Time

Physics has very little knowledge about time. There definitely is time -- otherwise everything would happen at once. Time also clearly has direction. More entropy, less useful energy, is always later. But there's no clear rules about why time goes the way it does. In fact, there's no obvious rule disallowing time travel to the past, other than it blows all our ideas about causality to hell. Also, because of time and entropy, aging is inevitable.
We also know that time is sort of limited in that more than about 13.7 billion years ago, there were no possible differences between one moment and another, and therefore no time. (Although time also theoretically existed even back then in the extent that if you could somehow import something to back then, that thing would have changes and hence time.)
Time is also blocky. Physicist Max Planck determined that there's a very small interval of time and any intervals smaller than that make no physical sense. Hence, this period of time is called Planck time after him. The same exists for space, with a smallest possible unit and any lower makes no physical sense, and this is called Planck distance. Curiously enough, 1 planck distance divided by 1 planck time equals exactly c, the constant of the speed of light in a vacuum and the maximum possible speed in the universe. (I can imagine faster, with something somehow traveling 2 planck distance units in 1 planck time, but it has all kinds of insane implications, including using more energy than exists in the universe, weighing more than the universe, and being so compressed in time that time goes backwards. So...not happening.)
So physicists describe time as a unit of change, essentially. Change with direction, from orderly to disorderly, from useful energy to useless energy. Time is relative, as we are aware from experiments in special relativity, which verified it, and yet going backwards somehow never happens. So time is not exactly a dimension.
The big problem with time travel is the immense paradox. Let's say I go back to the 1800s, and save a man's life. He ends up having a daughter, who proves more attractive to my great-grandfather than my historical great-grandmother was, and so he marries this lady instead. As a result, my grandfather and his entire line, down to me, never existed in the first place, which undoes the entire change. (And yet if I don't exist to save the man's life in the first place, then the man died and the daughter was never born and so I end up existing.) This is the "grandfather paradox." Similar paradoxes can be imagined, where a rolling ball on a desk is struck by its future self, thereby causing it to not travel back in time, which undoes the entire chain of events. Take that, causality. Another paradox is the information origin paradox. I bring Shakespeare his famous plays, which means that he plagiarized them, which means that no one ever wrote them, which is unspeakably insane. (Or, in the technology field, I bring Charles Babbage my desktop computer, he "invents" it despite it relying on technologial principles that only exist because of researched piled on research that Mr. Babbage has now never done.) Faced with So the usual resolution is to proclaim the entire thing impossible in the first place, full stop.
So...how do we best investigate the nature of time? And what kind of bizarre truth waits for us when we do investigate?