# Faster than light

## Main Question or Discussion Point

hi there looking for answers/explanation for this thought

if a space ship was to travel 10 light years at 75% the speed of light how long would it take(from the person inside the spaceships point off view) to travel 10 lightyears and what would be the average speed

thanks

Related Special and General Relativity News on Phys.org
russ_watters
Mentor
Here's the Lorenz factor equation: http://en.wikipedia.org/wiki/Lorentz_factor
Pluging and chugging yields a factor of about 1.5.

So if what you are looking for is using 10 ly from the stationary frame (say, measured before he left earth), he'd measure the distance traveled to be 6.67 ly and the time to get there to be 8.9 years.

how can the distance ie 10 lightyears between two stars change?

Fredrik
Staff Emeritus
Gold Member
how can the distance ie 10 lightyears between two stars change?
Because if you change your velocity, you will also change what "slice" of spacetime you think of as "space". If you're not moving relative to the stars, then what you think of as the space between them is a particular line through spacetime. When you are moving relative to the stars, then what you think of as the space between them is a different line. Both lines have endpoints on the world lines of the two stars, but they don't have the same endpoints.

You will find this sort of stuff much easier to understand if you learn about spacetime diagrams.

will it not appear to the person when he gets to point b that he has travelled faster than light,thats whats bugging me ?

thanks for the replys i will dig deeper into spacetime/lorentz info

thanks

Now comes a tricky part you should find interesting:
Lets assume the spaceship is traveling from earth to a space station.
We can ask – how fast is that space station only 6.67 ly away coming towards us in the spaceship. The math is easy 6.67 ly distance divided by the 8.9 years Russ provided as our navigator gives 0.75c just as we planned before departing Earth 75% the speed of light.

But on the space ship we can also ask “how fast are ‘we’ traveling?".
Well wrt the ship we are in we are not traveling at all we are stationary wrt that reference frame, so the question only makes sense by measuring our speed wrt to the Earth-Space Station reference frame. That can be a bit confusing because before departure we had planned on traveling 10 ly not the 6.67 ly the station is now away from use.
But as we pass Pluto we take a measure of a ten mile long distance marker to give our navigator a physical reading, so Russ can calibrate the gamma factor to be used for his near light speed trip planning. We advise Russ that the 10 mile marker measures only 6.67 miles long.
This actually makes sense – since the marker is reading as shorter me know that the actual length we will be covering, in and wrt to the Earth – Space Station frame, is still 10 ly. That length just fits into the distance we know measure to Space Station.

So for our own speed we must use the 10 ly length to be traversed in 8.9 years -- this gives our Proper Speed as 1.12c! Yep this is faster than light. This “Proper Speed” is important to our near light speed navigator. Remember although it can be “faster than light”; from our space ship the fastest things we see are Earth going away from us and the space satiation coming toward us at 0.75c nothing is observed as moving FTL. “Proper Speed” is strictly how we measure our own speed, based on our time on the space ship, wrt some other reference frame.

For more detail you can look up "Proper Velocity" on wikipedia.

Last edited:
Fredrik
Staff Emeritus
Gold Member
What happened is that he traveled from point A to point B. That's a coordinate independent fact. If you describe that using a coordinate system in which the stars are stationary, you will say that he traveled 10 light-years in 13.3 years. If you describe it using a coordinate system in which the rocket was stationary when it was going at full speed, you will say that he traveled 6.7 light-years in 8.9 years.

No matter which of the two coordinate systems you use, you won't have a reason to say that he traveled faster than light (10/13.3=6.7/8.9=0.75). It's only if you mix the two descriptions (never a good idea) that you get a weird result. The first coordinate system describes the distance as 10 light-years. The second coordinate system describes the time as 8.9 years. Divide that length with that time and you get a speed that's faster than light, but that doesn't mean anything since you got the numbers from two different coordinate systems.

when he gets to point b , the distance between a and b will still be 10 light years and he travelled it in less than 10 years?

