually possible?

[leaf]

Probably not. I realized a bit after posting it was impossible and I was wondering if anyone would actually catch me on that before I got to fix it =p

Anyway, for an accurate solution, that can be fixed by making the sphere of mass = m1 and the cube of mass = m2 = m1^2, where m1 = infinity. The new boundary conditions become m1 always has v > 0 in the positive x direction and m2 always has v = 0, a = 0, and x = 0 with respect to an inertial reference frame.

Or at least, that's one possible fix to the gravity problem. Another fix would be to have a third mass of mass of m3 = m1 approaching the cube from the opposite direction. There is also an infinite spring of zero mass and zero stiffness extended in this direction. Then, the two unstoppable objects and the one immovable object will remain unstopping and unmoving, respectively.

So, to summarize, the unstoppable object is defined as a sphere of arbitrary size, arbitrary (and finite) velocity in the positive x-direction, and mass m1 = infinity. The immovable object is defined as a massless infinite spring with zero stiffness that extends in the negative x-direction from the origin, which is attached to a cube of arbitrary size with mass m2 = m1^2 and a = 0, v = 0, x = 0 with respect to an inertial reference frame. The sphere collides with the spring and compresses the spring infinitely, never slowing down or changing direction. The cube does not move from its inertial reference position.

Q.E.D.

---

To answer your questions: An object of infinite mass could occupy a finite space if it also had infinite density. You are also correct that the space it occupies cannot be defined, since infinity divided by some finite value is still infinity, and infinity divided by infinity is undefined.

[zman9000]

more infinite

eh well... ok

I always thought of it like this, before i put more thought into it.
[spoiler]two objects that are exactly the same.
they are 100% solid in the true meaning of the word, and they them self's are solid and none moving with in them self's
one is fixed to a plain and can not move nor transfer energy. a perfect unmovable object.
the other is sent toward the other on a straight linear path that it can not deviate from and the path directly intersects the center of the non moving object.
the speed doesn't matter.
the rules are:

Object 1 must stay where it is no matter what.
Object 2 must stay on the path and must never slow or stop.
lastly matter may not intersect other matter.

to bad this its self is truly something impossible to think about or even replicate since the collision of the two objects following these rules brake the rules.[/spoiler]

This is the same thing as a few other variations I've heard.
[spoiler]A sword that can cut through anything meets a shield that can not be cut.
A force that can destroy anything meets an object that can't be destroyed.
Glue that sticks to everything and an object that doesn't let anything stick to it.

The only thing we know is we can never know what would happen.[/spoiler]

Saying that an object is "immovable" assumes a static universe of finite space where everything has an exact position. What constitutes an immovable object?

I think the bigger question is what constitutes a point within said universe for said object to reside?

Can an object of infinite mass exist within a finite space?

I've already said, an infinite number of infinite objects can fit in an infinite space EDIT::(and density doesn't have anything to do with it). but it is also possible for only 8 to do so, or 4, or 2, or 1, or a certain number. as long as you are talking about 3d space this holds. cause i don't want to get into 4D talk again... that was a nightmare.

[leaf]

Yeah, you're overconstraining the problem, which is why you get a paradox. It's the same as if you were to say y = 2x and you decided you wanted to make y = 1 and x = 2 instead of the other way around. If there were a z term in there, say, y + z = 2x, then you could do this and the equation would still hold (in that case, z = 3). But, if there is no z, the problem is overconstrained and no solution can be found; the result is just nonsense. 1 does not equal 4.

Since you assume both objects to be rigid bodies, a solution is impossible. One of the objects has to be a spring.

Alternatively, the "unstoppable object" isn't an object in the truest sense of the word, but is instead a wave. The problem is waves experience interference and such, so I'm not sure if it would be entirely accurate to call waves "unstoppable." Especially since they require something to propagate through.

edit: And zed, you misread the question. He was asking if it could fit in a FINITE space, not an infinite one.

A sword that can cut through anything meets a shield that can not be cut.
A force that can destroy anything meets an object that can't be destroyed.
Glue that sticks to everything and an object that doesn't let anything stick to it.

These are less scientific, but... okay.

The sword will cut anything that it strikes. The shield will not be cut by anything that strikes it. The solution is trivial. The sword will miss at any attempts to strike the shield.

