Like evolution, time travel is not a supposition, for it has a scientific basis. Disbelief in time travel is akin to those who, for religious reasons, believe in Creationism in spite of there being no hard science to back it up.
Before delving into the science behind time travel let us briefly mention some classic works dealing with time travel.
The first such title is historian H.G. Wells' "The Time Machine" (1895). Predating the publication of Albert Einstein's Relativity theories it, of course, can't be said to have suggested Einstein's suggestion that time travel might not be completely baseless given the proper technological advances. Nevertheless, Well's the "Time Machine" has contributed its share of importance to the concept of time travel.
The television series "The Time Tunnel" is also another work dealing with the subject of time travel. The impact of the this series is negligible. It did, however, focus on the subject of the causality paradox in episodes where the time traveler found himself aboard the Titanic hours before it sank. He endeavored unsuccessfully to change the course of history. There is an unwritten rule in time travel literature that suggests that changing history via time travel is somehow impossible even when attempted.
The movie "Return to the Future" also presents the problem of causal paradoxes which we will later present and study the views of Cosmologists Stephen Hawking  and Misio Kaku . The causality paradox can best be summarized in the question if a time traveler goes back and prevents his mother from marrying his father, wouldn't he then never have been born? If he had never been born due to history having been changed how could he then have been able to travel back in time to prevent his parents from marrying?
There are several adjustments to this conundrum. One solution is that there are different time lines. While the time traveler may have altered the particular time line which no longer includes his conception by his parents, in a separate, but equally valid, timeline his parents did marry and his mother did, in fact, give birth to him.
This paradox has been offered by some cosmologists, as well as detractors of the theory of time travel, as making time travel into the past, at least, unfeasible and causally problematic.
Briefly, let us outline the simplest type of time travel into the future but not the only one. It has been proven by experiments in space that when people travel faster than people on the ground the astronaut's passage through time actually slowed down the aging process but at a minuscule amount. Therefore, this theory which was foreseen by Albert Einstein, has now been experimentally verified.
In order to take this concept and make it true time travel imagine, if you will, a space ship travelling at incredible speeds towards the nearest star. On board is a space traveler whose other twin remains on Earth. Once the star traveler has returned to Earth he will have found, if his twin has not died of old age, that he or she has aged only a few years while the twin (s)he left behind has aged considerably. The other amazing outcome of this experiment is that the time-star traveler will be seeing decades as a younger person and all the technological advancements and historical outcomes than if (s)he had stayed on Earth with his or her twin.
Though some would find this cheating at time travel since it uses laws of science to slow down the aging process and thereby propel the star traveler into a future that s(he) would otherwise never have seen, it is, nevertheless, as bona fide time travel as may be possible in the foreseeable future.
To contrast future travel in time with backward travel in time, we have a thornier problem. It is believed that you can attempt traveling back in time by building a wormwhole whether by harnessing an actual black hole singularity or by creating a "baby wormwhole" in the laboratory and using that to create a closed loop from the time of creating the wormhole to some future time. Backward travel in time would only be as far back as the time that the wormhole was created and no further.
The ease with which the famous time traveler of H.G. Wells' "The Time Machine" flitted back and forth, whether venturing millennia into the distant future or travelling back to his own time, remain speculative fiction. The literary construct of his novel has other significant points which we will not go into here.
Finally when all the evidence, theories and concepts have been presented, some will still choose, as they do in the evolution vs. creationism issue, that it depends on what you choose to believe and not what scientific proofs, concepts or theories suggest what may or may not be possible.
In the mean time, enjoy your slow travel through time in your own life. It may very well be the only type of time traveling that most, if not all of us, will ever experience.
[This post needs more footnotes.]