Various Musings on Time Travel

Table of Contents

  1. Introduction
    1. What Is Time?
    2. The "Flip Book" Model
  2. Travel Into The Future
    1. Boooring!
    2. Easy!
  3. Travel Into The Past
    1. Might Be Possible
      1. Tachyons
      2. Black Holes, Rotating Cylinders, and the Empty Torus
      3. Wormholes?
      4. Slow Light?
    2. Various Objections to Time Travel
      1. Where Are All The Time Travelers?
      2. Various Conservation Laws
      3. The Chronology Protection Conjecture
      4. The Paradox Problem
  4. The Question
    1. A Changeable Past
      1. Models of a Changeable Past
        1. The Change-Wave Model
        2. The Many-Worlds Model
      2. Chaos Makes It Uncontrollable
      3. Historical Inertia
      4. No Self-Causing Loops
    2. The Unchangeable Past
      1. It "Already" Happened
      2. But What About Free Will?
      3. Worse Than Paradoxes
      4. Causality and Perpendoxes
  5. Time Phones Are Just As Good
    1. Energy Is Always Transferred
    2. Energy Is Easier Anyway
    3. The Time Modem
  6. Societal Effects
    1. Change-Wave
    2. Many-Worlds
    3. Single-Timeline
      1. High Availability, High Bandwidth
        1. Everything's Obsolete
        2. The Satisfaction Principle
        3. Triumph of the Whiny
      2. Low Availability - The Eternal Dictatorship
      3. High Availability, Low Bandwidth
  7. Examples in Books and Movies
    1. Change-Wave
    2. Many-Worlds
    3. Single-Timeline


The notion of time travel in various forms has existed probably for as long as humans have been able to ponder time itself. Legends of prophecies (which ultimately involve information moving from the future to the past) are as old as humanity.

What Is Time, Anyway?

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, it's hardly satisfying.

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?

The "Flip Book" Model of Spacetime

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.

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.

An interactive example of this idea can be found here. There's type of two-dimensional simulation called "Conway's Life", and this fellow has created 3D sculptures by stacking the 2D 'generations' on top of each other.

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 "spacetime". 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. As Einstein himself said, "Past, present, and future are illusions, if stubborn ones."

Time normally proceeds at the speed of light - one second ago is one light-second (186,000 miles; 300,000 kilometers) away. Note - that means two seconds ago is farther away than the surface of the moon! Any time machine would have to be a pretty good transportation system, too...

In any case, Relativity tells us that "spacetime" 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 below.

Time Travel Into the Future


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.

It's easy, too.

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 currently available technology.)

Time Travel into the Past

It Might Actually Be Possible

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.


It's widely believed that Relativity theory forbids travel faster than light. This isn't strictly true. Basically, the formula that relates mass to speed takes the square root of a constant minus the speed of the object. Looked at a certain way, what it actually states is, "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." Mathematicians have a term for the square root of a negative number - it's called an imaginary number. (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.)

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.

Again, tachyons are theoretical entities, and none have ever been proven to exist, nor has anyone thought of a way to generate them. But they are not forbidden by current theory, and if they could be discovered or generated they could be used for time travel.

Black Holes, Rotating Cylinders, and the Empty Torus

As noted before, mass and energy distort space and time. One familiar consequence of this effect is gravity. Gravity, in general relativistic terms, is a distortion of spacetime caused by mass or energy that alters the trajectories of other mass-energy systems.

But in our solar system, we don't get to see the really funky effects of this distortion. When you have really dense objects (like collapsed stars or black holes), and really high speeds (like over half the speed of light), things get decidedly odd.

Black Holes

If a black hole is rotating fast enough (a "Kerr" black hole, named in honor of the physicist who first explored the math involved), it's possible to plot an orbit around it that will take you to your starting point, not just in three dimensions of space but also in time. That's right, if you followed such a path you'd meet yourself coming, as if our flip book frog were to find himself returning to the first page of the book. (Imagine if the book were bound with rings like looseleaf paper...) Such paths are called Closed Timelike Curves or "CTCs". Of course, other paths can take you further backward (or forward) in time.

Lots of physicists don't like CTCs. But, again, if our current understanding of the universe is at all correct, they are not forbidden. Indeed, recently NASA discovered good evidence that at least some black holes do, in fact, spin.

Some people may object, "But you can't get that close to a black hole! You'll be torn apart!" However, it turns out that there are ways to counteract tidal forces and gravitational stresses for such a trip. While the actual implementation is, um, beyond the current state of the art, some physicists, on a lark, worked out a way to counteract up to 6760 G's. But even given the current state of the art, they note:

"It is interesting that, using only normal matter, we may in principle counteract tidal forces encountered in extreme situations. This might also find application in trips near neutron stars or small black holes (without falling in) where an adjustable-radius, actively-oriented life preserver might enable you to venture closer than would otherwise have been the case and still return safely home from the adventure."

