Cleonis
Gold Member
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In physics, we use the concept of mass, and we use a unit of mass.
It would appear that we must first define the concept of mass, to get to a position where we can establish a unit of mass.
Mass not rigorously defined
To my knowledge the concept of mass is not rigorously defined in Physics. We can opt to make equivalence of inertial mass and gravitational mass part of the very definition of mass, or we can choose to define mass independently. That is not codified.
(Incidentally, it's remarkable that enormous effort has gone in deciding on a definition of 'planet' that would make Pluto either a planet or not a planet, but the concept of mass is pretty much left free.)
If we want to know whether two objects have the same mass then we put them on a balance, a procedure that compares their respective gravitational masses.
Assumption of equivalence of gravitational mass and inertial mass is everywhere in our procedures. Therefore in effect equivalence of gravitational and inertial mass is part of the very definition of mass, even though there's no formal statement to that effect.
As I said, in physics defining the concept of mass is left free. Then how do physics student learn what mass is? Well, they absorb the concept; they learn by osmosis. In any discipline the most pervasive concepts tends to remain undefined, because those concepts are everywhere anyway.
In a recent thread on this forum I saw someone insisting that to define the concept of mass only the concepts momentum and velocity ought to be used. Implicitly (but nowhere explicitly) that person was arguing that the concept and unit of mass should work with the concept of inertial mass only, disregarding gravitational mass.
It would appear that we must first define the concept of mass, to get to a position where we can establish a unit of mass.
Mass not rigorously defined
To my knowledge the concept of mass is not rigorously defined in Physics. We can opt to make equivalence of inertial mass and gravitational mass part of the very definition of mass, or we can choose to define mass independently. That is not codified.
(Incidentally, it's remarkable that enormous effort has gone in deciding on a definition of 'planet' that would make Pluto either a planet or not a planet, but the concept of mass is pretty much left free.)
If we want to know whether two objects have the same mass then we put them on a balance, a procedure that compares their respective gravitational masses.
Assumption of equivalence of gravitational mass and inertial mass is everywhere in our procedures. Therefore in effect equivalence of gravitational and inertial mass is part of the very definition of mass, even though there's no formal statement to that effect.
As I said, in physics defining the concept of mass is left free. Then how do physics student learn what mass is? Well, they absorb the concept; they learn by osmosis. In any discipline the most pervasive concepts tends to remain undefined, because those concepts are everywhere anyway.
In a recent thread on this forum I saw someone insisting that to define the concept of mass only the concepts momentum and velocity ought to be used. Implicitly (but nowhere explicitly) that person was arguing that the concept and unit of mass should work with the concept of inertial mass only, disregarding gravitational mass.
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