# Time Dilation Questions

1. Nov 17, 2005

### EngineeredVision

Hey everyone,

This is my first post and I'm not sure if what I have to ask has been addressed before, but I thought I would give it a try anyway. I've been playing around in my head with the notion of pseudo faster-than light travel. I'm currently working on a science fiction project and was trying to figure out how time dilation would apply to a vessel that is able to arrive at a destination faster than light can travel, but without the vessel itself actually traveling faster than the speed of light. The concept is that if it were possible to stretch the space-time curvature opposite of the vessel's motion and compress the space-time curvature in the direction of the vessel's motion that the vessel could actually warp space around it so that it could actually arrive at a destination faster than light that is traveling in non-warped space. Almost like a wormhole, but a wormhole that actually grows/travels through space while pulling the vessel with it.

So here's my question. If this type of travel were possible what time dilation effects might occur?

It seems that a distant observer to this event would still experience time dilation, but would this actually result in any time travel effect? That is, if the vessel with the ability to jump ahead of light returned to the planet from which it left would it actually travel back in time? I'm sorry if I'm missing an obvious point to this discussion or concept. I know that this is only for science fiction but I would still like the concept to be somewhat plausible, or at least non-contradictory.

Any thoughts on this subject would be greatly appreciated.

2. Nov 17, 2005

### EngineeredVision

Sorry guys.

I just realized that there is a seperate section for relativity questions. I was wondering if an Admin could move this thread to that section.

Thanks.

3. Nov 17, 2005

### Danger

Although I'm not at all certain about this, I suspect that manipulating space-time curvature would merely result in artificial gravity gradients. As mentioned elsewhere, some NASA folks were fiddling with the theory of creating a 'bubble' of artificial space-time around a ship, within which the ship would be at rest or low velocity. The bubble itself is to be accelerated (I have no idea how) to superluminal velocity because there is theoretically no speed limit on space-time itself (as proven by +c expansion).

4. Nov 18, 2005

### Galileo

This is a bit vague, but something like it might already happen!
As seen from the point of view of the travelers and the spaceship there is no time-dilation. What they experience if they set of to a star some million lightyears away is that the space contracts in the direction of motion. This means that the distances measured in the direction they are going are shorter than when they were standing still wrt the star (and the objects). So space actually 'folds' or contracts. They will see the planets and stars flattened in the direction of motion and the distance to the star will also be shorter. Depending on how fast they go, this distance can get very short. If they go at 99% of the speed of light wrt the star, then the distance will be 14% of the distance when they were standing still.
From their point of view they can reach a star that is a million lightyears away in a few hours. For someone standing still wrt the star it will take over a million years before the ship reaches the star, because of time dilation.

5. Nov 18, 2005

### EngineeredVision

Thanks you Danger and Galileo for your responses.

They didn't quite address my question about potential time travel effects from this type of travel, but maybe I'm missing a subtlety in your responses. I think Danger closely hit the concept of this currently ficticious type of travel when mentioning that the vessel would be near rest velocity but accelerated through some sort of space warping bubble that surrounds the craft.

Galileo, I think you explained the time dilation that would result from the observers fairly well, but I'm still confused as to whether or not there would be a physical time difference for someone who traveled 1000 light years to a distant destination then returned the same distance to the location from which they initially left. Would the traveler still be younger than the observer that remained on the planet during this trip after returning? Again, I'm sorry if this isn't obvious to me.

6. Nov 18, 2005

### RogerAshford

This sounds like something I was playing with (mentally). As I understand it, relativistic effects such as time dilation & Lorentz contraction apply only when two observers are moving relative to one another *through* space: If the space between them is expanding or contracting (and therefore making them become nearer or further apart), then these effects are not apparent.

This is how galaxies can be further apart now than would be possible in the time since the beginning of the universe if they were limited to a relative velocity of c (I recently read that the size of the universe - whatever that means - is about 74 billion light years, while the age of the universe is less than 15 billion years).

In fact, although the distance between distant galaxies is increasing at a great rate of knots (as per Hubble), they are in actual fact not moving relative to each other (in the relatavistic sense): i.e. they are not moving *through* space (or at least not to any great degree).

My idea was: develop a means of causing a local contraction or expansion of space (it's easy if you say it quickly!), put it aboard a spaceship, then:

(a) contract a small volume of space in front of the spaceship (say by a factor of a million)
(b) travel across that space at, say c/1000 - relativistic effects would be negligible
(c) re-expand the volume of space you've just crossed (which is now behind you). You have now travelled the expanded distance at an effective speed of 1000c
(d) repeat (a) to (c) as many times and as rapidly as necessary.

I am sure that someone will very quickly point out the snags in this idea, but bear in mind that we ARE talking science-fictionally here!

