Up the River of Time, Without a Paddle

The science fiction author Larry Niven once wrote an essay on the practical aspects of time travel (“Theory and Practice of Time Travel,” collected in his out-of-print anthology, All the Myriad Ways), mostly concluding that it wasn’t practical, and that even if it were both possible, and practical, it couldn’t be invented. Hence the essay’s conclusion: If the universe of discourse permits the possibility of time travel and of changing the past, then no time machine will be invented in that universe.

I no longer have that essay lying around (the book was in one of several boxes I donated some years ago to create space in my small apartment), so I can’t consult it for this little amateur post on temporal physics. But Niven was getting at all those paradoxes that you need to deal with when you go back in time and kill your parents before you were born and all that fun stuff. But let’s skip the paradoxes and, just for shits and giggles, consider time in the Einsteinian sense, being a dimension just like the other three spatial dimensions.

There’s some heavy math involved here, which is beyond my capabilities. So feel free to disprove or work out the equations on your own; I won’t be upset. What if, as they say, time is a river, and we’re caught up in its flow. Well, as someone who spent a considerable period of my youth on a river (the Shenandoah; “life is old, there, older than the trees”), paddling both upstream and downstream, you can see that the metaphor falls apart, since we can’t paddle upstream through time (i.e., go into the past). We only go into the future, at a constant rate of one second per second.

But what if the metaphor does hold? Paddling upstream requires significantly more energy than paddling downstream. In fact, paddling downstream requires almost no energy at all other than that which is exerted to raise the beer can to your mouth or swat away the mosquitoes. If I were to get up from my chair and walk across the room I’m in, I would be exerting energy to move through three spatial dimensions.

Math question: How much energy E must be spent to move a body of mass M a certain distance along the X, Y and Z axes of this room?

Whatever E is, suffice to say that I have the ability to generate that amount of energy, even if the variables change from time to time, such as M increasing by 20 pounds over the last couple years, and therefore so does E to compensate.

But if there’s one thing that Einstein taught us, is that all motion is contextual. While it may seem that the E figure isn’t much, that it’s not too difficult to navigate this room, what I’m actually doing is changing my body’s (M) vector of motion, relative to everything else around me that is moving. So while change that I made, moving across the room, may be significant in that I can now reach my drink, or the cat can now move into the chair I vacated, compared with the motion of the Earth’s rotation I’ve hardly moved at all. Why? The Earth rotates at a certain speed. Where I am physically located (Seattle, 47.606 degrees north latitude), that speed comes to (break out the calculator here– cosine(latitude) x 1,000 m.p.h., which is the approximate speed of rotation at the equator) 674 m.p.h. and change. There 3,600 seconds in an hour. In 3 seconds, I am able to navigate about 8 feet across a cluttered den, but in those 3 seconds, the Earth has rotated (i.e., my position on the surface of the planet relative to the space above the Earth) 988.5 feet. It wasn’t my energy that caused me to actually move 988.5 feet in one direction. My energy was spent moving 8 feet in another — specifically, west, which is opposite the direction that the Earth rotates. To have only moved eight feet west relative to the Earth’s rotation, I would somehow have to move 996.5 feet west relative to this room. In 3 seconds.

Even discarding the amount of energy required to go through several layers of concrete wall in multiple buildings and up a slight rise so I don’t wind up underground, we’re talking about an enormous amount of energy, more than my humble body has the ability to generate.

Math question 2: Just how much energy would be needed if we needed to correct not just for the rotation of the Earth, but the movement of the Earth around the sun?

The Earth moves around the Sun at 66,000 miles per hour. Meanwhile, the Sun and all its planets are moving through the Milky Way galaxy at about 43,000 miles per hour (in yet another direciton, toward the star Vega). What is more, the entire galaxy is rotating, much like the Earth does, but at a relative speed (given our position out on one of the galactic arms) of 483,000 miles per hour, adding yet another vector on top of the others. And the Milky Way itself is not stationary: it is moving through our universe… at what rate? Well, as they say, everything is relative. All galaxies, star clusters, gas clouds are moving through the universe. The only frame of reference we possibly have comes from the Big Bang theory, which puts out that not only did the universe get born in a big bang some 13-14 billion years ago, but that it’s been expanding ever since, at a rate that is somewhat less than the speed of light (because according to Einstein, nothing with mass can exceed the speed of light), but that means that the universe is probably some 13-14 billion light-years across, which comes to something above (lessee, trillion miles times 13 billion is…) 76.7 quadrillion miles.

