Nikola Tesla was the quintessential mad scientist, an unparalleled and unrestrained mad genius, fortunately for humanity he was not an evil or immoral one. His madness and inability to conform to the norms of the scientific community rendered him somewhat of an outcast and recluse. Perhaps it was his intellectual prowess and inability to conform, that led to his keen ability to think outside the box and devise or inspire the development of much of civilizations modern miracles.
He had a white female pigeon that he was in love with, allegedly he saw light rays shooting from her 'gorgeous violet eyes', that others could not see . 
Perhaps his love for his pigeon was a product of his difficulty in interacting socially with ordinary human beings. He also suffered from OCD - obsessive-compulsive disorder, he was adamant that every meal should include exactly 17 folded linen napkins - not 16 and not 18 but 17. He constructed a tower in New Jersey in an attempt to communicate with aliens and at one point claimed to have contacted beings from Venus. 
A large swath of Tesla's works never saw the light of day, or so we are led to believe. Although Tesla developed technology that he believed would be financially rewarding, he also engaged in projects that simply stoked his intellectual curiosity.
Very little is known of these projects. He commonly published many of his findings without regard to profit potential, some were simply committed to paper and never disseminated and still more festered in his over burdened burgeoning mind never to see fruition. He designed, constructed, and tested many of his inventions using only the power of mental concentration. Without making a single sketch.
He pondered about gravity, anti gravity, free energy, invisibility and the physics of time as well the potential of time travel.
Work on his step-up transformer and transmission of electrical energy through the atmosphere led him to believe that time and space could be manipulated by using rotating, highly charged, magnetic fields.
In March 1895 a NY Herald reporter found Tesla in a cafe visibly shaken after being accidentally zapped by over 3 million volts of electricity. "I am afraid, that you won't find me a pleasant companion tonight. The fact is I was almost killed today. The spark jumped three feet through the air and struck me here on the right shoulder. If my assistant had not turned off the current instantly in might have been the end of me." said Tesla.
Tesla claimed that contact with the electromagnetic charge put him outside his time-frame. He claimed that was able to see the immediate past, present and future simultaneously, but unable to act as he was paralyzed within the electrical field.  A few days later Teslas Lab burnt down, uninsured and with very little resources he was in effect ruined - temporarily at least.
His assistant, by switching off the electrical current cut off his journey in space-time and also saved his life. Detractors speculate that like the rays of light from his pigeons eyes, this phenomena was something only Tesla himself would see, while others believe that it was duplicated years later in the Philadelphia Experiment with hideous results.
Merchant seaman Carlos Miguel Allende  , claimed to have witnessed a similar experiment, also in 1943, of a ship being made invisible using strong electromagnetic force fields as described in the Philadelphia incident.
Whether or not Tesla continued research into space-time or time travel is not certain, he did however issue a statement at the age of 82 that hints he may have.
'I have worked out a dynamic theory of [a] gravity in all details and hope to give this to the world very soon. It explains the causes of this force and the motions of heavenly bodies under its influence so satisfactorily that it will put an end to idle speculations and false conceptions, as that of curved space. According to the [b] relativists, space has a tendency to curvature owing to an inherent property or presence of celestial bodies.... 
Einsteins theory of relativity is what Tesla is referring to when he states - [b] relativists - Einstein delved into 4 dimensional physics when he determined that massive objects cause a distortion in space-time, which we experience as [a] gravity. He basically added a new dimension to the definition of gravity as well as time and space.
1. Interview with Nikola Tesla from 1899
2. The Lost Journals of Nikola Tesla Page 124
3. Tesla and the Aliens
4. The Case for the UFO Page 9
5. Skeptoid Questions the credibility of Carlos Miguel Allende,
6. OCCULT ETHER PHYSICS Page 95
Modern Mechanix Magazine in a 1933 article tells of a 1920 gathering attended by Edison and his associates where Edison demonstrated a photo-electric cell that revealed spirits in a beam of light. The American Magazine in 1920 interviewed Edison and he stated 'I have been at work for some time building an apparatus to see if it is possible for personalities which have left this earth to communicate with us.'