# Speed of light, observed speed while travelling at the speed of light

I was watching Discovery channel the other night, they were telling that time slows down when you travel at a higher speed. This means there is a difference between the actual speed you travel at, and the perceived speed.

Does anybody know what the perceived speed is, the speed it seems you're travelling at?

What does this imply? Does it have any meaning, in some theories perhaps, that the perceived speed is lower? Does this mean that you can never actually travel at the speed of light?

(All this is if we don't account for the fact that's impossible to reach the speed of light.)

I'm also not into physics, so try to keep it simple...

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@ Willie; so this is special-relativity? Didn't know what that meant at first, thanks. – Simon Verbeke Jul 10 '11 at 15:23

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I think you should start reading books about relativity. If you don't read anything, you will never understand anything. I recommend to start with Taylor, Wheeler "Spacetime physics". – Physicsworks Jul 10 '11 at 17:39
If I can find anything at the local library I will ;) Thanks for the suggestion – Simon Verbeke Jul 10 '11 at 20:40

## 2 Answers

I apologise, this answer as it stood originally was sloppy and flat out wrong on key points, and probably still needs attention from a physicist.

When you travel close to the speed of light, you experience less subjective time, according to the Lorentz transform. Moreover, external distances are contracted by the same transform.

The factor by which time slows down for a rapidly moving object is $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. As velocity $v$ increases it approaches equality with the speed of light, $c$, and the factor approaches infinity.

This means that if you had an arbitrarily fast spacecraft (I assume you don't) you could tour the universe in (from your reference frame) a few years, however you may return to find humanity extinct and continents in unexpected locations. You would actually perceive yourself as travelling at arbitrarily high speeds, in terms of the subjective time it takes to travel from point to point. However, in making measurements against objects you move past, you would see that your subjective velocity does not exceed the speed of light as the rest of the universe appears length-contracted. There are other limitations in your ability to enjoy your tour of the universe - if you set your sights on a star that is millions of light-years away it may well rapidly age (again, from your reference frame) and die before you get there.

References:

Lorentz factor at wikipedia

Relativistic Doppler Effect at wikipedia

The 3rd book of Tipler Physics also has a great primer on relativity, albeit with neglect of acceleration, which is critical in generating discrepant clocks between two observers a la the twin paradox.

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Wow.. This is really hard to understand (I mean it in the way of "How the *** is it possible?", not that I don't understand what you mean." – Simon Verbeke Jul 10 '11 at 16:01
– Richard Terrett Jul 10 '11 at 16:30
So, if they wouldn't move, their lifespan isn't long enough to reach us. But their great speed reduces time for their p.o.v., so they CAN reach us? Wow, very interesting – Simon Verbeke Jul 10 '11 at 16:43
@ Simon Verbeke: Yep, that's it. – Richard Terrett Jul 11 '11 at 3:19
@ Simon Verbeke: I was wrong on the 'see the external universe sped up' bit - Carl is correct that two observers moving past each other at high speed will see each others' clocks slowed down. Acceleration breaks the symmetry. – Richard Terrett Jul 11 '11 at 8:12

Your perceived speed is the same as the speed you travel at. That is, if you travel at 0.8c past the earth, people on the earth will measure your speed as 0.8c, and you will measure the speed of the earth going past you also as 0.8c. Thus you will conclude that you are traveling at 0.8c. So there is no difference between the speed you travel at and the speed you perceive that you travel at.

On the other hand, the people on the earth will see you as slowed down (relative to themselves). Similarly, you will see the people on the earth as slowed down. The two of you can't come to agreement on this because you don't have a consistent way of comparing your watches. Whichever one of you does the comparison will conclude that the other is slowed down. This is related to the fact that in relativity there is no way to determine time in an absolute fashion. It's always relative. There's no way to figure out which of you is moving and which is standing still. It is only when you get back to the earth that you might decide that it was you who was moving and it was you who was experiencing a slowing in time.

The fact that when you get back to the earth you determine that you were the one that was slowed down is only due to the fact that you were the one who changed course and returned to the earth. If instead the earth were somehow sped up and caught up with you, everything would be reversed. It would you who grew older than the people on earth.

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