The force is infinite. The object can withstand infinite stresses. According to your theory of infinity (which is wrong, btw), the object that cannot be destroyed wins, since the stresses in the object did not surpass their limit (which is infinity). The actual winner depends once again on which is "more infinite": The force or how much force the object can withstand. This is basically the problem statement you made before but with rigid bodies (which is, as stated, unsolvable).

Glue that sticks to everything would stick to the object that nothing sticks to, but it would easily wipe off. =p

[zman9000]

Yeah, you're overconstraining the problem, which is why you get a paradox. It's the same as if you were to say y = 2x and you decided you wanted to make y = 1 and x = 2 instead of the other way around. If there were a z term in there, say, y + z = 2x, then you could do this and the equation would still hold (in that case, z = 3). But, if there is no z, the problem is overconstrained and no solution can be found; the result is just nonsense. 1 does not equal 4.

well i get what you mean, but just because the result is nonsense doesn't mean its not a result. but i think i get what you...

Since you assume both objects to be rigid bodies, a solution is impossible.

what i mean about th...

One of the objects has to be a spring.

or...

the "unstoppable object" isn't an object in the truest sense of the word, but is instead a wave.

maybe you don't...

i feel like your solution is kinda is off but... idk... but reading it gave me another idea.
what if one of the objects was "dark matter" and the other normal. (and maybe i'm just going end up with the same answer you got just slightly different.)
If you don't know, dark matter now refers to something we have actually found and studied. dark matter only interacts with normal matter through gravity, but it has the same amount of gravity as normal matter.

with one object dark matter and the other one normal matter, both can have the same mass and size, and follow all three rules i said in my other post. but they don't collide.
but also with this, gravity would still be a factor... and since i really haven't been doing to well with the math... eh i'll leave it up to leaf.

Despite how this post started, he might be on to something...

[Misery]

Saying that an object is "immovable" assumes a static universe of finite space where everything has an exact position. What constitutes an immovable object?

I think the bigger question is what constitutes a point within said universe for said object to reside?

That's the point exactly, since the universe (presumably) expands infinitely in all directions, we have no way of knowing wether the "immovable" object actually remains at the same position. I already mentioned the only possibility I can think of, an object occupying an infinite space, but that would mean the other (unstoppable) object cannot exist unless it's inside the immovable one.

Since you assume both objects to be rigid bodies, a solution is impossible. One of the objects has to be a spring.

By disregarding molecular motion, the immovable object could be just about anything. And of course a solution is impossible, the initial question doesn't describe anything that could actually happen in reality to begin with, not even theoretically. We're not here for an answer, we're here for discussion ;)

edit: And zed, you misread the question. He was asking if it could fit in a FINITE space, not an infinite one.

Adding to that, I think infinite density would be a result rather than a condition. It probably doesn't matter though.

but they don't collide.

The question implies that the two objects must collide.
Edit: No wait, the question clearly states that they must collide.

[zman9000]

That's the point exactly, since the universe (presumably) expands infinitely in all directions

nononononono stop there... that isn't the reason... like you said "presumably". My point is, even with two objects the only way to know location is to reference something else. but i pointed it out more or less as a joke as since there are only two objects being in play, you would only need relative location for said experiment to work.

By disregarding molecular motion, the immovable object could be just about anything. And of course a solution is impossible, the initial question doesn't describe anything that could actually happen in reality to begin with, not even theoretically. We're not here for an answer, we're here for discussion ;)

you don't mind if i thumbs you up and give you a coin do you?

Adding to that, I think infinite density would be a result rather than a condition. It probably doesn't matter though.

it only depends if you are trying to place this in the real world physics, or if you are taking the exact meaning of the words Immovable and unstoppable.

The question implies that the two objects must collide.

this brings up another good point. since when does matter collide?

[leaf]

i feel like your solution is kinda is off but... idk...

How so? Unless you can find something I forgot to account for, it accommodates all conditions of the problem.

this brings up another good point. since when does matter collide?

Son, you just went full retard.

Since you assume both objects to be rigid bodies, a solution is impossible. One of the objects has to be a spring.

By disregarding molecular motion, the immovable object could be just about anything. And of course a solution is impossible, the initial question doesn't describe anything that could actually happen in reality to begin with, not even theoretically. We're not here for an answer, we're here for discussion ;)

Not true. While certainly, if you only needed an immovable object, you could make do with a rigid body. But the the point was to come up with a way for an immovable object and an unstoppable object to collide, while still keeping true to the conditions of being immovable and unstoppable. One or both objects could not exist in the same world if they did not properly interact with each other, after all. There may be other solutions that don't involve a spring, but that doesn't change the fact that using a very specifically defined spring (massless, infinite, and zero stiffness) will give a working solution.

