Pentcho Valev
2011-12-08 20:16:45 UTC
A twin paradox scenario where acceleration is avoided:
http://www.people.fas.harvard.edu/~djmorin/book.html
Introduction to Classical Mechanics With Problems and Solutions, David
Morin, Cambridge University Press, Chapter 11, p. 44: "11.19. Modified
twin paradox *** Consider the following variation of the twin paradox.
A, B, and C each have a clock. In A's reference frame, B flies past A
with speed v to the right. When B passes A, they both set their clocks
to zero. Also, in A's reference frame, C starts far to the right and
moves to the left with speed v. When B and C pass each other, C sets
his clock to read the same as B's. Finally, when C passes A, they
compare the readings on their clocks. At this moment, let A's clock
read TA, and let C's clock read TC. (a) Working in A's frame, show
that TC = TA/(gamma). (b) Working in B's frame, show again that TC =
TA/(gamma). (c) Working in C's frame, show again that TC = TA/
(gamma)."
Note that in this scenario, up to the moment when C sets his clock to
read the same as B's, A has been a genuine travelling twin who has
completed the outward part of his journey in B's frame. A's clock has
been running slow relative to clocks in B's frame, as judged from B's
frame.
A will remain a genuine travelling twin in C's frame and will perform
the rest of his journey if, as C sets his clock to read the same as
B's, simultaneously (in B's frame), at the location of A, another
clock belonging to C's frame is set to read the same as another clock
belonging to B's frame (it is assumed that clocks in B's frame are
synchronized). Then, as A moves between the two clocks belonging to
C's frame, his clock is running slow as judged from C's frame.
According to Einstein's special relativity, time dilation is
RECIPROCAL. This means that, in a twin paradox scenario where
acceleration is avoided, the sedentary twin CAN be interpreted as a
travelling twin. Needless to say, such an interpretation amounts to
REDUCTIO AD ABSURDUM - at the end of the journey, either twin proves
both younger and older than his brother.
Pentcho Valev
***@yahoo.com
http://www.people.fas.harvard.edu/~djmorin/book.html
Introduction to Classical Mechanics With Problems and Solutions, David
Morin, Cambridge University Press, Chapter 11, p. 44: "11.19. Modified
twin paradox *** Consider the following variation of the twin paradox.
A, B, and C each have a clock. In A's reference frame, B flies past A
with speed v to the right. When B passes A, they both set their clocks
to zero. Also, in A's reference frame, C starts far to the right and
moves to the left with speed v. When B and C pass each other, C sets
his clock to read the same as B's. Finally, when C passes A, they
compare the readings on their clocks. At this moment, let A's clock
read TA, and let C's clock read TC. (a) Working in A's frame, show
that TC = TA/(gamma). (b) Working in B's frame, show again that TC =
TA/(gamma). (c) Working in C's frame, show again that TC = TA/
(gamma)."
Note that in this scenario, up to the moment when C sets his clock to
read the same as B's, A has been a genuine travelling twin who has
completed the outward part of his journey in B's frame. A's clock has
been running slow relative to clocks in B's frame, as judged from B's
frame.
A will remain a genuine travelling twin in C's frame and will perform
the rest of his journey if, as C sets his clock to read the same as
B's, simultaneously (in B's frame), at the location of A, another
clock belonging to C's frame is set to read the same as another clock
belonging to B's frame (it is assumed that clocks in B's frame are
synchronized). Then, as A moves between the two clocks belonging to
C's frame, his clock is running slow as judged from C's frame.
According to Einstein's special relativity, time dilation is
RECIPROCAL. This means that, in a twin paradox scenario where
acceleration is avoided, the sedentary twin CAN be interpreted as a
travelling twin. Needless to say, such an interpretation amounts to
REDUCTIO AD ABSURDUM - at the end of the journey, either twin proves
both younger and older than his brother.
Pentcho Valev
***@yahoo.com