Subjective FTL travel (relativity thread)

[Jarvitä]

What would be the implications of that on causality, anyway? Assuming you still have to accelerate right up to within nanometers/second of c, then perform magic to cross c and find yourself on a complex time plane. Where/when would you reappear once you unmagic the ship and the velocity is below c?

 

[Fizyk]

Depends on what you do while going faster than c and on the frame of reference. That's connected to the breaking of causality, too.

The problem is, if you go faster than c in some frame of reference, there exists another frame of reference (travelling slower than c relative to that first frame) in which you are going back in time. In that frame, you start your journey before you finish it - the cause is before the effect and causality is broken.

So, if you start from Earth, perform magic and do some maneuvers while going FTL, you might find yourself travelling back in time relative to Earth (or going infinitely fast, that's possible too). With proper maneuvers, you may finish your journey at any point in spacetime (in arbitrarily short on-board time, too).

 

[jedidia]

So ftl is only possible on a complex time plane?

At this point, you're pretty much making the math used to describe the physics to the physics themselves... not a good basis. The Lorentz-equation is not in itself the problem, it just shows one of the problems nicely in an abstract way.

At this point general relativity kicks in, and that is a bit above my head. As far as I gathered, however, the problem of the Lorentz equation is resolved there, and time comes up negative. What'sjust as bad, the size of the universe as seen from the ship comes up negative too, if I'm not mistaken. navigating could get a bit tricky...

And, of course, there's the small problem that the mass of the ship undergoes a similiar "expansion" and reaches infinity if v = c, so you get into trouble long before actually reaching c.

 

[hribek]

The crew will only perceive the distance between origin and target to be much shorter than they're used to from earth, as it contracts (or, as seen from earth, the ship expands in the direction of travel).

No, it does not. The ship contracts (seen from Earth) by the exact same factor everything else contracts (seen from ship).

 

[Fizyk]

At this point general relativity kicks in, and that is a bit above my head. As far as I gathered, however, the problem of the Lorentz equation is resolved there, and time comes up negative. What'sjust as bad, the size of the universe as seen from the ship comes up negative too, if I'm not mistaken. navigating could get a bit tricky...

In general relativity it's the same problem. Simplifying it a bit, what you can always calculate is the square of the interval (let's denote it by [math]\Delta s^2[/math]) in spacetime between two events. You get positive square of interval for time-separated events and negative square for space-separated ones (or the opposite, it's a matter of convention - it's called "choosing the signature of the metric"). Depending on the convention, the actual interval is being calculated as [math]\Delta s_{actual} = \sqrt{\Delta s^2}[/math] or [math]\Delta s_{actual} = \sqrt{-\Delta s^2}[/math]. Either way, you get an imaginary number for spacelike intervals.

Now, when you have a travelling ship, starting at event A and finishing at event B, the journey can be represented as a curve in spacetime. Calculating the time that passes on the ship is equivalent to calculating the length of the curve (which is integrating the interval over that curve). This is where we run into a problem with FTL travel - we start getting imaginary numbers for the time passing aboard the ship.

It can be pretty easily fixed, though. Instead of integrating [math]\sqrt{\Delta s^2}[/math] (or with the opposite sign, depending on the convention again) we can integrate [math]\sqrt{|\Delta s^2|}[/math]. Bam, no more imaginary numbers. Everything works, time passing on a ship travelling FTL is well-defined and real. That doesn't fix the problems with causality, though, that's why this is the main issue

No, it does not. The ship contracts (seen from Earth) by the exact same factor everything else contracts (seen from ship).

True.

 

[Jarvitä]

No, it does not. The ship contracts (seen from Earth) by the exact same factor everything else contracts (seen from ship).

So you're saying you the ship perceives itself as travelling faster than light?

 

[Fizyk]

He's saying that the situation is symmetric. Relative to the ship, everything else contracts (because everything else is going at a near-c speed relative to the ship). Relative to everything else, the ship contracts, because in that frame of reference it's going at a near-c speed.

It's very similar to the situation where you are watching TV at an angle. You perceive faces of the people on screen as being "contracted" by the perspective. But, if they were also looking at you in your room, it would be you who would be "contracted" by the perspective to them (well, at least if your face was flat ).

 

[jedidia]

No, it does not. The ship contracts (seen from Earth) by the exact same factor everything else contracts (seen from ship).

ooops, sorry. Yeah, that bloody symetry always confused the heck out of me. I'm always able to just grasp it with the corners of my mind when I do all the math involved, but haven't really developed an intuition for it...

the journey can be represented as a curve in spacetime. Calculating the time that passes on the ship is equivalent to calculating the length of the curve (which is integrating the interval over that curve). This is where we run into a problem with FTL travel - we start getting imaginary numbers for the time passing aboard the ship.

And that's pretty much where I had to throw the towel, as my math sucks pretty hard :lol: