Inertial Mass vs. Gravitational Mass

[runningninja]

An interesting idea that my physics teacher posed to us yesterday, and apparently one that scientists have been puzzling over for quite a while: why is the mass as a measure of inertia equal to the mass in terms of gravity in our universe? My teacher said that this doesn't need to be the case, but it just so happens to be. Why?

 

[harrylin]

An interesting idea that my physics teacher posed to us yesterday, and apparently one that scientists have been puzzling over for quite a while: why is the mass as a measure of inertia equal to the mass in terms of gravity in our universe? My teacher said that this doesn't need to be the case, but it just so happens to be. Why?

To me that always sounded (and still does) somewhat as misunderstanding. In classical mechanics it was found that both inertia and gravitation depend on "amount of matter" as measured with a balance (read Newton); by next finding equations for these effects, by definition there was only one kind of "mass". I can't find a logical reason for wonder about that simple fact.

The real question, I think, is why the inertial effect of mass is proportional to its gravitational effects (there are two); but if I correctly understand it, this is not the case in GR for fast moving objects (and if I'm mistaken, I'll be happy to hear a detailed correction!).

 

[TurtleMeister]

An interesting idea that my physics teacher posed to us yesterday, and apparently one that scientists have been puzzling over for quite a while: why is the mass as a measure of inertia equal to the mass in terms of gravity in our universe? My teacher said that this doesn't need to be the case, but it just so happens to be. Why?

I've heard statements similar to the one from your teacher. However, according to everything I've read, a violation of the equivalence principle, as it relates to active gravitational mass, would result in a violation of Newton's third law of motion and the conservation of momentum.

This wikipedia section shows the classical reasoning as to why the three different types of mass must be proportionally equivalent.
http://en.wikipedia.org/wiki/Equivalence_principle#Active.2C_passive.2C_and_inertial_masses