Can you transfer momentum to an immovable object

Let us, now, consider some special cases. Suppose that two equal mass objects collide elastically. If then Eqs.

Suppose that the second object is much more massive than the first i. In this case, Eqs. Suppose, finally, that the second object is much lighter than the first i. Let us, now, consider totally inelastic collisions in more detail.

In a totally inelastic collision the two objects stick together after colliding, so they end up moving with the same final velocity. In this case, Eq. However, its velocity is mindbogglingly small, and approaches zero as the mass of the barrier approaches infinity.

We could show this more rigorously with painful limits and epsilons and such, but the intuition shown here should suffice. Sign up to join this community.

The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why does momentum appear to be not conserved in this elastic collision? Asked 2 years, 9 months ago. Similarly an observer located on the irresistable force may also consider himself to be at rest and the immoveable object to be moving, he may also accept that he may be moving through space as this irrestable force, either view is valid.

If we represent each by a snooker ball, lets call the red one the force and the white one the immoveable object. Following impact, momentum is conserved so the objects both adopt new trajectories within the same universe.

The guy on the white ball still thinks he is immoveable albeit the universe has started to move differently. The collision shock may be interpreted as an effect of the whole universe suddenly changing direction while he stays still. Therefore the paradox only exists for a third observer who starts off in the frame of reference of the universe because both terms are paradoxical from that relative viewpoint.

This becomes most obvious when the third observer is stationary compared to the white ball. To be a valid argument the basic precepts of causality, and conservation need to be upheld and these examples do this. The Prof, after explaining that two such objects could not exist in the universe, theorised that either:. Juggernaut would bounce off be redirected of the Blob.

There by they both would retain their titles. Juggernaut would be stopped dead in his tracks and the Blob would go flying off. There by they both lose their titles. Though it does defeat the purpose of the question, which is to have no answer. Lets just say that there is an unstoppable force, which hits an unmovable object. And both are to big to redirect the other. Would the resulting exchange of energy simply just distroy the universe. Both are true. When trying to understand God, you have to remember that God is farther above us than we are above microbes.

Do you think a microbe understands much of anything that you can? So it should not be a surprise that what we call logic often fails when trying to understand God.

I actually maybe have an answer for it… The unmovable object meets the unstoppable one and it reverses it direction. Just my theory. Might be or might not be true…. Neither can really exist at all. An immovable object would have to push back on any force with equal and opposite strength to remain truly immovable. This cannot happen because there is a set amount of energy in the universe that cannot be exceeded.

If an object were able to push back equally on any force regardless of its size it would in theory have to contain equal energy to the entire universe because if it is truly immovable the entire combine energy of the universe should not be able to move it. An unstoppable force on the other hand assuming that by unstoppable we mean nothing is able to affect its movement in any way , cannot exist due to the idea that every action has an equal and opposite reaction.

If a force acts upon an object or another force, no matter how small would cause the force to lose energy, therefore breaking our definition of unstoppable. Many wonderful theories! I was curious what if the immovable object was a black hole and the unstoppable force was the matter being sucked into it?

Another thought. It is very possible for both to exist at the same time, however the only constant is the immovable object. The unstoppable force can only be stopped or de-flected by the immovable object but only the immovable object. I seem to be obsessed with this question, i keep thinking about it. I really like johns theory of the the universe shifting or accommodating to both properties.

Each encapsulates a vivid and intriguing challenge to our metaphysical theory. Footnote 2 Achilles and the Tortoise, for example, takes as a premiss that space and time are infinitely divisible and the putative impossibility of Achilles catching up with the tortoise is a reductio of that premiss. The Stadium takes as a premiss that space and time are finitely divisible and the conclusion that half the time equals twice the time is a similar reductio. Whether modern analysis Footnote 3 fully resolves these challenges has continued to be debated by philosophers.

Footnote 4. A man decides to walk one mile from A to B. A third god … etc. Benardete , pp. Since for any place after A, a wall would have stopped him reaching it, the traveller cannot move from A. The gods have kept him still without ever raising a wall. Yet how could they cause him to stay still without causally interacting with him?