Rotating Cylinders

A physicist named Tipler worked out a method that doesn't even need a black hole, and published it in a paper titled "Rotating Cylinders and the Possibility of Global Causality Violation" [Physical Review D9, 2203-2206 (1974)]. Just construct a long cylinder made of neutronium (collapsed-star matter) and spin it along its axis so it's moving at over half the speed of light. This will also form CTCs. You orbit around the cylinder, and each trip takes you a bit further back in time. (Or forward, if you go in the other direction.)

The Empty Torus

Recently, a professor named Amos Ori of Israel's Technion came up with yet another potential design for a time machine. It basically involves a sphere of normal matter, where the inside is a vacuum, and on the outside extremely massive objects (e.g. black holes) are orbiting. Within the sphere, a toroidal (donut-shaped) area is formed that contains CTCs. The gory details are here.

The interesting thing about this particular time machine is that it doesn't require any particularly unusual physics and appears to get around some fairly abstruse objections that physicists have raised to time machines in the past.

General Considerations

Note that these kinds of "time machines" can't take you any further back than the point in time where the black hole (or cylinder or whatever) was first "spun up". So you can't take the plans for a time machine back into the past and use them to build the first time machine. Oh, well.

Sadly for time travel research, but perhaps fortunately for everything else on Earth, we don't have any black holes handy for experimentation. Maybe in a few hundred years (a few thousand? a few hundred thousand?) we'll be able to travel to black holes and/or make our own. Or perhaps there's another way...


Somewhat related to black holes and Tipler cylinders are "wormholes", a theoretical "subway" between two distant points in physical space. Imagine if you folded one of the pages of a "flip book" over, and punched a hole through the sheets. There would be a "shortcut" between two points on the page that were originally far apart.

Now, if you take one end of a wormhole and accelerate it for a while, and then bring it back to the other end (which stayed in one place), there will be a time difference between them. (Consider each end to be one of the twins in the so-called Twin Paradox.) Walking into one end of the wormhole takes you to another point in space and time. Wormholes and their time-travel implications are also discussed here, and here.

In any case, like tachyons, no one knows how to make one. The typical solutions involve some kind of "negative matter" that puts out antigravity instead of gravity. Until we figure out how to make negative matter, we probably won't be seeing any wormholes.

Slow Light?

Recently scientists working with odd quantum-mechanical substances called "Bose-Einstein condensates" have discovered ways to slow light to a crawl, and even, in a sense, stop it altogether. It's possible to build, in such substances, close analogs of black holes and other phenomena that are rather difficult to work with when light's moving at its normal speed.

At least one scientist has proposed that it might be possible to induce time-travel behavior in such an environment. I'm not so sure, but it's worth noting as a possibility. If it works, it'll be interesting to see how it pans out.

Common Objections to Time Travel

When the subject of time travel comes up, several common objections to the entire idea are made. These objections vary in their validity; some result from simple misunderstandings while others raise important questions.

Why Don't We See Time Travelers?

One very common objection to the notion of time travel goes something like, "If time travel were possible, they'd be here already! We'd be overrun with tourists from the future!"

However, almost all of the possible methods of time travel noted above have something in common: you can't go back any further than the construction of the first time machine. In the case of black holes or Tipler cylinders or whatever, you can't go back any further than when the time machine was "spun up". A slow-light time machine has the same problem, as does a wormhole-based time machine.

A tachyon-based time machine might not have this problem. However, it's at least possible that lots of tachyon-based messages from the future are coming at us, but we haven't built any receivers yet that can detect them. Our sun has put out an astonishing number of neutrinos every second since the Earth formed, but we've only been able to detect them for a few decades, and we still miss all but an infinitesimal fraction of them. Tachyons may be similarly difficult to pick up.

So the simple answer to this objection is that we haven't built any time machines or tachyon receivers yet. Once we do, we may be flooded with visitors and messages.

Conservation of Mass, Energy, Momentum, etc.

Another common objection to time travel is that "it violates the Law of Conservation of Mass and Energy", along with some variations like conservation of momentum, etc.

First off, natural "laws" are not like governmental "laws". A governmental law is a prescription for how things ought to behave. It may be illegal to speed on the highway, but you are still able to do it. But a natural law is a description of how things do in fact behave. If you see a rock violating the law of gravity, then the law is wrong, not the rock!

Newton's laws of motion are extremely accurate for most things that happen on a human scale. Engineers use them all the time to develop cars, bridges, airplanes, and more. But when you start dealing with things well outside the human scale, they break down. Look at very massive things (like black holes), very fast things (like particles in an accelerator), and/or very small things (like electrons in a semiconductor) and Newton's laws don't work. In these realms, you need things like Relativity (where time doesn't work like Newton supposed) and Quantum Mechanics (where conservation of mass and energy are sort of "average" conditions that can be locally violated).

