Chapter 12: Q11P (page 518)
Chapter 12: Q11P (page 518)
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Get started for freeFind the invariant product of the 4-velocity with itself, . Is localid="1654516875655" timelike, spacelike, or lightlike?
(a) Equation 12.40 defines proper velocity in terms of ordinary velocity. Invert that equation to get the formula for u in terms of .
(b) What is the relation between proper velocity and rapidity (Eq. 12.34)? Assume the velocity is along the x direction, and find as a function of .
Obtain the continuity equation (Eq. 12.126) directly from Maxwell’s equations (Eq. 12.127).
In classical mechanics, Newton’s law can be written in the more familiar form . The relativistic equation, , cannot be so simply expressed. Show, rather, that
where is the ordinary acceleration.
The coordinates of event Aare and the coordinates of event B are. Assuming the displacement between them is spacelike, find the velocity of the system in which they are simultaneous.
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