Invariance of Newton's laws.

[Henrique Mello]

Hey, guys

 

What are the arguments that show the invariance of the First and Third laws under the galilean transforms?

[ajb]

You can just pick some coordinates and explicitly apply the Galilean transforms to Newton's laws. You can see how the second law is shown to be invariant here.

[elfmotat]

Well, the first one is very easy. Take an object moving at a constant velocity [math]v[/math] in your coordinate system (can be a vector). Now boost to a new coordinate system moving at constant velocity [math]u[/math] with respect to the original (again, can be a vector). The acceleration of the object in this coordinate system is:

 

[math]\frac{d}{dt}(v+u)=0[/math]

 

So the object is still inertial in the new inertial coordinate system.

 

 

The third law is more of a postulate that can't be "proven" one way or another, except that experiment supports it. The third law is also explicitly local, so I don't see how a boost would affect it.

[ajb]

The third law is more of a postulate that can't be "proven" one way or another, except that experiment supports it. The third law is also explicitly local, so I don't see how a boost would affect it.

Okay, but does not the fact that it is invariant under changes of inertial frame follow from the invariance of the second law? You just need to be sure that the two forces do not change under the transformations in question. This would show that the third law, if it holds in one inertial frame, will hold in all inertial frames.

 

In fact the same comment goes for all of Newton's laws. Showing that they are invariant under Galilean transformations does not really prove they are valid.