Fredrik
Staff Emeritus
Gold Member
when he gets to point b , the distance between a and b will still be 10 light years in one coordinate system and he travelled it in less than 10 years in another coordinate system
This is exactly what I explained in my previous post. There's no coordinate system in which both of your statements are true.

will it appear to the person that he has travelled faster than light, yes /no please

russ_watters
Mentor
will it appear to the person that he has travelled faster than light, yes /no please
No, it won't.

jtbell
Mentor
Look at it this way: Suppose when the traveler starts out, a light pulse is also sent from his starting point towards his destination. From any observer's point of view, including the traveler's, the light pulse arrives at the destination before the traveler does.

will it appear to the person that he has travelled faster than light, yes /no please
No, it won't.
Hold on there Russ.
Take a look at your post #2.
You made it clear that passengers and the clocks they bring with them will experience 8.9 years as the travel to the Station 10 ly away. So when they get off and check the local mile markers and look at their watches just how is it going to “appear” to them.

Post #2 made you navigator of this little trip so when one of the little old ladies starts to freak out over traveling FTL; we are putting you in charge of explaining that the “Proper Time” she recorded on her watch and the real distance she traversed may make it “Appear” she traveled FTL. At no time during the trip looking out of any window did she ever see anything anywhere move FTL. And the appearance of a FTL change in position is consistent with the scientific “Proper Velocity” you logged for this trip. It is just part of the reality of how SR works.
(Plus don't forget to tell them to reset their watches by using the local clocks - with the info we have we don't realy know what that might be!)

Last edited:
russ_watters
Mentor
Hold on there Russ.
Take a look at your post #2.
You made it clear that passengers and the clocks they bring with them will experience 8.9 years as the travel to the Station 10 ly away. So when they get off and check the local mile markers and look at their watches just how is it going to “appear” to them.
I was quite clear - as were others - to say that there are two different distances being measured from two different frames. I said explicitly in the last sentence how far he traveled and how long it took. Again: you cannot take a distance measured from one frame and a time measured from another and calculate a speed.
Post #2 made you navigator of this little trip so when one of the little old ladies starts to freak out over traveling FTL; we are putting you in charge of explaining that the “Proper Time” she recorded on her watch and the real distance she traversed may make it “Appear” she traveled FTL. At no time during the trip looking out of any window did she ever see anything anywhere move FTL. And the appearance of a FTL change in position is consistent with the scientific “Proper Velocity” you logged for this trip. It is just part of the reality of how SR works.
I've never heard of someoneone taking a cross-country plane trip across time zones and exclaim 'wow, looks like we just traveled at 900 mph!. People understand different frames of reference in that context and never make such a calculation. That's all the problem is here.

If the OP is asking if it is possible to fool someone who doesn't understand Relativity into thinking he might have violated it, I'm sure it is. But I really think the OP is actually trying to understand Relativity and is simply missing the issue of mixing frames.

Fredrik
Staff Emeritus
Gold Member
Russ is obviously right. The answer to the question in #10 is definitely NO. There's no coordinate system such that the distance divided by the time is >c. It's 0.75c in both of the two frames that we would normally consider.

I like the example with the time zones. It's very clear. I tried to think of a good example myself yesterday, but gave up when I couldn't think of a good one in less than 10 seconds.

how can the distance ie 10 lightyears between two stars change?
Unless one or both of them accelerates the distance between them only depends on the velocity between them. But this only applies to flat spacetimes. In curved spacetimes the distance between two stars not only depends on the velocity between them but also on the resp. wordlines in spacetime. Think for instance about an apple falling from a tree or the expansion of spacetime.

Look at it this way: Suppose when the traveler starts out, a light pulse is also sent from his starting point towards his destination. From any observer's point of view, including the traveler's, the light pulse arrives at the destination before the traveler does.
from the light pulses point of view how long did it take to travell 10 lightyears?

ZapperZ
Staff Emeritus
from the light pulses point of view how long did it take to travell 10 lightyears?
Here's something you should consider before you ask that question:

If a distance in S is 10 ly, and you transform yourself to a frame S' that is moving very close to c relative to S, what would you measure the SAME distance to be in S'? If you can do this, then maybe you'll realize why your question isn't valid.

Zz.

