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From: DSeppala on 8 Nov 2009 08:25
The following seems contradictory.
There are two identical rockets separated a distance L as measured on
the x-axis in an inertial reference frame. Let the two rockets be on
parallel lines to the x-axis. An observer in a frame moving at V
relative to the x-axis turns on the thrusters of both rockets
simultaneously as measured in his frame. As viewed in this frame the
tip of each rocket remains a distance L away from the tip of the other
rocket even as the rockets accelerate. This occurs because both
rockets undergo identical simultaneous accelerations, so as one rocket
changes position the other does the identical motion at a different
location in space as measured in this frame.
How do people on board the rockets view things? In the inertial
reference frame the rockets were initially in, the turning on of the
thrusters of each of the two rockets were not simultaneous events.
The thrusters of one rocket were turned on before the thrusters of the
other rocket. Let's say you are in the rocket where the thruster was
turned on first, and you start accelerating toward the other rocket at
some constant acceleration rate. After T seconds as measured in your
accelerating rocket, the thrusters of the other rocket are turned on
so that both of you are now accelerating in the same direction. You
note that at this time you had a closing velocity of V (you and the
other rocket were approaching each other). You know the other rocket
is identical to yours, and you are still accelerating at the same
constant rate. If the closing rate continues at least at V or
greater, after some point in time the tip of your rocket will pass the
tip of the other rocket. But we've already established that as
measured in the inertial reference frame where turning on the
thrusters were simultaneous events, the tips of the two rockets never
are at the same point in space at the same time, and hence can never
pass each other. It seems to me at some point in time the rocket that
started accelerating first must pass the other rocket.
Thanks for explaining this from the point of view of someone in the
first rocket.
David Seppala
Bastrop Texas
From: rotchm on 8 Nov 2009 10:54
Whoah... so many errors in the formulation of your question.

On Nov 8, 8:25 am, DSeppala <dsepp...(a)austin.rr.com> wrote:
> The following seems contradictory.

Yes, "seems".

> There are  two identical rockets separated a distance L as measured on
> the x-axis in an inertial reference frame.  

Ok, so both are ON the x axis. The usual config.

>Let the two rockets be on
> parallel lines to the x-axis.  

? Now you mean that they are both NOT on the x axis but on parallel
lines *to* the x axis?



>An observer in a frame moving at V
> relative to the x-axis turns on the thrusters of both rockets
> simultaneously as measured in his frame. As viewed in this frame the
> tip of each rocket remains a distance L away


? They are a distance L in which frame, the "initial" frame you
referenced or this new frame V ? make up your mind.

At this point, you must completely rephrase your problem because it is
too badly posed.

From: eric gisse on 8 Nov 2009 11:23
DSeppala wrote:

> The following seems contradictory.

Wow! David Seppala doesn't understand an example that slightly different
from the last 50,000 he has posted in the previous decade. Imagine that!

[...]
From: BURT on 8 Nov 2009 12:24
On Nov 8, 8:23 am, eric gisse <jowr.pi.nos...(a)gmail.com> wrote:
> DSeppala wrote:
> > The following seems contradictory.
>
> Wow! David Seppala doesn't understand an example that slightly different
> from the last 50,000 he has posted in the previous decade. Imagine that!
>
> [...]

You're moving ahaed faster so light has more distance to travel to
reach you. Accelerate toward light in absolute space and you get
closer so light has to travel a shorter distance. This is the cause of
the appearence of the relativity of simultaneity.

Mitch Raemsch
From: DSeppala on 8 Nov 2009 12:55
To clarify your confusion caused by my phrasing.
The two identical rockets are positioned to travel along lines
parallel to the x-axis (as if they were racing side by side once they
start accelerating). The tip of one rocket is at x = 0, and the tip
of the other is at x = L'. In another inertial reference frame that
is traveling at velocity V with respect to the inertial reference
frame the two rockets are initially in, the distance between the tips
of the rockets is measured as L. At time t0 in this moving reference
frame, observers in this frame turn the the thrusters on both rockets
simultaneously. The accelerometers on board each rocket show a
constant and identical acceleration. As measured in the moving frame
(where the thrusters were simultaneously turned on) at any instant of
time, the tips of the two rockets are always L meters apart since both
rockets simultaneously go through identical motions (but at different
points along the x-axis).
Now in the original rocket inertial frame, the thrusters weren't
turned on simultaneously. The thrusters of one rocket was turned on
before the thrusters of the other rocket. From the point of view an
observer in the first rocket, how does he describe what happens during
the constant acceleration? First he starts accelerating toward the
other rocket. Then at some point in time as measured by the first
rocket's clocks, the other rocket starts to accelerate. At time t1
(as measured by the first rocket's clocks) when the other rocket
begins its acceleration, the two rockets were approaching each other
with some velocity. As they both continue to accelerate along the x-
axis, why doesn't the tip of the first rocket ever reach the same x
position in space as the tip of the second rocket and eventually pass
the second rocket?
Hope that clarification removes your confusion.
David
On Nov 8, 9:54 am, rotchm <rot...(a)gmail.com> wrote:
> Whoah... so many errors in the formulation of your question.
>
> On Nov 8, 8:25 am, DSeppala <dsepp...(a)austin.rr.com> wrote:
>
> > The following seems contradictory.
>
> Yes, "seems".
>
> > There are  two identical rockets separated a distance L as measured on
> > the x-axis in an inertial reference frame.  
>
> Ok, so both are ON the x axis. The usual config.
>
> >Let the two rockets be on
> > parallel lines to the x-axis.  
>
> ? Now you mean that they are both NOT on the x axis but on parallel
> lines *to* the x axis?
>
> >An observer in a frame moving at V
> > relative to the x-axis turns on the thrusters of both rockets
> > simultaneously as measured in his frame. As viewed in this frame the
> > tip of each rocket remains a distance L away
>
> ? They are a distance L in which frame, the "initial" frame  you
> referenced or this new frame  V ? make up your  mind.
>
> At this point, you must completely rephrase your problem because it is
> too badly posed.

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