# How is time distributed through space?

I was greatly confused when I saw video saying that if two wormholes were separated by time instead of distance, it would allow time travel. My question is what did they mean by this statement? What do they mean by time instead distance? How is time distributed through space?

• Maybe this will help en.wikipedia.org/wiki/Light_cone . It is four dimensional space you have to consider, and wormholes live in four dimensional space if they live at all. – anna v May 9 '14 at 3:48
• I'm surprised at all the downvotes. It's far from obvious that we could have two ends of the same wormhole at similar spatial coordinates but different time coordinates. The only related question on the SE reveals not even the experts are in agreement on the issue. Before you downvote I think you should consider whether you would be able to answer the question. – John Rennie May 9 '14 at 11:22
• Could you post a link to said video? – Kyle Kanos May 9 '14 at 12:50
• There's a great explanation buried in the heart of Kip Thorne's book Black holes and time warps. – rob May 9 '14 at 13:12
• Here is the video youtube.com/watch?v=SLUzJeto0Wo – user122083 May 10 '14 at 2:58

To start with let me emphasise that this is all highly speculative. Wormholes almost certainly don't exist, and if they did there's no proof they could be manipulated in the way I'm about to suggest. Still, this is the argument for how they allow time travel.

To start with suppose we can create a wormhole with one end here and the other end at the star Kepler 186, which is 490 light years away (you'll see why I've chosen that star in a moment). Assuming the Sun and Kepler 186 are stationary (or moving only slowly) relative to each other we can define a time coordinate covering both stars so the time would be the same at both ends of the wormhole. So it's currently about 8 a.m. on May 10th 2014 here in my study and it is the same time at Kepler 186.

Now this is the tricky bit. Suppose we can move the ends of the wormholes around. let's not worry exactly how we do this, just accept that we can can. In that case we can take the end of the wormhole at Kepler 186, put it in a rocket accelerating at 10g and bring it back to Earth. The point of choosing Kepler 186 is that I showed in a previous question that for a rocket accelerating and decelerating at 10g the trip back from Kepler takes 490 years as observed from Earth but only 2 years for the peole (and the wormhole end) on the rocket. The time flows differently for the two different sets of observers because of relativistic time dilation.

Now we have the strange situation that the time at the end of the wormhole that stayed at Earth has changed by 490 years, so it's now the year 2504, but the time for the other end of the wormhole has only changed by 2 years so it's now the year 2016. But the two ends of the wormhole are right next to each other. That means someone in 2504 can jump into the wormhole and emerge from the other end in 2016 (and kill their ancestor!).

I am sorry but I have to disagree with John Rennie at this point. I understand that he is saying that you take the Kepler 186 wormhole (the end of the wormhole pair that is on Kepler 186, lets call it Kepler-wormhole) as as 'device' and you can just put it onto the deck of the spaceship and transport it back to Earth.

Now he correctly says that the spaceship (and the Kepler-wormhole) would travel for 490 Earth-years, so you are right, on Earth it would be 2504 by the time the wormhole arrives on Earth with the spaceship.

Now he also correctly says that for the people (and for the Kepler 186 device) on the spaceship, time would pass slower, and their clocks would only show 2 years passing, so by the time they arrive, their clocks would show 2016. Their body's would also age only 2 years. The Kepler 186 device's 'body' would also only age 2 years. This means that the massless gluons inside the bodies (of the people on board the spaceship and inside the Kepler 186 device) in some confinement would only move (oscillate) less throughout the trip and thus the clocks (for example a photon clock) would only tick 2 years total.

Now the misconception (or misunderstanding) is where we say what the wormhole exactly does. As I understand the wormhole would only be in this case a device that works like a teleport. You enter one end at a spacetime (so space and time) location, and it will teleport you to the other end in spacetime wherever the other end of the wormhole is (note that that point is in spacetime not just space).

Now if the wormhole is on Kepler (before we move it back to Earth) then it is in space at Kepler and in time in 2014.

But here is the error we are making, intuitively thinking that the wormhole itself is where we are traveling in it. It is not. It is just a port. We are traveling wherever it points in spacetime.

Again, before the move it points to Kepler in space and 2014 in time.

As we move it on the spaceship, we relocate the kepler 186 wormhole device itself. We relocate it in space and time.

Where do we exactly relocate it to? To Earth in space. And to 2504 in time. Why?

Because the error we are making is that we think that the wormhole will lead to it's own timeline. It will not. The Kepler 186 wormhole device itself will age 2 years.