7. Nov 18, 2005

### EngineeredVision

Thanks Roger,

I think that you illustrated what I'm beginning to think on the subject after reading some of the threads here in the forums. That is, if the traveller isn't actully traveling at a significant speed in the same space-time inertial frame as the departing location resides in than time dilation effects are negligible. Not being a physicist, I haven't really taken it upon myself to study relativity in great depth, but my intuition has always told me that the usual time dilation effects experienced between a stationary observer and an observer traveling at a velocity approaching c is a result of the way biological, chemical, and nuclear reactions occur in different inertial frames. Unfortunately, intuition can be a dangerous thing in science, so please correct me if I'm wrong.

It seems that if someone leaving Earth only ages a year while traveling at a high velocity, but someone remaining on Earth ages 2 years in the same time it takes the traveler to accelerate to a distant destination and return that there must be a fundamental difference in the way biological, chemical, and physical systems operate in different inertia frames. I think though that if the stationary observer and the traveler were in the same or closely similar inertia frames that they would not experience a significant age difference in this situation if the traveler's ability to reach the distant destination and return relied on compressing and decomperessing space-time rather than actually traveling through uncompressed space-time near c. Any more thoughts on this?

Last edited: Nov 18, 2005
8. Nov 18, 2005

### JesseM

Your proposal sounds a lot like the "Alcubierre warp drive" proposed by a physicist named Miguel Alcubierre--see here for some info. This isn't a crackpot idea, Alcubierre was trying to propose something that would make sense in the context of general relativity, but from what I've read elsewhere it seems his proposal makes use of some approximations, and it has never been proven definitively that an FTL "warp bubble" is actually an allowed solution to the equations of GR. See section 5 of this paper, for example:
As for time travel, I would imagine that if we think of a small warp bubble moving on an otherwise flat spacetime background, the analysis of tachyons in SR would apply to the warp bubble as well, and therefore it would leave open the possibility of time travel. See this thread for a short discussion of tachyons and why they would violate causality in relativity.

9. Nov 18, 2005

### EngineeredVision

Thanks for the article link Jesse. The warp drive described is very similar to what I had in mind. I guess since I'm using this technology in the context of science fiction I could probably get away with stating that the observer and traveler could remain on the same time plane despite FTL travel achieved through this effect. I also realize that this type of technology is reliant upon unsurmountable amounts of exotic material and energy, but this too may be derived from my imagination as the type of device that is necessary for extracting the energy necessary for this operation.

Basically, I'm trying to come up with a semi-plausible FTL travel technology that allows an observer and traveler to remain on the same time plane after FTL travel.

10. Nov 18, 2005

### JesseM

If you want a plausible form of FTL travel that avoids causality violations, it might be better to go with wormholes, there's an actual physics argument that at soon as one mouth of the wormhole gets within the other mouth's light cone (which is when time travel would become possible), vacuum fluctuations would build up and destroy the wormhole at that instant. For example, see this article, for example:

http://www.aleph.se/Trans/Tech/Space-Time/wormholes.html

See here for a paper by Matt Visser on this form of "chronology protection". The article above says "Visser's work is not complete" so I guess this is still fairly speculative, and Visser has also proposed a more complicated way of using wormholes for time travel that may get around the virtual particle problem (although he adds at the end of the paper that he thinks this just shows that the semi-classical assumptions used in this proposal are probably not reliable), but for the sake of a science fiction story this would be a plausible way to allow FTL travel without time travel, and also without the need to seriously rewrite the laws of physics.

11. Nov 19, 2005

### RogerAshford

No, time dilation is not due to differences in the rate of biological/chemical/physical processes in different reference frames - one of Special Relativity's raison d'etre is to make sure that these processes are always the same in any inertial frames. Time dilation (and, in fact, Lorentz contraction too) are due to the relativity of simultaneity. If you move from one inertial frame to another (i.e. you accelerate from one state of being at rest to another), then the total collection of space-time events that were simultaneous with your "consciousness" after acceleration are different from before acceleration.

An example (related to an explanation of the twins paradox): If the 20-year-old you, on Earth, is at rest relative to your 20-year-old twin who happens to be situated 8.6 light years away on planet Faraway, and you accelerate instantaneously toward him to a velocity of 0.86c, during that instantaneous acceleration your twin "ages" instantly by 7.5 years: he is now 27.5 while you're still 20. (Had you accelerated in the opposite direction, your twin would instantly "un-age" by 7.5 years, to 12.5 years old.)

This is nothing to do with biological processes: in the initial inertial frame, the event "you being 20 years old on Earth" is simultaneous with the event "your twin being 20 years old on Faraway". In the "travelling" inertial frame, the instant after your acceleration has completed, the event "you being 20 years old on Earth" is now simultaneous with the event "your twin being 27.5 years old on Faraway". As you travel toward your twin, he will age at half the rate that you do - again this is nothing biological, it's because of the rate at which your "personal now" (see below) intersects his world-line.

