On 17 Feb 2016 at 11:59, Jeffrey Schwartz wrote:

> Right, understood, but please bear with me, I'm having trouble putting
> the image in my  mind into words.
>
> Let me try this way -
> Classic Flatland analogy.
>
> From one corner of the "paper" to the other would take the Flatlander
> 7 years to travel in his N-space only ship.
> But... he has the amazing 3D drive, so it only takes 168 hours by
> traversing the 3 dimensional tunnel.
>
> To any Flatlander, the ship vanishes and reappears, and there's no way
> the light cones in the corners of the page connect.
>
> To one of us, though, looking at the paper, and the 3D space around
> it, we see the folded paper tunnel, and can see that the actual
> distance traveled across the "Fold" is less than 168 light-hours.
>
> So... since the actual travel distance is less than light by the same
> path, isn't Flatlander still in the "light cone" when he exits Fold
> and arrives at the far corner of the paper?

The problem is that spacetime *isn't* flat. and they way it is curved
is counter-intuitive.

the distance between two points in space (x1 y1 z1) and (x2 y2 z2) is
given by
d = sqrt( (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2)

The equivalent for spacetime is called interval. And of course,
involve xyzt coordinates.

i = sqrt( (t1-t2)^2 - (x1-x2)^2 - (y1-y2)^2 - (z1-z2)^2)

with time in secoinds and distances in light seconds.

The problem is that at different velocities, what is "space" and what
is "time" changes. Effectively you are rotatiung the coordinate grid
thru an angle.

The result of this is for some observers, that ship will come out of
jump *before* it enters jump.

And their point of view is just as valid as the folks who see the
events in the opposite order.

This is known as "violation of local causality".

So FTL and time travel are equivalent ways of describing the same
thing.

If causes must always precede the events they cause, then you can't
have FTL/time-travel.

If you allow them to invert the order in some frames of reference,
then you can have FTL (and time travel *will* be possible!).

There are also some "interesting" consequences of allowing this sort
of thing.

If events must have causes, but can be in either order depending on
reference frame, you still have "conservation of global causality".

And some physicists are perfectly fine with viol;ating local
causality as long as you conserve global causality.

If you violatiote golobal causality, then you get things like events
happening without causes, or their causes getting erased while the
event persists. That's the sort of thiong you get in time traval
stories where you can change the past and have the changes stick.

With global conservation, you can still "change" the past, but only
to the extent that your info about the past was missing or incorrect.

> From another angle, suppose I have a spool of fiber optic cable 300km
> long, with an input on one end and output on the other. I pulse light,
> and 1/1000 of a second later, out it comes from the other end.
>
> I set up a light that will both go into the fiber input, and will
> travel straight past the spool to a pair of co-located detectors at
> the exit end of the cable.
>
> If I define the spool as a frame of reference, then the straight beam
> is "Faster than light" and isn't in the light cone.
> If I define the straight light beam as the frame of reference, life is all good.

You haven't got "frame of reference" right. To the extent that the
cable is a "frame of reference" it's an *accelerated* frame of
reference (because the light is forced to curve in it). As such, just
like the twin (non)paradox, simultaneity and all that don't apply.

Only *un*accerlated frames of reference are equally valid. Because
there's no way to "prove" which one is moving relative to the other.

*Everyone* in *any* non-accelerated frame of reference can agree that
an accelerated frame of reference *is* accelerated and on what the
acceleration is (adjusted by the tau factor between the two
non-accelerated frames)

--
Leonard Erickson (aka shadow)
shadow at shadowgard dot com