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From: KFL@MX.LCS.MIT.EDU
Newsgroups: sci.physics
Subject: Accelerating elevator
Message-ID: <255@sri-arpa.ARPA>
Date: Fri, 21-Nov-86 21:50:42 EST
Article-I.D.: sri-arpa.255
Posted: Fri Nov 21 21:50:42 1986
Date-Received: Sun, 23-Nov-86 07:01:27 EST
Lines: 134

From:  "Keith F. Lynch" <KFL@MX.LCS.MIT.EDU>

    From: ucbcad!ames!nike!ll-xn!mit-eddie!husc6!ut-sally!ut-ngp!melpad!reality1!james@UCB-Vax.arpa (james)

    Hmmm...  I take it you mean that if the rider measures acceleration in
    terms of the gravity the rider feels, then it is constant.  But if the
    rider measures acceleration in terms of the observer that was left behind?

  The observer who was left behind may be:

1) Left behind in empty space, in which case he would observe the
   elevator accelerating away from him, which it really would be.  The
   observer would be weightless because he is not accelerating and
   there are no large masses nearby.

2) Left behind in an elevator shaft on Earth, in which case he would
   observe the elevator accelerating away from him.  Actually, HE is
   accelerating away from IT, but he can't know that without peeking.
   The observer would be weightless (until he reaches the bottom of the
   shaft!) because he in unsupported.

  Once again, there is no way to tell which is the case without looking
"outside".

    I guess it all depends on how you want to define acceleration maybe?
    After all, since the rider can't see the observer recede faster than
    the speed of light, eventually the change in velocity between the rider
    and observer would have to fall off.

  This relativistic decrease in acceleration would be observed in either
case, so it can't be used to distinguish between them.

    One other thing that confuses me about all of this.  The rider takes off
    from the planet at relativistic speeds, and the observer on the planet
    sees the rider "suffer" time dilation: the rider appears to move more
    slowly through time.  ...  But what does the rider see of the planet?
    Since the planet is also receding relativisticly from the rider, the
    rider observes the planet suffering the same fate: time dilation by the
    same factor as the planetary observer measured.

    Now, when the rider arrives at the destination, the rider must conclude
    that the rider's clocks are *ahead* of the planet's, since the rider
    clearly observed the planet's clocks "slow down".  Similarly the planetary
    observer must also conclude that the rider's clocks are *behind* the
    planetary clocks.  ... it seems to me that I have to be able to view the
    situation from both the rider's standpoint and the planet's and get the
    same answers (that's what relativity is about in this example?).

  The flaw is the assumption that they ever get together again.  The
rule about clocks slowing down is strictly true only for unaccelerated
observers.  And if two unaccelerated observers start in the same place,
they will never meet eachother again.
  I know it's kind of hard to imagine that both are correct in
considering the other one's clock to be running slower that their own.
The best way to see it is to draw two perpendicular lines on a piece of
paper, one line representing time, the other line representing the
direction in space in which the two observers are seperating.  The lines
you have drawn are the space and time axes as seen by one observer.  To
represent the space and time axes seen by the other observer, draw two
other lines, which are not perpendicular, but which angle inwards from
the lines you have by the same amount.  Of course the other observer
"sees" those lines as perpendicular, and the original two as angled
inwards.
  One of my favorite thought experiments is to imagine a large set of
synchronized clocks, all at rest relative to eachother, set up at
arbitrary grid points in empty space.  Someone sitting on one of the
clocks observes a clock 186,282 miles away and observes it striking
the hour one second late, which he correctly explains as the speed of
light delay.  But now a second similar set of synchronized clocks
comes hurtling through this set.  Does the observer see these clocks
as being synchronized with eachother?  He does not.  He sees the
trailing clocks as lagging behind, and the leading clocks as being
set ahead.  But an observer at rest with respect to the second set
of clocks will see that his set are in synch and the FIRST set are not.
Which observer is right?  They both are.
  A similar paradox is the garage door paradox.  This relies on the
concept that things in rapid motion are shortened in the direction of
motion.  The driver of a very fast 10 foot long car sees his car as
still being ten feet long, but sees a garage, normally 10 feet long,
as being only 5 feet long.  The garage operator sees his garage as
being ten feet long, but sees the fast car as being foreshortened to
only five feet long.  The paradox is that the garage operator thinks
that he can have both garage doors, front and back, (briefly) closed
while the car is passing through.  But the driver is equally convinced
that he cannot pass through the garage unless both doors are open.
Think about it.  I won't answer it for now.  Remember, the rules are:

1) Motion in a straight line is relative, i.e. no experiment can show
   which state of uniform motion is at rest (from which it is concluded
   that the concept of "at rest" is bogus).  This comes from Newtonian
   physics.

2) The speed of light in a vacuum is the same to all observers.  This
   can be deduced from Maxwell's equations (1861) and was confirmed
   directly by Michelson and Morley in 1881.

    Special Relativity is the simplest theory with these as axioms.  It
can all be derived by high school algebra.  The fact that it wasn't for
over 40 years shows how reluctant people are to question things that
have been long taken for granted, such as the constancy of space and of
time.
  By the way, it can also be proven that if these axioms are true, that
sending information faster than light is not possible without reversing
causality (i.e. time travel).  SF authors would do well to accept time
travel if they postulate FTL travel, unless they instead explain which
one of the two axioms turned out to be wrong despite overwhelming
evidence.  A plausible case could be made that the cosmic background
noise defines an absolute frame of reference.  I suspect that Doug
Gwyn's vehement rejection of the cosmic background explanation for the
noise might be at least partly due to his heavy emotional investment in
relativity theory, and due to a perhaps subconscious perception that
this cosmic background presents a threat to that investement.  Then
again perhaps my eager acceptance of the cosmic background explanation
for the noise is for the same reason, since I *WANT* FTL travel to be
possible but can't bring myself to accept reverse causality.
  Of course facts are facts, and are not influenced by our hopes or
fears or misconceptions.

    When the rider returns to the planet, every cutsey story says the rider
    is much "younger" than the contemporaries left behind because of time
    dilation.

  This involves general relativity, not special relativity.  General
relativity expalins the interactions of ACCELERATING and GRAVITATING
objects, while special relativity only applies to objects moving in
straight lines at constant speeds in the absense of gravity.
  These cutesy stories are correct, according to general relativity.
  In addition to the above two axioms, general relativity has a third:

3) Acceleration is indistinguishable from gravity.

  Which is where I came in, so I'll climb down off my soapbox now.

								...Keith