Traveling through time according to the laws of physics as propounded by our foremost scientists is probably going to be a near impossible feat for any human being, as a result of the complexity of the variety of theories governing its realization.
Necessity, they say is the mother of invention. We have probably not found any reason for traveling in time, hence the reason why we have erected a diverse string of complicated theories against realizing it. Perhaps when we are ready, we will keep it simple and realize that it is not as complicated as it seems.
I am not very competent when it comes to quantum physics, or string theory or even Einstein's theories of general or special relativity. I am a great fan of science fiction though and my most favorite science fiction show of all time is the Star Trek Series. I believe the transportation technology utilized in this show is the key to time travel. The principle underlying this technology seems to indicate that it is based on the dual nature of light; that is the ability of light to alternate between being a waveform and particle streams. As most scientists are aware, the microcosm is an overblown image of the macrocosm. Electrons revolve around a central proton in virtually all the elements of the periodic table just like planets revolve around a central star.
So called living things are more or less a derivative of this commonality. It is possible that human beings have an innate ability to transform themselves into waveforms from the rigid form that they are, or an external agent like laser energy could be used to effect the same change. If such a thing were possible, without the loss of consciousness or the sense of perception, then as a light wave, it will probably be a matter of modulating a ray of light from a distant star with our perceptive waveform and following it either forwards or backwards to our time destination. In the same vein, Einstein's idea of an ever increasing mass will become irrelevant, since we well become one with whatever vessel we design to take us to our destination. Such a vessel will become light waves and each individual on board will transform into light waves at the very high velocity of light and above. No one on board will notice the change in structure, since such changes between cellular and waveform are instantaneous and alternating possibly every nanosecond of less.
So in the Star Trek series then, the true sequence of events when a crew member is beamed out of or back on board the Star ship is not that the individual is being reduced to their particles and then beamed out, but that the individual actually has control of their atomic structure and are self conscious and perceptive at all times, and actually initiates the conversion of themselves into a waveform, which uses the beaming light as a guide to get to their co-ordinates, just like we currently travel in cars over highways to get to our destinations. An ancient human being from 2000+ years ago would not have believed the ability of humans to drive cars either.
The question is how do we arrive at this point. As humans, we do believe in a great deal of ideas like reincarnation, spirituality, being born again and a whole category of esoteric ideas. In which case, we are probably on the right path. For those of us who do not believe in religion, we probably need to find the threshold of pain. There is a level of sound that human beings cannot hear, but which can damage their hearing if directly exposed to same. Perhaps, in the same vein there is a wavelength of high intensity light on the electromagnetic spectrum that can resonate with and alter our constitution from flesh to waveform without killing, disabling or making us lose perception of what we are. I believe this may be what the trekkers mean when they make reference to "sentient beings".