"Wormholes" are common staples in science fiction. Would travel through a wormhole violate causality the way other faster-than-light methods do?
"Wormholes" are common staples in science fiction. Would travel through a wormhole violate causality the way other faster-than-light methods do?
Yes. It doesn't matter how you travel faster than light, doung so in any manner violates causality. If the wormhole allows transit from one end to the other faster than a photon could have travelled through normal space, then there exists a frame of reference in which a ship entering the wormhole will exit the other end before it enters.
edited for brain fade.
Actually it is possible to have a wormhole which does constitute a shortcut in time and space but does not constitute a time machine; if you are careful with the geometry, you can make sure that time does not reverse itself in any direction ('along any geodesic' or otherwise) and so is safe to use.
Jim Wisniewski has written this essay and diagram to show that wormholes can be used without paradox if certain restrictions are observed.
please note- I do not mean to say that traversable wormholes are necessarily possible; this is a thought experiment only.
Jim Wisniewski doesn't seem to understand the nature of the problem. The problem lies in the fact that in relativity simultaneity is reference frame dependant. Two events which appear to be simultaneous in one reference frame may not be in another. If everything stays below the speed of light, causality is preserved in all reference frames. If anything travels faster than the speed of light in one reference frame, there will exist another reference frame in which causality is violated. Jim Wisniewski seems to be addressing the issue of going back in time directly through a wormhole, which is a different matter entierly and doesn't address the fact that in relativity, any use of FTL is mathematically equivalent to time travel.
Yes. If we have wormhole point A=entrance and we have wormhole point B=destination, then if we travel to point B instantly we can then wait the appropriate amount of time for the light from point A to reach us and observe ourselves departing. In our frame of reference we exist in two places at once. That is a paradox. The only way a paradox can be avoided is if the world lines will never intersect.
I really must remember to not try thinking about this stuff after a couple of glasses of wine...
I'm going to hate myself for asking this, I'm sure...Originally Posted by Evan
I don't get reletivity... But this paradox seems to me like this:
I see a flash of lightning a few miles away. Several seconds later I hear the clap of thunder produced by it. I know the lightening bolt happened in the past and it just took time for the thunder to get here.
Now, in the above paradox, why do we really exist in two places at the same time? Why don't we just recognize that the image hasn't gotten here yet?
It's worse than that.Originally Posted by Evan
If the situation was merely as you described, it wouldn't be a violation of causality, merely look odd to see yourself doing something somewhere else while you're here. You could simply chalk it up to the limited speed of light, similar to the limited speed of sound here.
The problem comes when you try to define "instantly". In relativity, two events which are simultaneous in one frame may not be simultaneous in another. This applies even if you take lightspeed delay into account! It's simply the nature of relativity - time is not absolute, and there is no way to make a universal time reference that holds in all reference frames.
So, if you have a wormhole that allows instantaneous travel from one end to another as seen in one reference frame, it will allow travel back in time as seen from another refernce frame. Furthermore, by travelling the wormhole in one reference frame, then appropriatly changing your reference frame (such as by accelerating to near-relativistic velocities relative to when you emerged from the wormhole), then traveling back the other direction through the wormhole, you can arrive back at the entrance before you went into the wormhole in the first place. Thus, FTL violated causality.
(The actual math proving the above is complex, but it follows unavoidably from the theory of relativity.)
Is there a prayer of a wormhole to an alternate history, something like the novel Drakon? Could I use it to visit a 2005 where Hitler died in the First World War (as he nearly did, once)?
It's taken as do-able by many authors. Can you give an example of how to violate causalty with a single bi-directional wormhole where the ends are not too close together re that limitation?Originally Posted by TinFoilHat
His thesis boils down to the assumption that whether or not a particular configuration of wormholes provides for causalty violation is invariant of reference frame. That is, for all observers, a particular configuration is either safe or illegal.
Looking at Wisniewski's drawing, I think he might be right, actually. The first thing I note is that the wormholes he's describing exist at a specific point in time as well as space, so he's talking only about a highly constrained example (you can't arbitrarily go back and forth between the two locations, for example). For the wormhole with spacelike separated ends, these should be safe from causality violation, since the two events can't be causally linked by normal means. Note that although all observers will agree on the order in which two timelike separated events occur, differently moving observers may disagree on which of two spacelike separated events happened first even without the wormhole.
