On 31 Aug 2005 05:04:35 -0700, "Spoonfed"
wrote:

Kim B wrote:
On 30 Aug 2005 09:11:50 -0700, "Spoonfed"
wrote:


Kim B wrote:

In the space-time diagram, any uniformly accelering object will have a
45° asymptote. Any events on the other side of this asymptote will
never be visible to the object


Any event that can be seen by an inertial observer should also be seen
by a uniformly accelerating observer sitting right next to him, passing
him, or coming to a momentary rest adjacent to him.

If that conflicts with whatever you just said, you should let me know.

Take a look at http://micki.dk/diverse/accel.jpg - it shows 4 points
accelerating, which all could belong to the same rigid rod (David, you
may have a look too!).

The event at the red dot is never seen by any of these points.

Kim

Thanks, Kim

Your diagram at http://micki.dk/diverse/accel.jpg looks very similar to
the hyperbolic arcs in the upper right quadrant of this animation:

http://www.spoonfedrelativity.com/files/world-lines.gif

While I don't know for sure that the two diagrams are derived from the
same place, I do know what the same arcs represent in my diagram, so
forgive me if this seems off-the-mark.

Take a set of simultaneous events, occurring at
(x,t) = (1,0),
(2,0),
(3,0),
(4,0)

Perform Lorentz transformations around the origin to find points
(x',t')

t' = gamma*t - v*gamma*t/c^2
x' = gamma x - v*gamma*t

(where gamma=1/sqrt(1-(v/c)^2)

By varying the velocity and plotting each new set of points, map out a
locus of points which form hyperbolic arcs which are similar to the
ones in your diagram.

Though we are varying the velocity, this is not acceleration.
Acceleration involves the passage of time. This animation applies
repeated transformations at time t=0, whereas an acceleration should
apply transformations at incrementally increased times.

I will try to interpret the red dot in this schema. Assuming there is
an observer at the origin, the red dot could represent an event in the
observer's future.

The observer accelerates until the red dot is directly above the
origin. As time goes by, the observer will see each of the four events
well before he reaches the red dot. The light from those events
travels at a 45 degree angle up and to the left, and when it crosses
the path of the observer, he will see it.

The hyperbolic lines in my diagram ARE the worldline of 4 observers on
a uniformly accelerating rod -- and none of these will ever see the
light from the read dot.

Kim