
The Question
(Submitted July 01, 1997)
Time dilation is at least several times stated to be a function of
acceleration rather than velocity.
The Lorentz transformations do not deal with acceleration, just velocity.
I started to calculate the time dilation effect of mass and velocity as
functions of energy in the system.
I wonder if anyone has an analysis I can read. My math stops short of
tensor calculus, but I can usually comprehend other's work.
The Answer
Time dilation is a function of velocity. It is a function of the relative
velocity of two inertial reference frames. However, to get from one
reference frame to another, you have to change your velocity, you have to
accelerate.
In the twin paradox, Romulus stays home on Earth, while Remus travels at a
good fraction of lightspeed to Alpha Centauri, then turns around and comes
back. When they get back together again, they find that Remus is younger
than Romulus. However, during the out bound leg of the flight, Remus sees
Romulus aging more slowly than him, and during the return leg, Remus also
sees Romulus aging more slowly than him. Since Remus always sees Romulus
aging more slowly, how did Romulus get to be older? (Romulus always sees
Remus aging more slowly, so he has no reason to be surprised.)
The explanation is that when Remus turns around and comes back, he shifts
from a frame where Romulus is younger than Remus, to a frame where Romulus
is older. It is this changing of frames, rather than the physical effects
of acceleration, that results in Remus ending up younger than his
stayathome twin.
Understanding this type of explanation makes it easier to understand the
confusing explanations often found in books.
Tom Bridgman and David Palmer
for "Ask an Astrophysicist"
