Why is momentum conserved (or rather what makes an object carry on moving infinitely)?

Question

I know this is an incredibly simple question, but I am trying to find a very simple explanation to this other than the simple logic that energy is conserved when two items impact and bounce off each other.

The question is this: how do particles, atoms, objects just carry on moving in space in their free will (in a "vacuum")? When I am throwing a ball and let go of it (imagining that myself and the ball are in a vacuum of which I am impervious) why does it keep pushing itself forward? I know there's a logic to it that says "what's there to stop it" but really, what is keeping it going, infinitely through a real vacuum?

So there's potential energy inside it. It moves... Is it really just the simple logic that "nothing is there to stop it"? Or could there be propagation?

Edit: I can't vote up yet by the way, else I would on all these great answers! Thanks everyone.

Answer 1

Well a beautiful way to understand why would we choose a quantity and say that it is conserved is looking at symmetries.

If you look at the Euclidean space, $\mathbb R^3$, with only one particle. You clearly see that space is homogeneous, i.e., there's nothing that differs from a point in space to another (right?). Well, symmetry implies that there is a conserved quantity as the Noether's Theorem states. The quantity that is conserved due to that symmetry (space homogeneity) is what we call Momentum.

This can be readily checked if you formulate classical mechanics using the Hamilton's Principle known as Lagrangian Mechanics. For example, conservation of energy is verified by the homogeneity of time, i.e., if any instant is equivalent to any other, and Angular momentum conservation is due to isotropy of space.

More on this topic can be seen in Landau&Lifshitz Course of Theoretical Physics - Volume 1: Mechanics Chapters 1 and 2.

Answer 2

Suppose a box is pushed in a vacuum. Due to this push the box at rest starts to move. But, in a vacuum, there are no other forces which oppose the motion of the box so it will continue to move. Or to think in energy terms, once we gave the box energy there is no mechanism for the energy to transfer from the box. The energy has been "trapped" in it.

Answer 3

The idea that "kinetic energy is being used" is a false one.

Anything in motion has this kinetic energy (which you might as well call 'potential inertial energy') because it has momentum, and it is only converted into another kind of energy, when its in interaction with something else, like a collision with a mass, or the gravitational field of another mass or electromagnetic fields, for example.

Actually we all have kinetic energy at the moment, because we rotate together with the earth. But in our daily context it is pointless to mention it, that's why we say we have no kinetic energy. So it all depends on what inertial reference frame you choose.

Answer 4

From a mathematical point of view you might like to look at Noether's theorem. I have to agree with AED that the kinetic energy idea goes into the wrong direction. With respect to Noether's theorem vacuum is space where one point is no different to any other. So if there are no forces and no reference for your moving ball, it is always in the same "environment". That is sort of relativistic thinking. So from the ball's point of view it does not keep moving, but stays at rest. Then you can come back to the start and ask: why a body at rest stays at rest, and the thing starts all over again. Although that might be easier to accept.

Answer 5

I think the real reason is because if you change your velocity then everything that used to be at rest should now continue just as they did before you changed your velocity.

You can call it indifference, nothing cares how you move unless you interact with it. Or you can call it relativity.

What this does is reduce the case 1) of things at constant motion staying at constant motion to they have to do that because of the case 2) things at rest stay at rest when nothing interacts with them.

Well, why do they do that? Then you can give the potentially unsatisfying answer of where would they go? What direction? How fast would they accelerate or what would the velocity jump to or where would it teleport to? There isn't a reason for it to do something else.

Answer 6

The reason to anything cruising is nothing but the fact that acceleration is a consequence of force. In absence of any force, there cannot be an acceleration (or retardation) hence the velocity remains constant. This is linked very closely to the quintessential definition of force as being the cause of change of linear momentum, which in the absence of force remains invariably constant( ALSO PROVED by quantum mechanics and Noether's principle) and therefore, the velocity is also constant.

you need to understand that it doesn't require anything to keep it moving and your question about what keeps it moving is hence contradictory to the fact that it doesn't need anything to keep moving. You can understand it in this way that uniform motion(constant velocity) and rest are completely equivalent(and relative) and are therefore the "natural" state for any body in which the body stays when not forced out of those states. The definition of force is inseparable from the idea of inertia, i.e, unwillingness to go out of these "natural" states.

Answer 7

Energy is inversely related to stability. If something has more energy than required, it will have less stability than required. That lack of stability can be seen in the form of its motion.

The only problem here is...why is energy inversely related to stability? Maybe an intuitive answer would convince you...the BASIC law of physics states that energy can neither be created nor destroyed. So, anything cannot "gain" energy...so it must loose that in the form of lack of stability in one form or the other...

This basic law has been taken by observations! So, I guess we're back to square one....?