# Now i'm getting all confused

## Main Question or Discussion Point

Rocket flies from Earth to a star, 4.5 light years away, at 8.66C (the actual numbers are irrelavent, so they might be wrong). When the rocket gets up to speed, instantly, the distance between earth and the star contracts to about 2.3 light years. So the journey only takes about 3 years. Bargain.
Then, when the rocket reaches the star and stops, the distance ebtween the star and Earth expands back to normal size - 4.5 light years.

So, the rocket has travelled 4.5 light years in only 3 years. I.e. faster than the speed of light.
This is what i dont understand. Any help would be much appreciated.

Thanks : )

## Answers and Replies

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Ich
So, the rocket has travelled 4.5 light years in only 3 years. I.e. faster than the speed of light.
Just make sure that you take distance and time from the same reference frame. An important point: there is no "reference frame of the rocket", as SR allows only inertial frames. Choose either the "moving" frame or the "stationary" frame, but don't mix them.

Doc Al
Mentor
So, the rocket has travelled 4.5 light years in only 3 years. I.e. faster than the speed of light.
As Ich says, if you stick to a single frame of reference for measuring both distance and time you'll always find that the speed is less than light speed. No one observes anything moving at greater than light speeds.

But the quantity that you calculated by mixing earth frame distance with moving rocket frame time does have its uses--it's called proper velocity (or celerity).

As Ich says, if you stick to a single frame of reference for measuring both distance and time you'll always find that the speed is less than light speed. No one observes anything moving at greater than light speeds.

But the quantity that you calculated by mixing earth frame distance with moving rocket frame time does have its uses--it's called proper velocity (or celerity).

Thanks for the replies guys. Took a break from replying because i had the lurgy and couldn't concentrate.

So.... maybe i get it now. Rocket has 3 frames. Stationary at start, moving at C, and stationary at end.

At the start and end nothing is moving, so no speed. In the moving rocket frame the length contracted universe appears to be moving at 8.66C. No problemo.

So, in the stationary rocket frame at the end, the universe has expanded and it appears that a much greater distance has been travelled. This results in an apparent 'proper' speed greater than C?

And does this mean that given speed close enough to C we could cover huge distances in much less time than we'd expect when calculating distance/speed from a stationary point of view?

And then, as the rocket's moving frame is non-intertial, do we assert that the earth is stationary, and therefore not experiencing time-dilation, so back on earth everyone is about 5 years older, while the rocket is only 3 years older. And on earth the observe the same as to them the rocket IS moving and therefore experiencing time dilation.

If, somehow, this is correct so far, then the only thing that's getting me now is why the distance covered experiences length contraction if we've already asserted that the rocket is in motion and the earth + destination point are stationary.

akarian
. When the rocket gets up to speed, instantly, the distance between earth and the star contracts to about 2.3 light years.

Thanks : )
Why do they contract?

I just had a thought...

Is it that the time dilation DOES occure with regards to the moving rocket frame observing earth, BUT, the clocks are offset by the rocket accelerating up to speed (instantly in this case) and decelerating to a stop, so that the end result looks like there was no time dilation?

Ta.

Why do they contract?
Are you asking why I think they contract, because you don't think they would? or just asking about length contraction in general?

Rocket flies from Earth to a star, 4.5 light years away, at 8.66C (the actual numbers are irrelavent, so they might be wrong). When the rocket gets up to speed, instantly, the distance between earth and the star contracts to about 2.3 light years. So the journey only takes about 3 years. Bargain.
Then, when the rocket reaches the star and stops, the distance ebtween the star and Earth expands back to normal size - 4.5 light years.

So, the rocket has travelled 4.5 light years in only 3 years. I.e. faster than the speed of light.
This is what i dont understand. Any help would be much appreciated.

Thanks : )
If by C you mean the speed of light, then you mean the rocket is moving at 0.866c because the velocity of anything with mass is always less than c.

Now if the distance is 4.5 lightyears in the Earth frame, then in the rocket frame the distance is 4.5*sqrt(1-0.866^2/c^2) = 2.25 lightyears.

The time taken according to the Earth frame is 4.5/0.866 = 5.196 years.

The time taken in the rocket frame taking time dilation into account is 5.196*sqrt(1-0.866^2/c^2) = 2.595 years.

The velocity according to the observer on the rocket is then 2.25/2.598 = 0.866c

Both agree the velocity is 0.866c and no one sees the velocity as greater than c.

He could reason that while he was travelling his clock was ticking slower than when he was stationary OR he could reason that the distance was length contracted while he travelling, but he can not be sure which.

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