Time is not an arbitrary, manmade concept, the means by which we measure time are. Time does exist, and it only flows one way. Take a ball and drop it. It lands on the floor after you release it from your hand. It takes a certain amount of time to do so. You can measure it in seconds, microseconds, years, or an arbitrary unit of time you just made up, but it does not change the amount of time elapsed. It also does not change the fact that the ball hit the floor after you let go, not before or at the same time.
And this opens up another can of worms: thermodynamics. Entropy. The irreversability of certain processes. Could the ball have suddenly flung itself off the floor and landed in your hand? Certainly, but it is highly unlikely. Could the coffe cup have reassembled itself, scooped up the puddle of coffee, and landed back on the table? Even more unlikely, but still possible. However, once you get into subatomic physics, certain things become completely irreversible. There is a certain particle (can’t remember which one, will have to look it up), that forms out of two particles, but decays into three of the exact same particles (or vice versa). The arrow of time always points in one direction. You could never put it back the way it was.
There’s also the issue of black holes, and their singularities. A singularity is defined as something whose past can not be extrapolated from its present condition. If you took a compacted car, you could conceivably figure out whether it used to be a Honda or a Mercedes. No matter how much you crushed it, you would still be able to find out what it was before, up until it collapsed under its own gravity and became a singularity, at which point there is no hope. Essentially, it has been reduced to its basic properties, mass, angular momentum, charge, etc. What it used to be is a complete unknown.
Time travel into the past would violate both these principles, since from the observer’s frame of reference, thermodynamics would be disobeyed, and singularities would be spitting things back out. Unless some loophole is discovered (and a number of scientists are working furiously on finding one), time travel into the past is impossible in this universe as we now understand it.
(P.S. I do not claim to be an expert. If anyone finds any flaws in my argument, do point them out, so I can use it again, New and Improved. Like I even have to ask…)
Modest? You bet I’m modest! I am the queen of modesty!