4D-Space-Time Warping, as said by Einstein is the cause of Gravity, in the Special Relativity, which I think is just an artifact of Gravity, and also seen in the Electro Magnetic and Atomic Fields but not talked about. One day I shall present a paper on this aspect which is underway.
Space-Time Entanglement is possible at a particle level, a particle from Past can appear in Present and Future, and vice versa, but this also needs crossing of 3D World, which I do not think Human Beings can cross in the Physical Body Frame. There has been some talk about Astral Body, or Soul doing the Time Travel, among the UFO Research Community, Yogis, and some clairvoyants/spiritualists/saints etc.
One law of Thermodynamics, which says most of, if not all, the reactions are irreversible, (I forgot the exact technical name but this is the essence), are it also related to all entities trying to reach their lowest state of entropy, and for them to reverse that trend is almost impossible. In other words, once you destroy or age you body, I do not think there is any machine that can bring you back!
What Einstein said is badly misconstrued, and based on a misunderstood principle that Space Time Fabric is curved and is the cause of gravity. It is just a mere effect.
The only way it may be possible if you get help of some extra dimension and it is a two-way Quantum Entanglement Tunnel of Macroscopic size!