The Force, FTL and causality

[NecronLord]

I've been unable to find a video of Brian Young talking about the Jedi Crash incident being proof of time dilation, it's not mentioned in his main one on the website or any of the youtube videos I've looked at, but it almost certainly has to be given the distance traveled.

[Adam Reynolds]

I've been unable to find a video of Brian Young talking about the Jedi Crash incident being proof of time dilation, it's not mentioned in his main one on the website or any of the youtube videos I've looked at, but it almost certainly has to be given the distance traveled.

I believe it was with regard to sublight speed traveled by Star Wars vessels. IIRC it was in the ship to ship combat page on the Federation vs Empire section. My current internet is too slow to download a half gig file to check.

[Khaat]

I think (but I've been wrong before) Grumman is tripping over the "from the frame of reference of a photon" thing: for the FTL traveler, there has been no "back in time", their [edit: temporal] frame of reference hasn't reversed, it continues in one direction. They may appear from the outside to have traveled back in time, but that's just causality breaking down.

DOCTOR: Oh. My, God! Oh, it's bigger!
RIVER: Well, yes.
DOCTOR: On the inside,
RIVER: We need to concentrate.
DOCTOR: Than it is
RIVER: I know where you're going with this, but I need you to calm down.
DOCTOR: On the outside!
RIVER: You've certainly grasped the essentials.
DOCTOR: My entire understanding of physical space has been transformed! Three-dimensional Euclidean geometry has been torn up, thrown in the air and snogged to death! My grasp of the universal constants of physical reality has been changed forever.
(River has gone down the stairs.)
DOCTOR: Sorry. I've always wanted to see that done properly.

[Paolo]

Nyrath's website has a good explanation of this. Here.

I like Atomic Rockets, but his main point at the start of the FTL section is incomplete, and in two cases outright wrong.

The technical term for time travel isn't "closed timelike curve." A CTC certainly is a class of time machine, but the name says it defines a class of geometries in which timelike trajectories intersect with their past light cone. There are also spacelike trajectories. Then there are all the trajectories in spaces that are not locally Minkowskian.

Also, chronology protection concerns paths that approach CTC. It is insufficient for determining the implausibility of wormhole-like geometries in general; for that, you need an argument that has nothing to do with causality at all.

[NecronLord]

Very interesting, you should write to him. While he's on SDN I've not seen him for a bit and he might miss this but he does update regularly.

Does it alter the point of 'FTL, causality and relativity; pick one?' It seems not to from where I am sitting, but that's a cursory glance.

[Cykeisme]

The counter-intuitive nature of how space and time relate to each other is mind-bogglingly fascinating.

I found this useful reading for a layman (it's presented in steps such that concepts are introduced early and then invoked later as it builds upon previous things taught):
http://galileoandeinstein.physics.virgi ... elist.html


Going from "The Speed of Light" through to "Time Dilation: A Worked Example" is pretty good reading.

[Paolo]

Very interesting, you should write to him. While he's on SDN I've not seen him for a bit and he might miss this but he does update regularly.

Does it alter the point of 'FTL, causality and relativity; pick one?' It seems not to from where I am sitting, but that's a cursory glance.

As you've (and AR, to be fair) state it, no (with the correction that you have to pick two). In special relativity, you're options are certainly limited to two. All spacelike motion (straight forward FTL), for example, yields at least one from of reference in which effect is perceived to be proceeded by cause regardless of whether it results in a closed trajectory. Therefore, all causal paths must be either timelike (slower than light) or light-like/null (speed of light). This is one form of acausality, one specific to local geometry of special relativity.

The issue is acausality encompasses far more than what we commonly refer to as time machines, which (in sf circles at least) means trampling over your own past light cone (i.e., closed timelike curves). These don't offend special relativity, but they do offend the principle of causality. Unfortunately, this principle--while as firm as anything can be in our direct experience--is defined largely by what we believe does not occur. An ongoing problem in physics is to find either mathematical proof or experimental evidence that a class of potentially causality violating geometries are either ruled out entirely by laws of nature or constrained by causality through some as of yet unknown mechanism.

[Paolo]

The counter-intuitive nature of how space and time relate to each other is mind-bogglingly fascinating.

I found this useful reading for a layman (it's presented in steps such that concepts are introduced early and then invoked later as it builds upon previous things taught):
http://galileoandeinstein.physics.virgi ... elist.html


Going from "The Speed of Light" through to "Time Dilation: A Worked Example" is pretty good reading.

For me, building on geometry helped. We all pretty much have at least a fair notion of how the world works based on high school geometry. From there, it's basically figuring out some tools (like vectors and matrices and operations there on) to represent that common 3 dimensional experience with a time parameter.

Then you eliminate the time parameter and introduce a fourth coordinate that is simply time scaled by the speed of light (or, stick to units where c=1 and make your life easier). From there, you start with the observation that the speed of light is constant in every reference frame, and you derive your laws of energy and momentum from there. Basically, this is the hardest leap, but once you have the foundation in linear algebra it's a hell of a lot easier to make the jump. I recommend MIT'S 18.06 OCW, and the [url=http://math.mit.edu/~gs/linearalgebra/]Strang book ain't bad{/url]. There are several free texts online as well if you search for them, many with more of a connection to geometry than Strang.

As for general relativity...well, I've yet to find a gentle introduction.

[Terralthra]

I think part of the confusion is that all of the various explanations of the possibility of breaking causality involve instantaneous communication. There's no succinct explanation of how, say, being able to go 3.0 * 10^8 m/sec breaks causality. It's easy to see how instantaneous travel or communication is a problem. It's far less clear that slightly-above-light-speed breaks it.

[Simon_Jester]

The real problem is this.

As long as there is NO way to send objects or information from event A to event B faster than light*, the mathematics of special relativity tell us that in all possible frames of reference, we can agree about whether event A or event B happened first chronologically.

If ANY degree of faster than light transportation or communication exists... special relativity is no longer consistent in this way. Different frames of reference can always be found, for any events with 'spacelike' separation, where people in one frame will think A happened after B, while people in the other frame think B happened after A.

This disagreement may not arise between your frame of reference and mine... but it may well arise if we compare my perceptions with those of a relativistic spacecraft moving nearby. Or a cosmic ray particle traveling at a few cm/s short of the speed of light.

This is in turn problematic because in special relativity there is no privileged frame of reference. There is no one perspective, position, or chosen speed that we can use as the 'master copy' to determine which event happened first. From your point of view, the question "well, what does this look like from the perspective of a cosmic ray particle zooming past at insane speeds?" may seem irrelevant. But from physics' point of view, the sequence of events observed by the fast particle is as valid as the sequence of events observed by you... and neither can be said in an objective sense to be 'illusory' or anything like that.

So in effect, if FTL travel is possible, special relativity informs us that A happens before B, and B happens before A, and that both these descriptions of the sequence of events are equally true at the same time, with no way of telling in any 'objective' sense which is right and which is wrong, because they're both right!

This leads to logical contradictions, and to the 'causality' breaking in the famous "relativity, causality, FTL' trio.

The only way for this to be bypassed is if the way special relativity interprets and explains causality is completely wrong, which seems... a bit unlikely. There are other reasons to think this interpretation is correct.
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*Note that an "event" comes with specification of both time and space.