# Conservation of linear momentum (classical mechanics and special relativity)

How did Newton deduce the law of conservation of linear momentum? Can it be derived only by Newton's laws, or does it follow from practical experiments?

If the law of conservation of linear momentum could be deduced by Newton's laws, why did Einstein try to redefine the linear momentum of a particle, assuming this law is true?

• The law of conservation of linear momentum is deduced from Newton's laws. Indeed, by experiments relating to momentum provide evidence for Newton's Laws (and in many cases, are easier to test). – PyRulez Jan 10 '16 at 23:07
• Also, I presume it was Einstein's intuition. He knew his momentum should be a lot like classical momentum, and so he partially found its definition based on the fact it should be conversed. – PyRulez Jan 10 '16 at 23:08
• What has this to do with special relativity? For the relation between Newton's laws and momentum conservation, see this question and this question, I'm not sure what your precise question here is. – ACuriousMind Jan 11 '16 at 0:54
• @user1717828 I didn't really answer it. A full answer would include the derivation, and probably some other equations. – PyRulez Jan 11 '16 at 1:28

"If the law of conservation of linear momentum could be deduced by Newton's laws, why did Einstein try to redefine the linear momentum of a particle, assuming this law is true?"

Ans: No, Newton's law of conservation of momentum is not true. Einstein discovered that it is not $mv$ that is conserved, but $\gamma mv$.

• Just to add to this, Newtonian Mechanics deals with speeds much slower than the speed of light, so in the limit where $v<<c$, $\gamma \rightarrow 1$, so for Newtonian Mechanics the fact that $mv$ is conserved was a good approximation. – Sreekar Voleti Apr 23 '17 at 5:56

From Newtons second Law which tells that force equals rate of change of momentum. If external force is zero then rate of change of momentum is zero which means momentum is conserved.