I Object Moving Faster Than Light?

[swampwiz]

I had read in the Time-Life Science Library book "Man And Space" about the possibility of a very, very ambitious mission in which an astronaut would go to a galaxy 200 million light-years away, with the spacecraft simply being accelerated at 1 g during the whole time (in the direction of the galaxy for half of a leg, then in the other direction for the other half), and thus going for the most part at nearly the speed of light as observed from the Milky Way, with the net effect that the astronaut would experience about 26 years of time pass by for each leg. This astronaut would start his trip by observing that galaxy as being 200 million light-years away, but then reach the galaxy in only 26 years, thus he would conclude that the galaxy appears to be moving at about 8 times the speed of light. What gives?

 

[BvU]

Hi Wiz,

Could you formulate your actual question a bit clearer ? 'What gives' can be replied in umpteen ways, e.g. with: it is not possible to exceed the speed of light

 

[swampwiz]

This is basically part of the "twin's paradox". Yes, the astronaut & light from the galaxy would not be exceeding the speed of light, but nonetheless the net effect of traveling near the speed of light and the increase in the length contraction would make the galaxy appear to be traveling at greater than the speed of light.

 

[BvU]

Did you read https://en.wikipedia.org/wiki/Space_travel_using_constant_acceleration ?

 

[Ibix]

This isn't the twin paradox because it's not a round trip.

I think you have length contraction wrong. To an observer in the rocket the distance between the galaxies is length contracted, sufficiently so that 26 years is enough time for the destination galaxy to reach the rocket.

We're being a bit sloppy here because the rocket frame is not inertial, but the gist of it is as above. Edit: do note that the speed of light is not constant in non-inertial frames, so the rocket observer may see the galaxy travel very quickly (whether it ever exceeds c depends on the simultaneity convention used, I suspect). It will never overtake light, however.