Quote from http://forums.lycaeum.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=9&t=000979 :
How can something move in time? It can move along the x-axis and it's velocity is dx/dt. If it moved along the time axis it's velocity would be dt/dt or 1. dimensionless one, at that. There can be no time travel.
(IMHO = in my humble opinion / OTOH = on the other hand)
Defining Travel : travel is a movement in some dimension. A movement is a change in the position of that dimension(s). A change can't happen on it's own; it must follow some external change. One would ask, the external change would need another change too. Yes, IMHO that it is an infinite loop. The change in X would affect Y which will affect Z which on the end would affect X and so on.
So to describe movement, we need to describe what changes can affect it. Before we do that we must say how was the movement described before. It was described in terms of displacement. But displacement is not enough. Because it does not uniquly identify a movement. I can move 10 meters north, or west, each is a different movement. So we need to make it more specific. We add direction. Which as may jump to the readers mind as a vector of X,Y and Z. Yes. But this is also not enough. One moving to USA in a plane at 500 KM/H and one is also moving but in a boat of 50 KM/H. Is not analogous types of movement though at the end will be the same place. At this point we needed velocity (speed). First, we ask, now we have that movement depends on displacement, thus if change in displacement = 0, there will be no movement. Direction depend on movement; if there is no movement there is no direction. Velocity introduces a new parameter. Time. If change in time = 0, there will be no displacement. But what does changes time ?
So far we defined Movement as undirectly depending on changes of time. Thus time restricts movement. There is some different argument : if movement = 0, will time change ? Some one will say 'Sure'. It may be changing. But how can you tell ? Movements will exists as long as time changes. So, if one can STOP movements, all movements. He theoritically will STOP time. OTOH, argument would say : which by contradiction, is proved if larger changes of Movement will cause time to change with the same amount. Einstien proved that, as one approaches light speed, time will shrink until it reaches zero. This is contradictory. As meaning if you are Moving in light speed, you will STOP time. But as concluded earlier this will make Movements = 0. As far as i conclude, this means that once you reach light speed, your speed will equal zero. OTOH, as your speed increase, time changes will dicrease. which lead to dicreasing in your speed. Actually time shrinking will not make your speed dicrease. If speed = dx/dt, as dt approaches zero, speed approaches infinity.
From the above one can conclude that if your speed increase then the displacement is still the same. Directly from what did Einstein proove. Given that time changes depend on the speed, and speed depends on the displacement per time unit; meaning that speed is inversly proportional to time unit. That is true if Displacement per time unit is constant. But in real life, speed only increases when the displacement per time unit increases. Which means that if we can increase the speed, while keeping the same displacemnt per time unit, then we can decrease the time unit. which will force us to recursivly decrease displacement to keep the ratio constant. When displacement reaches zero, time unit will equal zero. This is undefined as displacement zero is undefined. This was to shrink the time unit. Shrinking the time until means that we move faster relative to other slower entities. Ironically, in a race moving faster means that you reach the finish line first, which is other racers future . Meaning if you can increase the speed and decrease the displacement you will move to future. Descreasing the displacement is only meaning to decrease the new disp/t after t decrease, so it means slowing down while you increase your speed. This is moving to future. Moving to past means jumping over the zero time barrier, which is met when you are moving at the speed of infinity and not moving out of your place (note that this means going to infinite future). Jumping over the barrier requires you moving at negative infinity , while you are moving "inside you place" (displacement zero). As you reach -n speed where n <>
This all is an argument which expresses the conditions for Time travel IMHO. It shows a lot of contradictions. Which if sometime is solved it might happen to travel through time.