Is it possible for momentum to be conserved in one direction and not in other directions? Explain your answers with reasons. This was the question given to my classmates and I to solve. However my group and I had several very different takes on it, and I was wondering if someone could justify that I was right or explain perhaps why I am not right. My take on it Quantum mechanics proves that momentum is conserved. The assumption is that space is homogeneous in all directions - this leads to conservation of momentum. If I were to take everything in the universe, and move it to the right, then the laws of physics should still be the same. That means momentum is conserved in the x-direction. Similarly for whatever direction you want to show conservation of momentum, you would displace the universe in that direction and argue from homogenity of space that the physics stays the same. What happens is because the physics is symmetrical under the operation of moving it over a little (the Hamiltonian commutes with the displacement operator), and hence the momentum operator, which is the derivative of the displacement operator with respect to position, is also commutable with the Hamiltonian. So your state will always return the same eigenvalue (the value of definite momentum in your case) at anytime: P[H[State 1]]=H[P[State 1]]=H[momentum*State 1]= momentum*H[State 1]=momentum*State 2 (there's one detail, since the Hamiltonian H is the derivative of the time operator, and not the time operator itself, but you can show that if H commutes with another operator than U - the time operator - commutes with the operator too] Similarly conservation of angular momentum is a consequence of the isotropy of space (if I rotate the whole universe then the physics is the same), and conservation of parity is ambidextrousnes of space (if I make the mirror world of the universe - parity is actually no conserved for beta decay), and conservation of energy is...well I'm not sure I can make up a catchy label for this one - how about I call it the "patience" of space (if move time backwards a little, then the laws of physics are still the same). Classmates take on it Law of conservation of momentum: “The momentum of any closed, isolated, system does not change” It is possible for momentum to be conserved in one direction and not in the other. For example, If I were in an “isolated system” roller-blading, with no help of external forces, and were to slide into someone else in that system who was at rest, we would continue with the same momentum. If I were going 4.4 m/s, the momentum would be split between the two bodies in the system, but the momentum would remain the same as it was before I pushed the other body. In order for the momentum to be conserved in that one direction however, no external forces could have been present. If an external force acts, the system would change, and the momentum would not be conserved.