. We can then measure out time upward in the direction perpendicular to the “map,” so that with the two dimensions of space and the one dimension of time, there are only three dimensions in total, which is easy enough to draw and visualize. Now, if you did not move at all, your world line would be just a straight line going straight up because you would still be evolving through time, but if you move around, your world line will twist and turn, tracking your position as shown in .
. The idea of projection can be generalized to any number of dimensions. So, while we might not be able to visualize say ten dimensions, we can always examine and draw their projections on any one particular dimension that we are interested in—and this notion will be very relevant to us here, as we now see.
Figure 17.2 Possible projections of personal world lines on the dimension of wealth are shown. Such projections of world lines can be shown for every dimension of life. Each projection is like a shadow of the full multidimensional world line on that particular dimension of life, while we ignore all other dimensions.
In , we assumed that we are only interested in your location in space-time. Well, keeping track of the location alone might work fine with things we usually encounter in physics, but people are a lot more than just inanimate objects. So to really describe how we change and evolve over time, we need to do more than just keep track of our location. This means that we need to generalize the concept of the world line by going seriously multidimensional, so that in addition to the usual physical dimensions that determine our position, we also add in additional dimensions to keep track of everything else about us (everything that we would care to keep track of)—such as our state of mind, wealth, job, relationships, spouse, children, feelings, emotions, and actions—over time. Each additional feature would add an extra dimension to the three dimensions of space and the one dimension of time we started with. That would be a pretty complicated trajectory, and we won’t get far trying to visualize it in all its multidimensional glory! But it is not hard to get the general idea, and of course we can always look at particular projections corresponding to each dimension of our lives while we ignore all other dimensions, in exactly the same way we did in , where we tracked the east-west dimension and ignored the north-south and up-down dimensions. In the same spirit, in we see some possible world lines showing only the projections that correspond to the “dimension” of wealth.
, we see a wide range of possibilities reflected in the financial dimensions of personal world lines, including being a multibillionaire. While the range of possibilities can be wide, it is important to keep in mind that not every possible world line is available at any particular point in space-time—in life as well as in the natural world. The physical limitations on world lines can help us appreciate that not all destinies are ever open to us.
World lines are often used in Einstein’s theory of relativity to visualize the locus of an object or person in space-time. In such visualizations, illustrated in , light-cones separate the possible world lines from the impossible ones; in , space is projected on to a two-dimensional flat plane while the vertical direction tracks time. As mentioned before, the world line of a stationary object would be just another vertical line, since it evolves in time without changing position in space. But any sort of motion in any direction will tilt the line from the vertical indicating displacement in space—and the faster the motion, the larger the tilt. There is a maximum tilt, however, corresponding to the maximum speed possible in the universe—the speed of light, as we saw in . Thus, at any point in space-time, the possible paths of light, in all possible directions that pass through that point, mark out two cone-like shapes with their edges having the maximum tilt possible, as drawn in —the past light-cone is defined by all the possible paths of light arriving at that point in space at that instant, and the future light-cone is defined by all possible paths of light leaving the point at that instant. Any world line that passes through that particular point in space-time has to lie inside both the light-cones; any line that lies outside, or even deviates outside, either of them even for a bit is strictly not allowed in the theory of relativity, because that would indicate that there is motion faster than the speed of light even if momentarily.
. At each point in space at any given instant in time, like at the point marked as “Present,” there are two light-cones—the past light-cone defined by all possible paths of light arriving at that point at that instant in time from all directions, and the future light-cone defined by the paths of light leaving it at that instant. Since nothing can move faster than the speed of light, all possible world lines passing through that point have to lie entirely inside the two light-cones. Any line that lies even partially outside them is forbidden by the theory of relativity, because they would correspond to motion faster than the speed of light. Note every point in space-time will have its own particular pair of light-cones.
