# Thread: A superluminal thought experiment

1. RBG
Established Member
Join Date
Apr 2003
Posts
429

## A superluminal thought experiment

Two spaceships are situated 1 light-year apart, with Earth to be exactly midway. If they travel at the speed of light, I would assume it would take each craft half a year to reach Earth. But does that mean the ships travelled faster than the speed of light relative to each other?

RBG

(The "Of-course-not" answer is going to hurt, isn't it?)

Intuitively I would think the answer is related to who is doing the initial accelerating and who is not.

2. Of course not. But, there's much more to this. First of all, one must distinguish the words "the speed they travel at relative to each other" versus "the rate that the distance between them is changing for the central observer". That these are not the same is the whole key-- the former can never be > c, the latter is 2c here.

3. Order of Kilopi
Join Date
Dec 2004
Posts
11,832
Could someone less math-averse than I provide a simple calculation
with more realistic values than assumed in the original post? Perhaps
the two spacecraft are moving at 0.98 c relative to Earth. They
could each pass "space bouys" which have been placed at a distance
of one-half light-year from Earth, with big clocks on them so that the
passing spacecraft can determine that their initial speed and time of
passage are correct. Assume that the spacecraft first become visible
from Earth when they pass the bouys. That is-- one-half year after
they pass the bouys, observers on Earth will first see the two craft
passing the bouys. Use a speed other than 0.98 c if another value is
more convenient.

-- Jeff, in Minneapolis

4. Everyone's favorite relativistic speed is 0.8c, because the Lorentz factor then comes out simply as 1/root(1-0.82) = 5/3. The stationary observer sees the "rate of closing" of the two rockets as being 2*0.8c = 1.6c, whereas each rocket sees the other rocket approaching at a speed of 2*0.8c/(1+0.82) = 40/41 c.

The clocks on the rockets would appear to be slow by 3/5 relative to the clock on the stationary observer, and each rocket would see the central observer's clock as slow by a factor 3/5, and the other rocket's clock would be slowed to 9/41 of normal. Any problems this would appear to cause when all the clocks meet at the center are resolved by simultaneity disagreements-- each observer thinks the other is mistaken about what "now" meant globally prior to their union.

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