- #1
James MC
- 174
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The most common definition of mass, at least in the Newtonian context, is in terms of a measure of inertia: The mass of an object is a measure of, and gives rise to, its resistance to changes in motion.
F=MA presumably quantifies this idea of inertial mass.
I'm wondering whether any property (at all) in special relativity exactly fits this definition, and therefore deserves the label "inertial mass".
In relativity, F=MA no longer holds, because the relationship between F and A depends on the orientation of F with respect to V. When F and V are perpendicular, F=##\gamma##MA, and when F and V are parallel, F=##\gamma^3##MA.
Consider a spaceship firing its constant-thrust engine (constant F in the direction of V); even though F and M are constant, A continually descreases such that v never reaches C. (Incidently, if you understand how merely cubing gamma achieves this, please say.) Hence, M cannot be a measure of acceleration resistance.
What, if anything, is the inertial mass, in SR? Here is one answer: the best one can say is that there is an "inertial mass" associated with the F that is perpendicular to the V, which is equal to ##\gamma##M, and there is an "inertial mass" associated with the F that is perpendicular to the V, which is equal to ##\gamma^3##M.
Is this the only way to make sense of inertial mass in SR?
F=MA presumably quantifies this idea of inertial mass.
I'm wondering whether any property (at all) in special relativity exactly fits this definition, and therefore deserves the label "inertial mass".
In relativity, F=MA no longer holds, because the relationship between F and A depends on the orientation of F with respect to V. When F and V are perpendicular, F=##\gamma##MA, and when F and V are parallel, F=##\gamma^3##MA.
Consider a spaceship firing its constant-thrust engine (constant F in the direction of V); even though F and M are constant, A continually descreases such that v never reaches C. (Incidently, if you understand how merely cubing gamma achieves this, please say.) Hence, M cannot be a measure of acceleration resistance.
What, if anything, is the inertial mass, in SR? Here is one answer: the best one can say is that there is an "inertial mass" associated with the F that is perpendicular to the V, which is equal to ##\gamma##M, and there is an "inertial mass" associated with the F that is perpendicular to the V, which is equal to ##\gamma^3##M.
Is this the only way to make sense of inertial mass in SR?