<p>Let's restrict to <a href="http://en.wikipedia.org/wiki/Introduction_to_special_relativity" rel="nofollow">special relativity</a>, meaning two <a href="http://en.wikipedia.org/wiki/Inertial_frame_of_reference" rel="nofollow">inertial frames</a> moving in a <a href="http://en.wikipedia.org/wiki/Minkowski_space" rel="nofollow">Minkowski spacetime</a>.</p>

<p>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.</p>

<p>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.</p>

<p>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 <em>the dimension</em> of a velocity; it is not a velocity with respect of any of the two inertial frames.</p>

<p>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 <a href="http://en.wikipedia.org/wiki/Relativistic_Doppler_effect" rel="nofollow">relativistic Doppler blue-shift</a> when moving towards the observed object.</p>

<p>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.</p>

<p>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.</p>

<p>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.</p>

<p><a href="http://en.wikipedia.org/wiki/Twin_paradox" rel="nofollow">More on the twin paradox on Wikipedia</a>.</p>

CC BY-SA 3.0
2014-02-10T14:52:49.923Z
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
CC BY-SA 3.0
2014-02-10T15:08:03.817Z
To clarify; I think I am trying to use local time on proper distance.
frodeborli
CC BY-SA 3.0
2014-02-10T17:27:45.630Z
It would be 43.4 days for the clock: 4.5 years x $\sqrt{1-0.999^2}$
Gerald
CC BY-SA 3.0
2014-02-10T17:31:04.443Z
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
CC BY-SA 3.0
2014-02-10T20:39:42.697Z
@Gerald The only thing I don't get is why would external events appear slowed down to a traveler. If stationary observer sees traveler slowed down because his time is moving very slow, wouldn't traveler see stationary observer speed up, since hit time is moving very fast.
this
CC BY-SA 3.0
2014-02-10T20:54:54.897Z
No, the way time passes is not absolute, but bound to the respective inertial frame. For the traveler the stationary observer moves. Even simultaneity is relative to the frame: http://en.wikipedia.org/wiki/Relativity_of_simultaneity
Gerald
CC BY-SA 3.0
2014-02-10T22:42:39.047Z
The wiki didn't help. :( If both see time of the other appear slower. Then if traveler sees stationary moving slower in time, how is stationary going to end up older that him. It is not logical.
this
CC BY-SA 3.0
2014-02-11T09:44:05.920Z
@self Imagine watching an analog clock on the wall. At the same time imagine moving away from it at the speed of light. The clock must appear to stop. If you hold a clock in your hand, it must also appear to stop for the other observer. This is simplified and only uses the doppler effect in 3 dimensions. Relativity uses the time-dimension in a much "deeper" way, and adds time dilation on top of the doppler effect. From these I've understood that a lot of other effects must be expected, such as length contraction and the headlight effect.
frodeborli
CC BY-SA 3.0
2014-02-11T11:10:14.817Z
@self. That's the twin paradox (actually no paradox), the clue is the change of inertial frames due to acceleration/deceleration: http://www.csupomona.edu/~ajm/materials/twinparadox.html
Gerald
CC BY-SA 3.0
2014-02-11T12:08:44.467Z
@Gerald Great link, I think I get it. It has to do with apparent space( and time ) contraction for the traveler. The time is slow for both, until the traveler starts to slow down( or accelerate ). While decelerating( changing the frame ) the stationary time is moving very fast compared to traveler.
this
CC BY-SA 3.0
2014-02-11T13:14:09.013Z
@self. ... The more distant the faster.
Gerald
CC BY-SA 3.0
2014-02-10T12:55:51.863Z
2014-02-10T17:53:26.607Z
2014-02-10T17:53:26.607Z
Gerald
<p>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.</p>

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

CC BY-SA 3.0
2014-02-15T04:37:40.230Z
2014-02-15T04:37:40.230Z
Erokhane
<p>When a clock travels close to the speed of light as observed by us, it should tick slower.</p>

