Image of bear looking into bucket of maple treesap Brought to you by
   Sugar Tree Ridge

Time Travel: Why You Can't Get There from Here

by Thomas L. Atwood
March 10, 2007

Return to our home page

The Classic Paradox of Time Travel

My mother and father met at a dance, began dating, fell in love, were married and had two children, the first of whom was I. I grew up, studied physics and actually built a time machine. I used it to travel back through time to the day my mother and father first met. Having had the foresight to take some old coins with me, I bought a bottle of black indelible ink. I went to my mother's house, arriving shortly before she was to leave for the dance. I knocked at the door and asked to see her. When she came to the door, I took out the bottle of ink, opened it, and tossed the ink all over her and her beautiful new dress. Then I turned and ran back to my time machine and returned to the present.

My mother was horrified. She burst into tears, running back into the house, leaving a trail of black indelible ink drops from the front door to the kitchen, where her mother intercepted her and daubed up as much of the ink as she could with a dish cloth. To this day if you visit that old house, you can still make out those ink stains on the hard wood floors.

And so, because of my intervention, my mother didn't go to that dance, and she never met my father. It was during the war, and he was a soldier. He shipped out with his unit a few days later. Since they never met, my mother and father never fell in love and were never married. Though each of them later married other partners and had other children, they could never have had me. Therefore, because of my intervention through time, I never existed. Ouch!

This is a classic paradox of time travel. It has been presented in one form or another in a large number of science fiction stories and movies. If time travel became possible at some time in the future, then people would eventually travel back in time. Intentionally or unintentionally, they would introduce minor differences from the original flow of events upon which their existence depended. These differences would propagate into our present, like a ripple across a pond.

When Did I Cease to Exist?

When would the change in the past affect the people making the change? In my example, when would I cease to exist? Would it be the moment I tossed ink on my mother to ensure she wouldn't go to the dance? Would it be the moment I returned to my "present" time? Would I have to wait awhile for the change to propagate forward in time?

Perhaps I would live out my life completely before the effects of my intervention could catch up with me. Perhaps those changes would evolve in some kind of parallel universe; and my future here, in this universe, would never be affected. Who knows? I, for one, have trouble believing that my going back in time could trigger the formation of a parallel universe. Come to think of it, I've never even seen a parallel universe. Maybe they don't exist.

Nevertheless, you can deduce some information about time travel from my example. We don't see people popping in and out of existence in our world, as we might expect if their past was being tampered with by agents from the future. Therefore, if time travel is possible, either the method for it will never be discovered, or else it will be prohibitively expensive and never be used, or else there is some kind of natural law that intervenes and prevents the time traveler from interacting with the past. At best, he or she could only watch the events of the past, but could not alter them. Maybe our species will become extinct before the method for time travel is discovered. Anyway, there are no people popping in and out of existence. None that I've seen anyway.

What Time Is It?

There are good reasons why contemplation of time travel may be wasted effort. These reasons go well beyond the paradoxes that time travel would introduce. These reasons relate to the fundamental nature of time itself.

If we want to understand the concept of time, we need to examine what we know about how time is measured. These days, we measure time with clocks and calendars. Before our ancestors had the knowledge to construct these devices, they measured time by looking at the angle of the sun from the horizon, by counting periods of daylight, by recording how long it took the moon to return to a certain location among the field of stars, and by looking at the changes in the apparent north-south position of the sun's circuit across the sky during the course of a "year".

All of our mechanisms for telling precise time involve the observation of regular, repetitive motions. Whether we use the apparent positions of heavenly bodies or the periodic behavior of a clock's pendulum or the vibration of a crystal or the regular motion of atoms within a molecule, our method involves the counting of regular intervals of motion.

What Is Time?

Why do we want to measure time? The simple answer to this question is something like, "so we'll know when to show up at the dance". We use measurements of time to schedule and to pace our activities. Let's look a little deeper. If we were all statues and the world was frozen, so that nothing ever changed, we wouldn't need to measure time. If nothing ever moves, if nothing ever changes, who cares what time it is? One time is as good as another.

