Can Relativity Theories Actually Permit Faster-Than-Light Travel?

[Citizen247]

Hello, recently elsewhere on the interwebs I was subjected to a discussion on whether it is possible to travel faster the light under relativity. My general rule of thumb is that if you ever think you've found a way to travel FTL under relativity then you don't understand relativity. Especially on the internet, because some guy from somewhere with a degree in talking gibberish is unlikely to have done in their bedroom what some of the smartest physics doctorates have dedicated their lives to do in some of the most sophisticated laboratories ever built.

My dilemma is, though, that I'm fairly sure I'm wrong and don't understand relativity, even if I'm also certain I'm less wrong than others, but that's a hard position to argue a point from. I'm pretty sure trollers are going to troll, so have already written off the originator of this "argument" but I'd like to learn something myself. So was hoping that someone more knowledgeable than me could explain the following scenario presented to me as "proof" (their words) that you can travel faster than light :

A spacecraft leaves its source point at 1g and accelerates for 10 years. It then flips around and decelerates for a further 10 years at 1g. To the crew, they have traveled for 20 years but their source point is much further away than 20 ly, so they have traveled FTL.

My rough calculations indicate that the ship would be about 340ly from its source point and would have taken about 344 years to get there, according to an outside observer. My belief is that in order to come to the conclusion that the ship traveled FTL, you have to cherry pick measurements taken in different frames of reference, which makes that conclusion meaningless. The rebuttal was that this is not the case because "the ship returns to its original IRF".

I'm pretty sure this is complete nonsense, but I'm not confident enough in my own understanding to say why.

 

[Ibix]

You are right (I haven't checked your maths!). Taking the distance in one frame and the time in another is like measuring distances northwards using the north star for direction and distances east using magnetic east for direction, then wondering why your roads never quite meet up at right angles.

Edit: or, better, claiming that your roads must meet at right angles and blaming fact that they don't on your boring conventional insistence on using a set-square.

 

[Dale]

My belief is that in order to come to the conclusion that the ship traveled FTL, you have to cherry pick measurements taken in different frames of reference,

You are correct. The measurement that they are talking about is called celerity. It is the coordinate distance divided by the proper time. Speed is coordinate distance divided by coordinate time. Even though they have the same units they are different quantities. The speed is strictly less than c in an inertial frame, the celerity may be infinite.

Your friend did not find a speed faster than light, but did find a celerity faster than c.

 

[Nugatory]

To the crew, they have traveled for 20 years but their source point is much further away than 20 ly, so they have traveled FTL.

Would they have won a race with a flash of light traveling between the same points they did? No, so whatever their experience is, it's not FTL.

 

[Grinkle]

The ships crew will agree that they did not arrive at their destination ahead of any light signals sent co-incident with their departure. Think about a laser beacon on Earth that the ships crew observes as they travel and what they observe as they travel - they will never think they are moving faster than a signal received from the beacon. If the beacon is an hdmi bit stream of tv episodes, the ships crew will never stop receiving the bit stream, but they will see that the bits per second they can decode from the stream lowers as they travel. By the time they come to rest relative to the start of their journey, they will see that they are once again able to decode the hdmi bitstream at the rate expected by the broadcasters, but they will see (I think) that the accumulated lag over their journey is equivalent to the discrepancy you calculated.

So during their journey they were perhaps watching a tv episode at 1 frame per hour (or whatever) but they never outran the signal.

 

[Citizen247]

Thank you all, that helps :).

 

[Wes Tausend]

I just finished reading about FTL in my latest library book, FASTER THAN LIGHT; SUPERLUMINAL LOOPHOLES IN PHYSICS by Nick Herbert, Ph.D. (3.7 stars). He has a knack for explaining broad concepts to untrained laymen, lighter on abstract math, heavier on visual geometry.

Of course Herbert's mind may be wired a little differently from some of his experiences. While my small area library system generally has less than half the books I seek on the relativities, it has some truly odd books. This book was published way back in 1988, back in the pre-Hubble scope-explosion time, when I surmise research trends were more interested in the FTL subject. Still, I find the book seems pretty thorough on FTL and I would recommend it to further ones SR/GR and QM understandings. His earlier book, QUANTUM REALITY (4+ stars), is probably better known... and it's now on the local shelf!

Questions on the subject of FTL are never done full justice here on PF. There just isn't enough room. Thus the value of a book... to methodically explain why some pretty ingenious schemes (even such as quantum entanglement) are highly unlikely to work. No doubt biased as a leading researcher, I feel Herbert still does a pretty honest job, logically analyzing years of high end proposals.

Wes