🚀 go-pugleaf

> james@reality1.UUCP (james)
>> mouse@mcgill-vision.UUCP (der Mouse)
>>> galins@trwrb.UUCP (Joseph E. Galins)

>>> So with a constant (or even increasing but finite) force, wouldn't
>>> the acceleration necessarly slow down as the rider approched 'c' and
>>> hence notice that he was in an elevator?
>> Yes, EXCEPT that as the rider views it, the acceleration is constant.
> But if the rider
> measures acceleration in terms of the observer that was left behind?

How would you suggest the rider do this without looking outside?

>> Note another difference.  If the elevator rider measures his velocity
>> with respect to "the universe", whatever that means, he will find it to
>> be steadily increasing.  The guy on the planet will not.

Well, one thing it means is looking outside the elevator.

> One other thing that confuses me about all of this.
> [description of classic twin "paradox", omitted]
> My high school physics isn't letting me in on the secret...

My college physics DOES let me in on the secret... but just how many
times should I post the same thing over and over?  Well, maybe just once
more, since this aspect of it hasn't come up in this particular
newsgroup for a while (though you'd already know the answer if you were
paying close attention to the "instant message channel" exchange).  This
is a repeat of a talk.philosophy.misc fragment, with a small correction
pointed out to me by ucbvax!brahms!weemba.

We have a stay-at-home A, and a passing traveler, B.  A says something
like "First, take the event on B's timeline that I consider simultaneous
with 'now' on my timeline.  Second, take another event on B's timeline
that I consider simultaneous with a point N seconds ago on my timeline.
B will think that M seconds have passed between these two events, and M
will be less than N." Fair enough.  But change the B's to A's in the
above statement, and it must be *just* *as* *true* when B says it.  How
can this be?  Well, note that the point on A's timeline M seconds ago
(according to A) doesn't *HAVE* to be simultaneous with the point on B's
timeline of M seconds ago (according to B).  How does it all work? See
the diagram below.  Events are 1, 2, 3, 4 and 5.  Worldlines are A and
B.  A and B cross at 3, so event 3 is on both A's and B's timeline.

        |                .     .          .   .
        |                .    .           .  .        *
        |                .   .            . .     *
   ^    |                .  .             ..  *
   |    |       A ****** 1 2 ************ 3 ************
 space  |                ..           *  ..
        |                .        *     . .
        |               ..    *        .  .
        |              . 4*           .   .
        |             5  .           .    .
        |       B *  .   .          .     .
        +-------------------------------------------------
                           time -->

Note that in this diagram, events located along the vertical dotted
lines are considered to be all simultaneous by A, and events located
along the slanted dotted lines are considered to be simultaneous by B.
This is a space-time geometric cosequence of the
generally-given-as-algebraic "laws" of special relativity.

So what have we got?  Well, the time interval 1-3 is what A considers N
seconds.  A considers 1 and 4 to be simultaneous.  The interval 5-3 is
what B considers N seconds.  B considers 5 and 2 simultaneous.  We can
see that A considers 2-3 to be less than N seconds long, B considers 4-3
to be less than N seconds long.  So, lo and behold, A thinks that B is
slower, and B thinks that A is slower.  And all because space and time
are (to a limited extent) interchangeable, just as various spatial
dimensions are.  Fancy that!

Note that all these relationships stay the same from any point of view,
whether A's, B's, or somebody else going a different constant speed.  Of
course, none of these others will agree that 1-3 or 5-3 is N seconds
long, but so what?  Even A doesn't think that 5-3 is N seconds (A thinks
it is longer!), nor does B think that 1-3 is N seconds (again, B thinks
it is longer!).

Ok.  Fine.  But how does all this hoo-hah relate to the twin "paradox"?
After all, either A or B has to be "really" slower, right?  Wrong.  As B
travels away from A, B considers events on slanted lines to be
"simultaneous".  When B accelerates to stop at some distance from A, B
has changed reference frames, and now considers events on vertical lines
to be "simultaneous".  Thus, for any stretch of the trip with no
acceleration (and with B and A moving relative to each other), both B
and A think that the other has slowed down.  But during B's
acceleration, B skips large parts of A's history, because B's line
through space-time indicating what is the "present moment" rotates, and
sweeps along a large part of A's history.  The same occurs when B
accelerates to return home.

The difference in the twin's timelines is that A didn't change inertial
frames, and B did.  Simple as that.

--
Our tool is diagram and explanation... uh, two, our TWO tools are
diagrams and explanataions, and appeal to authority... uh THREE our
THREE tools are diagrams, explanations, appeal to authority, and...
AMONG our tools ARE: diagrams, explanations, appeal to authority, and a
fanatical devotion to Physics!
                --- (NOBODY expects the RELATIVISTIC INQUISITION!)
-- 
Wayne Throop      <the-known-world>!mcnc!rti-sel!dg_rtp!throopw