Even before the advent of modern physics established by Max Planck, Niels Bohr, Albert Einstein and many more in the opening decade of the 20th Century, the idea of time travel had already been playing in the minds of notable science fiction writers lead prominently by Jules Verne and H.G. Wells.
The Time Machine by H.G. Wells brilliantly chronicled the idea and possibility of time travel. He argued that time is a dimension exactly identical to the three dimensional space we are moving back and forth and up and down in our real world, thus possibly in time- forward and backward travel. Well's succeeded to create a compelling fiction of time travel on the strength of this argument, but a plain science fiction writer he was and without proper background in the natural sciences, his book did not offer any sort of scientific support to his idea.
As far as science history is concern, Albert Einstein did not mention reading Well's; in fact he did not like science fiction. But, his theory would later provide a compelling evidence of the theoretical possibility of time travel, described by Well's short novel.
His Special Theory of Relativity published in 1905, theoretically speculated that traveling close to the speed of light (300,000,000 meters per second) would physically alter time by dilating it. Any relativistic traveler would find his time running slowly than any one at rest on earth. The effect of which when he landed, would be himself too distant in the future. The people his age when he left would have aged a couple of decades his senior. This seeming backward travel in time was never been confirmed yet by any actual relativistic traveler as the spacecraft that could travel close to the speed of light remains a technological marvel, but, Einstein's prediction of time running slower has been experimentally confirmed.
In 1916, General Theory of Relativity was published as an extension of the Special Theory published in 1905 to include gravity. One of the tenets of the new theory was the physical and mathematical underpinnings of time being the fourth dimension in addition to the common three dimensional space where we are moving in the real world up and down or forward and backward.Thus, laying ground to Well's pioneering and fictional idea that one may travel forward and backward in time; up and down as well, since time and the ordinary space we live and move were the same thing according to the new theory. Without question, General Relativity was extremely effective and successful in explaining previously unexplained natural phenomena. But, Einstein himself being completely aware that not all consequences of a scientific theory is valid, he passed way in 1955 far from being convinced of time travel in factual occurrence.