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Originally Posted by Zanket
The equivalence principle implies that the laws of motion for a uniform gravitational field are the same as the laws of motion for a relativistic rocket.
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Can you show us how this implication works?
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Originally Posted by Zanket
To get to another galaxy within their lifetimes, the crew of a relativistic rocket must effectively exceed the speed of light.
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Why?
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Originally Posted by Zanket
This is doable thanks to length contraction.
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I thought
time was the problem.
Isn't it sufficient that the relativistic rocket's speed is close enough to
c, so that the travel time measured by the crew is less than their lifetimes?
Quote:
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Originally Posted by Zanket
For instance, when the rocket has accelerated to a velocity of sqrt(0.5) ≈ 0.7071c the crew observes length contraction to a percentage given by eq. 8.13, ≈ 0.7071.
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What happens to the time?
Quote:
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Originally Posted by Zanket
One light year as they measured before they began accelerating now measures as 0.7071 proper light years along their axis of motion. At 0.7071c a distance of 0.7071 light years is traversed in one year.
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0.7071 ly is the distance as measured by the crew.
The speed of the rocket
as measured by the crew is zero.
How do you get
one year travel time, and in what frame of reference is this time measured?
In the frame of reference of the gantry, wouldn't they take
~1.4142 years to cover
1 ly at
0.7071c speed?
Wouldn't it take
~0.293 years from the point of view of the crew?
(Of course I could have made mistakes in my calculations.)
How did you obtain those numbers?