Is there a physical reason why conservation of momentum HAS to happen?

[Simfish]

It's a fundamental principle. But *why* does it have to happen? I can easily intuit why conservation of energy has to happen, and I can also intuit why conservation of mass has to happen. But with conservation of momentum, I can't intuit why.

 

[A. Neumaier]

It's a fundamental principle. But *why* does it have to happen? I can easily intuit why conservation of energy has to happen, and I can also intuit why conservation of mass has to happen. But with conservation of momentum, I can't intuit why.

It is a consequence of the more fundamental principle that physics doesn't depend on shifting the whole universe by some amount. This is called the translation symmetry of the theory, and leads to momentum conservation because of Noether's theorem. http://en.wikipedia.org/wiki/Noether's_theorem

 

[Geremia]

It's a fundamental principle. But *why* does it have to happen? I can easily intuit why conservation of energy has to happen, and I can also intuit why conservation of mass has to happen. But with conservation of momentum, I can't intuit why.

Because something cannot come from nothing without the action of an external agent, viz., something cannot cause itself.

 

[SprucerMoose]

I can easily intuit why conservation of energy has to happen, and I can also intuit why conservation of mass has to happen.

Why is that?

 

[vanhees71]

Obviously mass conservation is not a necessary property since it is not realized by nature. Only in the non-relativistic limit there is something like "mass conservation", but in Newtonian physics mass is a pretty subtle concept. On the most fundamental level it is the central charge of the unitary ray representations of the (universal covering of the) Galileo group that lead to physcally meaningful quantum dynamics, cf. Inönü and Wigner.

Thus, although related to symmetry principles, the mass as an observable in non-relativistic physics, plays a special role. E.g., the above considerations lead to the obviously wrong super-selection rule that forbids the superposition of states of different mass. On the other hand unstable particles exist, and the description of their decay involves the necessity to describe particles as quantum excitations with broad mass distributions as it turns out to be very natural in relativistic quantum theory, where the mass is a usual Casimir operator of the underlying symmetry group of space and time, i.e., the proper orthochronous Poincare group. Here, no conservation of mass follows.

The (approximate) conservation of mass in non-relativistic physics in the relativistic context is subsumed in the generally valid conservation of energy which follows from time-translation invariance as part of the Poincare symmetry.

 

[Cleonis]

It's a fundamental principle. But *why* does it have to happen? I can easily intuit why conservation of energy has to happen, and I can also intuit why conservation of mass has to happen. But with conservation of momentum, I can't intuit why.

I suppose you need to turn your predicament upside down. Chances are that the way you are intuiting conservation of energy is actually circular reasoning.
If anything conservation of energy is more baffling than conservation of momentum.While it's not possible to explain momentum and conservation of momentum, it is possible to put things in a bigger picture.

We have Newton's second law: F=ma
This law defines the concept of inertial mass. To find the inertial mass of a particular object you exert a precisely known force upon it, the force accelerates the object, and then m = F/a yields you the object's inertial mass.

This procedure works everywhere, and gives consistent results everywhere. The same force on the same inertial mass gives the same acceleration anytime, anywhere.

That uniformity anytime, anywhere, that is in itself sufficient to imply the law of conservation of momentum.Example:
Take two spacecraft s, A and B, floating in space, a cable connects them, they are reeling in the cable. Let A be the one who is reeling in the cable, Let B be the one that is being reeled in. The inertial mass of the two spaceships is comparable, let's say one may be up to two times more massive than the other, but no more.
Spacecraft A, who is reeling in the cable, is itself also accelerating. As you know, in space there is no such thing as digging in your heels; you can't grab space and hold on. Still, you can tug at another spacecraft , it's just that your own tugging is at the expense of accelerating yourself towards the other.

The most straightforward way to graph that reeling-in-a-cable setup is to graph each spacecraft s motion with respect to the common center of mass.
F=ma applies for both spacecraft s. The spacecraft that is the most massive will have the smallest acceleration with respect to the common center of mass. So that is the connection that I can describe. If you grant that F=ma gives consistent results anytime, anywhere, then by implication you have granted the law of conservation of momentum.