Newton's laws are approximations, quite accurate for some things but not precise enough for others. Even General Relativity and Quantum Mechanics have problems, and areas where they don't match up. We know that more progress will be made, and we even have some ideas about where the problems are. Some involve really dense, small things - like black holes. It wouldn't be too surprising if we saw some truly odd behavior there.

Anyway, that isn't the strongest response to this objection. The correct answer to this objection is to point out that the Law of Conservation of Mass-Energy is a local condition, not a global one. If I put more styrofoam peanuts in a box, it doesn't mean that conservation laws have been violated in the box! As long as you get the mass or energy from somewhere else, where it already exists, there's no problem.

But remember the model of the universe that we're dealing with. Time is another dimension like length and width and depth. And a black hole or a wormhole or even a "slow light" warp bends space and time around. When something comes from the future in a time machine, it doesn't just "blip" into existence. It physically moves from somewhere, just like moving styrofoam peanuts from a bag into a box. It covers distance.

Again, think of it like the flip-book. If the substance of the book were twisted in three dimensions, like a Mobius strip, and some parts of the book linked to other parts, it wouldn't be a violation of conservation laws for a 2-dimensional object to follow a three-dimensional path along those twists and end up in the book "before" it left. The "worldline" that it follows may be unusual but is not "prohibited".

In this model, what the conservation laws do prohibit is "worldlines" that have end-points. Every particle or quanta of mass-energy "starts" way back at the Big Bang, and continues in an unbroken stream into the future and the end of the universe (if any). Matter and energy are not created or destroyed along the way, though if there's time travel they might make a lot of "loop-the-loops" along the way. (One possible exception is "matter loops"; see below. But even they have no endpoints.)

Note that even this limitation isn't strictly accurate. According to Quantum Mechanics, "virtual particles" are created out of nothing and disappear into nothing. Sort of. In any case, conservation laws are more complicated than they might at first appear.

The Chronology Protection Conjecture

This one is fairly abstruse and technical, but one of the more credible obstacles to building a time machine. The potential time machines we listed above are based mostly on General Relativity, which is a solidly-tested theory that has been shown to be extremely accurate in a very wide range of circumstances. However, it doesn't work well when it comes to extremely small scales - for that, you need to bring in Quantum Mechanics.

The problem is that GR and QM are, in their current formulations, fundamentally inconsistent. They make radically different predictions in certain areas. Many of those areas have to do with extremely small, dense, fast objects... which is where time machines are predicted, at least by GR.

Some physicists, Stephen Hawking among them, are pinning their hopes on QM to prevent time machines from being constructed. It has been shown that, in the general case, the amount of energy to actually construct some time-travelling regions tends to infinity, just like the amount of energy needed to accelerate something to the speed of light tends to infinity.

But we don't have a solid theory of Quantum Gravity yet, and as this summary states (less technical version), it's not clear that there are no possible ways to actually make a time machine. The current math is rather complex and full of approximations and simplifying assumptions. Until we have a dependable, more fully-developed theory of quantum gravity, we just can't be sure.

Again, this is an argument against time travel that should be taken seriously, but there's still plenty of room for doubt. Some formulations of QM, so-called "Feynman Diagrams", accept time travel in a sense already - a particle of antimatter is, mathematically, like a particle of matter moving backward in time. Perhaps we'll find a way (via large rotating masses?) to amplify this effect out of the quantum level to have macroscopic consequences. Other quantum effects have been similarly 'macroized'; see, e.g. Bose-Einstein Condensates and Superconductivity.

But There's the Paradox Problem

The key problem with travel into the past is paradox. Probably the most famous paradox is the so-called "Grandfather Paradox". You travel into the past and kill your grandfather before he meets your grandmother. Therefore, of course, one of your parents wasn't born. Therefore, you were not born. But in that case, you never went back and killed your grandfather. So, naturally, you were born. Which means, of course, you weren't.

A paradox is a self-inconsistent series of events. It's when you take an action that ends up precluding that action being taken. Scientists and logicians and others get very upset about paradoxes. Many believe that since time travel apparently allows paradoxes, it is therefore forbidden by the Laws of Nature - "Time travel can't happen because it would have terrible effects." Whether it is actually Nature or merely the scientists who actually abhor paradoxes is a topic of some debate, however.

In any case, if we assume that time travel is possible, then we must at some point address the question of paradoxes. There are answers to this question, but they fall into two main types, as we shall see.

The Question

Once we assume time travel is possible, to describe the consequences we must make an additional assumption. We must answer the question, "If one travels back in time, can one alter the past?" Answering "yes" or "no" leads to fundamentally different notions of how time travel works, and, in fact, what time travel actually is.

