inside Ninja's Brain

The more one thinks about time travel, the more one is brought up against fundamental concepts of being. What exactly do we mean by “time”, anyway? The simplest definition I’ve heard has been “that which keeps everything from happening at once”, but while amusing and logically implicative, it’s hardly satisfying as a definition.

Time is probably best thought of as a dimension, an extent. Objects have length, breadth, depth, and duration. Even in day-to-day life, people intuitively understand this. When you want to meet someone, you tell them where (locating a spot in three physical dimensions) and when (locating a spot in a time dimension). To specify an event, we need all four dimensions. This leads to the common statement, usually unexamined, that “time is the fourth dimension”. What does this actually mean? To simplify this lets look at this with reference to a real world example: the flip book model…

    Have you ever seen a “flip book”, or made one? This is a simple kind of animation that even a child can understand. You draw frames of a sequence in the margins of a book, like the individual frames of an animated cartoon. Then you rapidly flip through the pages, and the drawings seem to move. For example, the animation might consist of a frog that hops up and comes back down. Each drawing has the frog in a slightly different position. Perhaps the initial and final images are the same, in which it would become a circular flip book. Consider the “flip book” world. It has two dimensions – the length and breadth of the pages. It also has a “time” dimension – the thickness of the book. Each two-dimensional instant (an individual drawing on a particular piece of paper) is arranged in three dimensions. When you flip through the book, you scoot along the time dimension of the flip book. Consider the frog in our hypothetical flip book. It jumps up, and comes down again, returning to the same spot. But, actually, it doesn’t return to exactly the same point – it’s the same point in terms of the two dimensions of the page, but it’s displaced in the third direction, perpendicular to the pages.

Now, we can extend this model to our world. We can imagine that our universe consists of three-dimensional moments arranged in a four- dimensional sequence. Even if we walk in a circle, we haven’t returned to the same point – it’s the same point in the three space dimensions we normally use, but it’s displaced in the fourth, time dimension. Note that this is exactly the model used by General Relativity. The universe, which we normally think of as being made of “space” and “time”, is actually a single something called “space-time”. In Einstein’s view, the world really is a four-dimensional flip book, and time really is, in a real sense, another measure of distance. Time normally proceeds at the speed of light – one second ago is one light-second (186,000 miles; 300,000 kilometers) away. As Einstein himself said, “Past, present, and future are illusions, if stubborn ones.” More interestingly, “space-time” is warped by matter and energy (or really, “mass-energy”, one substance with different aspects). If one follows the current equations to their limits, they imply some very odd consequences, which we shall explore later. People are quite familiar with the space-time continuum, thanks to various science fiction books, movies and documentaries but are quite illiterate about the hidden secrets they withhold.

Time Travel???

Time travel to the future is no big deal. Heck, we’re always doing it automatically. It doesn’t lead to any paradoxes or any really unusual consequences. It might be nice from a practical or educational standpoint to get to the future faster than one second per second, but it doesn’t bend the brain the way travel into the past does. We can think of several ways today to travel into the future. You can either fake it with some form of suspended animation, or go for the gusto and spend some time going fast, preferably as close to the speed of light as possible. (I didn’t say they were trivial, but we can think of ways to do them with some not so currently available technology.) Moreover, it is at this point that most people think or fantasize about stopping time. From what I understand, I don’t think it is possible to stop time as such, you can only accelerate yourself to an as-close-as possible speed of light thus making time appear to have stopped for you. Now psychological implications of whether you will be able to accelerate you brain activity also to that speed is highly questionable, still everything is worth a try, isn’t it?

This one is the confusing part. Imagining it, itself, would break down most people’s mental boundaries. Let’s see it as an example. Imagine a Boeing 737 flying at 500 MpH. Now imagine it flying at 10000 MpH. I am guessing both pictures would have formed quite comfortably in your mind. Now try imagining the same hovering in mid air like a helicopter. Tough??? Now try to think the plan flying backwards at 500 MpH… this is exactly the problem with time travel. But as always nothing is impossible. Since mass-energy can alter space-time, theorists have found several ways that might allow travel into the past. None of them have been experimentally verified, but none of them are ruled out by any known means either logically implying that one of these methods might actually work.

