Question Relativistic speed question

[Topper]

Hello I have had some thoughts and a resulting question regarding hypothetical interstellar traveling...

Assumed I want to travel to Alpha Centauri and back to Earth, what is the best speed to chose, if I can travel anything between 0 and c under the condition, that I want to be back on Earth so that there is less as possible dt gone on Earth?

I mean, when I travel very slow, let's say whith a speed of 0, the dt on Earth is infinity (I will never arrive and be back). If I travel a speed of c, dt (at Earth) is also infinity (as far as I understood).
If I travel with 0.99999c, I'm back as fast as possible for the travelers point of view, but there is much dt gone at earth.

So the optimum speed has to be something between them... what is the best speed to choose?

 

[jedidia]

That's not how it works. You're not suddenly slower because you travel faster.

You'll be faster back on earth the faster you go (common sense, really). You will experience the journey as much shorter, so at your arrival you'll think that you should really have been back earlier, but you won't magically get back earlier by moving slower. There will merely be less difference between the time that passed on earth and for you, so it will seem more "normal". It will still be slower though, from both the earths and your perspective.

 

[Topper]

That's not how it works. You're not suddenly slower because you travel faster.

You'll be faster back on earth the faster you go (common sense, really). You will experience the journey as much shorter, so at your arrival you'll think that you should really have been back earlier, but you won't magically get back earlier by moving slower. There will merely be less difference between the time that passed on earth and for you, so it will seem more "normal". It will still be slower though, from both the earths and your perspective.

Ok I understand you but I don't know if I can belive this but maybe you are right....

Let's say Alpha Centauri is 4 light years away.
If I travel with 0.1c, I need 80 years to get to alpha and back right?
I gues at 10% c, we can neglect relativistic effects, so the time passed at earth is similar or am I wrong in this point?

But if you travel at 0.9999999999 c, you can't neglect relativistic effects and there are much more than 80 years passed on earth when you are back. Because I guess, If you travel at 1c, the dt passed on earth becomes infinity right? That were my thoughts...

[edit]
Ok I think I've got my mistake:
-> because I guess, If you travel at 1c, the dt passed on earth becomes infinity right? That were my thoughts...
Thats not true. If you travel with exact 1c, you exactly need 8 years to go to alpha from earth and back to earth, without any dt in the spaceship right?
Because the space dilation will effect that the distance between the systems will srink to 0 right? I know it's impossible to reach c but this is the mathematically result or isn't?

 

[donatelo200]

No, if you traveled at 0.9999999999 c to Alpha Centauri it would take ~4.37 years from Earth's perspective. However, from your perspective, it would take just over two days.

 

[jedidia]

Thats not true. If you travel with exact 1c, you exactly need 8 years to go to alpha from earth and back to earth, without any dt in the spaceship right?

Correct. It's called the Lorentz contraction, after all.

 

[Topper]

No, if you traveled at 0.9999999999 c it would take ~4.37 years from Earth's perspective. However, from your perspective, it would take much much less time to reach Alpha Centauri. However, from your perspective, it would take just over two days.

Ha that depents how you define "from Earth's perspective".
If you follow the spaceship from earth with a telescope, you will see the "arrival" 8.74 years after the start right?

But if then the spaceship travels back with c as soon as it has arrived at alpha, will you see the spaceship twice? Because you see the ship which arrived at alpha, and you see the ship which is back at earth (It has traveld back at the same speed as the signal)... That's confusing...

 

[jedidia]

But if then the spaceship travels back with c as soon as it has arrived at alpha, will you see the spaceship twice?

Mathematically yes, but since you can't travel at c, the question is moot...

 

[Thorsten]

Because you see the ship which arrived at alpha, and you see the ship which is back at earth (It has traveld back at the same speed as the signal)... That's confusing...

You may want to google the term 'light echo' in astronomy ... This is about the light from a bright sudden source (supernova) reflecting off a surrounding dust cloud, and by a geometrical effect this appears as if the light front is expanding faster than light for the viewer - because of the timing of the signal arrivals from direct vs. reflected signal.

So yeah, this is how it works.

 

[jedidia]

By the way, if you're confused about special relativity, I'd recommend this course. It's what taught me the subject many years ago.
It's a bit of a time investment, since you really have to do the mathematical examples yourself to really understand what's going on (math is very basic though, nothing that goes beyond basic trigonometry).

 

[RisingFury]

I think a ship travelling away from you at c would be completely invisible. The wavelength of any signal it emits would extend into infinity because of Doppler shift, so the frequency would be 0. So in effect, it wouldn't emit any signal. We can see that effect in action when we observe distant galaxies that are receding from Earth at nearly the speed of light and they're redshifted.

You could still know it's there, though. If the ship was between you and a star, it'd block a part of the star's light.

 

[steph]

Thinking of it, wouldn't there be a speed at which the ship's emissions would basically blend into the background radiation, for an observer left behind? Not too fast, since the same effect as if it were in front of a star would happen ,but just fast enough

 

[Urwumpe]

Thinking of it, wouldn't there be a speed at which the ship's emissions would basically blend into the background radiation, for an observer left behind? Not too fast, since the same effect as if it were in front of a star would happen ,but just fast enough

Yes. A pretty high speed but yes (But only if it flies straight away from you)

 

[Linguofreak]

Yes. A pretty high speed but yes (But only if it flies straight away from you)

Actually, relativistic time dilation contributes to the doppler effect, so for any arbitrary angle other than flying straight towards you an object can be redshifted to an arbitrary amount if it's traveling fast enough.

freq_observer = freq_source / (gamma * (1 + (v/c) cos(theta_observer)))

Where theta_observer is the angle between the path of the light arriving at the observer and the path of the source in the reference frame of the observer. Gamma goes to infinity in the limit of v going to c, so freq_observer goes to zero in that limit unless theta_observer is 180°, in which case the cosine is -1, making (1 + (v/c) cos(theta_observer))) zero.

(For anyone unfamiliar with relativity, gamma is 1/(1-(v/c)^2), where c is the speed of light)

 

[PhantomCruiser]

This kind of conversation is yet another reason why I really like this forum.