SP2171 and 72: Time travel, is it possible?

In the year 2009, three SPS (Special Programme in Science) students investigated the previous research of time travel and made a small discovery of their own. They found that time travel, allowed by the General Theory of Gravity (GR) because of curved spacetime, is self consistent in curved space time itself!

The tale of time travel may seem absurd and discarded by most as impossible due to the Grandfather Paradox (you can go back in time to prevent your own existence if time travel is possible). However, there are solid Physics behind time travel. It started when Willem Jacob van Stockum first showed that one solution of the GR equation by Einstein allows for time travel. The whole van Stockum Universe was just an infinitely long rotating cylinder whereby the spacetime outside is so curved that the light cones tipped and allows one to move back to where one started by travelling around the cylinder.



The vertical axis is time. An observer in any point in spacetime can only travel to the future of his or her light cone (as no one can travel faster than the speed of light), and thus when the light cones tipped sufficiently, one can travel around the cylinder back to the exact point in time and space where one started.

This provides a way to create a Closed Time-like Curve (CTC), a physicist way of saying time travel. With GR producing potential time travel paradoxes, there are four ways that the physics community are dealing with it.

1. The Radical Rewrite Conjecture: from multiverse to saying time can be rewritten, this is the radically rewriting the laws of physics and causality conjecture. (Science Fiction series Doctor Who falls under this category)
2. Self-Consistency Principle: the basic tenet is that whatever is recorded down in history cannot be changed. So if one travelled back in time, one would have already done it. It also means either restricted free will or no free will.
3. Chronology Protection Principle: all the ways of allowing time travel cannot yet work in our universe because of the impossible requirements like: infinitely long cylinder, negative energy etc... there maybe a deeper law, like quantum gravity that will protect causation and prevent all forms of time travel.
4. Boring Physics Conjecture: time travel has not been shown to be practical or possible yet with 100% certainty, so there are better things to worry about.

Obviously Science fiction writers has explored the first way, physicists like Novikov had proposed the self-consistency principle using wormhole as the time machine (in flat space-time background), while others likeStephen Hawking had proposed the Chronology Protection Principle and most of the rest of us chose to adopt the boring physics conjecture. However, until 2009, no one has yet tried to see if the self-consistency principle could work in fully curved spacetime itself.

There comes our three students, Han Weiding, Jani Hariom Kirit, and yours truly who investigated this case for the van Stockum Universe. What we had found was that there exist at least one self consistent path for a billiard ball inside the van Stockum Universe to go back in time and hit its past self so that the past self can go around the cylinder, back in time, to become the future self that did the hitting in the first place.

Therefore, we concluded that time travel is still possible under the self consistency principle and that GR has not contradicted itself.

This however does not tell us in absoluteness if time travel is possible or if it is, will it require the radical rewrite conjecture or self consistency principle. The search for an answer goes on.

Note: at the time of literature review and research, the three students were in their 2nd and 3rd semesters in NUS.