We use time to measure things that involve change. We use time to measure motion. If we want to know how fast Billy can run, we have him run a measured distance. When he begins, we start counting the ticks of a clock. When he reaches the end of the measured distance, we record the total number of clock ticks that occurred during Billy's run. By dividing the distance by the number of clock ticks, we can calculate Billy's average speed and compare it with the average speed of other runners.

Anne is going to cook for her new boyfriend for the first time. She chooses well-tested recipes, and makes sure to carefully set the temperatures and to measure the duration of each item's exposure to heat. If she successfully counts off the correct number of clock ticks, she will impress this guy big time.

Sam is irate that I would use such a sexist example of time measurement. Sam calculated that there were three more days in which a letter to the editor could be sent in time to be printed in the next issue. But now the time is almost up. After more than a dozen attempts to say it with just the right mix of anger and wit, Sam is still pounding on the keys. Will Sam's efforts come to naught? The clock is ticking.

Things Change

By counting the clock ticks, we are indirectly counting the number of times a crystal vibrated back and forth inside the electronic watch during the course of Billy's running or Anne's cooking or Sam's writing. If we used a mechanical watch, we would be indirectly counting the number of oscillations of the hairspring as it twists back and forth in its regular, periodic motion. If we were on the Mayflower and we wanted to time the trip to the New World, we would watch the motion of the Sun and count the number of times it moved across the sky, leaving alternating periods of light and darkness.

If you think about it, when we measure time, what we are really doing is comparing the regular motion of standard (clock) systems with the motions and changes in our lives and the world around us. We measure change by calibrating one motion or change against another. Therefore, when we are talking about time, we are inevitably talking about motion.

What we can truly say about time is that things move, things change. This we know for sure.

Time Is (Like) Money!

You've probably heard the expression, "Time is money!". When a person is being paid by the hour to load a truck, the sooner he finishes, the less the loading dock boss has to pay him. If he takes more time to do the job, the boss is out more money. This is one way time is like money. There is another.

Suppose I print up 100 pieces of paper. On each piece of paper I write, "This piece of paper is worth one dollar." What happens if I take this stack of paper to the grocery store and offer to exchange it for $100 worth of groceries? Well, just because I say it's money doesn't necessarily make it so, does it? But what happens if I execute a legally recognized document where I guarantee that each and every piece of that paper can be exchanged for one dollar's worth of gold? Hmmm. I might just be able to exchange those previously worthless pieces of paper for groceries.

If you think about it, a dollar bill has no intrinsic value. We can use this otherwise worthless piece of paper as money because a government guarantees its value. In fact, we can individually create money any time we want by simply writing a check. We put our guarantee of payment on an otherwise worthless piece of paper.

We use money as a "medium of exchange", as the economists would say. Using money is much more convenient than exchanging items by bartering. I can sell a few hours of my labor to my employer in exchange for money, which I can exchange for groceries at the grocery store. In all probability the store would have no use whatever for my labor. But the store will exchange groceries to me in return for the value of my labor to my employer. Wow! What a neat system!

The concept of "time" plays the same kind of role in characterizing changes as money plays in characterizing exchange value. "Time" is not a tangible, physical quantity itself, any more than paper money has intrinsic value. The real physical manifestation associated with time is "motion". You can see motion. Motion is a perceivable fact.

We use motion to mark off time, then we use time to measure motion. What happens if we eliminate the middleman? What's the difference in just using one motion to directly measure another? "Time" doesn't really pass. Instead, things move. We just use the concept of time to measure the motion, like we use money to measure the value of what we buy and sell.

Time Travel?

So what do most scientists think about time travel? You don't exactly hear a chorus of denial such as occurs whenever someone seriously tries to substitute the teaching of religious beliefs for evolution in the public schools. Why isn't the scientific community audibly skeptical about time travel? Let's explore.

All the physical sciences, especially physics, are based on the concept that the universe in which we find ourselves behaves in accordance with "natural laws". Most of this regular behavior of the universe can be deduced from a few relatively simple basic principles through the careful application of measurement, analyzed by rational thought. This application of logical analysis uses as its primary tool that body of symbolic logic we know as mathematics. In other words, our knowledge about the physical universe can be largely explained in terms of mathematics. Mathematics is a natural language for expressing natural law.