<p>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?</p>

<p>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? </p>

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

<p>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.</p>

CC BY-SA 3.0
2014-02-10T15:32:43.013Z
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
CC BY-SA 3.0
2014-02-10T18:51:22.337Z
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
CC BY-SA 3.0
2014-02-10T20:15:10.493Z
I tend to agree, the question should better be moved.
Gerald
CC BY-SA 3.0
2014-02-10T21:27:42.930Z
This question appears to be off-topic because it is about physics
Eduardo Serra
CC BY-SA 3.0
2014-02-11T09:49:57.587Z
How do I move it?
frodeborli
CC BY-SA 3.0
2014-02-11T13:12:22.053Z
That can be done by moderators. Other users can just vote for migration (above some reputation count).
Gerald
<general-relativity><speed>
A clock travelling "faster than the speed of light"
frodeborli
# A clock travelling "faster than the speed of light"

(Asked by: username_0 on 2014-02-10)

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.

**Tags:** general-relativity, speed
> **Comments:**
> **username_1**: 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.  
> **username_2**: 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.  
> **username_3**: I tend to agree, the question should better be moved.  
> **username_4**: This question appears to be off-topic because it is about physics  
> **username_0**: How do I move it?  
> **username_3**: That can be done by moderators. Other users can just vote for migration (above some reputation count).  

---

## 2 answers

### Answer by username_3 on 2014-02-10. Score: 4

Let's restrict to [special relativity](http://en.wikipedia.org/wiki/Introduction_to_special_relativity), meaning two [inertial frames](http://en.wikipedia.org/wiki/Inertial_frame_of_reference) moving in a [Minkowski spacetime](http://en.wikipedia.org/wiki/Minkowski_space).

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](http://en.wikipedia.org/wiki/Relativistic_Doppler_effect) 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](http://en.wikipedia.org/wiki/Twin_paradox).

> **Comments:**
> **username_0**: 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.  
> **username_0**: To clarify; I think I am trying to use local time on proper distance.  
> **username_3**: It would be 43.4 days for the clock: 4.5 years x $\sqrt{1-0.999^2}$  
> **username_3**: 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.  
> **username_5**: @Gerald The only thing I don't get is why would external events appear slowed down to a traveler. If stationary observer sees traveler slowed down because his time is moving very slow, wouldn't traveler see stationary observer speed up, since hit time is moving very fast.  
> **username_3**: No, the way time passes is not absolute, but bound to the respective inertial frame. For the traveler the stationary observer moves. Even simultaneity is relative to the frame: http://en.wikipedia.org/wiki/Relativity_of_simultaneity  
> **username_5**: The wiki didn't help. :( If both see time of the other appear slower. Then if traveler sees stationary moving slower in time, how is stationary going to end up older that him. It is not logical.  
> **username_0**: @self Imagine watching an analog clock on the wall. At the same time imagine moving away from it at the speed of light. The clock must appear to stop. If you hold a clock in your hand, it must also appear to stop for the other observer. This is simplified and only uses the doppler effect in 3 dimensions. Relativity uses the time-dimension in a much "deeper" way, and adds time dilation on top of the doppler effect. From these I've understood that a lot of other effects must be expected, such as length contraction and the headlight effect.  
> **username_3**: @self. That's the twin paradox (actually no paradox), the clue is the change of inertial frames due to acceleration/deceleration: http://www.csupomona.edu/~ajm/materials/twinparadox.html  
> **username_5**: @Gerald Great link, I think I get it. It has to do with apparent space( and time ) contraction for the traveler. The time is slow for both, until the traveler starts to slow down( or accelerate ). While decelerating( changing the frame ) the stationary time is moving very fast compared to traveler.  
> **username_3**: @self. ... The more distant the faster.  

---

### Answer by username_6 on 2014-02-15. Score: 1

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.


---