Consequences of a Changeable Past

If you can change the past, what does that mean? Imagine you go back in time to, say, 1000AD, and give a bunch of North American tribes smallpox and a few other nasties, and maybe teach them to distill alcohol. Now, when Chris Columbus arrives, it's a much tougher job to conquer them; they're resistant to the diseases the dirty Europeans bring and they have more genes for resistance to alcoholism.

So, now we have two four-dimensional continuums, the "before" where North America was conquered with relative ease, and the "after" where it's a much tougher fight. We have two different four-dimensional states. When we had different three-dimensional states, that implied four dimensions; wouldn't changes to history imply five dimensions? We would need a "hypertime", another time dimension for changes in timelines to happen in.

Models of a Changeable Past

The Change-Wave Model: One Universe, Many Complications

Many stories assume that there's only one four-dimensional continuum, (you have to assume four dimensions for time travel to be possible at all) and when you make a change in the past, that change has to "propagate" forward. Examples: Frequency, Back to the Future.

This makes a sort of intuitive sense, but this model ends up being fraught with problems and paradoxes. For example, how fast does the "change wave" propagate forward? How many seconds per second? (The units there should give you a clue that something strange is going on - that would be a dimensionless number.) Why wouldn't the "change wave" move backward along with a time-traveler and end up changing the change?

The details of what the "change wave" is supposed to do are, so far as I've seen, inconsistent and ad-hoc, and certainly not supported by any known theory. For example, in "Back To The Future", why would a "change wave" remove a person's head from a picture first, and then their torso, and then their legs? For that matter, if there was a "change wave" at all, how could it possibly affect the picture before it "arrived"? It seems more reasonable to assume that the entire picture should change "at once", when the change wave "arrived" back in the past.

But, of course, if such a "change wave" had arrived, it would have eliminated the hero, and therefore all his actions, including the ones that put his existence in jeopardy. So we'd just have a Grandfather Paradox.

It's frequently part of a story that, if one actually did the time-traveling, one would be immune from the effects of the "change wave", and would remember the "old" past. (Not always, though - a 1948 story "The Brooklyn Project" has experimenters oblivious to the changes they are making.) In the extreme, one might perform a Grandfather Paradox and end up a person with no parents. You show up, an 'extra', a person who never existed.

But this points out a problem. Let's assume this model is true. Now, you borrow a gold brick for a few minutes, say from 12:00 to 12:10. Then you get your time machine going. You jump to 12:09, and take the brick. Then you jump to 12:08, and take the brick. Then 12:07, then 12:06, etc. Finally, you jump forward to 12:10, and hand the lender a gold brick. You have nine other bricks to play with. Where did these bricks come from if there's only one history? The Law of Conservation of Mass/Energy is totally out the window.

What if you leave those nine gold bricks laying around for ten minutes, then do it again? At the end, you have ninety bricks...

Note that, in principle, you could keep duplicating gold until you'd paved the world with it, until you'd created an Earth coated in thousands of miles of gold, until the Earth weighed as much as the Sun. In principle, you could create enough mass to reverse the universe's expansion. Where'd the matter come from? (BTW, remember the bit above where I said that conservation laws could be violated in QM under certain circumstances? That doesn't help here; if a virtual particle is 'created', it must be 'destroyed' later; in the long term, the books balance. The point of this thought experiment is that, in the change-wave model, the books don't balance.)

Some people like to keep to one timeline in order to avoid "many worlds" and the idea of new universes being created all the time. But if you're worried about conservation laws, well, the change-wave model still violates that law. It's a difference of degree, not kind.

Another example: in Caleb Carr's "Killing Time", a genius sends himself into the past, and his compatriots suddenly find themselves in a world affected by his actions, but remembering the "old" world. How could this be? If they didn't do any traveling, why would they be exceptions and remember the "original" past? Indeed, why would they even exist, their origins being so far divorced from the world as they "now" find it? (More matter creation...)

Another problem. If time exists in four dimensions, so it's possible to travel back and forward in time... then 'when' does a change in history happen? If someone was going to come from the future to the past to change something, then they would 'already' have done so/be doing so.

(English really isn't built to discuss time travel very well. These sorts of things are hard to talk about in English, but fairly clear in mathematical terms. Ah, well, for now we're stuck with English, so we'll try.)

For example, consider a timeline like so:


Time moves normally, from moment A to B to C to D. At time D, someone goes back in time to B and changes things, so that now we have a new history, E to F to G. Now, what does someone at time C observe?

If the future 'already' exists, if we have a four-dimensional continuum (which we pretty much have to assume for time travel to be possible at all), then from the perspective of moment C, the time travel event at D 'already' exists. But that means that moment E 'already' exists, and therefore moment C 'already' doesn't exist. We have a contradiction. The point is that a change in history can't come from within that history, because it would already have come.