Here's something you should consider before you ask that question:

If a distance in S is 10 ly, and you transform yourself to a frame S' that is moving very close to c relative to S, what would you measure the SAME distance to be in S'? If you can do this, then maybe you'll realize why your question isn't valid.

Zz.
S would be different if you measured it while travelling but when you get to point b it will be 10 lyrs

is it possible to travell great distances at close to the speed of light that would give you the appearance that you travelled faster than light??

yawn

ZapperZ
Staff Emeritus
S would be different if you measured it while travelling but when you get to point b it will be 10 lyrs
You do know that a "light-year" is a distance, don't you? So, if a length is 10 light-years in its proper frame S, and if S' is at, say 0.99c, what is that length observed in S'? You seem to not be able to figure out this straightforward question to understand why your question isn't valid here.

is it possible to travell great distances at close to the speed of light that would give you the appearance that you travelled faster than light??

yawn
"appearance"?

Either you can, or you can't. There's no "appearance" here. If you can work out that first part, you'll know that the answer is a definitive NO.

Zz.

Fredrik
Staff Emeritus
Gold Member
is it possible to travell great distances at close to the speed of light that would give you the appearance that you travelled faster than light??
Russ and I both said no (and explained why) when you asked the same thing earlier in the thread. Did you not believe us since you're asking the same thing again?

S would be different if you measured it while travelling but when you get to point b it will be 10 lyrs
I have also explained a couple of times why this is irrelevant, and I'm guessing Russ did too. (I didn't read every word in his replies to you, so I don't know exactly what he said). What kind of answer do you want if those explanations weren't enough?

If you didn't understand our explanations, that's OK, but it would be better to tell us what part of the explanations you had difficulties with than to just repeat your questions.

You do know that a "light-year" is a distance, don't you? So, if a length is 10 light-years in its proper frame S, and if S' is at, say 0.99c, what is that length observed in S'? You seem to not be able to figure out this straightforward question to understand why your question isn't valid here.

"appearance"?

Either you can, or you can't. There's no "appearance" here. If you can work out that first part, you'll know that the answer is a definitive NO.

Zz.
will the watch on the person show that he has taken less than or more than 10 years to travell?

when he gets to point B will the distance between point B and A still be 10lyrs??

could you answer these 2 points please without going of on a tangent i am new to this

thanks

all i want to know is if you travel a couple of thousand lyrs at close to the speed of light that you wouldnt die of old age before you got there

"i dont think you can travel FLT"

or is my understanding of this wrong?

russ_watters
Mentor
will the watch on the person show that he has taken less than or more than 10 years to travell?
Less.
when he gets to point B will the distance between point B and A still be 10lyrs??
If he measures the distance he traveled, he will measure it to be less. If he measures the distance again when he arrives and stops, it will be 10 lyr.
could you answer these 2 points please without going of on a tangent i am new to this...
You appear to be trying to push the conversation in a particular direction with a particular line of reasoning. We are not going off on a tangent, we are explaining to you why your line of reasoning is faulty.

Fredrik
Staff Emeritus
Gold Member
will the watch on the person show that he has taken less than or more than 10 years to travell?

when he gets to point B will the distance between point B and A still be 10lyrs??

could you answer these 2 points please without going of on a tangent i am new to this

thanks
all i want to know is if you travel a couple of thousand lyrs at close to the speed of light that you wouldnt die of old age before you got there

"i dont think you can travel FLT"

or is my understanding of this wrong?
I have to ask: Why do you keep asking the same questions over and over, after they have been answered many times?

LESS than 10 years.

YES, the distance will still be 10 light-years in the frame where points A and B are at rest, and NO, it won't be 10 light-years (and has never been) in the frame where the rocket was at rest during most of the trip. (There's no "absolute" answer to this question. The answer depends on what frame we're talking about. Actually the question is ill-defined since you didn't specify a frame in the question).

NO, you can't, but you can travel to a star that's 10000 light-years away in Earth's rest frame without dying of old age. Those two don't contradict each other even though at first glance it looks like they do. The reason for that can be found in most of my posts earlier in this thread.

Edit: Just testing if I can still edit this (more than 9 hours after I wrote it). Apparently I can.

Last edited: