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

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.

• My answer to another question here : physics.stackexchange.com/questions/59448/… covers your question too. In a few words: Physics does not answer "why" . Physics starts from observations and creates axioms and mathematical models dependent on these axioms will answer questions of "how", which most "why"questions within a physics framework are really "how" questions. This question addresses one of the axioms of classical newtonian physics. The only answer is "because". Apr 4, 2013 at 13:52
• Isn't this basic acceptance a bit bad, that it's just about observation? Doesn't that mean that everything is just recorded but not explained other than down to a base cause? Apr 4, 2013 at 13:56
• Good answer though although rather disappointing. Apr 4, 2013 at 13:59
• Thats the way the cookie crumbles in physics. is not a philosophy. It is a mathematical description of the world as we find it. The ultimate "why" enters the realm of "metaphysics" Apr 4, 2013 at 13:59
• But when I ask why I am asking for a depth as to "how" they remain in motion... so that's where PML's answer comes in I guess. Apr 5, 2013 at 8:23

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.

• Great :) I will look into these and see if I can find anything else to irritate people with on this question. Apr 4, 2013 at 14:12
• @marksyzm This is a really interesting topic that is used thoroughly not only in Classical Physics but also in more advanced topics such as Quantum Mechanics, Standard Model, etc. Symmetries is the way to go so read and ask as much as you see fit. =)
– PML
Apr 4, 2013 at 14:16

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.

• Okay, so why does it keep moving? Lets say there are other things in it's field that are also in the same state but moving in the opposite direction and always dodging said ball... why do they move in one direction and the other in the other direction? Why are they moving, other than just the logic behind the Newtonian observation? Apr 4, 2013 at 13:58
• Well you could view the mass as a linked structure like a train and each particle is moving forward and backwards pushing and pulling each other. This has different names depending on what scale you use, and since I'm not a Quantum scientist, I'll just call it cohesion. Imagine yourself in a space shuttle and blowing a bubble of water or throwing a water balloon, it will keep stretching itself and then compressing itself, just like a longitudinal wave. This goes on and on, but after some time it will reduce to a quantum scale, and we make it easy for ourselves and just call it momentum.
– AED
Apr 4, 2013 at 15:14
• Obviously if you consider a train, it will stop vibrating after some time, since it dissipates its energy via friction/heat due to vibrations etcetera, but at a quantum scale, the system is more homogeneous and symmetrical (as others have pointed out) these losses reach zero and the phenomenon of conservation occurs. From a mathematical point of view, the function reaches a point of stability, where it goes in cycles and settles to a certain 'mode', where it features a certain threshold in order to be influenced and change this 'mode'.
– AED
Apr 4, 2013 at 15:33
• Does that have anything to do with this? en.wikipedia.org/wiki/Geodesic_(general_relativity) Apr 4, 2013 at 19:11
• It could be, geodesics involve continuous motion. Though I think that might be a too concrete concept for this topic - unless geodesics are also observed at quantum level. In reality there are always losses due to friction due to its environment, but I don't think a force on a mass alone will increase friction or entropy (as with the example of a mass in space). I think to understand this, you have to understand quantum theory - in my oppinion it all boils down to that. So everyday forces, lead to vibrations, which in turn lead to attribute changes at quantum level, thus causing momentum.
– AED
Apr 10, 2013 at 0:37

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.

• I agree about K - thanks for updating me on that though Apr 4, 2013 at 14:16

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.

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.

• Isn't this just the same as simple acceptance of the third and first law then? How does this work in (sorry to bring this which I know little about) string theory, where waves of quarks move (again little knowledge) along to maintain movement... surely something is involved there, where things are moving along? I know it is contradictory to the understanding that it doesn't need anything to keep on moving but then that doesn't hold any explanation other than observation as mentioned by anna v. Apr 4, 2013 at 14:09

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....?

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.

• Doesn't quite cover it like the accepted answer of supersymmetry does. This is just an acceptance of how something works without definition. Aug 29, 2015 at 8:00
• @marksyzm The accepted answer wasn't "because of supersymmetry" and not many physicists care for supersymmetry (one way or another) and it generally has nothing to do with classical physics. The accepted answer appeals to Lagrangians which leads to asking "why are there Lagrangians?" A Lagrangian is a better answer for "what is momentum?" Or why is it conserved. But it doesn't explain why a particle stays at constant speed. That requires that there be no interaction. Since, say, a muon at rest can decay it also doesn't carry on moving indefinitely so this shows I'm appealing to the right idea. Aug 29, 2015 at 13:49
• Yes, you're right - sorry, my mind was mixed up with another question which had more to do with the relevance of direction, reasons why magnets have poles, which pole is which and is one really doing the pull over the other and so on, not so much about continuous movement. I did mean Langrangians. Unfortunately just saying "there's nothing in the way" doesn't really give a reason - but some might say "there's no reason in physics, just observation"... which just pains me. Geodesics, on the other hand, does sound interesting. Aug 29, 2015 at 20:26
• I think that with "quantum tunnelling" (which doesn't technically exist any more) is what I was getting at - vibrations having effect through quantum states and the forces applied to the multidimensions. Aug 29, 2015 at 20:29
• @marksyzm Quantum tunnelling exists. It's how the sun can burn at such a relatively low temperature and how radioactive nuclei decay and lots of other things happen. I'm saying that things move at uniform velocity when not acted upon because things at rest stay at rest when not acted upon. And that is the true reason. And when things don't stay at rest they won't stay in uniform motion either. People get too excited by geodesics, things don't move on geodesics as often as people like to say they do. And I do think you have a bias that things need to be made to keep moving. Aug 29, 2015 at 20:40