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I CLosed Timelike Curves

  1. Sep 25, 2015 #1
    Would someone explain to me in lay men's terms exactly what a CTC is. I understand that it is a closed timeline curve and that it allows( in theory) time travel to one's past. My question is how does one get into a CTC: Do you have to be traveling in space and at a certain speed? Does one have to enter a black hole?
    What exactly is the physical thing?
  2. jcsd
  3. Sep 25, 2015 #2


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    First let's define a timelike curve. Suppose some object is moving at less than the speed of light. Then if we use consistent units for space and time, such as light-years and years, the distance it covers is less than the time. If you trace out the object's track through spacetime, called its world-line, we call this a timelike curve. It's called timelike because it covers more time than space. All material objects have timelike world-lines. Since observers are material objects, they have timelike world-lines. Because space is mostly empty, most timelike curves are not actually the world-line of any object, but you could consider them as hypothetical world-lines.

    A closed timelike curve is a timelike curve that forms a closed loop rather than a line that stretches off indefinitely into the past and future. If it was the world-line of an object, it would describe a case where the object revisited the same location in the past and took over the world-line again from its own past self. (This is unlike the science-fiction scenario where you go back to the past and there are two of you at once.)

    In most spacetimes that possess CTCs, the CTCs are a common, ordinary type of timelike curves -- there is nothing special or dramatic going on in the region of spacetime where they occur. For example, suppose you take a piece of lined notebook paper and turn it sideways, so that the blue lines are upright. This is a spacetime diagram, and the blue lines are timelike curves. If you now wrap the paper into a tube, so that the blue lines join up with themselves, then each blue line is a CTC. This is a universe where time repeats. In this universe, you're still looping through time regardless of whether you're following a CTC. A CTC describes the case where you happen to revisit the same point in space again.
  4. Sep 25, 2015 #3
    Thank you bcrowell,
    I am still a bit confused. I understand the general concept but would you elaborate on the specifics of(theoretical) time travel: for instance, say I want to travel into my past, just how would this be accomplished- I understand this is all in theory. Would I myself have to be traveling in space, at a certain speed along this curved space time so as to link up with my past like the tubed paper? Would I have to be approaching the speed of light or overcome it to accomplish this? Would I have to be traveling in space at all when you consider the earth is moving?
    I guess, I would like you to explain how exactly the theorists describe this happening.
  5. Sep 25, 2015 #4


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    Unfortunately, there are no specifics.

    Loosely speaking, the equations of General Relativity (the Einstein Field equations or EFE) describe various ways in which bcrowell's figurative sheet of paper might be folded and twisted. Some of these (such as bcrowell's example of rolling the paper into a tube) lead to configurations of space-time that contain closed time-like curves. However, just because something is a solution to the EFE doesn't mean that it necessarily can be made to happen - all real-world configurations of spacetime must be solutions of the EFE, but not all solutions of the EFE are possible real-world configurations of spacetime. As far as we know, the solutions that contain interesting CTCs also require other conditions that are more or less physically impossible. "Set up some impossible initial conditions" is not a happy start for anything specific.

    Another approach is to note that we don't need to do any warping, curving, twisting of spacetime to produce time travel. If you google for "tachyonic antitelephone" you'll see how just the assumption of faster-than-light travel can lead to that possibility - but again, that's an impossible initial condition.
  6. Sep 25, 2015 #5


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    In that example, everybody in that universe is a time traveler. You don't have to do anything special to be a time traveler. It happens to you automatically, and you can't avoid it. Your state of motion is only relevant in determining where you end up after you complete a loop.
    Last edited: Sep 25, 2015
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