Isaac Newton, perhaps the greatest of all physicists, used mathematics to describe the motion of physical objects. He found that the same law of gravity that keeps the moon in its orbit around the earth is also the governing law that describes the accelerated fall of an apple from an apple tree. Up until that time, such a thing was not at all obvious.

Mathematically, Newton took the approach that we live in a world of three spatial dimensions. You can think of these three dimensions as (1) left - right, (2) front - back, and (3) up - down. You can locate any point in the universe relative to your position and orientation by giving its distance in each of these three perpendicular directions.

For example, suppose you are calling me from a phone booth on Main Street, asking for directions to my office. I tell you to go north on Main six blocks, take a right on Elm and go three blocks. Enter the Court House building on your right and go up 3 floors. I'm right across from the elevator.

I specified my location by telling you how far north to go, then how far east, then how far up. This specifies my location in three dimensions, relative to your phone booth. You don't need a fourth dimension to locate a point anywhere in space.

But Newton also used a mathematical time parameter to index the motion of physical systems. So, his mathematics describes motions of physical objects in three space dimensions together with a time measurement.

Then along comes Einstein, that clever dude! He and his friends extended Newton's physics by recognizing that the speed of light plays a fundamental role within natural law. In working out the mathematical consequences of this new understanding, called the principle of special relativity, they observed something really elegant. The mathematical equations that describe the natural law regarding particle motions, forces among particles, electrical charge, and so forth, became much simpler if you treated "time" mathematically as if it were some kind of fourth spatial dimension.

When the equations become simpler, more symmetric, more elegant, this is serious stuff for a physicist. It's an indication of the mathematical model's getting closer to the absolute truths of the real world. For whatever reason, it often seems to be the case that the simplest mathematical model of the natural world, consistent with measurements, is the most correct one, all things considered. In physics, Occam's razor gives any theory a smooth, clean shave.

OK, we have this simple, elegant model of the universe existing and moving in a 4-dimensional "space-time", right? So if I can move back and forth in the other three dimensions, why can't I move back and forth in this fourth dimension, time? Mathematically, they're more or less equivalent, space and time. After all, it's in the equations of natural law. Furthermore, if you look at what the equations predict would happen if you ran the time backwards (and reversed the charges - of electrons and protons and such - and reversed a few other things) the laws that govern the universe would be essentially the same as if time were running forward. This is why you don't hear the scientific community complaining much about the idea of time travel. The mathematics doesn't rule it out.

Just the Ticket for Speeding!

"Time" is just a way of measuring motion. If you don't believe it, re-read the earlier parts of this article. What the mathematics of Einstein's special relativity is telling us is not about "time", which has no physical reality. These equations are telling us about "motion", which we use "time" to measure.

In fact, when we look at those lovely, elegant four-dimensional equations that govern so much of natural phenomena, whenever the time occurs as if it were a fourth dimension, it is always multiplied by the speed of light. So, what actually is manifested as a fourth "dimension" is the distance that would have been traveled by a beam of light during whatever time interval you happen to be discussing.

The distance traveled by a beam of light during the motion of any natural system is the most natural way of parametrizing that motion. The four-dimensional mathematical description of natural law suggests that the distance covered as a beam of light propagates through space is some sort of universal clock.

In other words, we are right back to using one standard type of motion to calibrate other motions. The speed of light in a vacuum differs from essentially all other types of motion. To the best of our knowledge, it is a constant throughout the universe. It doesn't matter how fast you may be moving. If you measure the speed of light relative to yourself, it is always the same. If you double your speed, then again measure the propagation speed of your beam of light, it's still the same as before.

If these were sound waves you were measuring, they would go slower ahead and faster behind. If you kept accelerating, eventually you would "break the sound barrier", traveling faster than any sound wave could propagate ahead of you. But light waves are different from sound waves. You can't break the light barrier, because no matter how fast you travel, the speed of light which you measure will always be the same. Regardless of your speed, the speed of light is the same for a beam shone ahead of you as it is for a beam shone behind you. It is also the same as measured by someone else moving at a different speed from yours. The speed of light is a universal constant for everybody. It's the law. It's the natural law!