Only a wall can stop him and no wall is ever raised, since for each wall he must reach it for it to be raised but he would have been stopped at an earlier wall. So he can move from A. Footnote 5. Supertasks can be set up in Newtonian universes of point particles with classical dynamics hereafter, Newtonian universes in which actual infinities of particles are permitted but each must have a finite speed.

Where has it got to one hour after it started? Infinitely far from its starting place? But there is no such place. It has gone out of existence. Yet how can mere increase in speed result in non-existence? Perez Laraudogoitia has shown how this can be modelled in a Newtonian universe by arranging an infinitude of particles to successively collide with a single particle, doubling its speed on each collision.

Perez-Laraudogoitia also created the Beautiful Supertask within a Newtonian universe. Since this last was the original inspiration for this paper and we make partial use of it I shall outline it briefly. It will collide with the 1st particle and thereby stop, imparting its velocity to the 1st particle, which in turn will collide with the 2nd particle and thereby stop, imparting its velocity to the 3rd particle Hence after one unit of time all the particles are stationary, thereby showing how.

Some people reject altogether the application of classical Newtonian mechanics to actually infinite systems. More broadly, for those who are skeptical of metaphysics that is not very severely disciplined by our current best physics, a position most recently advanced by Ladyman and Ross , such applications may have no interest.

In response, it may be said that metaphysical possibility is very broad, broader than mere physical possibility, and broad enough to include Newtonian universes of all varieties. Granted the possibility of infinite duration for the universes there is little to object to the initial conditions posited: they are merely the conditions convenient to start with and the entire history of the universe leading to those conditions could easily be given if necessary.

Footnote 7 Newtonian supertasks in the literature are of this type. They have no need of a creator nor instant of creation but are just the possible worlds with a certain specifiable history that leads to the moment from which we start our explorations. That being said, there are also possible worlds that have an initial instant Footnote 8 and such include Newtonian universes with various distributions of particles at that instant. These are all issues about Newtonian universes that can be contended but for reasons of space they are not contended here.

Footnote 9 This paper is in the tradition of previous papers that have treated such systems on the assumption that exploring the metaphysical possibilities of Newtonian universes, and in that way testing the metaphysical principles manifested therein, has philosophical significance. Previous supertasks in Newtonian universes have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism.

They have usually offered only a single argument to their paradoxical conclusions, making them vulnerable to single rebuttals. In this paper I present a novel supertask that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism.

Furthermore, the paradox can be based on each of four different continuity principles and as a result there are four independent arguments to the paradoxical conclusion. Consequently it raises significant challenges to the metaphysical principles on which it rests, with a special robustness because there is no single path to its resolution. This has often been thought to be simply contradictory and therefore a weak paradox, and we shall see a question arises over the exact relation of our model to the paradox that our ancestors had in mind.

Nevertheless, the fact that a version of it can be given a formal model shows the easy dismissal may be too quick. Our supertask is set in a one-dimensional Newtonian universe without gravity, containing point particles with unit mass.

Nothing turns on it being one-dimensional, but all the action happens in one dimension so it might as well be. Space and time are continuous and we use a reference frame with a spatial x -axis and a temporal t -axis. Particles have continuous paths; have inertia, so they continue at uniform velocity unless and until colliding with another; are impenetrable, so if a particle is on one side of another it can never reach the other side.

Collisions are perfectly elastic so result in particles exchanging velocities. We have two countably infinite pluralities of particles, which I shall call the M s and the F s.

I give here a picture that I hope is an aid to the reader. This and the later pictures use blue for Ms and purple for Fs , arrows to represent velocity, and are not to scale Fig. So our initial condition is based on well known examples in the literature investigating puzzling phenomena in classical particle dynamics. Individually, then, the Ms and Fs are possible. Can they co-exist? Footnote 11 This shows that there is nothing objectionable per se about a universe in which an infinitude of stationary particles coexists with an infinitude of particles in motion nor need such coexistence imply obscurity about the future of that universe.

Granted the cases in the literature, this other universe seems also possible and that alone proves the possible co-existence of a pair of pluralities like the Ms and Fs.

Finally, we should note that there is nothing special about the initial condition of our Ms and F s being initial. So the initial condition is possible. The consequence of the initial condition is that the M s and F s will undergo a series of collisions, which for brevity I will call the meeting of the M s and F s. What happens when the M s and F s meet? This results in a chain of collisions.