Wisniewski's essay seems to be pointing out that certain classes of FTL transport, though functionally time travel (as in the travel back in time from point A to point H in his drawing) do not violate causality if the destination it outside the light cone of the source. This is correct. It doesn't disprove the matter of FTL being equivalent to time travel, just points out that in some cases time travel doesn't violate causality.
The problems with violation of causality generally require a round trip, in which you travel FTL, change your frame of reference, then travel back. You can arrange to return before you arrived. Alternatly two FTL travelers in different reference frames can be used to create an unsolvable paradox.
Although it has a lot of math, the following link explains the matter in detail:
True, though the original post was specifically asking about violations of causality. It's also worthwhile pointing out that whether point A is earlier in time than point H is reference frame dependent, but it is earlier in at least some references frames.Originally Posted by TinFoilHat
I generalize that to the wormhole mouths producing world-lines too, and they are not moving relative to each other, and the angle on the page of the connection between mouths is constant. So if the diagram has point (event) A as the entrence and point (event) B as the exit, then if the mouths continue to exist there is also point A' and B' with the same change in Y coordinate.Originally Posted by Grey
If the original post was asking about the standard science fiction wormhole, a stable conduit to go from one place to another faster than light would travel in the outside universe, then the answer is yes - it can be used to violate causality.Originally Posted by Grey
No, if this is the case, I think TinFoil Hat is correct. If the wormhole continues to exist and allows traffic back and forth, I think you'll violate causality.Originally Posted by John Dlugosz
How? Can you come up with the diagram?Originally Posted by Grey
Grey is right; Tinfolihat is wrong. (I think).
The point is that a wormhole only connects two points in space; if the geometry allows closed time like curves, there is a violation of causality, a paradox, and the wormhole probably closes down, either by the formation of a Cauchy horizon or a virtual particle fountain; therefore causality is preserved, but the wormhole is unusable.
If the geometry is such that a closed timelike curve cannot form, then the wormhole does not violate causality; as long as you keep the wormhole mouths further apart than the time differential between their mouths, there can not be a violation of causality.
No time machine is formed by the establishment of a wormhole, as long as the distal mouth is kept further away from the proximal mouth than the difference beteween the duration of a trip through the hole and the time taken to travel that distance in ordinary flat space.
Build a network of wormholes and you will quickly run into trouble. Visser calls this a Roman ring, for some reason; if the geometry allows the formation of a closed timelike curve, the ring (probably) closes and does not allow travel at all;
if not, not.
Like I said, careful geometry allows certain formations of wormholes; the lack of simultaneity alone is not sufficient to cause a violation of causality.
And you're still not seeing the problem. The issue is not about causality violations due to one end of the wormhole being within the light cone of the other. The issue arises when you take a round trip, traveling from one end of the wormhole to the other, undergoing a frame of reference shift, then traveling back and arriving before you started.Originally Posted by eburacum45
Consider the following throught experiment. You have a wormhole with openings A and B. Entering one opening causes you to pop out at the other instantaneously. The two wormhole openings are outside each other's light cones, so a single traverse of the wormhole wil not cause a causality violation in any frame of reference, as per Wisniewski's diagrams.
Assume you leave an observer at wormhole mouth A, stationary with respect to the wormhole mouth, to record the experiment. Now, you get in your space ship, which is located inbetween the two wormhole mouths. You accelerate towards wormhole mouth A, and enter it travelling at a large fraction of the speed of light.
When you undergo a reference frame shift, you have to apply a Lorentz Transformation to your universal time and space coordinate frames. As a result of this, you and the stationary observer you left behind will disagree on the time and distance between points in spacetime. The only thing that will be constant for both of you is the speed of light. The Lorentz Transformation is such that you and the stationary observer will no longer agree on whether two events in spacetime were simultaneous - even if you into account the time it takes for light to get to you from the event. And since there's no prefered frame in relativity, there's no way to say that one of you is right and the other wrong.
Now you enter the wormhole. From your point of view, you travel from point A to point B instataneously. From the point of view of the stationary observer, you appear at point B before you entered point A. However, since point A is outside of point B's light cone, the observer won't see you exit point B until after you entered point A, so causality is conserved.
