functionally faster than light.

[Didymus]

Was watching an SR lecture and the professor gave an interesting example:

 

Traveling at a speed of .99C, time dilated and space shrinks by a factor of about 7. Therefore, if I pick a point 7 lightyears away and head that way at a speed of .99C... Everyone watching me will see it take a little more than 7 years to make it. However, from my perspective, I'd see something 7 lightyears away, travel for about a year.... Then stop, seeing that I've traveled to a point 7 lightyears away in what was, to me, about 1 year (but was only 1 lightyear away while I was moving at that speed because of space contracting while I move that's way).

 

He left it off here, but, my question is.... Does this not make velocity change relative to itself? I.e. the closer youget to C, the more you accelerate past it. While an outside observer could only detect you going .99999C.... As time and space shrink, one may be able to travel megaparsecs away nearly instantly because of the perceived shrinkage of space. Thus, while light moves at C, because time is stopped, it experiences both being emitted and absorbed as instantaneous even if it were 10 billion lightyears away.

[elfmotat]

Does this not make velocity change relative to itself? I.e. the closer youget to C, the more you accelerate past it.

 

I have no idea what that's supposed to mean. In the spaceship frame the distance is 1 ly, and you measure time at its regular rate. In the Earth frame the distance is 7 ly and they notice that your clock is running slow.

[Didymus]

This traveler doesn't care about anyone else. He picks a point 7 ly away, starts moving at .99C. This 7 instantly shrinks to 1 LY, and it takes him 1 year to get to it. He stops after traveling for 1 year, space grows behind him and he's traveled 7 LY in 1 year.

 

Just a fun paradox.

[elfmotat]

This traveler doesn't care about anyone else. He picks a point 7 ly away, starts moving at .99C. This 7 instantly shrinks to 1 LY, and it takes him 1 year to get to it. He stops after traveling for 1 year, space grows behind him and he's traveled 7 LY in 1 year.

 

Just a fun paradox.

 

No, he only traveled 1 ly in a little more than a year. When he stops he's in a different inertial reference frame. You're mixing the times and distances of two different frames.

[swansont]

This traveler doesn't care about anyone else. He picks a point 7 ly away, starts moving at .99C. This 7 instantly shrinks to 1 LY, and it takes him 1 year to get to it. He stops after traveling for 1 year, space grows behind him and he's traveled 7 LY in 1 year.

 

Just a fun paradox.

 

Not a paradox at all, though. Nobody in an inertial frame sees that anything has traveled faster than c. The clock and length disagreement is calculable and straightforward.

[Moontanman]

From the point of view of the guy in the space craft he has traveled at 7xC, is this not correct?

Edited February 22, 2013 by Moontanman

[swansont]

From the point of view of the guy in the space craft he has traveled at 7xC, is this not correct?

Not while he's moving.

[Moontanman]

Not while he's moving.

 

While he is moving he experiences one year of time while he covers 7 light years... how is this not experiencing 7xc?

[imatfaal]

While he is moving he experiences one year of time while he covers 7 light years... how is this not experiencing 7xc?

 

 

he doesn't measure or experience it as 7 light years . Either it is his frame (ie moving with respect to start and finish) in which the distance isnt 7 light years or it is a frame at rest with respect to the start and finish point and it doesn't take 7 years. In no single frame is the distance 7 light year AND the time one year. I hope.

[elfmotat]

While he is moving he experiences one year of time while he covers 7 light years... how is this not experiencing 7xc?

 

You're mixing the times and distances of two equally valid frames. It seems like you think 7 ly is the "real" distance, but both distances are equally valid in their respective frames.

[Moontanman]

You're mixing the times and distances of two equally valid frames. It seems like you think 7 ly is the "real" distance, but both distances are equally valid in their respective frames.

 

 

Are you suggesting that the distance of 7 light years is relative and not an actual distance?

[swansont]

Are you suggesting that the distance of 7 light years is relative and not an actual distance?

 

All distances depend on the frame from which you measure them.

[Moontanman]

All distances depend on the frame from which you measure them.

 

 

Ok, my understanding was that time was distorted by speeds close to the speed of light not the actual distance...

[Didymus]

Basically, he stands on a planet and sees something 7 light years away. He wants to make it to that object 7 lightyears away, so he travels at .99c for about 1 year... traveling about 1 lightyear in about 1 year... stops, and looks back at his starting point 7 lightyears away.

 

While moving, he's only traveling 1 lightyear. When he stops, the entire universe expands around him changing the distance traveled to 7 lightyears.

 

Outside observers would just see him traveling 7 lightyears in 7 years. What makes this concept interesting is the change in reference frames from a single observer.

 

...now imagine you are the point being travelled to. There is no preferred frame of reference, so, when I begin traveling toward you at .99c, your speed relative to me suddenly increases to that amount. Do you see my trip taking 1 year, or 7?

Edited February 22, 2013 by Didymus

[Moontanman]

I know this is off topic but I would love to know how this applies to warp travel... The proposed warp bubble effect seems to turn this whole thing upside across...

