How does closed timelike curve work?

In a closed timelike curve, the worldline of an object through spacetime follows a curious path where it eventually returns to the exact same coordinates in space and time that it was at previously. In other words, a closed timelike curve is the mathematical result of physics equations that allows for time travel.

What would a closed timelike curve look like?

A closed timelike curve wouldn’t actually “look” like anything because it’s an abstract thing. You can’t actually see any lightcones or worldlines. A metric is an abstract thing too, to do with your measurements of distance and time, typically made using the motion of light.

Who Discovered closed timelike curve?

Kurt Gödel
The ‘closed timelike curve’ concept, introduced by Kurt Gödel, had highlighted logical inconsistencies with the concept of time, as we know it. These potential problems regarding time were further explored in the 1960s, when interest in general relativity was growing among scientists.

Is the universe a closed timelike curve?

It turns out that general relativity allows for closed timelike curves to exist. In 1949 Kurt Gödel devised a rotating universe that has CTCs and is perfectly allowed by relativity.

What is a timelike vector?

A timelike vector connects two events that are causally connected, that is the second event is in the light cone of the first event. A spacelike vector connects two events that are causally disconnected, that is the second event is outside the light cone of the first event.

What is timelike interval?

The value of a timelike interval determines the proper time between the two events—that is the the time between the events as measured in a frame of reference where they occur at the same position.

Do all objects follow geodesics?

It is this curvature of spacetime that gives rise to what we interpret as gravitational acceleration. Note that there is no mass in this equation – it doesn’t matter what the mass of the object is, they all follow the same geodesic (so long as it’s not massless, in which case things are a little different).

Are geodesics straight?

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines.

What is a closed timelike curve?

Closed Timelike Curve. In a closed timelike curve, the worldline of an object through spacetime follows a curious path where it eventually returns to the exact same coordinates in space and time that it was at previously. In other words, a closed timelike curve is the mathematical result of physics equations that allows for time travel.

Can black holes have closed timelike curves?

In the 1960s, solutions to the field equations were found that describe not only stationary black holes, but also black holes that are rotating or spinning. To the surprise of many, these solutions appear to show that the space and time immediately surrounding a rotating black hole can also contain closed timelike curves.

What are timelike and spacelike events?

Any single point on such a diagram is known as an event. Separate events are considered to be timelike separated if they differ along the time axis, or spacelike separated if they differ along the space axis.

What happens to the light cone in curved spacetime?

In curved spacetimes the light cone will be “tilted” along the spacetime’s geodesic. For instance, while moving in the vicinity of a star, the star’s gravity will “pull” on the object, affecting its worldline, so its possible future positions lie closer to the star. This appears as a slightly tilted lightcone on the corresponding spacetime diagram.