For this to work, time would have to have a "leading edge" that left a trail behind it, a bit like paint dripping down a wall. But this has its own paradox. What if you invent a time machine, and want to determine if you're at the leading edge or not? You try to travel forward in time, (say it's 2050 and you try to travel to 2051) but you can't because the future you're trying to travel to doesn't exist yet.

But, "one year later", that future will exist. What happens back in 2050? Do you suddenly "have succeeded" back then, although you failed "before"? Does it matter if you only try to travel a nanosecond into the future? The point is, as soon as you determine if you're on the "leading edge", you're not anymore, so you both succeed and fail. Contradiction again.

This "change-wave" model resolves no problems (paradoxes still happen) and creates so many new complications that it seems we must abandon it. What if we return to the idea of a "hypertime", a fifth dimension for such changes in history to happen in? (Note that, when we made a change to our one-dimensional ABCD timeline, we needed two dimensions to draw it in...)


This is a very common theory about how to resolve paradoxes. When you travel back in time, you really create a whole new universe where your changes take place in. You don't kill your grandfather, you kill someone who would have been the grandfather of someone just like you.

As noted, you need (at least) five dimensions to properly make room for all this. Four dimensions for a given three-dimensional history, and a fifth "hypertime" dimension for changes in history to take place. Personally, this seems a little untidy to me, but it dovetails pretty well with some interpretations of quantum mechanics.

And, of course, it's not really "time travel", is it? You don't travel into your past, the past that gave rise to you. All you do is travel to another universe that bears a remarkable resemblance to the past. In any case, it's the only internally consistent model of anything like a changeable past that I'm aware of.

It handles the notion of "matter creation", too. If you do the gold brick experiment listed above, you still end up with nine extra bricks. It's just that those bricks came from other universes. You end up in a universe with extra bricks, and nine other universes are shy some gold. (However, assuming there were an infinite number of other universes, there might be schemes that would allow you to multiply gold endlessly in all the universes. Adapting and implementing such a scheme is an excercise left for an advanced relativistic quantum mechanic.)

You Must Change the Past

One problem (often overlooked in fiction) with the ability to change the past is that it isn't terribly practical. Chaos theory shows that if you can change the past, then you must change the past, and the further you go the more unpredictable the results.

A "chaotic" system is one that exhibits extreme sensitivity to initial conditions. That is to say, even a tiny difference in a single variable in such a system eventually leads to large differences in the observed behavior. (For some examples, see here and here.)

Not all systems in the world are chaotic, of course. But one that appears to be is weather. Even a very simple model of atmospheric convection (the distribution of heat via air circulation) displays chaotic behavior. Discovered by Edward Lorenz, the Lorenz Attractor is such a model, and among other things spells the doom of long-range weather forecasts.

Because weather is chaotic, in order to predict it far in advance, we would need to know the exact state of the entire weather system of the Earth, down to well past a millionth of a degree of temperature. Any mistake, however small, in our model will be exponentially amplified as we run through the calculations, and eventually (probably on the order of a few days (see here, at the bottom of the page)) our predictions will look nothing like the actual weather.

This has been called the "butterfly effect", the notion that a butterfly flapping its wings on one side of the world can change the weather from sun to hurricane on the far side of the world within a few days or weeks. The weather depends on everything.

Now think what this means for time travel. If you appear at all, and you can change the past, then simply the act of appearing will disturb the atmosphere around you, right? Within a few days or weeks, the weather will be completely different, from sun to rain and vice versa.

Imagine you put on your time belt, jump back to 1850, pick an apple, then return to your origin time. By the time the Civil War comes about, battles happen on different days because the weather has changed. Maybe a drought is added into the mix, or an unusual amount of rain. Different people die in these battles. Perhaps the war goes quite differently.

Even if the outcome of the war is similar, the weather will affect when people make love, and even a tiny change in position, much less timing, would make a different sperm reach the egg first, right? Perhaps a son is born in 1867 instead of Marie Curie. Hitler is never born, but neither is Winston Churchill, Albert Einstein, or Ghandi.

So even if we can change the past, it's not practical to do so with a definite purpose in mind. There's no possible way to predict what changes you'll cause; all you know is the further back you go, the greater they will be.

Historical Inertia

Some fiction writers have invented a notion of "historical inertia", which I like to call "historisis", after "hysteresis" in electrical circuits. The idea is that time itself somehow works to resist change, that changes you make tend to be damped out. Perhaps you kill Hitler, but someone very like him takes his place, does very similar things, and the future that results looks quite similar to the original one.

No plausible mechanism for such a phenomenon has been proposed; indeed, the chaos argument above argues strongly against it. But even if it's true, Larry Niven pointed out something. If time wants to resist changes, what's the simplest course of action? Right, prevent time machines! So if there is historisis, we'd never prove it because we'd never manage to make a working time machine. (This is similar in spirit to Hawking's Chronology Protection Conjecture above.)

No Self-Causing Loops

One common theme in some time-travel stories is that of self-causing events. Imagine you take some of Van Gogh's paintings back in time, and show them to the artist. He likes them so much, he copies them. The question arises, where did they come from?

In a many-worlds model, the answer's easy. They came from a universe where a Van Gogh originally dreamed them up. Things get more complicated if we can't posit multiple timelines, however...

What if the Past is Unchangeable?

It may not seem intuitive to propose that you couldn't change the past. After all, you're there, you have free will, why wouldn't you be able to affect the outcome of events?

It "Already" Happened

Imagine, however, that you are traveling, not into an alternate universe, but into the past, the past that gave rise to you. For this to be the case, your trip into the past must "already" have happened, must "already" be a part of the history that gave rise to you and your trip. (English again.)

In this sort of view, our history, our timeline, is a static, 4D sculpture, like the 3D flip book our frog lives in. If you travel into the past, you can't change it, because you didn't; or more precisely, any changes that you make are part of the history that you left.

To give this a practical example, let's return to the Grandfather Paradox. You go back in time with the full intention of killing Grandpa. We know, because you exist, that you didn't kill him. Perhaps your gun jams. Maybe the records are inaccurate, and you kill the wrong person. Maybe you do kill Grandpa, and then (assuming you're male), you take his place. After all, you were jealous of his relationship with Grandma, and you've got the right genes...

In a practical sense, this can be thought of as a sort of "super-historisis"; no matter how unlikely it may seem, whatever you do in the past will not change anything about the "present" you came from. In another sense, you can think of the future as the same as the past; neither can be changed.

On the other hand, neither can be known fully, either. We know a fair amount about, say, ancient Egypt, but a whole lot of really funky things could have happened back then and we'd never know today. Perhaps some records were forged. Possibly the memories of the people who wrote the records were biased, or just mistaken. You go back and kill Ramses II, and it just turns out that the guy histories record as Ramses II was in fact an impostor put up by the royal families to maintain the line of succession.

But What About Free Will?

A lot of people don't like this model because it would seem to eliminate any possibility of free will. Personally, I don't particularly worry about whether I have free will or not. If I do have free will, then I don't have to worry about it. If I don't, then there's no point in worrying about it. Either way...

But this model doesn't necessarily pose problems for free will. Consider normal ideas about time and free will. Your parents freely chose to have you, right? At the very least, their free choices led them to the point where they did have you, though hopefully they were happy about it.

Now, assuming no time travel, those choices cannot now be changed, right? They cannot now decide not to have had you. The moment of choice was back then, somewhere in the past. Once that choice was made, it was fixed. Assuming free will, it was not totally determined by what led up to it in some physical deterministic sense, but once made it could not be changed. This is not a constraint on free will.

Now, just by adding in time travel we needn't change anything about this. Choices are freely made at the moment they are decided. It's just that now it's possible to know what those free choices "were" at a point in time "before" the choice "will be" made. (English again forces us to use strange tenses to speak about this. Oh, well.) Remember, in this model, there is no privileged point we can pick out and call 'the present'. Every moment is past to some instants, future to others. Every moment is a "present".

(Note that some people use this idea to reconcile the idea of God knowing what we will do with the notion of free will. God, existing outside of time, doesn't ordain what people do, It just sees them doing it. I only bring it up to point out that lots of people have no problem in principle with the idea that they both have free will and yet someone knows with certainty what they will do. I don't see why it's any different if someone besides a God has that knowledge...)

If you see a movie of yourself from the future doing certain things tomorrow, from a certain perspective it doesn't mean that you are "fated" to do those things. It just means that you know, when that time comes around, that doing those things will seem to you to be the best available choice.

Perhaps the future choice seems silly, or even terrible. Well, can't you think of a moment where you've made a choice, and then later (perhaps only a second later) thought, "What was I thinking?" The fact that it seems unlikely to you that you will make that choice doesn't mean that you won't make it. People do things they never expected to do, even said they wouldn't do, all the time.

If this isn't convincing, oh well. Sadly, the universe is not constrained to behave in only the ways we'd like it to. As I said before, there's no practical point in worrying about it either way. You might as well debate about irresistible forces meeting immovable objects.

And You Thought Paradoxes Were Bad...

But whatever other consequences this model of time travel has, it allows for one of the strangest consequences - "causal loops", a chain of events that causes itself. These have been called "perpendoxes" (by Andrew Plotkin on rec.arts.sf.science) because they are an orthogonal notion; they are "perpendicular", or "at right angles", to paradoxes.

Let's return to the Van Gogh story from before. Again, you bring back copies of Van Gogh's paintings and show them to the artist. He likes them, and copies them. "Later on" (English again), you show them to Van Gogh...