, we can say that at any given point in your life, you can view your future as a “superposition” of all the possible paths your world line could possibly take. At the moment of your birth, nothing has been defined, so technically all possible world lines are available, no matter how unlikely most of them are—unless of course you were born into utterly hopeless conditions, but in that case you probably would not have made it far enough in life to be reading this book anyway, so we will leave out that possibility!
. The first couple of homecoming reunions reaffirm that—most of your fellow alumni are not that far off from you in their life situations; you can still connect with them and relate to them. With each subsequent homecoming, you are generally farther and farther apart—and everyone’s life trajectory is a possible world line that might have been yours.
Figure 17.4 Visualizing how world lines diverge with time.
Changes are easy early on. As a recent graduate, if you are not happy with your career path at that point, you can change jobs; if you want to move to another city, you just pack up your stuff in a U-Haul and move out of your apartment; if you are having relationship issues, you just break up. Now, try doing all of that twenty years later: If you hate your career, too bad, you are stuck with it, it is next to impossible to seek out a new one now; if you hate the city you are in, well, your job, your house, and your family are all there, so you are stuck there; if you are having marital problems, well, now you need to go through legal channels for a divorce, and the prospects for a new relationship are not what they used to be, so you are forced to deal with it. You just can’t jump to another world line so easily now, because the world lines are farther apart, and there are fewer available—there is real risk of falling into some very unattractive ones in between if you attempted such a jump at a later stage in your life, just as you risk going under if you try changing horses in midstream. There is so much more at stake.
From this perspective, it is easy to understand why as teenagers and twenty-somethings most of us are so cocky and so full of attitude—because we are absolutely certain at that point that one of those high-flying successful world lines we envision is bound to be our destiny, for after all everything is possible, and there is so much to choose from. With all those choices, our eyes are only for the high road, and it is easy to ignore the predominance of the middling or low roads all around. We are quite sure we won’t turn into our parents, and we look with impatient bemusement at our older relatives and friends, wondering how and why they ever settled for so much less in life. Not for you the boring job, the nagging spouse, the little house, and the beat up old car. You will be driving an eye-catching import, living it up in some fancy place, earning millions in some position of authority. Without any serious failures to look back upon, as yet, you are certain of success where others might have failed. We all view our open world lines through the lens of our own hopes and dreams that blocks out the paths we would much rather not think of—call it the tunnel vision of youth!
Midlife crisis is just the onset of realization that you are on the wrong world line, and it is too late to jump to another; the world line you thought you would be on has seemed to have faded away completely, lost over the horizon. It is also the realization that changes are not so easy to make now. You might be able to buy the Porsche convertible if you are lucky enough, but your skin and your gray hair give it away as a prop for midlife crisis. If you are still single, you might dye your hair and try to play the dating field, but the chances are you will be seen as a potential sugar daddy or a cougar on the prowl. Well, the crisis blows over for most, and we learn to see and appreciate the good things in the world line we are on—once we accept that we are stuck on it, anyway.
It is best not to know of alternate possible world lines, but that knowledge is often forced upon us despite our best attempts. That is why reunions can be tough, and why we so often measure ourselves against how the friends of our youth are doing. Ever notice that there are lots of successful folks on the planet whose success never troubles us, but when we hear that someone we grew up with has made it big, has become much more successful than we ever will be—someone just like you and me, someone we always thought we were better than—that never fails to trigger a sense of “it could have been me,” no matter how broadminded and altruistic we think we are. That is because they represent our very probable alternate world lines, because we shared very similar initial conditions for some time, but choices, circumstances, and fate took us on separate world lines.
So when they say, “the world is your oyster,” to a youngster, they are really saying, “Hey kid, most of your world lines are still open.” Act on it! If you are starting out in life, you should be aware that those world lines start closing fast, much faster than you might think, and small decisions you make now, that you might not think twice about, can have tremendous impact on which world line you end up on for the rest of your life. The lesson here is that the time to really engineer your fate is when you are young, that is, when you have the maximum choice of paths, and you can easily jump between them. With the right choices and some help from Lady Luck, your optimism just might last you a lifetime!