And measured against the Cosmic Background Radiation, which is as close to a frame of reference to the initial Big Bang there is, the Milky Way is moving through the universe at 1.3 million miles per hour (in the direction represented by the constellations Leo and Virgo; which is different from the star Vega in the constellation Lyra). Calculate that downward to our room: In the 3 seconds it took me across the room, the galaxy moved 1,083 miles. In that context, 8 feet is nothing on a cosmic scale, and there’s no way I, you, or anyone else on this planet, can counteract all those different vectors without expending an enormous amount of energy.

(For some of the math behind this, and a good explanation of this, this page at AstroSociety.org does an excellent job.)

Back to the river.

If, as Einstein says, time is simply another dimension like our three spatial dimension, and that all objects in the universe can be expressed by their motion through those three dimensions plus time, why is it that we only experience time going forward? Why is time so special?

Well, the answer is time is not special. We perceive its movement as we perceive the wind in our face when we ride in a car with the windows open. We are traveling through time, at one second per second. In order to, in the science fictional sense, travel through time, we need to expend enough energy to change our vector relative to the one second-per-second vector we are currently traveling on.

Math question 3: How much energy is needed to change that vector?

I’m not even going to attempt to Google an answer to that question. Moving across the room requires a measurable if small amount of energy, but actually moving relative to the motions of the Earth, solar system and galaxy requires quite a significant amount more. So much more that, so far, our only attempts have been limited to strapping ourselves on the tops of powerful rockets, which are pointed upward just so we can escape Earth’s gravity. Changing all those other vectors to reach an absolute standstill relative to the universe is beyond us, much less to reverse those vectors, or manipulate those vectors. And we haven’t even started in about how to counteract or otherwise alter the motion of us, the Earth, the solar system and the galaxy through the universe in the time dimension.

So the reason we can’t travel through time? Perhaps it’s only a question of energy. In other words, we haven’t tried hard enough. Because one-second-per-second, as it turns out, is very, very fast.

Again, I’m a dilettante when it comes to this stuff. Someone with more letters after their name can punch holes through all my musing on this subject.

One final thought: Returning to Einstein, we find that space-time (all four dimensions) can be changed and distorted by gravity as well as motion. That’s why if you in your spaceship got close to a very massive body, such as a black hole, and survive such an encounter (i.e., you didn’t actually cross the event horizon and disappear forever, or get torn apart by the tidal forces the curvature of space-time exerts on your body, or get fried down to your atoms by the radiation in the area of the black hole), you would find that your position in time as well as space would likely have changed, because the mass of the black hole is enough to distort all four dimensions to a point that you might not actually move through its field at a rate of one second per second. You might actually be moving faster, relative to the rest of us. Meaning, that while you spend what you think is a few minutes playing around dangerous black holes, for the rest of us, hours, days, months or years might have passed, depending on how close you got and how long you got there.

As far as time travel goes, extreme levels of gravity provide one way of doing so, the only way that’s permissible under the laws of physics as we know them. But that’s not a way of generating the energy required above as it is distorting the time dimension so much that we actually perceive the distortion as different from where we are. But even then, that seems to only account for time going in one direction. Perhaps in the arcane mathematics of negative energy or dark matter or quantum physics or whatever is something that would explain how time could be distorted in the other direction. If it’s out there, it’s sure to be weird.

But perhaps the best way of looking at it is this is this quote, also from Einstein: “When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute and it’s longer than any hour. That’s relativity.” Maybe he was not just creating a pithy example (for a 1938 scientific paper) but was really figuring out an easier way to travel through time. He certainly tested his theory a lot.

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