Everyone knows the relativity equation proposed by Einstein. Using the concept of rest mass and relativistic momentum, the total energy of a particle would be where V is the velocity of the particle and m, the mass. Re arranging the equation we get mass would be a factor multiplied by the square root of C²-V². This segment implies that if the V is bigger than C, then the value is negative. And simple mathematics would tell you that you cannot have the square root of a negative number. Now again, more advanced mathematics would tell you that if you have the imaginary number ϊ defined as the square of (-1) (Note that the term “imaginary” is not pejorative, any more than quarks actually have color or flavor. Imaginary numbers are used for real every day in electrical engineering). The implication of this statement would be that the mass of the particle would have to be negative. More easily put “Objects that have real mass travel slower than light. Objects with zero mass travel at precisely the speed of light.” And, maybe, “objects with imaginary mass travel greater than the speed of light.” What a particle with imaginary mass would look like isn’t clear. None have been detected or generated so far. But such a particle would, according to Relativity, move faster than light. And it’s possible to show that if things can travel faster than light, they can in some circumstances travel back in time.

The entire “FTL (Faster than light) implies time travel” meme has to do with what’s sometimes called “failure of simultaneity at a distance”. In addition to the effects that pop treatments of relativity mention (that is, time dilation and length contraction), relativity proposes that the definition of “right now” is also different, depending on which observer’s coordinate system you use. This is an effect much like the revolution of deciding that the direction “up” wasn’t the same everywhere, but varied from place to place on earth. With relativity, the revolutionary notion is that the direction “futureward” (or “now-ward”) isn’t the same everywhere, and varies with velocity of the observer. This is quite confusing so lets visualize it yet again.

Consider a duel with tachyon pistols (not the star wars one.. in this case pistols which fire tachyon particles). The plan being that two duelists, A and B, are to stand back to back, then start out at 0.866 light speed for 8 seconds, turn around, and fire. So, the duelists both set out — at 0.866 light speed each relative to the other, so that the time dilation factor is 2 between them (implying that 1 second is seen as half a second by the other one). Duelist A counts off 8 lightseconds, turns, and fires. Now, according to A (since in relativity all inertial frames are equally valid) B’s the one who’s moving, so B’s clock is ticking at half-speed. Thus, the tachyon round hits B in the back as B’s clock ticks 4 seconds. Now B (according to relativity) has every right to consider A as moving, and thus, A is the one with the slowed clock. So, as B is hit in the back at tick 4, in outrage at A’s firing before 8 seconds are up, B manages to turn and fire before being overcome by his fatal wound. And since in B’s frame of reference it’s A’s clock that ticks slow, B’s round hits A, striking A dead instantly, at A’s second tick; a full six seconds before A fired the original round. Now the question remains, why did A have to fire coz he would not be hit by B bullet as B is dead just two seconds after the duel started. This example show one of the most famous and significant paradox of time travel called the Grandfather paradox. It is due to the fact that, in Special Relativity, the question of what occurs at the “same time as” something else is observer dependent.

As A fired that first show at tick 8, the bullet effectively teleported from A’s gun to B’s back instantly — instantly according to A. But for B, who was moving at 0.866 lightspeed with respect to A, B was hit in the back by the bullet 4 seconds BEFORE the bullet was fired. And again note, this is NOT due to the optical illusion of lightspeed delay in viewing A’s turn-and-shoot; the light form that event wouldn’t reach B until MUCH later, not tick 4. Here’s a spacetime diagram of a referee (O3) and two duelists (O1 and O2). Space is up/down, time is left/right, in the diagram.

The paths O1 and O2 take through space-time are the blue and Green colored arrowed lines. The events in space-time that each considers “simultaneous” and “8 seconds after the start” are along the thinner, non-arrowed blue and green lines. So we see that, each of the three observers thinks the other two have slow clocks, and that if we are allowed to move faster than a lightcone, we’ll end up going “pastward” in somebody’s reckoning. (It means that what you do at a time would be seen as only a smaller time period by someone else, remember time dilution???) We can trace out the shots on this diagram, also. Step through it one more time: if green shoots at 8 seconds out, the shot will go along the green “line of simultaneity”, and hit blue at 4 seconds elapsed. If blue returns fire from there, it will return along a line parallel to the blue “line of simultaneity”, and catch green napping at 2 seconds elapsed (this is not shown in the diagram.).

    I am guessing its been confusing enough now.. will be continued in further parts.

-Ninja-