Solution Found!
We have seen that there are processes in which the mass of
Chapter 15, Problem 15.85(choose chapter or problem)
We have seen that there are processes in which the mass of an object varies with time. (a) Starting from (15.85), prove that dmIdto= u K1c2, where to is the object's proper time, u is its four-velocity, and K is the four-force on the object. (b) This means that the necessary and sufficient condition that a force doesn't change an object's mass is that u K = 0. It is an experimental fact that if a charged particle is at rest in an electromagnetic field (even instantaneously) then dE/dt = 0. Use this to argue that electromagnetic forces do not cause a particle's mass to change.
Questions & Answers
QUESTION:
We have seen that there are processes in which the mass of an object varies with time. (a) Starting from (15.85), prove that dmIdto= u K1c2, where to is the object's proper time, u is its four-velocity, and K is the four-force on the object. (b) This means that the necessary and sufficient condition that a force doesn't change an object's mass is that u K = 0. It is an experimental fact that if a charged particle is at rest in an electromagnetic field (even instantaneously) then dE/dt = 0. Use this to argue that electromagnetic forces do not cause a particle's mass to change.
ANSWER:Step 1 of 4
a)
Differentiating the relation \(E^2=(pc)^2+(mc^2)^2\) we find that: