Eclipse proves space warps exist
The first experiment to test Albert Einstein's 1915 assertion of warped space—embodied within his general theory of relativity—occurred on May 29, 1919 during a solar eclipse. The calculations made after the observation proved that mass warps space. In the case of the eclipse, the sun's mass warped space and the light of nearby stars was displaced by that warp exactly to the degree predicted by Einstein's equations. The light waves followed the curvature of space bending around the massive gravity well of the sun. 
While the reality of space warps had been established, time warps remained merely scientific speculation and the fodder of science fiction literature.
The science of space-time warps finally got a firm footing with another experiment that measured the dilation of time between two jetliners flying in opposite directions around the circumference of the Earth.
Accelerating mass and time dilation
During October 1971 two physicists, Hafele and Keating, installed cesium atomic clocks-exactly synchronized with the master atomic clock at the US Naval Observatory—on two jet aircraft. The respective aircraft were flown around the circumference of the world: one eastward the other westward. After the flights the scientists compared the time of the aircrafts' clocks to the time on the clock at the Observatory.
Because one plane flew with the rotation of the Earth while the other flew counter to our planet's rotation, the difference in their velocity affected space-time. The two scientists were able to measure a disparity in time between the two jetliners: the minutest fraction of a second. The jetliner traveling with the rotation of the Earth had been accelerating closer to the speed of light. Again, as Einstein's equations predicted, time slows as mass accelerates towards the speed of light. The dilation of time is caused by the warping of space-time.  
The ability to warp time either naturally or artificially has been a dream of Man since time immemorial. Ever since H. G. Wells' "The Time Machine" popularized the notion of time travel, the public has been enamored with the idea of breaking free of the constraints of time. Later, in cinematic works like "Forbidden Planet," "The Fly" and the television series "Star Trek," the concept of warping space and manipulating or transmitting matter using warped space has been explored.
Despite space and time warps being a reliable standard in many works of popular fiction, the physical reality of warped space-time is stranger than the fiction that envisions it. If, for example, space could be warped back upon itself then time could be looped. The looping of time would violate the assumed law governing causality.
For centuries it was assumed that under the law of cause and effect a cause must precede an effect. Yet if space-time could be warped by creating a loop or tunnel then, theoretically at least, it might be possible to have an effect precede the cause.
Effects preceding causes seem to violate common sense and an orderly universe. After all, if such a thing were true in the real world it would be feasible that you could arrive back home from a dinner out before you even left for the restaurant!
Although an effect occurring before its cause seems paradoxical, mathematically the physics allowed for it. Therefore, a landmark experiment was created. In an experiment that predated John Singleton's polarization synchrotron project at the Los Alamos National Laboratory, European experimenters transmitted sub-atomic particles across the European continent at faster-than-light speed.  The results were shocking. Researchers discovered that some of the particles arrived before they had been sent. The time span only covered billionths of a second, yet there was no denying that the law of causality had been violated. Indeed, the experiment seemed to reveal that causality could work either way.
Retrocausality and quantum superarrivals
“"If you have the block universe view, the future and the past are not any different, so there's no reason why you can't have causes from the future just as you have causes from the past." 
That statement, made by Australian physicist David Miller lays the foundation for time warps, retrocausality and the possibility of time travel.
Experiments conducted with particle accelerators have revealed hints of sub-atomic particles that regularly travel backwards in time. Matter and energy, two forms of the same quanta expressed as either waves (energy) or particles (matter), are governed by the ebb and flow of space-time. Everything in the universe—everything that is—is simply a transfer of information from one state of existence to another. The understanding that time can flow in either direction and already does so in nature is a monumental breakthrough in knowledge that may one day lead to technologies capable of tapping into information from what we currently term “the future.”
The study of quantum superarrivals, lays the groundwork for the exploration of that area of quantum physics wrestling with the evidence of information leaking from the future into our present. It lends credence to the suspicion that the universe itself is operating as a natural time machine on a massive scale. But rather than time marching inexorably forward (as had always been assumed), the actual nature of space-time is a two-way street. Causality is valid, but so is retrocausality.
