|Source: see "here" after Type IV and V below|
I used a reference to the Kardashev Scale to answer the following question (proposed to me by a friend on Facebook):
"Do you think mankind will ever master time travel?"
Short answer: no, with caveats.
I did qualify my "no" also with the 2nd Law of Thermodynamics, and gave a link on Entropy. I also pointed out that every moment of our existence, we are time travelers - the motion of course, traveling forward.
In the series "Hannibal," the infamous Dr. Lecter discusses his longing for Mischa, his sister (you'll have to read "Hannibal Rising" by Thomas Harris to get the back story). In a nod to "Rising," he spoke of dropping a teacup in one scene of the season finale (most of which as someone who read the book series I did NOT predict coming), and hoped to see it reassemble, presumably witnessing the flow of time going in reverse, thus he would see his beloved sister again. That is a longing for something Entropy doesn't allow - backwards time travel.
I also pointed out as a species, we're not even at Type I on the Kardashev Scale:
Type I: able to marshal energy resources for communications on a planet-wide scale, equivalent to the entire present power consumption of the human race, or about 1016 watts. Here, Carl Sagan begged to differ, due to power gradation, we're more like (on his measure) a 0.7 civilization, or 7 x 1015 watts. We have pockets of deployed resources, but definitely not "planet-wide," else there would be no economic distinctions: east/south side to west side; 1st and 3rd worlds. Perhaps we could edge up our score with renewable alternatives?
Type II: surpasses this by a factor of approximately ten billion, making available 1026 watts, by exploiting the total energy output of its central star, using a Dyson sphere.
Type III: evolved enough to tap the energy resources of an entire galaxy, ~ 1036 watts.
Type IV and V here (along with the source of the shway photo above)
Let's take Chris Pine - the current Captain James T. Kirk. He weighs 175 lbs or 80 kg.
The Trek transporter converts humans into pure energy, ignores Heisenberg Uncertainty (via a Heisenberg compensator, of course...o_9), and somehow miraculously reassembles them perfectly, managing not to create horribly misshapen"Kirk-copies."
Utilizing the famous (Special Relativity) E = mc2:
80 kg x (3 x 108 m/s)2 = 7,200,000,000,000,000,000 N-m = 7.2 x 1018 Joules, or 7.2 x 1018 Joules per second (watts), clearly putting 23rd Century Warp Tech somewhere between a Type I and a II (I'm calling it "1.12"), at least to accomplish "scattering a man's atoms" about the universe (gotta love Bones McCoy's wordplay).
However, Wormholes are theorized to exist, as were once Black Holes (see Kip Thorne's "Black Holes and Time Warps: Einstein's Outrageous Legacy"). I was astonished to find out that Einstein and other physicists of his day did-not-want Black Holes to exist (at that time, they were called Schwarzschild singularities). It was pointed out in Kip's book that the solutions in General Relativity predicting Black Holes were initially themselves astonishing.
Wormholes, if detected, are probably very tiny and would take some kind of "exotic matter" to stabilize it for anything like the Enterprise, Defiant or Voyager to traverse it safely. That would put us squarely in Type II and out of the fossil fuel choke hold, plenty of food, world peace; "tea: Earl Grey - hot." A Wormhole would be a bridge in time as well as space, (Heimdall! Open the Bifrost!), but I think your time travel would be limited to the manufacture date of your Star Gate, i.e., if you made it 7 June 2014, this is as far backwards that one could travel (no reverse-breaking teacups or grandfather paradoxes).
So in essence: like any good Trekkie, or the mourning Dr. Lecter: I'd love to see it, but I don't think I will in my lifetime. We'd have to get smarter as a species than we've currently demonstrated in science.