Causality(?)/Time FTL Question

RichardGarfinkle · May 10, 2013

The hyperspace = Hell bit is sort of the premise behind the game Warhammer 40,000. Actually, Hell would be nicer.

King Neptune · May 11, 2013

No, that's what makes time travel such an interesting concept and plot device. It is malleable; you can make it do what you want.

Causality is a different matter.

As for Hell, try looking at Qabbala.

jshughes · May 11, 2013

The concept of the time cone can be applied here. You can think of it as all the points in spacetime that can be affected by an event at a given point in space time.

If we were somehow allowed to "blink" to a new point in space time nothing would be ary as long as you remained in the forward cone of the departure point.

You could see weird effects, like receiving messages from your past self, if you jump out of that cone.

Also, a cone emanating from your destination should not intersect your timeline, or reverse time cone, or you could cause a paradox. e.g. kill your grandmother before she conceives your father.

FOTSGreg · May 12, 2013

But, jshughes, if you're *blinking* to a different point in space-time, doesn't your forward time cone also change with relation to the distance *blinked*?

That is, if I'm here now and there a heartbeat later how does my change in 3-dimensional space affect my position in time.

I can see the possibility for multiple overlapping time cones and, to paraphrase a popular TV show, "a wibbly wobbly tangle" of multiple possibilities if time cones are affected by frames of reference.

RichardGarfinkle · May 13, 2013

FOTSGreg said:
But, jshughes, if you're *blinking* to a different point in space-time, doesn't your forward time cone also change with relation to the distance *blinked*?

That is, if I'm here now and there a heartbeat later how does my change in 3-dimensional space affect my position in time.

I can see the possibility for multiple overlapping time cones and, to paraphrase a popular TV show, "a wibbly wobbly tangle" of multiple possibilities if time cones are affected by frames of reference.

I fear that you're still trying to think in old fashioned Newtonian terms. Three dimensional space is not a meaningful concept in spacetime. It's not as if points in spacetime have definite coordinates assigned to them. Their coordinates are always relative to a chosen observer.

One of the consequences of relativity (I'm fudging this slightly) is that if you have two events (that is points in spacetime), you can find an observer with position and velocity chosen to perceive those two events as happening simultaneously.

In other words, you can't make a slice of spacetime that contains all events happening at the same time, because that slice would depend on the position and velocity of an observer.

To repeat, there is no meaningful concept of space apart from time.

Maxx · May 13, 2013

FOTSGreg said:
Oh, oh, oh!

And, since, as we perceive the universe, everything is moving away from everything at anything like light year ranges, the relative change in time becomes negative if you move toward an object moving away from you at FTL.(?)

Thus, you move backwards in time relative to where you and they were at the moment you went FTL(?).

The metric tensor (the measure of what the gravitational field is doing in some region of space) is actually even more convoluted. There is (for example) no simple overall expansion. For example -- the Andromeda galaxy is heading toward us so overall there is no cosmological redshift (bestowed by the metric) for some huge region between us and Andromeda.

You can see this convolution of the metric leads to lots of possibly very convoluted topological and causal problems. For example -- if the metric is blueshifting overall in a region -- how does that "come to terms" with the cosmological redshift -- I mean somewhere the metric must get pretty flat (approach a kind of zero) to get from one overall shift to another. A way to state this is to ask "Can the metric lock itself up? So the overall field coming in or out of an area would be very very small despite the fact that it includes many galaxies?"

jshughes · May 13, 2013

Yeah, so the time cone is a 4-D construction (that is itself curved in space-time). You can consider all events in the reverse cone as "observable" at a point in space-time - or vice-versa. Another thing that could happen, is that a black hole might create a shadow in a time cone, thus creating space-time events that are close, but unobservable from a given frame.

If d = (x,y,z,t) is your departure point and p = (x',y',z',t') is the destination point, then if p is in the reverse time cone (by the above definition) then paradox happens.

I hope that's more clear.

As far as Andromeda, its pretty darn close as far as these things go. What's a few million light-years between colliding galaxies? From a more philosophical physics perspective, we might ask if non-causal solutions to the Einstein equations represent real physical solutions.
Its pretty common to "throw out" non-causal solutions in E&M to great effect. Much of what we know about material science is based on that principle.
KK relations : http://en.wikipedia.org/wiki/Kramers–Kronig_relations
Basically, this is a consequence of causality.

I'm sure there are theoretical physicists that have attempted to use this basic mathematical principle in application to GR. I could imagine that might have some implications on time-travel.

Maxx · May 14, 2013

jshughes said:
Yeah, so the time cone is a 4-D construction (that is itself curved in space-time). You can consider all events in the reverse cone as "observable" at a point in space-time - or vice-versa. Another thing that could happen, is that a black hole might create a shadow in a time cone, thus creating space-time events that are close, but unobservable from a given frame.

If d = (x,y,z,t) is your departure point and p = (x',y',z',t') is the destination point, then if p is in the reverse time cone (by the above definition) then paradox happens.

I hope that's more clear.

As far as Andromeda, its pretty darn close as far as these things go. What's a few million light-years between colliding galaxies? From a more philosophical physics perspective, we might ask if non-causal solutions to the Einstein equations represent real physical solutions.
Its pretty common to "throw out" non-causal solutions in E&M to great effect. Much of what we know about material science is based on that principle.
KK relations : http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations
Basically, this is a consequence of causality.

I'm, sure there are theoretical physicists that have attempted to use this basic mathematical principle in application to GR. I could imagine that might have some implications on time-travel.

The wikipedia on casual relations says something like only expansions developed from a Cauchy surface of R X S (ie model continuity) are considered physical in GR as a rule.

So there is this (note the Cauchy surface):

http://en.wikipedia.org/wiki/Causality_conditions

Warning -- large PDFs follow:

And things like this (note the K-causality condition -- which is pretty seminal for later work on causality):

http://arxiv.org/pdf/gr-qc/9508018v3.pdf

Nice slide-show summary of relativity and causality:

http://www.umpa.ens-lyon.fr/~geodycos/Documents/Causeries/minguzzi.pdf

jshughes · May 15, 2013

Awesome. This is why I diverged from Physics to Math to Software development. I loathe researching these things. Surprisingly, I enjoy it when I am writing fiction. Then again, if I don't agree with something, I can chuck it out.

King Neptune · May 15, 2013

jshughes said:
Then again, if I don't agree with something, I can chuck it out.

That's what I like about writing fiction also.

Causality(?)/Time FTL Question

RichardGarfinkle

Second Edition and Second Laughter

King Neptune

jshughes

FOTSGreg

Today is your last day.

RichardGarfinkle

Second Edition and Second Laughter

Maxx

Got the hang of it, here

jshughes

Maxx

Got the hang of it, here

jshughes

King Neptune