Space Travel & Relativity: Is it Possible?

[mccraggen]

I had a bit of a thought experiment the other day, does relativity mean that technically you couldn’t travel faster than the speed of light to the observer. But if you were traveling from Earth to another planet, could you technically be traveling faster than the speed of light relative to the earth?

And if you did manage to be traveling faster than light relative to the Earth would this distort time to the observer and from the perspective of the earth?

 

[tnich]

I had a bit of a thought experiment the other day, does relativity mean that technically you couldn’t travel faster than the speed of light to the observer. But if you were traveling from Earth to another planet, could you technically be traveling faster than the speed of light relative to the earth?

And if you did manage to be traveling faster than light relative to the Earth would this distort time to the observer and from the perspective of the earth?

Whenever you consider questions like this, you need to ask yourself, "What is the reference frame of the observer?" In this case, is the observer traveling to another planet, stuck at home on earth, or moving in some other direction? You can even consider observers in different reference frames, so you could for example have one on Earth and one on the spacecraft going to another planet. Once you settle that, you can answer your question, and the answer is this - no matter what the reference frame of the observer, nothing can move faster than the speed of light in that reference frame.

 

[tnich]

Whenever you consider questions like this, you need to ask yourself, "What is the reference frame of the observer?" In this case, is the observer traveling to another planet, stuck at home on earth, or moving in some other direction? You can even consider observers in different reference frames, so you could for example have one on Earth and one on the spacecraft going to another planet. Once you settle that, you can answer your question, and the answer is this - no matter what the reference frame of the observer, nothing can move faster than the speed of light in that reference frame.

Now, that said, in your observer's reference frame, two objects can be moving in opposite directions each at a speed greater than 0.5C so that their relative velocity in that reference frame is greater than c.

 

[Nugatory]

Now, that said, in your observer's reference frame, two objects can be moving in opposite directions each at a speed greater than 0.5C so that their relative velocity in that reference frame is greater than c.

Careful - that's not a "relative velocity". A relative velocity is always relative to an observer who considers themselves to be at rest while the other thing is moving. If A is moving to the left at .5c relative to me, and B is moving to the right at .5c relative to me, then they are both moving at .5c relative to me and the distance between them in the frame in which I am at rest is increasing by one light-second every second... but their speed relative to one another is not (.5+.5)c. To find their relative velocity you have to ask how fast one of them is moving in a frame in which the other is at rest, and that will be .8c by the relativistic velocity addition rule.

 

[sweet springs]

Velocity addition rule
$$V/c=\frac{u/c+v/c}{1+u/c\cdot v/c}<1$$ ,where $$0<u,v<c$$,
gives speed of less than light speed because
$$(1-u/c)(1-v/c)>0$$
$$1+u/c\cdot v/c >u/c+v/c$$
$$\frac{u/c+v/c}{1+u/c\cdot v/c}<1$$

 

[mccraggen]

I have never studied physics so this may be a silly question, but if I’m already traveling at half the speed of light, and since relativity is in regards to the observer or relative reference points could I technically be stationary?

If this was the case as you moved away from one person object faster and faster your speed relative to the object would change but not your own speed perhaps relative to other objects.

I was just thinking that traveling towards something at faster than the speed of light could actually mean traveling back in time relative to the object you are traveling towards, would this be correct?

 

[sweet springs]

There's nothing like "own speed". Speed is always relative to objects. Everyone feels he/she is staying still even if he/she is on car, train or plane. Is his/her own speed is zero?

Say Two rockets between of which the Earth lies, are traveling against each other. For Earth they have speed of 0.9c and -0.9c.
For Rocket#1, Earth travels -0.9c reciprocally but Rocket#2 travels -0.99c not exceeding c.
For Rocket#2, Earth travels 0.9c reciprocally but Rocket#1 travels 0.99c not exceeding c, reciprocally to Rocket#1.

 

[Orodruin]

I have never studied physics so this may be a silly question, but if I’m already traveling at half the speed of light, and since relativity is in regards to the observer or relative reference points could I technically be stationary?

There is no such thing as “stationary” without further specification. You can only be stationary relative to something else. This is true both in classical mechanics and relativity.

I was just thinking that traveling towards something at faster than the speed of light could actually mean traveling back in time relative to the object you are traveling towards, would this be correct?

Since this is impossible in relativity you should not expect relativity to give you any answer to this. It is like asking what the traffic laws tell you to do when the stop lights show blue.

 

[Orodruin]

#7 and #8 being said, it should also be pointed out that you can tell if you are accelerating or not.