Wormholes, time travel, and time dilation

Question

I believe I understand the "wormhole time machine" now, but still have one question regarding what happens if you enter the stationary mouth.

A wormhole is created and (of course) has two mouths, $x$ and $y$.

$x$ remains stationary on Earth while $y$ is sent away at relativistic speeds (.99c) for (example) five years as measured on Earth (observer at the stationary mouth $x$).

The spaceship with mouth $y$ returns to Earth. Mouth $y$ and any occupants of the spaceship have obviously aged less than five years, though observers on Earth and wormhole mouth $x$ have aged 5.

What now happens if someone enters into wormhole mouth $y$?

As explained below by Ben Crowell, you would exit mouth $x$ at a time in the past. This happens because the time (as measured by clocks, if you wish) inside the mouths of the wormholes remains syncronized. So, when you enter $y$ (the younger wormhole mouth), it takes you to the mouth of $x$ when it was the same age. You end up in the past.

What happens if someone enters into wormhole mouth $x$?

I can't find a definite answer on this, so I'll try to work through it. I think you would emerge from mouth $y$ - the one in the present time (5 years old). Because the time inside remains synchronized between the wormholes regardless of the outside age, then entering $y$ takes us to $x$ in the past (sometime between <5 and 5 years ago); however, entering $x$ does not take us to the future because mouth $y$ (outside) has not yet aged beyond 5 years since we started our experiment.

Can someone confirm if my reasoning is correct or not?

Answer 1

This seems to be called the eternal-time-machine spacetime, and I believe the original paper was Morris 1988, which is available online and not paywalled. On p. 1447, they claim:

...at late times by traversing the wormhole from right mouth to left, one can travel backward in time (i.e., one can traverse a closed timelike curve)...

The question says:

I've read conflicting info -- some say that entering y will send the traveller back in time. Others say entering x will send the traveller back in time.

I'm not aware that this aspect of the idea is controversial at all. In your notation, the paper is saying that entering y and emerging at x sends you back in time. If there's some source that says it's the other way around, please tell us what the source is.

Here's a diagram showing what I understand them to be saying.

The wormhole is created before the diagram begins. The left-hand black line is the world-line of one mouth (x), and the other black line is the world-line of the other mouth (y). An observer's world-line ABCD is shown in red. B is the point where the observer enters y. C is the point where he exits x. The observer's world-line contains a closed, timelike curve. In the paper, they label the wormhole's mouths with time coordinates, which I think are the readings on a clock that's inside the wormhole. Since the wormhole can be assumed to be internally short, one can synchronize these clocks without any of the usual ambiguities -- even relativistically, one can absolutely synchronize two clocks that are at the same location. So B and C are simultaneous according to a synchronization process that's carried out inside the wormhole.

Morris, Thorne, and Yurtsever, "Wormholes, time machines, and the weak energy condition," Phys Rev Lett 61 (1988) 1446; http://authors.library.caltech.edu/9262/

Answer 2

Entering at x does take you to the future.

If this is not explicitly stated in Morris and Thorne 1988, Thorne does explicitly state this in his 1994 book Black Holes and Time Warps -- Einstein's Outrageous Legacy. You'll find the following sentences on page 504,

"The wormhole has become a time machine. If I now (on 1 January 2010) climb into the wormhole mouth in the spaceship, I will emerge from the other mouth in our living room on 1 January 2000, and there I will meet my younger self. Similarly, if my younger self climbs into the mouth in the living room on 1 January 2000, he will emerge from the mouth in the spaceship on 1 January 2010.

This assertion is commonly taken for granted and has been repeated in other pop science books on the subject (e.g. Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension by Michio Kaku and The Physics of Stargates -- Parallel Universes, Time Travel and the Enigma of Wormhole Physics by Enrico Rodrigo).

Answer 3

Wormholes, time machines, and the weak energy condition by Morris, Thorne, and Yurtsever contains the following description and illustration:

Figure 2 is a spacetime diagram for the conversion of a spherical, traversible wormhole into a time machine. Shown unstippled is the nearly flat spacetime outside the wormhole, with Lorentz coordinates $T,Z$ (shown) and $X,Y$ (suppressed). Shown stippled is the wormhole interior, i.e., the region of large spacetime curvature. The central lines of the stippled strips are the wormhole throat, parametrized by a time coordinate $t$ introduced below.

At $T=0$, the wormhole's mouths are at rest near each other. Subsequently, the left mouth remains at rest while the right mouth accelerates to near-light speed, then reverses its motion and returns to its original location. The advanced beings can produce this motion by pulling on the right mouth gravitationally or electrically. This motion causes the right mouth to "age" less than the left as seen from the exterior. Consequently, at late times by traversing the wormhole from right mouth to left, one can travel backward in time (i.e., one can traverse a closed timelike curve) and thereby, perhaps, violate causality.

Based on this diagram, it appears that traversing the wormhole from left to right (e.g. entering at point 11 on the left) would cause you to emerge in the interior of your future light cone (point 11 on the right).

Answer 4

Gravity has its effect on time as well. Everything we know about matter quality in space is a mere assmption. So I am as well as you sir are assuming about the above question. First before starting with the above mentioned subject we should know a little about time. What is time ? Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as the fourth dimension, along with the three spatial dimensions.So I think , you will have a clear understanding about right now. But first of all we have tho tell about the existence of wormholes. For the existence of Wormhole exotic matter should be present which you can say is a kind of hypothesis.Now the question that will pop up in your head is that what is the relation between wormholes and time. Now what i am trying to tell you is that wormhole itself is a gravity. Now consider the sun , the planets are revoloving arund it mercury being the fastest and the pluto being the slowest.Now you can think that it is because of the orbits are small and large. But what exactly holds the orbits in their place . The gravity of the sun. So as you see gravity also controls distance. Geodesic is the straightest possible way in a fabricating space time. Wormhole can be described as a geodesic. It is the hypothetical topological feature connecing two distant points in the universe.It is a bending singularity in the fabric of spacetime . Scientists tells that gravity has its effect on the objects that has mass. But in the case of wormholes, it is the gravity. I meant to say that gravity is the wormhole. And as you gravity attracs time. So gravity at the wormhole (from the event horizon ) is the maximum , as a result the time is also passing fastly. As a result the subject coming from the wormhole will be performing time travel. As the subject is younger than the subject approaching the event horizon it is performing time travel . So as gravity attracts time we can say that tme ravelis possibel.