We are all time travellers as time is just a measure of the rate at which the universe is running down, i.e. increasing entropy, so is always in that direction.
If time travel was allowed in the reverse direction then we would need to send an observer back to experience it as such. Unfortunately this would also mean that, as far as this observer is concerned, it would have to put the WHOLE of the universe, i.e. every particle, each and every one in its original position and each with its original momentum and ground energy as they were back at the time the observer makes the journey INCLUDING the particles that make up the observer! This might be the reason for the observer (the time machine) vanishing in a violent explosion as its constituent parts tear of to their various origins at that distant time and place.
I am well aware that I am missing the theoretical knowledge and the mathematics to describe what the above words mean but I am pretty sure this is the way it works no matter how many mathematical fuddles are used to get over this simple concept of why we cannot fight the whole of the universe and the universal increase in entropy as we are part of it and cannot stand apart from it such a way that we are not torn to shreds as our atoms are dispersed through time and space to regain their positions at the time we seek to visit. This is what it really means to go back in time to a universe as it was, back then. If you had at your disposal a universe full of energy, the knowledge about all its constituent particles, and the wit to control all of this, then you might, just, have a chance.
OR, am I missing something?
I am also aware, as are others in the earlier comments, that what we called time is not a real thing it is just the measure of the rate of change of entropy which we also know can vary, relatively, in the forward direction simply by accelerating, relative, to another body such that our rate of change of time is different to the body that is not accelerated. Time appears to be a construct of the mind to enable us to comprehend change and exchange ideas about such change in much the same way as we agree about colours as we can never be certain that the colours we perceive are the same as those perceived by others. Time also flows differently according to mood which also seems to suggest it is a construct of the mind and not a real phenomenon.
There have been designs for interstellar ram-jets that collect hydrogen nuclei using huge electrostatic collector/compressors to fuse these together to make heavier nuclei which they expel out of the back at very near the speed of light thus propelling the ship at, say, a constant 1g using the energy from the, free, interstellar hydrogen fuel. This, if perfected, could make the Nebulae in Andromeda about a lifetime away for the travellers but about 2.5million years, each way, for those living on Earth. There is, of course, the ablation and radiation due to the extremely high energy particle flux (blue shifted, to overcome - maybe we would have to convert a trillion tonne asteroid into a spaceship - or, just maybe, it is all just a pipedream! In any case this is still time travel into the future, not the past.
I would be very much obliged for a critique on the above ideas as I have long (50 years or more) wondered why I have not seen this idea posited anywhere else as it seems such a reasonable rebuttal to the question of the possibility of time travel into the past.
John Barton Wood
Leeds, West Yorkshire