In the many-worlds model, there were at least two histories, one where Van Gogh created the paintings and a "later" (in hypertime) history where he merely copied them. The paintings have a definite origin, just in another universe. But in a single-history model, the paintings don't have a beginning or an end! They more-or-less cause themselves. (Robert Heinlein took this to an extreme in a story called "All You Zombies...", and invented a character who was his own father and mother.)

Remember, a paradox is a self-inconsistent series of events. A "perpendox" is consistent, but it's self-causing. When cause and effect are reordered, effects can be their own causes. This can go even further, and you can have loops of matter. What if you don't just show Van Gogh the paintings, but instead you give him the originals?

There is a problem with matter loops, however. Consider that a painting is made up of many billions of atoms, all of which are moving around. At some point in the loop they have to come back to exactly the same configuration, down to the subatomic level, so that the loop can "match up".

But paintings, and really all macroscopic objects, age and break down and otherwise go through non-reversible transformations. A few electrons might make a plausible matter loop, but anything visible to the naked eye would be almost thermodynamically impossible. (The pocket watches in "Somewhere in Time" and "Timerider" are neat symbols but not terribly reasonable.)

Causality and Perpendoxes

Some people seem to have a problem with perpendoxes because in a direct sense they "violate causality", the idea that effects follow causes, and those effects in turn become causes, etc. A perpendox is not an effect of any cause from before the time traveler "arrived" in the past.

Even if you knew the entire state of the universe to the last detail at the point just before they arrived (thus allowing you to get around chaos theory), and assuming determinism (thus denying free will), you still couldn't predict a perpendox. It depends on events that "haven't happened yet". The effect of the perpendox comes from causes that happen "later".

Of course, this is hardly surprising - the whole definition of (backward) time travel is putting effects before causes! If you don't have effects coming before causes, you're not talking about time travel. Note that even in a perpendox, though, causality applies - effects have causes and so forth. It's just that causality is a local condition, not a global one.

In the absence of time travel, the relations between cause and effect are, in principle, pretty simple. They more-or-less follow a straight line: cause to effect, cause to effect, etc. If you allow effects to appear before their causes, though, we'd have to expect some pretty weird and non-intuitive behavior.

Of course, Relativity and Quantum Mechanics are pretty non-intuitive as well; we didn't evolve at speeds near light or sizes near an atom. But even if they're odd, they seem to match the data pretty well.

Quantum Mechanics and Perpendoxes

While normally quantum mechanics is associated with the many worlds model of time travel, it's worth noting at at least some interpretations of QM actually dovetail quite nicely with the idea of an unchangeable past. Indeed, this notion of nondestructive interference would tend to argue against the Chronology Protection Conjecture of Hawking.

Time Phones

Of course, you don't need to physically move back in time to get all the bizarre consequences of time travel. Even if you can only send information into the past, you too can create paradoxes or perpendoxes! Consider the (fixed-timeline) story of Oedipus. Or, for a more recent version, the (change-wave model) movie Frequency.

Energy Is Always Transferred

In order to transmit information, though, you do need to direct some energy so that it has an effect. Signals of any type (except possibly psychic signals, which nobody has any solid evidence for anyway) are composed of energy, either radiated like light or in solid packets of matter. In order to affect the past, energy will need to be sent.

But Energy Is Easier Anyway

Remember the Tipler Cylinder above? Obviously it twists up spacetime something fierce. In order to keep things like tides from smearing a person like Play-Dough, the total "twistiness" in any particular area has to be kept fairly small. (People are fragile things; a couple of dozen gravities and they fly apart!) To do that, you have to build a big cylinder, on the order of at least a few miles long. And it'll probably still be a bumpy ride, even with a life preserver.

But what if you want to transmit something smaller... a lot smaller? Like, say, a beam of laser light? You can make the wavelength as small as you like, maybe in the gamma-ray range if you're really worried about it. Then you don't need to build the cylinder so large. A visible-light laser pulse has a wavelength on the order of a few hundred nanometers. People are on the order of a meter or so. As a handwaving guess, something built to transmit a laser pulse into the past could be less than a millionth the size of one built to send a person.

Besides, as I noted above, to travel even one second into the past means travelling almost the distance from the Earth to the moon. It takes a lot less energy to shoot a laser at the moon than an astronaut.

No matter how time travel is finally invented, it will almost certainly send information back first, and then, much later if ever, people (assuming it's based on any relativistic model).

The Time Modem

Of course, if we can send a signal into the past, we can encode more than just morse code with it. Imagine a time-modem, able to send text, pictures, programs, databases, blueprints, recipes, and more. Given enough bandwidth, you could put on Virtual Reality goggles and see the past in... er... "real time". (English again.)

(Given a lot of bandwidth, you could have an "ISP of Time", which would let you communicate with any time in their range of existence.)

The Practical Consequences of Time Travel

But what would the world look like if time travel were available, even common? What changes would something like this force on society? Obviously we can't be sure, but there's room to speculate...

