# Math Help - The Mathematical Definition of Mass

1. ## The Mathematical Definition of Mass

This one's been on my mind for a while: how does one define mass mathematically?
I know balances measure strain using a strain gauge, but strain relates to weight (force) not mass. Does that make mass a function of weight and altitude? That's pretty counter-intuitive (it'd be nicer to say weight were a function of mass and altitude).

Maybe I've overlooked one definition of mass, but all the ones I can think of stem from force or velocity. That includes molar mass, because molar mess stems from the mole concept, which stems from measurements of Avogadro's number. The only determination of Avogadro's number I know of is Perrin's, and that one depends on velocity squared.

Any ideas?

Maybe specific heat? q = C m dT

2. Mass is based up the 1kg (definition) bar in Paris.

As an SI base unit it's one of the fundamental dimensions which the other units/dimensions are based off of. For example Force is a function of mass and acceleration which in turn is mass, distance and time.
I always thought Avogadro's number was the number of species in 12 grams of carbon-12

They (COPM) are meant to be looking at how to redefine the kilogram (and hence mass).

edit: the big bang theory would suggest that energy turned into mass so it could be tenuously linked using distance, time and energy. Of course if the Higgs Boson is seen then that could be used to help define mass a little less abitrarily

3. Maybe specific heat? q = C m dT
You could although you can get an expression for mass via energy (q) and some is always lost. Nuclear physics is more accurate so I'd still look for an $m = \dfrac{E}{c^2}$ style solution since the equation is used as a shorthand for mass (for example a proton has a mass of ~931.6 MeV/c^2).

4. "mass" is not a mathematical concept so there is no "mathematical definition". There are, of course, a number of formulas, such as those given by e^(i pi) that you could use to determine the mass of an object.