This should seem familiar, since it is a version of the aforementioned Beautiful Supertask. It will be useful if we can refer to the chain of collisions in the Ms initiated by the collision of p with m 1 as the wave w p. Because Ms are confined to the interval 0,1] so too is w p.

When the Ms and Fs meet, the meeting is constituted by an extended series of collisions. It looks as if the collisions constituting the meeting of the M s and F s are very complex, since each particle will be struck infinitely often by the particle to its right and will then move until it strikes the particle to its left.

In fact we can see what is going on by considering the waves of collisions that constitute the meeting of the M s and F s. Footnote 13 It may appear that one wave can catch another, i. But we cannot simply assume that the particles must be somewhere, i.

I am now going to show how, at least in the general case, this is misleading, thereby showing that the mere coincidence of infinitely many particles may not be an essential feature of the puzzle that the M s and F s meeting sets us.

So in that case there would be no temptation to think some part of the meeting was constituted by all the waves of collisions catching up at the same time and place since clearly they would have gone out of existence well to the right of where their equations of motion are equal.

So now having got clear of the essential features of the case and the way in which the meeting of the M s and F s can be understood in terms of thinking about infinitely many waves of collisions which cannot catch up with each other, we can leave behind mere mathematical detail.

Since waves do not catch up we can see that a universe consisting of an initial segment of the F s, F s n , Footnote 14 meeting M s would be like an n -fold repetition of the Beautiful Supertask. Footnote 15 There is no obvious fallacy of composition involved in taking an n -fold repetition to have the same outcome as the Beautiful Supertask. Can this be right? If we can assume a continuity principle, then the meeting of the M s and F s is the limit as n tends to infinity of the F s n meeting the M s.

In general continuity is a matter of the outcome being determined by nearby outcomes whereas discontinuity allows an outcome to be nothing like nearby outcomes. Footnote 16 Here the nearby outcomes to the meeting of the M s and F s are the meetings of the F s n and M s.

So we assume the universe under consideration and nearby possible worlds are continuous in this way. A similar argument can be formulated in terms of a within-world continuity principle instead.

Footnote 17 Each composition of F s n and M s is in a separate world and we are making a topological assumption about the structure of possible worlds, that nearby worlds are similar to one another in a special way that grounds the continuity assumption about the relation of the world containing the M s and F s and the nearby worlds of F s n and M s.

Footnote We can now prove that there is no position at which any of the M s can be. To have proved that there is no position at which any M s can be appears to be sufficient proof that the M s have gone out of existence. If there is some doubt we may appeal to Alper et al. Alper et al. Footnote 19 Footnote What has happened to the F s? So in the limit as k tends to infinity, by the argument just applied for the M s we can prove for each n that the first n constituents of the F s have gone out of existence.

Consider now a two-dimensional universe where each particle in the M s has initial x and y coordinates equal to the x coordinate in the original case. What happens to the M s and F s is the composition of these infinitely many exchanges and the upshot is that the M s and F s have changed roles: the F s are now a stationary plurality and the M s are a plurality in motion Fig.

This is plainly a case in which continuity holds, since what happens to the M s and F s just is what happens at the limit of the interactions of the F s n and M s. Furthermore, that continuity holds here supports our assumption that it holds for our supertask.

We needed the continuity assumption to conduct the critical parts of the immediately foregoing arguments. I cannot think of a simple reason why that assumption may be false. It seems reasonable but I would concede that it would require further investigation and defence.

We shall now consider some lines of analysis that do not depend on it. If we give up the assumption of continuity but retain the assumption that the meeting of the M s and F s is constituted by an infinite repetition of the Beautiful Supertask then we have another argument for the inexistence of the M s and F s from the paths of particles being continuous. It would be arbitrary to assume that what is constituted of an infinite repetition of the Beautiful Supertask could achieve what no individual or finite repetitions can.

Coalescence cannot be ruled out in particle mechanics: it happens at every collision. Footnote 24 This amounts to a different appeal to continuity: not that the meeting of F s and M s is the limit as n tends to infinity of F s n meeting M s, but only that the velocity of each particle at an instant is the limiting average velocity. Taking the velocity of a particle at an instant to be the limiting average velocity is the definition of instantaneous velocity.