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]

Re: [Phys-l] how to explain relativity



On 06/17/2010 08:00 AM, chuck britton wrote:

Note that if the rocketeers agree that the (changing) accelerometers
always agree with each other
then it must be true that those in the earth frame insist that they
do NOT agree with each other.

Huh?

I assume "always" means "at all times". But whose time
are we talking about?

A major result of the analysis is that the two rocket
captains -- like the infamous traveling twins -- do not
agree as to what time it is.

We know that timekeeping in an accelerated reference frame
is tricky.

This is exactly how people get ensnared in "paradoxes" in
relativity, by assuming things that aren't true. The fact
is that clocks are like odometers. The path length i.e.
the odometric length of a path from A to B depends on the
choice of path. Similarly the elapsed time depends on the
choice of path. Terrestrial pedestrian experience suggests
that elapsed time "should" be independent of path ... but
this is not true in general. Talking about "the" time or
talking about "always" is just begging for trouble.

I recommend that each rocket captain worry about sticking
to his own acceleration schedule as a function of his own
proper time, and not worry too much about the other guy
... unless he wants to /correctly/ calculate things from
the other guy's viewpoint. Doing this calculation in an
accelerated reference frame is tricky, laborious, and
unnecessary, but it can be done.

Calculating things like rope length is much easier in the
lab frame, because the lab frame is unaccelerated. And
any Lorentz scalar (such as proper length) calculated in
the lab frame will be correct in all frames.