Now you're in your ship, travelling at high speed out of the wormhole opening at point B in the direction of point A. You turn the ship around and accelerate hard back towards point B until you are headed back at it at a good fraction of the speed of light. This causes you to undergo another Lorentz Transformation, again chainging your frame of reference realtive to the stationary observer - reversing the shift you underwent earlier and shifting things back in the other direction.
Now you enter the wormhole mouth at B, and emerge at A, instantaneously from your point of view. Your stationary observer saw you emerge from B before you entered A, and now he sees you emerge from A before you entered B. Which means that he will see you emerge from the wormhole before you entered. Your ship then crashes into the prior instance of itself, which is traveling towards the wormhole at the time, destroying itself and prefeventing itself from ever entering the wormhole in the first place. There goes causality.
Two FTL trips through a wormhole with a reference frame shift in between can be used to violate causality, because there's no universal standard to say when two events are simultaneous.
(It's possible that I might have switched the directions above - the ship might have had to start accelering towards A in the direction of B, emerging at B and then reversing accelerating towards B in the direction of A to get the appropriate sign on the time shift.)
Brian Greene clarifies that wormhole "time machines" do not allow travel to a time prior to the construction of the first wormhole time machine itself. If the first wormhole time machine is built 10,000 years from now, all previous times, such as ours, will remain inaccessible. In the case of wormholes, Greene doesn't seem to consider this an FTL situation - or a causality problem.
In fact, Greene claims that even if one could "travel back in time", there could be no causality problems. The old example of going back and preventing your parents from ever meeting "fails to make sense because it assumes moments can change." With Greene's view of spacetime, moments simply can't change, they just are. He envisions spacetime as a block of ice with every moment forever frozen in place, as opposed to time as a river sweeping us forward from one moment to the next.
Ref: B. Greene, The Fabric of the Cosmos, 2004
Everyone is entitled to his own opinion, but not his own facts.
Yes, agreed. Nevertheless, you do not have carte blanche to say that this transformation is unlimited in scope; in fact there is a value for the maximum difference between the local times, which is dependent on how the wormholes were set up.When you undergo a reference frame shift, you have to apply a Lorentz Transformation to your universal time and space coordinate frames. As a result of this, you and the stationary observer you left behind will disagree on the time and distance between points in spacetime. The only thing that will be constant for both of you is the speed of light. The Lorentz Transformation is such that you and the stationary observer will no longer agree on whether two events in spacetime were simultaneous - even if you into account the time it takes for light to get to you from the event. And since there's no prefered frame in relativity, there's no way to say that one of you is right and the other wrong.
This is my thought experiment;
Imagine a Morris-Thorne wormhole, with two mouths, a few metres apart. Separate these two mouths, keep one at home, and put the other one on a spaceship to a distant destination. This ship travels at 0.707c, which is a convenient velocity, for reasons I will explain in a minute.
Now imagine a destination at 7.07 light years; this could be an (as yet undiscovered) red or brown dwarf. If the spaceship carrying the wormhole mouth sets off in 2010 Earth Time it will arrive at the destination star in 2020 Earth time; but because of time dilation the ship’s crew will have experienced only 7.07 years; by their watches it is now 2017.07 (some time in late January if they set off on new years day).
This is why I picked that speed; it leads to a time dilation so that a ship travelling one light year relative to its departure point experiences one year of time, making the maths a bit easier.
If someone passes through the wormhole they step instantly from 2020 to late January 2017; simultaneity is no longer applicable. But the difference in time is not unlimited; you have three years advantage on those poor souls back on Earth- but they are more than seven light years away. There is no way that you could now get back to the Earth without taking more than seven years; you cannot therefore arrive back at your departure point before you departed.
Now the crew of the spaceship can set off as fast as they like toward Earth in their craft, but as long as they leave the wormhole behind they cannot create a time machine.
They are protected by geometry.
If on the other hand they create another wormhole and establish a time differential of three years in the other direction, they will pretty soon come into a situation where a closed timelike path is possible.