Every observer carries around their "personal now", which is the volume of 3-D space that contains all of the events in the universe's 4-D space-time that are simultaneous with them at any particular point on their world-line. As they move relative to other observers, their personal nows "tilt" (I can't think of another word to describe it - it's more obvious on a space-time diagram), and intersect the other observers' world-lines at different points.

12. Nov 21, 2005

### EngineeredVision

Ok, so I understand why clocks would appear to operate at different speeds between an observer and traveler in different inertial frames, but what actually causes the difference in the so-called simultaneity? Does the actual curvature of space-time change as something approaches c? I can accept the princliples if this were the case, but usually that's not enough for me. I typically like to understand how things work or operate in a rationale way.

It makes sense that a stationary observer would observe that the clock of a fast traveling vessel is ticking slower because of the delay between ticks that is the result of the amount of time light takes to travel between observers. However, it seems that even though observations would differ between individuals that their actual "personal nows" as you called it would remain the same, so that upon reuniting after near c travel they would have experienced the same passage of time in their personal nows. Obviously it just seems this way, but why is this not the case? What about traveling near the speed of light causes two individuals to have different personal nows when at different inertial frames? Are there any good visualizations to help undertand this?

13. Nov 21, 2005

### JesseM

The idea of different observers having different definitions of simultaneity is part of special relativity, so it doesn't have anything to do with curved spacetime, which only appears in general relativity. The relativity of simultaneity shouldn't necessarily be thought of as a "physical effect" at all, it's just a consequence of how different observers define their coordinate systems, although the choice of coordinate systems used in SR is the most "natural" one to use physically because it insures that the laws of physics will obey the same equations in each observer's coordinate system.

When Einstein originally came up with relativity, he imagined that each observer would define the coordinates of events using purely local measurements, to avoid the issue of light-speed delays. Imagine I have a large grid of rulers that reach throughout space and are at rest with respect to me, with clocks attached to each marking on the ruler. Then if I see an event such as an explosion through my telescope, I can just look at the marking on the ruler that was right next to the explosion when it happened, and look at the reading on the clock that was attached to that marking at the moment the explosion happened, and this will give me the space and time coordinates I assign to the event.

For this to work though, I have to make sure that clocks at different locations along the ruler are "synchronized" with each other in some sense. Because of time dilation, I can't just synchronize them by taking them to the same point in space, making sure they read the same time, and then moving them apart--the act of moving them will cause them to change speeds. So Einstein suggested that each observer could synchronize different clocks in his system using the assumption that Maxwell's laws of electromagnetism are valid in his coordinate system, which means that light must travel at c in all directions in his system. So if you make this assumption, you can synchronize clocks using light signals--just set off a flash at the midpoint of two clocks, and if they both read the same time at the moment the light from the flash reaches them, they are defined to be "synchronized".

Now, there's nothing that says you have to synchronize your clocks using Einstein's synchronization convention. But if you do, you find an elegant result--if different inertial observers all synchronize their own set of clocks using this convention, then the all laws of physics will obey the same equations regardless of which observer's coordinates you use to express them. This is because all the known fundamental laws of physics have a mathematical property called "Lorentz-symmetry", which insures they will have the same form in different coordinate systems which are related by the Lorentz transformation--if we ever turned up a fundamental law that was not Lorentz-symmetric, it would no longer be true that all the fundamental laws obey the same equations in all coordinate systems constructed this way. But most physicists would consider this unlikely, it would seem a strange coincidence that all the most fundamental laws have happened to have this symmetry if it wasn't a symmetry that was built into the most fundamental laws out there waiting for us to discover (from which all our current 'fundamental' laws can presumably be derived). The fact that all fundamental laws of physics are Lorentz-symmetric also insures that the rate of actual physical clocks must match the rate that coordinate time passes in the clock's own rest frame--if there were some frames where physical clocks ticked at the same rate as coordinate time and others where they didn't, then clearly the laws of physics cannot be obeying precisely the same equations in both coordinate systems. To put it another way, if you were to create a computer simulation of a universe with different laws of physics than our own, as long as the equations you programmed in had the mathematical property of Lorentz-invariance, this would be enough to absolutely guarantee that you'd see relativistic phenomena like the twin paradox within your simulated universe--you wouldn't need to program in any extra "laws of relativity" or anything, in fact if you just programmed in the equations without noticing they had this particular mathematical property, you might be surprised by such phenomena (consider the fact that Maxwell's laws of electromagnetism are Lorentz-symmetric, even though they were discovered well before relativity was understood, and people were certainly surprised by things like the fact that light seemed to have the same speed in all directions regardless of which direction the earth was moving).