How can the speed of light be the same for every observer, no matter how fast she is moving? Don't ask. Einstein took this as a postulate, a starting point, for his theory of special relativity--and it worked! This is pretty strange stuff. Oh, well, so the distance traveled by a beam of light is the measuring rod, the clock for "universal time", right? Why not use it as a clock in real life? This is how it would work:

I drove my pickup truck to a lake about 120 miles from home. The trip took about two hours. My speedometer wasn't working--it's an old truck--but I can calculate my average speed. Divide the distance by the time interval and that's my average speed, about 60 miles per hour.

Now, suppose I want to calculate my speed using the new "universal time" based on the speed of light. Instead of dividing the distance by the time, I will divide it by the speed of light times the time. This will amount to the distance I traveled, 120 miles, divided by the distance a light beam would have traveled during my drive.

Well, light travels about 186,000 miles per second. That's a second and a half to the moon, a little less than nine minutes to the sun. It's about as fast as you can go. So, how far would light have traveled during my two-hour drive? If you work it out, it's about 1,340 million miles. So my average "speed" based on this universal time would be 120 miles that I traveled divided by 1,340 million miles that light traveled, or about 0.00000009.

"What do you mean, 0.00000009 ?" you ask. "What kind of speed is that?"

"But officer, I was only doing 0.00000009 !", I begged. "Yes, I know, son. But that speed limit sign that you just blew past says 0.00000006 !"

Look at it this way. If you had been traveling at the speed of light, your speed measured in this fashion would be 1. So describing motion in terms of this "universal time" is just expressing your speed as a fraction of the speed of light.

Well, maybe measuring our speed as a fraction of the speed of light is not a very practical thing to be doing. Too many zeros. But all we did to get to this way of measuring speed was to divide our speed as we usually express it in miles per hour by the speed of light, which is a universal constant. We just switched to a different scale of measurement, that's all. But in picking this particular scale of measurement, we effectively changed from computing speed as distance divided by time to computing speed as distance divided by what we might call "light distance". The idea of time as some independent "substance" just vanished. We don't need it anymore. We just need to see the light!

But what about the success of the four-dimensional space-time approach to physics? No problem. It's just that the fourth dimension isn't some mystical expanse called "time". The fourth dimension is the distance traveled by our "clock" reference system. We end up with more than three dimensions because we are describing the motion of two different systems, the system whose motion we are measuring and the "clock" system, whose motion we are comparing with.

Actually, the motion of the "clock" system, which I have arbitrarily chosen to be a beam of light, requires three dimensions to fully describe. In general, this would result in a six-dimensional "space-time", three spatial dimensions for each of the two systems involved in the comparison of motions. But all we need to know about the movement of the "clock" system is the distance it travels. Distance is a one-dimensional concept. Thus, the three spatial dimensions of the system whose motion we are measuring, together with the single distance dimension of the "clock" system whose motion we are comparing with, gives a four-dimensional mathematics for describing motion. It just needn't involve any mystical substance called "time".


Does this mean that scientists are mistaken in using a time parameter in their mathematical descriptions of motion? No, not at all. We believe in accepted scientific models because they account for all kinds of measurements we can make in the real world around us. Using time to parametrize motion and change has been very successful, and has led to immense increases in our understanding of the universe and our place in it.

Nevertheless, I think almost all scientists would freely stipulate that we use motion to measure time. Many would probably argue that time is not like money, a convenient means of representing something more fundamental, but is a true fourth dimension. What many of them may not have considered is that motion can be thought of as the fundamental concept and time as the derived one, instead of the other way around. Then the philosophical meaning of time changes in a big way. Time travel? Once the motion happens or the change unfolds, how are you going to undo it? Just a little food for thought. I didn't want you to waste too much time trying to figure out how to build yourself a time machine.

Anyway, instead of thinking about time as some kind of fourth dimension, perhaps we should instead be thinking of the motion, the changes that we witness in our daily lives. Things happen. The Earth revolves around the Sun, acted upon by gravitational force and moving according to natural law. Could the Earth "unrevolve" around the Sun? Isn't that what you mean when you talk about traveling back in time? Have you ever seen such a thing? I haven't.

Image of bear looking into bucket of maple treesap Brought to you by
   Sugar Tree Ridge