In fact they would only need to approach to within five light years or so of Earth with their time displaced wormhole on the way back, and they would come to a point where they are five years ahead of the people back home; drop the wormhole right there and a person could send a message from Earth, via the wormholes and across the light speed gap, to the exact moment of the sending of the message. Now extend the Earthbound wormhole a little further and the message can be sent further back, to a time before the message was sent.
There is your violation of causality; the single, simple wormhole I described at first does not allow a violation of causality- and there is no possible path (at any speed less than c), through any combination of gravity fields or reference frames which can lead to such a violation- unless you introduce another hole or move one, or both, mouths of the original hole again.
You still seem to be missing the point of the thought experiment I described. I am not claiming that a single trip through a wormhole would cause a causality violation. That would be impossible for the reasons you pointed out.
I am arguing that a round trip through a wormhole, in which a reference frame translation is made between the trips, can be used to violate causality. Unless the wormhole create is limited to a single trip, or travel in only one direction, or other special provisions such as a universe set up in such a way that casuality cannot be violated.
This doesn't make sense to me. Okay, so the light from the first trip meets up with the real you from the second trip. How does this constitute a "crash?" Your physical ship in the first trip is already gone, so there's no physical object to smash into.Originally Posted by TinFoilHat
It's like an afterimage produced by a flash of light in your vision. You might jerk back to avoid being 'hit', but you're seeing something that isn't physically there anymore... so there was no danger of a physical impact anyway.
Actually, in the simple, single wormhole configuration I described, you can go through the wormhole and back via normal space as many times as you like, and you will never acheive a causailty violation;
you will find that a ship making the circuit in one direction leads to a different observed rate of passage of time (compared to a stationary observer) to one making a circuit in the other direction, so there is no simultanety-
but they are both positive, ie both in the forward direction of time so no-one goes into the past.
This is because the light speed gap between the two mouths of the hole is greater than the difference between the reference frames at each end of the hole.
Go round the circuit in one direction and you gain three years in every seven- so the trip will take ten years relative to a stationary observer(assuming the trip in normal space is made at light speed)
Go round the other way and you lose three years- so the trip takes four years relative to a stationary observer.
Obviously there is no simultaneity between the observer and the ships, or between the ships themselves, but the light speed delay ensures that there are no closed timelike loops either.
These values are both positive- so you are always going forward in time, no matter which way you go, and there is no frame of reference which allows time travel.
Please actually read the thought experiment I described. In it you are not going through the wormhole and back via normal space. You are going through the wormhole, then going back through the wormhole, traveling very little through normal space. The real-space distance in time or space between the wormhole mouthes is irrelevent.Originally Posted by eburacum45
No, the light from the first trip doesn't met up with the real you from the second trip. The real you from the first trip meets up with the real you from the second trip, because you physically came out the wormhole entrance after the second trip before you physically went into it during the first trip.Originally Posted by Kesh
Let me ask once more...is there a ghost of a chance that wormholes could connect alternate histories?
I think I've noticed a subtle difference in the assumptions of how the wormhole behaves, and that may have an effect on whether or not causality can be violated. Let me see if I can phrase this clearly enough that it will make sense. I believe that eburacum45 is assuming that the wormhole links two points in space such that when travelling through, one reaches a point that would be considered simultaneous with the departure (or at least spacelike separated) when measured in the reference frame in which the wormholes ends are at rest. TinFoilHat, however, is assuming that travelling through the wormhole takes you to another location at a time which would be considered simultaneous with the departure when measured in the reference frame of the person travelling through the wormhole. Am I correct in these assessments? Note that these are actually two distinct behaviors for a wormhole, so it's entirely possible for one to allow violations of causality while the other does not.
Um, well, we don't really know whether wormholes exist. And we don't have any actual evidence that alternate histories exist in any real sense, apart from one possible interpretation of quantum mechanics and a lot of science fiction. But apart from those little problems, well, sure, why not? :wink:Originally Posted by Tom Mazanec
You are correct, at least as far as my assumption as to wormhole behavior. However, if it is the case that the wormhole transmits the traveler to a point instantaneous with respect to the framework in which the wormhole mouths are at rest, causality may still be violated. In that case you would apply the same thought experiment as I described above, but you would accelerate the wormhole inbetween the trips instead of the traveler to get the required shift in reference frames.Originally Posted by Grey