Nicholas asked:
Is one of the reasons there are no time travellers visiting us (the general public) in the past because time travel is never seriously researched, given the stigma attached to the subject, and thus is never invented ? Could there be other reasons, such as future government regulation/monitoring or limited use as another reason for no time travelling tourists in the past or present so to speak ? Thank you for your time.
Answer by Craig Skinner
Why indeed no time tourists from the future. No record of hordes of oddly-dressed strangers in the crowd in contemporary accounts of Christ’s crucifixion or Lincoln’s Gettysburg address, although both events would be enduring favourites on the must-see list of future time tourists.
Possible reasons are:
1. Time travel (TT) to the past is logically impossible.
2. TT to the past is metaphysically impossible.
3. TT to the past is nomologically impossible.
4. TT to the past is physically impossible.
5. TT to the past is possible, but no further back than the date of invention of the time machine.
6. TT to the past is possible but prevented/limited by future government or by lack of research (your suggestions).
Of these, I favour 4. and 5.
I will deal briefly with each.
1. Logically impossible: TT to the future presents no in-principle problem. First, we all do it, albeit at the same rate of one hour per hour. Secondly, time dilatation predictions of Special Relativity are well-confirmed: thus, were I to go on a space flight reaching near-light speeds, returning 10 years older, I would find the Earth thousands of years older. But I could never return to the earlier time. This effect has been confirmed for particles in accelerators, and the expected very tiny effect for big objects in ordinary flight.
But TT to the past allegedly yields logical impossibilities (grandfather paradox; free-knowledge paradox). I don’t think this is so. Remember that the actions of future time tourists are already built-in to the past, there is only one past, not different versions, the past can’t be changed, although TTs might have had a hand in bringing it about in the first place. Thus, you didn’t kill your grandfather when he was a boy, so no matter how often you go back in time intending to kill him, you always fail to pull it off.
So, in my view, TT is logically possible.
2. Metaphysically impossible: if the past doesn’t exist, there is no destination, so TT impossible. So argue ‘presentists’. But I favour the ‘block’ view of past/present/future all existing, and will assume this. In fact, even on a presentist view, a coherent story about TT can be told, but it is more complicated and I will leave it out.
So, TT is metaphysically possible.
3. Nomologically impossible: this means contrary to the laws of nature (as they happen to be in our universe). Most scientists believe that this is not the case. And I will go along with that.
So, TT is nomologically possible.
4. Physically impossible: although allowed by natural law, there may be insufficient resources in the universe to actually do it. Thus current suggestions as to how TT could be engineered (spacetime wormhole; colossal rotating cylinder) need incredible amounts of energy or large amounts of exotic matter, maybe more than a whole galaxy (or more) could provide.
So TT might remain forever a practical impossibility.
5. TT but no further back than time-machine invention: current schemes entail this, and of course it explains why no time tourists so far.
6. Government controls/ lack of research: I doubt the former would stop determined groups with the technical knowhow and resources. But it would be a lot of resources for little gain. After all, nothing would change, the actions of any visitors from the future have already been built in to all past events. I don’t think any stigma attaches to TT, or that research is or will be limited by apathy. It’s perennially popular with scientists, philosophers, writers and the public, and will remain so unless it’s shown to be impossible, and I doubt this will happen.
It’s amusing to speculate that in the distant future we, or our successors, whether biological or machines, might discover how to create universes with desired laws of nature, travel back to the singularity 14 billion years ago and destabilize it resulting in the Big Bang which starts off our universe.
Ask a Philosopher 
There are so many possible reasons, so many variables. In modern physics, time and space aren’t so different. Physicists speak of space-time, or the space-time continuum, because time and space aren’t actually two different and separate things. Currently, we don’t know much about time travel into the past, but there are a few things that we’re sure of. The H.G. Wells concept of time travel, where the time machine moves through time and not through space is naive. Travel through space-time means traveling through both space and time.
Since space is so incredibly huge, moving back just a bit in time could cause one to end up far, far from one’s starting point spatially. The hardest trick of time travel wouldn’t be going back in time. It would be staying on the same side of the universe while moving back in time. It could be that time travel is possible, but time-only travel isn’t. That would mean that, when people want to travel back in time, they’d have to go someplace far from their point of origin. If your point of origin isn’t well known in the big universe, and people who grew up there can’t travel back in time to it (via time-only travel), then few or no time travelers would ever end up visiting it. Why would anyone who didn’t come from our planet visit it? With all of the hundreds of trillions of other places in our galaxy alone?
If I stand in the middle of some mid-western desert for days and days, and nobody comes by, does that mean that it’s physically impossible for people to drive into the desert? Also, some destinations are harder to reach than others. If I’m standing in the middle of Antarctica, and no planes come by, does that mean that powered flight is impossible?
Then there’s the issue of windows of opportunity. Our planet is fairly young compared to the oldest parts of the universe, but it’s been around for a long time. Modern humans have only been around for tens of thousands of years, and civilization has only been around a few thousand years. Technological society is only a couple of centuries old. Any given historical event might only last for a few hours or at most a few days.
If you think of this temporal window as if it were a target in space, and consider how incredibly immense the known universe is, that’s a pretty tiny target to hit intentionally. It’s also too small to bump into by accident, given how many billions of other targets exist. In a sense, the answer to the question of why time travelers haven’t visited our time and why extraterrestrials haven’t visited our planet might be the same. The universe is very, very big, and we don’t live at the center of it, spatially or temporally. We live in the boonies. Until very recently, we didn’t even have cordless phones! And our video games sucked!
There is another possibility, that most people don’t want to consider. Time travel might be possible, and even fairly easy to achieve. But our species may die out before we ever build our first time machine.