Disclaimer: This is an opinion based on my current understanding, not a proof or a lack thereof, of the mathematics of time as a dimension.
I've always been fascinated by the concept of time travel and I'll admit my knowledge on the mathematics of the arena is quite minimal consisting of opinions of fellow google users. Nevertheless, I'm going to venture my views on why it simply won't happen.
Time travel via moving trains (A childhood fantasy):
In my childhood for some reason I thought that if I have enough small clocks and I can move them on different speeds through time eventually making some faster than time, I'll in theory be able to reverse time. My plan for this was to attach a clock to a toy train moving in a large circle on the rails, on the top of this train I'll have tracks and another train with another clock and so on. I did not decide on how many trains since I didn't even have one train at that moment or a clock, nor a way to get that. But the theory was, since the top most train will have the speed exponentially as large as the bottom most, the clocks would at least have some difference in their respective times eventually thus giving me a clue to formulating a more reliable way to actually time travel. Obviously, I did not account for reality i.e. any of the physical phenomenon like friction, air resistance, limitations of the measuring instruments or matter changing into energy (E=mc^2 is just so cool). Watching the sci-fi movies and the time machine always having something rotating around them, I'm assuming I wasn't too far off in my fantasies. Had I known some mathematics, I'm sure I'd have wasted countless hours obsessing over a formula to get time travel out of the way, luckily, I knew I couldn't get the set up so I dropped it in favor of my other musings which I assure you were equally removed from reality.
Buying into multiverse (The teenage obsession):
Yep, I bought into that one for a long time. You see, it makes sense, at any one instance in time, you can make countless choices and if that were true and nothing was influencing your choices, each would lead to an entirely different timeline (multiple movie references here so again I'm not being too far off albeit being close to science fiction.) That means, thanks to the methods provided by reddit's dimension jumping community (please don't be offended) that I now had a way to travel between these multiple dimensions because obviously they existed. So, yes I tried methods and recorded my observations and sure enough I for a while observed a shift in reality. Dimension jumping worked! A word to the wise, don't trust your brain or observations too much. I wasn't a world renowned neurosurgeon in any dimension.
Unfortunately, that's not, at least in my opinion, how it works. Yes at any one instances, theoretically you have infinite choices but studying too much psychology has made me realize that:
Our brains are very hardwired to think a certain way. It's more chemicals and neurons than conscious choice. (thank you, Freud and Jung)
We are very, and I can't emphasize this enough, very much influenced by our environment and external circumstances. (thank you, Darren Brown)
So, as disappointing as it might be to realize that your choices are not exactly your choices, you do not necessarily have as much freedom as you might think. No! I'm not absolving you of any responsibility for your actions because your actions are nevertheless your actions. (I know, this is a tough pill to swallow.)
But back to time travel in the next session.
Causal Determinism and Laplace's Demon (The mid 20's disappointment):
Next, I stumbled across causal determinism and the Laplace's Demon. Again totally bought that one. Was "obviously" convinced the Laplace's Demon was the new answer because it would explain a lot of my stray information nodes as well. Again, obviously I didn't bother to delve into the maths and believed the word of wikipedia and some online lectures on the topic. I even generated a few "ground breaking" ideas from that concept, one of them was something that I got so excited about that I thought it would be transformational for the age. Looking back I suspect this idea occurred to me at 2am because in the coming days I was rather embarrassed by my excitement for the idea.
But recently I started thinking in very basic terms. Considering time only a dimension and really looking into manipulating it like I might manipulate any other dimension. I've come to the conclusion that even if you could time travel, it would be extremely meaningless.
Why time travel would be meaningless (The wisdom of old age):
Let's start with two dimensions, a picture, which everyone is familiar with. Now let's add the time dimension and you can roughly call it a movie. We know that movies are comprised of countless pictures so at any single point that you stop the movie you get a picture. this picture in the sequence of pictures is one single, static, discrete instance of time. This concludes that at any single point of time, only one picture exists and it's the moving of time that sets the movie in motion.
In any movie, you again are not bound by the timeline of the movie, so the dimension of time inside the movie is not the dimension of time you live in and yes because it has been remade, you can go to any frame you want controlling time. But that is not the case in real world. The time in real world is a dimension you are bound by and of your life after a certain point is not yet created. Now let's assume you are halfway into the movie. Let's suppose you can time travel to the past but you're only "visualizing" a certain instance that has occurred, you in no way have a way to be observed by people in that movement or manipulate that movement because it's a static scenery. So, you can view the scenery but not really change it, unless:
You can move the time in the past, that would mean you have to continuously jump into infinitesimally apart time discrete time instances and maybe just maybe then you can be observable in the timeline.
Yes you have full discretion of how to change that single scene in time but it would not change the consequent events because you're only in a discrete interval which you can modify but the next instance is already formed. I'll go ahead and say that our world is a Markov chain so the instance you changed doesn't matter unless the next instance is created. Therefore to truly change the past and the future you'll have to modify every scene unto the point in present and even then you only do it for yourself. Funny right!
Future time travel is simply not possible because the movie of your life has not been constructed to that point and if we assume that universe is Markov then you do not know the next state unless you know this state, but I'll go ahead and assume only one timeline exists in future (bad news for free will) and you can jump to it but even though the point in time exists you don't have the mental faculties to see what is not visible.
Of course if you somehow attain a level such that you can mold all dimensions and "create" timelines, you can find a way to view the past and the future for those subsequent timelines and can tweak the present but only present and you yourself would be timeless.
Final Thoughts:
I am still processing a lot of these thoughts and I suspect that there might be beings in higher dimensions who we obviously can't see and maybe in some dimension there's a being that can actually create timelines but even they can't change the past because the next frame in the picture has been generated and we don't care about all the previous frames.
Funnily, you already time travel to past and modify the timeline in your memory. You even modify timelines in collective conscience through tweaking of history. But the whole perception theory is another monster, I think George Orwell captures a lot of it really well, my personal conclusions are still in the process though.
It should be liberating though because that means all the power lies in the present and by simply changing this moment in time you can actually change everything.
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