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When a clock travels close to the speed of light as observed by us, it should tick slower.

Does this mean that, when using this clock to measure a second - it could travel much more than 300 000 km during a second? In fact, this clock could travel infinitely fast when viewed only from its own perspective?

Does this imply that if I traveled on a space ship, at the speed of 99 % of light, I would age 4 years, but could reach a destination perhaps 400 light years away?

My friends and family on earth would have perished, but the people I saw on the destination planet as I started my journey will have aged only 4 years as well.

If the last assumption is correct; it means that we could watch a launching space ship at alpha centauri, it could arrive here in just 3-4 days - appearing to travel much faster than the speed of light, without breaking the laws of relativity. We would just say that it was relativistic blue shift that made it seem to travel faster than the speed of light.

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Yes, you would age by four years and travel very very far and everyone you know would get 400000 years older. However, you, having stopped at that distant location would have to wait for about 400000 years for these events to unfold as you point your powerful telescope at the Earth. Remember that when you look far you see the past, but not the present. –  Alexey Bobrick Feb 10 at 15:32
    
This seems more like a general physics question than an astronomy question. Sure, it uses a space journey as an example (which actually sounds more like Space Exploration) but the heart of the question is general physics. –  called2voyage Feb 10 at 18:51
    
I tend to agree, the question should better be moved. –  Gerald Feb 10 at 20:15
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This question appears to be off-topic because it is about physics –  Eduardo Serra Feb 10 at 21:27
    
How do I move it? –  frodeborli Feb 11 at 9:49
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closed as off-topic by Gerald, Eduardo Serra, frodeborli, Manishearth, TildalWave Feb 15 at 10:49

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2 Answers

Let's restrict to special relativity, meaning two inertial frames moving in a Minkowski spacetime.

A clock in the first inertial frame ticks slower, when seen from the second. A clock in the second inertial frames ticks slower, when seen from the first.

Now assume, that you are fixed to one of the two inertial frames. Usually you measure velocities within your own inertial frame, meaning measuring distance and time in your inertial frame to calculate the velocity of the other frame. In this case you'll get a velocity below the speed of light.

If you measure the distance in your inertial frame, and divide this distance by the time you observe on the clock of the moving inertial frame, you'll get higher velocities, which may exceed the speed of light. But this result has only the dimension of a velocity; it is not a velocity with respect of any of the two inertial frames.

The moving observer would observe a slow-down of external events, not a speed-up. The observer would observe a speed-up only in the sense of a relativistic Doppler blue-shift when moving towards the observed object.

The people on the destination planet age the same as on the Earth, provided they don't move relative to the Earth. It's just you, since you travel that fast, the distance gets shorter, and therefore the time for the travel also gets shorter. By the Doppler shift and space contraction you'll see them age faster.

From Alpha Centauri, it's again the space contraction for the traveller, making the distance shorter. Again we have a combined space contraction/Doppler effect looking the people on Earth aging rapidly for about 4.5 years.

For people on Earth observing the travel takes 4.5 years. For the traveller it may take just a few days. With an acceleration of just 1g you could traverse the Milky Way in about 20 years, seen from the spaceship. The same travel seen from Earth would take about 100,000 years.

More on the twin paradox on Wikipedia.

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So, considering a clock starting travel today from earth, traveling to Alpha Centauri at 99.9% the speed of light. After about 4.5 years it arrives and stops. How much time would have passed on this clock? I assume that the clock will have advanced somewhere near 40 hours - making the speed of light for that clock seem to be (4.5 light years) / (40 hours) = 2.95*10^11 m/s. –  frodeborli Feb 10 at 14:52
    
To clarify; I think I am trying to use local time on proper distance. –  frodeborli Feb 10 at 15:08
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It would be 43.4 days for the clock: 4.5 years x $\sqrt{1-0.999^2}$ –  Gerald Feb 10 at 17:27
    
The distance for the clock would contract the same factor making the distance only 43.4 light days. The speed would still be 99.9% the speed of light. –  Gerald Feb 10 at 17:31
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@self. That's the twin paradox (actually no paradox), the clue is the change of inertial frames due to acceleration/deceleration: csupomona.edu/~ajm/materials/twinparadox.html –  Gerald Feb 11 at 11:10
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One is always traveling. Even if traveling at the speed of light, one is still affected by the forces. If the clock depends on gravity, then inertia will have an affect on it. If the clock uses a battery, then maybe the clock will only affect itself if nothing else is nearby.

I'm not an expert, but even at the speed of light, forces will still have an effect.

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