So Einstein's synchronization convention is the most physically natural way to set up the coordinate systems of different inertial observers. But as a consequence of this convention, different coordinate systems will disagree about simultaneity. Imagine I am travelling past you on a rocket, and at the midpoint of the rocket I set off a flash, and set clocks on either end of the rocket to read the same time when the light from the flash reaches them, so that they are synchronized in my rest frame. But if you assume that light travels at constant velocity in all directions in your rest frame, then in your coordinate system the light from the flash cannot have hit both clocks at the same time--after all, the back of the rocket is travelling towards the point where the flash was set off while the front of the rocket is travelling away from that point, so the light should take longer to catch up with the front than with the back. So, if I have set the clocks so that they read the same time when the light hits them, in your frame my clocks must be out-of-sync. That's pretty much all there is to it.
That would just be the classical Doppler effect (The relativistic Doppler effect follows a different equation, because it is a consequence of both the fact that the distance to the source changes between signals, so the signals have further to travel, and the fact that the source is genuinely emitting signals slower in your frame). Time dilation can be seen even if you make purely local measurements to avoid the issue of signal delays, as on the scheme using a grid of rulers and synchronized clocks that I described above. I provided some diagrams of a specific example of two rulers sliding alongside each other with clocks attached to the markers on each on on this thread, if you're interested.

14. Nov 21, 2005

### EngineeredVision

Thanks JesseM for the thoughtful explanation. It reinforces what I have just come to discover about simultaneity and time dilation after performing some interesting computer simlulations. I was able to understand the fact that the laws of physics and the curvature of space-time in SR doesn't change between different inertial frames as I had once incorrectly assumed.

I'm a 3d animator and technical artist, and consequently a very visual person. So last night I began working on some visual simulations in Maya (3d modeling and animation appication) that would hopefully illustrate why different inertial systems experience different simultaneity. I used the classic train example first put forward by Einstein. I created a simple 3d scene with a train station platform occupied by a stationary observer and a passing train with another observer in the middle of the train. I timed the train to pass in front of the station platform right as both ends of the train were struck by lightning. I also animated a spherical representation of radiating light from the lightning strikes expanding outward. I then placed a camera for the stationary observer that had its extents set to the lightning strike positions and created another camera parented (attached) to the train that was also framed to fit the lightning strikes when they occured. It clearly illustrated the differences each frame (a seperat camera represented each inertial frame) experienced in the event of the lightning strikes. It's obvious that the stationary observer concludes that the lightning bolts struck at the same time, and also clear for the moving inertial frame that the front lightning bolt struck before the rear. This particular example I've never really had too much of an issue with, but seeing it visually represented solidified my understanding of different coordinate systems.

The next simulation I created helped illustrate how time dilation occurs. I created a large spherical vessel that had a radius of 0.1 c light seconds that left another stationary vessel traveling at 0.8 c. Both the stationary vessel and the traveling vessel had synchronized clocks that would flash a light at their center every 1/4 of a second (not quite sure why I chose that value, but it didn't really matter for demonstrating the point). I also setup up the scene so that the animation would run at 100 frames per second to make math a little easier. Additionally, I decided that 1 light second would be equaivalent to 100 units in Maya (the 3d application). At any rate, I knew that it each time the light for a vessel flashed that it would take 20 frames to emit from the vessel's center, reflect off the outside wall, and return to the source to be counted. So as in the lightning strike simulation I also created a radial light field for each flash of light that expanded outward at c. As I began to watch how the light was flashed and received it became obvious that the stationary vessel was receiving the flash return at a faster rate than the moving vessel. I wasn't just accepting this as fact, I was actually SEEING it! :surprised I was able to visually extrapolate that time was passing slower for the moving vessel. I didn't have to scale Maya's playback speed or create any "faked phenomena" to achieve the effect.

Anyway, I'm really excited that I finally understand what's going on in SR. I've always simply accepted it without fully understanding the relationships. It's more gratifying to figure it out and prove it to yourself.

If I have time I'll try to polish up the animations for presentation and try to find a website where I can upload them. I think the animations might help others like myself who prefer seeing visual relationships and representations as opposed to complex mathematical expressions and equations. The animations did the trick for me, but I had the advantage of being able to look at my simulations from any angle in real-time. If I create a pre-rendered avi or mov file I'll want to make sure that I have intuitive camera angles and discernable representations for abstract elements such as light.

After reading many of the other threads on these forums it appears that I wasn't the only one that didn't have a strong grasp, or weak one for that matter, on SR and topics such as simultaneity and time dilation. I think the animations may even help to persuade those few skeptics that still don't believe in the effects in special relativity.

Thanks everyone for responding to this thread.

15. Nov 21, 2005

### robphy

Last edited: Nov 22, 2005