 

[cosmik debris]

I'm not sure that asking "why" questions of mother nature is the role of physics, more for a philosopher. Have you ever been cornered by a six year old who keeps asking "why"? There is no answer that will satisfy.

 

[Curl]

Its a combination of Newton's third law and Newton's second law (for the classical conservation of momentum law)

Two bodies exert equal and opposite forces on each other for the same amount of time - therefore the impulses are equal and opposite - therefore, by 2nd law, their changes in momentum are equal and opposite.

 

[eczeno]

according to the internet, chuck norris seems to have something to do with it.

 

[Drakkith]

It's a fundamental principle. But *why* does it have to happen? I can easily intuit why conservation of energy has to happen, and I can also intuit why conservation of mass has to happen. But with conservation of momentum, I can't intuit why.

Conservation of mass, energy, and momentum are all the same thing. What's so hard to understand?

 

[SprucerMoose]

I'm not sure that asking "why" questions of mother nature is the role of physics, more for a philosopher. Have you ever been cornered by a six year old who keeps asking "why"? There is no answer that will satisfy.

I was that six year old. How can you say askying "why" is not the role of physics? I think you are confusing physics with engineering. If they didn't ask the questions, why would any physicists bother investigating anything? In my opinion, all the great physicists were deeply curious about the nature of reality and asked the "why" question of mother nature frequently.

 

[element4]

Conservation of mass, energy, and momentum are all the same thing. What's so hard to understand?

Please explain how conservation of mass, energy and momentum are equivalent!

 

[Drakkith]

Please explain how conservation of mass, energy and momentum are equivalent!

They are all things that must be accounted for before and after any interaction between particles. Any loss in momentum would be a loss of energy or mass and vice versa.

 

[Redbelly98]

Its a combination of Newton's third law and Newton's second law (for the classical conservation of momentum law)

Two bodies exert equal and opposite forces on each other for the same amount of time - therefore the impulses are equal and opposite - therefore, by 2nd law, their changes in momentum are equal and opposite.

My initial thoughts were along these lines as well, but you have expressed it clearly and concisely. Seems like the best explanation here.

 

[vanhees71]

Depends on what you consider as "fundamental". From a more modern point of view, symmetry principles are the best formulation of fundamental Laws of Nature. Newton's Laws then follow to a large extent from the basic symmetries of Galilean-Newtonian space-time (the Galilei group).

Historically, of course, the discovery of the fundamental laws has been in the opposite way: Newton's Laws were first, and then the symmetry principles have been derived much later.

 

[SpectraCat]

They are all things that must be accounted for before and after any interaction between particles. Any loss in momentum would be a loss of energy or mass and vice versa.

They are certainly not the same thing. You can conserve energy without conserving momentum ... consider a stationary object that suddenly breaks apart, converting part of its internal potential energy into kinetic energy of the fragments. All that is required to conserve energy is that the summed kinetic energies of the fragments be equal to the potential energy lost by the initial object. However, we physicists know that there is another conservation at work, namely conservation of momentum, and so since the initial particle was stationary (p=0), we know that the summed momenta of all the fragments must also equal zero. For example, if there are exactly two fragments, they must travel in opposite directions to conserve momentum.

 

[cosmik debris]

They are certainly not the same thing. You can conserve energy without conserving momentum ... consider a stationary object that suddenly breaks apart, converting part of its internal potential energy into kinetic energy of the fragments. All that is required to conserve energy is that the summed kinetic energies of the fragments be equal to the potential energy lost by the initial object. However, we physicists know that there is another conservation at work, namely conservation of momentum, and so since the initial particle was stationary (p=0), we know that the summed momenta of all the fragments must also equal zero. For example, if there are exactly two fragments, they must travel in opposite directions to conserve momentum.

In spacetime they are all components of the energy-momentum vector. The length of the vector is the mass, the 0th element is E/c and the rest are momenta in each spatial direction. In 3D these concepts become separated, this is why relativity was so important.