Mass - do we even know what it is?

Today in class we talked about a reading from chapter 3 in the Arons book.  He asked the differences between gravitational mass and inertial mass.  The participants were like, "Forget the differences, what ARE gravitational and inertial mass?"  I was like, "forget gravitational and inertial, WHAT IS MASS?"  Do we have an operational definition for mass?

No, really, do we have an operational definition for mass?  In all of the years that I've been teaching I never have come up with anything that made sense.  We have an idea of mass (at least we can say if an object has more mass than another) and even measure it in kilograms.  But what it is?

I've had to rely on the circular reasoning argument that "all matter is made of atoms and has mass" and then "mass is the amount of matter contained in an object".   These statements, unfortunately, make so sense at all!  We still don't have a good definition of mass.  WTF!

To make matters worse it turns out that we have no way to directly measure the mass of an object!  I asked in class and they suggested a balance - but that is a comparison between an already known mass based on a gravitational force; how did you establish the first mass?  Then they suggested the "inertial balance" which puts you in a position to measure the frequency of a vibrating mass and inferring the value for the mass.  Someone suggested we just push with a force and measure the acceleration; again inferring the mass.

We don't have a way to measure the mass of an object!  I am not sure that the participants have thought that deeply about mass as a concept before but we still have a long way to go with it.

I am thinking about an operation definition that allows us to use the mass but doesn't hinge on a origin.  How about this:

mass is the measurement of an object's resistance to change in motion

We know that the natural tendency of an object is to resist changes in its motion; an object at rest will tend to stay at rest and an object in motion will tend to stay in motion (in a straight line at a constant speed).  But which will resist changes more, a basketball or a bowling ball?  Obviously the bowling ball, but do we know why?  It is not because it weighs more - we're not trying to pick it up.    Its because it has more mass!  

The more mass the more resistant to changes in its motion.  We measure this in kilograms which is quite arbitrary but we've decided to go with it.  

I can't wait to see how the participants respond to this idea.