# Question on speed(of light that is)

if I am traveling in a craft at 95% the speed of light relative to everything outside this ship, is it possible to travel in the same direction as the ship is moving at 95% the speed of light relative to things inside the ship? making me travel faster than the speed of light relative to things outside the ship? I know there is more to it that that like time slowing down so I would appreciate it if someone could explain exactly what is going on here.

also if this is possible, what would happen if, while both objects were at full motion at 95% the speed of light, I reached the edge of the spaceship and burst out of it's confines?

I think I remember reading something saying that while it would seem to me like I was traveling so fast inside the ship, to an observer outside I would just be traveling slightly faster than the ship? is this due to the time slowing down at speeds near light? if so does anyone know why time slows down at these speeds?

these questions have made me think of another question hope Im not overloading anyone. lets think about the twin paradox. I am traveling away from my twin at 99% the speed of light. the nearest star is 4 light years away, but if I travel away from my twin at these speeds for only minutes, then years may have passed for him. does this mean that if we could achieve speeds close to light then we could travel to these stars or other galaxies in only minutes to days relative to those inside the craft, but it would be millions or billions of years before we reached these stars relative to everyone outside the ship?

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#### dicerandom

First of all, welcome!

Yes, it is possible to travel at 0.95c relative to your ship which is traveling at 0.95c, however you are correct that outside observers will not see you as going 1.9c, instead you'll be doing more like 0.999c. This has to do with the fact that distance, simultenaity, and time scales are all measured differently by the outside observers, the observers in the ship, and you. A full conceptual explination is rather complicated unfortunately, I would refer you to the existing literature and documented thought experiments for this.

As for your second question re: the twin paradox (which really isn't a paradox by the way, that's a bad name for these things), the answer is yes, someone who is in a ship which is traveling close to c will be able to reach objects which are far away while experiencing comparitively small ammounts of time. People back on earth would see this trip as taking a much longer time, exactly how long depends on the speed of the ship and the distance traveled.

Think about this: If you were in a ship which accelerated at one earth gravity it would take you roughly 20 years to reach the center of our galaxy (that's assuming you decelerate for the second half of the trip so that you're actually stopped when you get there). To the people who stayed back on Earth tens of thousands of years would have passed.

#### jtbell

Mentor
dicerandom said:
Yes, it is possible to travel at 0.95c relative to your ship which is traveling at 0.95c, however you are correct that outside observers will not see you as going 1.9c, instead you'll be doing more like 0.999c.
More precisely, using the equation for relativistic "addition of velocities,"

$$\frac{0.95c + 0.95c}{1 + (0.95c)(0.95c)/c^2} = 0.9987c$$

Hey, you were pretty close after all.

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jtbell said:
More precisely, using the equation for relativistic "addition of velocities,"

$$\frac{0.95c + 0.95c}{1 + (0.95c)(0.95c)/c^2} = 0.9987c$$

Hey, you were pretty close after all.

In fact, to the three places he gave, .999c was spot on.

#### dicerandom

Lucky guess :rofl:

#### rbj

In fact, to the three places he gave, .999c was spot on.
wow! an Englishman in Wisconsin.

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(maybe it's me, but "spot on" sounds like an expression from the UK or Ireland.)

"Question on speed(of light that is)"

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