On Mar 12, 4:08*pm, (Daryl McCullough)
wrote:
In article ,
says...



On Mar 11, 9:08=A0pm, "
wrote:
Hello again,

Assume I take a spaceship to Alpha Centauri, which is 4 light years
away. And the ship goes so fast, that the travel time seems to me to
be one hour. Will it not seem to me that Alpha Centauri made a journey
that started at x=4[ly] and ended at x=0, during a time of one hour,
and therefore its speed was much faster than lightspeed? Where is my
mistake?

Ram.

Is there anyone interested in answering my question?

First, note that your spaceship does *not* travel faster than
light: if you sent a light signal towards Alpha Centauri at
the same moment you launched your ship, the light signal
would get there first.

What your example illustrates is that the speed of light
is only 300,000,000 meters per second if measured in an
*inertial* coordinate system (Minkowsky coordinates).
In a noninertial coordinate system, or in a curvilinear
coordinate system, the speed of light can be position-dependent
or time-dependent.

From the accelerated coordinate system of a spaceship
undergoing constant acceleration in the x-direction (as measured
using on-board accelerometers), things seem very different from
any inertial coordinate system:

1. There is an apparent "gravitational field" pushing things
towards the rear of the spaceship. This field is not constant,
but instead is stronger towards the rear of the spaceship and
weaker towards the front of the spaceship.

2. The rate at which clocks advance (and the rate at which
people get older) is position-dependent. Clocks run faster
towards the front of the spaceship, and clocks run slower
towards the rear of the spaceship.

3. The speed of a light signal is not constant; it varies
with position. In the rear of the spaceship, the speed of
light is slower, and in the front of the spaceship, the
speed of light is faster.

From the standpoint of this noninertial coordinate system,
Alpha Centauri is in "freefall" under an enormous gravitational
field (remember point 1: the apparent gravitational field is
stronger the farther you get from the rear of the spaceship).
So Alpha Centauri appears to be accelerating towards your
spaceship at an enormous rate, quickly getting up to a
speed that is much larger than 300,000,000 meters per
second.

If all this seems weird, it's because it's all just
artifacts of using weird noninertial coordinates. That's
why it's important in General Relativity especially to
get clear about which effects are physical and which
effects are artifacts of your coordinate system.

--
Daryl McCullough
Ithaca, NY

Thank you Daryl!
I think I understand. Correct me if I'm wrong: The law that says that
objects can't move faster than light only applies when you are in an
inertial frame, i.e. a frame that is not experiencing acceleration.
When you are in an accelerating frame, things CAN go faster than
light. So, for example, we on earth will correctly measure certain
photons to be traveling faster than light, since we are in an
accelerating frame. Is that true?