[Misery]

That's the point exactly, since the universe (presumably) expands infinitely in all directions

nononononono stop there... that isn't the reason... like you said "presumably". My point is, even with two objects the only way to know location is to reference something else. but i pointed it out more or less as a joke as since there are only two objects being in play, you would only need relative location for said experiment to work.

The question of wether an immovable object can actually exist was unrelated to the unstoppable vs immovable question...

Adding to that, I think infinite density would be a result rather than a condition. It probably doesn't matter though.

it only depends if you are trying to place this in the real world physics, or if you are taking the exact meaning of the words Immovable and unstoppable.

Another one of my unrelated questions...

The question implies that the two objects must collide.

this brings up another good point. since when does matter collide?

two objects collide one cannot be stopped the other cannot be moved.

I assume these objects consist of matter, and the objects collide
But I'm not great with physics -.-

Since you assume both objects to be rigid bodies, a solution is impossible. One of the objects has to be a spring.

By disregarding molecular motion, the immovable object could be just about anything. And of course a solution is impossible, the initial question doesn't describe anything that could actually happen in reality to begin with, not even theoretically. We're not here for an answer, we're here for discussion ;)

Not true. While certainly, if you only needed an immovable object, you could make do with a rigid body. But the the point was to come up with a way for an immovable object and an unstoppable object to collide, while still keeping true to the conditions of being immovable and unstoppable. One or both objects could not exist in the same world if they did not properly interact with each other, after all. There may be other solutions that don't involve a spring, but that doesn't change the fact that using a very specifically defined spring (massless, infinite, and zero stiffness) will give a working solution.

Assuming you don't count molecular motion as motion, then sure, it's a working solution. And if you count collision with no mass as an actual collision, but then you could simply say the object itself has no mass.

[zman9000]

Quote from: zman
this brings up another good point. since when does matter collide?

Quote from: leaf
Son, you just went full retard.

maybe i should make another topic... but not until i figure out how that topic could last longer then one post of be talking about the facts...

Quote from: zman
i feel like your solution is kinda is off but... idk...

Quote from leaf
How so? Unless you can find something I forgot to account for, it accommodates all conditions of the problem.

well I just don't like your answer, while it is correct with the way it was set up... I just can't except your... spring... idea...
You don't know, but i once had a real life discussion on this, for about 12+ hours over a few day on a road trip... i had pulled the spring idea then...  and i was shot down like a fly with a nuke...

my take on it is, both have to be a solid zero energy object. one moves never stopping, the other never moves. I'm not sure if you are going for real world example or not... a spring like this... its just... the spring changes direction and speed... i don't know anymore

[leaf]

Assuming you don't count molecular motion as motion, then sure, it's a working solution. And if you count collision with no mass as an actual collision, but then you could simply say the object itself has no mass.

Well, saying the object has no mass is actually a problem in this case, since I wouldn't be able to pull the center of gravity voodoo. If both the mass of the cube and the spring were negligible, the center of mass would be wherever the center of the spring-mass construct is, rather than at the center of the cube.

And you kind of have to disregard molecular motion. The problem statement referred to an "immovable" object. Not an "unmoving" one. On a macro scale, at the very least, it is both immovable and unmoving, which is what is relevant to the problem. Perhaps a more accurate way to put it would be to say that it's unmovable through the application of outside force. No matter how much force you apply to that spring, the object's center of mass will always remain at the same coordinate position.

well I just don't like your answer, while it is correct with the way it was set up... I just can't except your... spring... idea...
You don't know, but i once had a real life discussion on this, for about 12+ hours over a few day on a road trip... i had pulled the spring idea then...  and i was shot down like a fly with a nuke...

my take on it is, both have to be a solid zero energy object. one moves never stopping, the other never moves. I'm not sure if you are going for real world example or not... a spring like this... its just... the spring changes direction and speed... i don't know anymore

But was your spring massless with zero stiffness? :awe:

And by definition, it's impossible for an object to be moving and have zero energy. In fact, it's impossible for an object to have mass and have zero energy, too.

The only way to solve this problem is to remove implied constraints. You have to define the objects independently. And if you're not going to try to work toward a theoretical solution, there's no point in even discussing it to begin with.