Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What Are Closed Timelike Curves?

  1. Aug 25, 2008 #1
    i was going over some relativity search online and came across what is called a closed timelike curve and that i actually allows time travel, am i right?
  2. jcsd
  3. Aug 25, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    A "curve" is a function [itex]c:A\rightarrow M[/itex] where A is some interval of real numbers and M is the spacetime manifold. "Timelike" means that if we call the tangent vector v and the metric tensor g, then g(v,v)<0 at all points on the curve. (If we define the metric with a +--- signature instead of -+++, it's ">" instead of "<"). "Closed" means that c(t+T)=c(t) for some real numbers t and T such that both t and t+T are in A.

    A timelike curve is the type of curve that can represent that path of a massive object through spacetime. If it's closed, the object will meet a younger version of itself at some point.

    Edit: I should probably add that the condition g(v,v)<0 can also be written

    [tex]g_{\mu\nu}v^\mu v^\nu<0[/tex]

    and that in a local inertial frame, this is just

    Last edited: Aug 25, 2008
  4. Aug 25, 2008 #3
    i was thinking it over,about the constant energy.ctc's would violate 2nd law of therodynamics,also i looked up that GR allows ctc's but QM does not.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook