Faster Than Light if You Want To
The effective velocity of travel in the pilot frame of reference in a speeding spaceship in special relativity is
V_effective = v/[1 - (v2/c2)]1/2,
where v is the pilot's ship
velocity in the stationary frame K, say the frame associated with the center of the galaxy.
That is, due to Lorentz contraction of the external stationary system of coordinates K, the pilot not only sees a coordinate velocity of magnitude v in his system of coordinates K', but an effective velocity of travel V_effective
that is amplified by the apparent shrinking of the external stationary system of coordinates K. That is why Einstein sometimes remarked that c plays the role of an infinite velocity in special relativity.
As v goes to c, V_effective goes to infinity.
The distance traveled according to the pilot within the external stationary system of coordinates is the integral
of V_effective*dt', where dt' is the time on the pilot clock. That is, the STAR WARS images of travel through "hyperspace" are not just completely far-fetched. With sufficiently powerful engines and the right architecture, travel to the stars should be possible using an approach which maintains an acceleration of 1G from the start of the trip to its midpoint, with reverse braking at 1G from the midpoint to the endpoint. However, the Twin Paradox results in simultaneous time travel into the future, with no realistic possibility of time travel into the past. I have software over here to compute interstellar and intergalactic travel times using the above acceleration scheme.
- James A.Green, Oct.14,2002.
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