All of this explosive information has left some physicists scratching their heads. They recall Einstein's assertion that “God doesn't play dice with the universe.” Yet the violation of causality, particles flipping forwards and backwards in time, and the credibility of the chaos theory seems to violate classical physics and the body of knowledge that has been painstakingly gleaned from hypothesis and observation over the past few centuries. What could account for the seeming paradoxes that now stare researchers in the face almost everywhere they look when investigating the sub-particle and quantum universe? Can this dilemma, unsolvable on the surface, be resolved?
Yes it can. If one accepts that our universe is only one of many universes—perhaps infinite universes—then the riddle of space-time goes a long way to being solved.
Space warps and time warps can be accounted for—and in fact must exist—if one postulates the interaction of our universe with many others. Thus, the mysterious actions of our universe that seem to violate established physical laws make perfect sense if there is interaction with other realities at higher dimensions. The way to prove this is to look at the disparities in space-time. These disparities are clues that can lead us to discovering the nature of the other realities our island universe is trading information with on a regular basis. This new physical branch is known as the study of the multiverse concept.
The existence of multiverses was first hinted at during 1970s laboratory experiments with a device known as a “Josephson's Junction”-a superconducting electron generator that permits researchers to study the properties of sub-atomic particles traveling through regions of near absolute zero temperature. At absolute zero all motion comes to a halt, therefore the closer the temperature is to absolute zero the more that matter and energy slow down.
Researchers observed during some of the experiments that particle streams shot between electrode gaps near absolute zero conditions briefly disappeared. The particles seemed to wink out of existence momentarily before popping back into existence. Where these particles went was hotly debated. The most likely answer is that the particles briefly passed into another dimension/reality, exchanged information, and then returned to this space-time continuum.
A measure for the multiverse
“ … the multiverse has developed rapidly from a being merely a speculative idea to a theory verging on respectability. There are good reasons why. Several strands of theoretical physics - quantum mechanics, string theory and cosmic inflation - seem to converge on the idea that our universe is only one among an infinite and ever-growing assemblage of disconnected bubble universes.” 
The multiverse theory fills the gap that Einstein sought for his failed Unified Field Theory. If there are many higher dimensions and those dimensions are interacting (exchanging information) with other universes then the creation of a unified theory of everything is brought much closer. Of course, as with everything in science, the solution of one mystery creates a plethora of new questions.
The resolution of dark matter, string theory, space warps and time warps can be accounted for by physical interaction between multi-universes. That space warps and time warps exist has been proven through the observation of nature and experiments in the lab.
Gravity wells, black holes and singularities
Kip Thorne and Stephen Hawking are two of the world's leading experts on a phenomena no one has ever directly observed: the black hole. Black holes are the remains of super-giant stars that have exploded in supernovaes and then imploded falling into a gravity well so deep that everything around them—including light and space—is dragged into them. Space around black holes is warped to an incredible degree, so much so that at the delineation between warped space and the hole itself (called the “event horizon”) also warps time.
Much speculation has revolved around the physics inside a black hole. Obviously whatever is inside it, termed a “singularity,” must exhibit pretty exotic physical properties.
A new thought, however, about singularities has recently emerged. Tied into the research of multiverses, this hypotheses speculates that black holes might be a safety valve and a major conduit connecting one universe (or a multitude of universes) together. In a way, black holes are networking in a mosaic of warped space-time and transferring information in the form of raw energy to other realities outside of our own.
As researchers gain more knowledge about the properties of warped space and time warps we will move to a day when artificially warping space to travel through it like the starship Enterprise will become a reality.
Thinking further, if we can get a firm grasp on the nature of time and how everything else is embedded within it, time travel will become possible. And if time travel too becomes a reality then time travelers may be walking among us even now.
4.“Physics Beyond the Speed of Light” Discover, article number 42.
5.Foundation of Physics Letters
6.David Miller of the Centre for Time at the University of Sydney in Australia. SFGate.com, “Science hopes to change events that have already occurred,” by Patrick Barry.
7.Discussion of Cramer's retrocausality experiment.
8.Of Josephson's Juncntions, Quasi-particles and Cooper Pairs
9.New Scientist, “A measure for the multiverse.”