Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Testing time dilation



On pp. 43 and 57 in

http://www.courses.fas.harvard.edu/~phys16/handouts/textbook/ch10.pdf

a modified twin paradox is analysed. The conclusion is that, even
in the absence of accelerations, the moving clock is slower. In fact,
the trip involves an obscure episode. Clarifying it leads to the opposite

conclusion: Time dilation is incompatible with the assumption that
neither frame is more fundamental.
In A's frame, B moves to the right with a speed v:

B-> A

Also, in A's frame, C moves to the left with a speed v:

B-> A <-C

When B passes A they both set their clocks to zero (or just set their
zero-reading clocks in motion). Then B and C pass each other and C sets
his clock to read the same as B's. Finally, when C passes A, they
compare the readings of their clocks. If, at this event, A's clock
reads T_A and C's clock reads T_C, it is shown that, in A's, B's and
C's frames,

T_C = T_A / gamma

The obscure episode in this story is when "C sets his clock to read
the same as B's". It is not clear how this could happen without wasting
time. So let us simplify the problem by assuming that, as B meets C, it
just sets C's clock (which has read zero so far) in motion.
With this simplification, let C's clock read t_C as C meets A.
The time t_C characterizes the movement of C between B and A. The
respective time on A's clock is T_A / 2. Since no frame is more
fundamental than the other, the conclusion is

t_C = T_A / 2

I don't see how time dilation could be introduced without declaring
either A or C as more fundamental.

Pentcho