Now the error is where you say that the wormhole that was this way transported back to Earth would still 'lead' to year 2016. No. It would 'lead' to Earth (in space) and it would 'lead' to 2504 as soon as you exited the wormhole.

So as soon as you exit the kepler 186 wormhole device on Earth, you will find yourself in 2504 Earth.

OK, here is another example. Let's say person1 is on Kepler 186 and person2 is on Earth. Let's say somehow they could synchronize their clocks with immediate info-exchange. Problem is they can't normally because however they would try, they would always be 490 years back leg in the info-exchange so if person1 would have 2014 on his clock, he could only send info to person2 about that in 490 years.

But let's say that person1 and person2 know SR so what they do is:

1. person1 looks at his clock, reads 2014, and sends this info to person2, and then person1 at the same time right away jumps into the spaceship and heads towards person2.
2. by the time person2 gets the info from person1 about the clock's info saying 2014, he would check his clock and see exactly 2504.
3. So person1 has 2014 on his clock, and is on the spaceship towards person2.
4. person2 has 2504 on his clock and is waiting for person1 to arrive.
5. obviously person2 would arrive in 2504 (on person1's clock) since by John Rennie's definition the spaceship would take 490years to travel.
6. But what would be on person2's clock, he would read 2016.
7. So they would meet in both space and time coordinates exactly on Earth in 2504 local time. They would not meet on Earth in 2016.
8. The question you have to ask yourself is, what would the person on the spaceship see, when looking at the people's clock on Earth? He would see those clocks tick faster then his own. So by traveling in space towards Earth fast, he would travel towards the Earth's 'future'. He would see Earth 'living' through 490 years. In other words, he is not able to reach Earth sooner then 490 years in Earth-time. So he would have to slow back (sorry, the opposite of catch-up) to Earth in the time-dimension, since in the time-dimension Earth is traveling faster then the spaceship. He has to compensate that difference by traveling faster in space on the spaceship, thus creating a slower speed for himself in the time dimension ( while Earth is moving still faster in the time dimension). But why has he to make up for that difference in the first place? Because the simultaneity you intuitively think of does not exist, it is shifted. How? Well, in this case, Kepler 186 is 490 ahead in time of Earth. Just because the spaceship wants to move from kepler to Earth (if it would want to move from Earth to Kepler, then Earth would be 490 years ahead). So that difference of being ahead on Kepler needs to be compensated for, throught the travel, and it is compensated by higher speed in the space dimensions. It slows down the spaceship in the time dimensions and so Earth will move faster in the time dimensions and will catch-up to the spaceship. They will meet in 2054 local time on Earth.
9. By John Rennie's statement he says that the Kepler 186 wormhole device would still lead to 2016 in time, just relocated to Earth in space. That is not true. The device itself would have aged 2 years only, but the device, as a port would lead to 2054 Earth, local time.

To make you understand this, I am starting with basics.

A point is zero-dimension. By stacking points, you'll get higher dimensional figures like 1-dimensional line. Similarly, by stacking lines, you'll get higher dimensional figures like 2-dimensional plane. Similarly, by stacking planes, you'll get 3-dimensional Space. For 4-dimensional Spacetime, do I need to say more? It's simply a stack of Spaces.

Think it in reverse: You can't imagine a plane without lines and you can't imagine space without planes. Similarly, you can't imagine Spacetime without space.

Then, what exactly is Time?
Think about it: To make space from plane, you've got only two direction. If plane is horizontal, you can either stack planes above or below the given plane. Similarly, for stacking space, you've got 2 directions. These directions are time: Forward time and backward time.

As for wormholes, let's discuss it on stack of planes (making space). If there're two wormholes on two different places, how would you measure separation between them? Clearly, it's not separated by distance defined on planes. It's separated by a distance defined in extra dimension viz. direction in which stacking is allowed.
Similarly, if there're two wormholes at different spaces, the separation between them wouldn't be defined in space, but rather in extra dimension viz. directions in which space stacking is allowed i.e. Time.

• Reasons explaining downvotes would be nice.. – Schrödinger's Cat May 9 '14 at 9:21
• I didn't downvote, but I have to say that your answer doesn't seem related to the question, and indeed I'm not 100% convinced it makes sense. An answer that made sense would be something along the lines of showing that $dt/d\tau$ could be different for the two ends of the wormhole. – John Rennie May 9 '14 at 16:31

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