[Didymus]

Edit for better judgement

Edited February 22, 2013 by Didymus

[md65536]

Basically, he stands on a planet and sees something 7 light years away. He wants to make it to that object 7 lightyears away, so he travels at .99c for about 1 year... traveling about 1 lightyear in about 1 year... stops, and looks back at his starting point 7 lightyears away.

Yes, but at least 7 years has elapsed on the destination object. It is functionally equivalent to having time slow for the traveler, though of course the traveler experiences time passing at a rate of 1s/s.

 

 

Using the traveler's measuring devices he's traveled 1 LY in about 1 year. Using others devices he's traveled 7 LY in about 7 years. Mixing up frames of reference doesn't make a lot of sense. The traveler could say "No, I really did that in 1 year, and look I've only aged a year!" and it's true, but you've measured it taking 7 years... the traveler can't convince you otherwise. And the traveler has measured that 7 years has passed for everyone else. Functionally, relative to the planet and destination, it's taken 7 years.

 

There are other measures of speed that are not limited by c, eg. rapidity and proper speed I think. You can use those if you want, but ordinary speed in SR is defined by measurements of distance and time from a common frame of reference.

 

I'm not suggesting futurama is predicting the future.

Science and science fiction often inspire each other. Often the idea behind some realistic sci fi is based on a scientific principle that may be decades old. Then, scientific imagining of how an idea might be implemented may borrow from the fictional imagining of it.

[swansont]

Basically, he stands on a planet and sees something 7 light years away. He wants to make it to that object 7 lightyears away, so he travels at .99c for about 1 year... traveling about 1 lightyear in about 1 year... stops, and looks back at his starting point 7 lightyears away.

 

While moving, he's only traveling 1 lightyear. When he stops, the entire universe expands around him changing the distance traveled to 7 lightyears.

 

Outside observers would just see him traveling 7 lightyears in 7 years. What makes this concept interesting is the change in reference frames from a single observer.

 

...now imagine you are the point being travelled to. There is no preferred frame of reference, so, when I begin traveling toward you at .99c, your speed relative to me suddenly increases to that amount. Do you see my trip taking 1 year, or 7?

 

I see it taking 7. Your clock is slow.

[ACG52]

Didymus, I think you did the same thing in the Alternate definitions of time thread, in that you mix frames of reference.

[Moontanman]

I see it taking 7. Your clock is slow.

I guess my mind just isn't flexible enough, it seems to be a time dilation problem not an actual distance problem...

[md65536]

One additional thought:

 

There are applications for using a traveler's clock and "rest" observer's distance to measure rate of movement: http://en.wikipedia.org/wiki/Proper_velocity#Applications

 

However, even with this measure, you're not at all functionally faster than light. Yes, you can say that the traveler covered 7 LY while aging only 1 year, but light makes the same journey without aging at all. With this measure, light's rate of movement is infinite (or undefined I guess, to be precise). So to claim "faster than light" not only do you have to mix frames of reference, you also have to compare two very different measures of speed.

 

 

... You can be faster than c in measurements where c is not the rate of light, but then that's not faster than light.

Edited February 23, 2013 by md65536

[swansont]

I guess my mind just isn't flexible enough, it seems to be a time dilation problem not an actual distance problem...

 

They are intimately connected because c is invariant. Time dilation in one frame is length contraction in the other.

[michel123456]

All these examples are completely unrealistic and we get wrong conclusions from it.

The traveler had to accelerate. acceleration is that thing that makes the transfer from earth's FOR to the traveler's FOR. in the examples there is no transformation from one FOR to the other and stating that the traveler goes at 0,99c 'instantly" is both unphysical, impossible and provokes misunderstanding.

 

the same happens when stating that the traveler "stops" and looks back to Earth. there is deceleration in order to go back to Earth's FOR, otherwise he doesn't "stop".

[swansont]

All these examples are completely unrealistic and we get wrong conclusions from it.

The traveler had to accelerate. acceleration is that thing that makes the transfer from earth's FOR to the traveler's FOR. in the examples there is no transformation from one FOR to the other and stating that the traveler goes at 0,99c 'instantly" is both unphysical, impossible and provokes misunderstanding.

 

the same happens when stating that the traveler "stops" and looks back to Earth. there is deceleration in order to go back to Earth's FOR, otherwise he doesn't "stop".

 

But the part about going 0.99 c is fine. That's not unrealistic at all.

 

The acceleration doesn't really matter all that much. If you want to integrate the time dilation over the path of the acceleration, go ahead and do it. It changes the numbers slightly, depending on what values you use, but the numbers are artificial anyway. They were chosen to simplify the problem. What more complicated numbers won't change is the underlying effect. If you're focusing on the parts we're ignoring for the sake of simplicity, you're missing the point.

[michel123456]

That reminds me an episode of looney tunes (was it the coyote and the road runner or bugs bunny?) where the main character is in a house falling from a cliff and steps out at the last moment before reaching the ground as if nothing happened, next to the crumbles of his house.

-----------------

OK forget acceleration.

So at the starting point and time T=0 you have an observer A on Earth (standing still) and an observer B traveliing at 0,99c. They both observe an object that for the observer A is 7 LY away and for observer B I guess is not.

Right from the beginning they will disagree on observations.