Change-Wave Model

No time travel happens. Or, rather, in accordance with Niven's Law, changes happen until someone prevents time machines from ever having been invented. After that, no time travel ever happens. Things may get a little weird "during" the "settling", but "in the end", no one ever sees that.

Many-Worlds Model

In this case, based on the analysis above, time travel (even in the form of a time phone) isn't practical for more than avoiding catastrophes. The chaos theory discussion showed that you can't predict what will happen when you try to change the past.

Besides, all you do is create a world where the disaster didn't happen, it doesn't solve your problem. For example, perhaps someone in 1940 might send a message back to 1930 saying "Do something about this Hitler guy!". In so doing, maybe they create a world where Hitler doesn't come into power; but the person who sent the message still has to fight in World War II.

And again, all you can be sure of is that you avoid a particular catastrophe. Perhaps Hitler doesn't become the leader of Germany, but someone else even worse does, and because of all the meddling, that German leader develops atomic bombs before the Allies. (Maybe the Allies don't even form until it's too late...)

So, if you are sending the message or the time traveler, it doesn't have any effect on you. And if you are receiving the message or the visitor, all you can be sure of is that the future won't look like they say it did. You might get some advanced technology out of it, or things like that, but it's basically from an alternate world, not a future or past time.

If you are able to physically travel and not just send messages, then there are some advantages if you're the traveler. You could travel into the past armed with high-tech stuff and set yourself up very well. But you might never be able to return to the "future" you left, depending on exactly which model of multiple-universes applies.

Then, of course, there's Niven's Law again. As all these changes happen, eventually a change will be made such that time travel doesn't get developed. After that, history doesn't change or branch anymore. In most universes, no one will ever encounter time travel, even if it's physically possible.

Single-Timeline Model

If changing the past isn't possible, then we still have to answer some questions before we can determine what the effects will be. First, how many people will have access to the time machines or time phones? And second, how much information can be sent?

High Availability, High Bandwidth

What if everyone had time phones (or access to one big time-internet), and calling another time cost no more than a long-distance call today? Anyone can send voice, text, and images across the ages. What are the consequences?

Everything's Obsolete

Try to think of any area of human life that wouldn't be changed. The stock market's gone. Las Vegas is out of business. You can't get life insurance. Who needs dating services? Paramedics are retired, though perhaps not doctors. Theft is virtually impossible, as is fraud.

If you doubt this, think for a moment - what would you do if you came home and found your house had been burglarized, and you had a time phone? Right, you'd call yourself in the past, and have the police waiting to arrest the thieves. But, of course, the thieves would also have a time phone, and with their one phone call they'd warn themselves not to go to your house.

But we're assuming that time can't be changed. Barring some thermodynamic miracle, if your home is burglarized these calls would take place. So, ipso facto, your home is safe. However it works out, you don't have a reason to call back and change things.

The Satisfaction Principle

The principle is that things will work out in such a way that people either have no motivation, or no ability (or both), to change the past. Let's look at another example that will hopefully make things clearer.

Imagine that one of the tires on your car is about to fail. Either you get a phone call warning you about this, or you don't. If you don't, the tire fails, and you are irritated, or your loved ones are sad that you died in an accident. Someone will call. But that would change the past, and that's not allowed.

Fortunately, there's a self-consistent alternative. What happens is, you get a call from yourself, saying, "Hey, your tire's about to blow, go get it replaced!" You take it in, and sure enough, you need a new tire. So you go home from the mechanic's and call yourself up in the past, and say, "Hey, your tire's about to blow..."

In essence, no one has any motivation to change the past to anything other than how it ends up. (At least, no one with access to a time phone has any motivation to change the way history worked out; more in the "Low Availability" section below.) Maybe they make calls to ensure that things happen the way they "did", like in the tire example above, but they don't try to change it.

Imagine you're an ad executive, who has to decide between using ad campaign A or B. You call yourself up in the future and ask, "What did I do?", and you tell yourself, "You went with campaign B, and sales went up 50%." So you go with B.

Now, perhaps A would have doubled sales. But what matters is that B was good enough that nobody had any reason to want to change things. Things don't have to work out optimally, they just have to work out well enough to satisfy the people involved.

Back in college, one night, some pipes froze in a building on campus and water leaked all over a bunch of expensive computer equipment. What if there had been time phones? Would a security guard have called back and said, "Hey, the pipes are going to freeze; set up a space heater over there"?

No, of course not. Really, someone would have called the architect and said, "Hey, those pipes are going to freeze! Design them with more insulation or reroute some heating ducts or something", right?

Again, nope. Imagine you're an architect designing a building. You know, because of the way time phones work, that the design you turn in will be at least good enough to prevent people from calling back and complaining; otherwise your phone would be ringing right now. But since that's true, why bother going to the trouble of designing it? Just call yourself up in the future and download the plans that you are going to turn in...

With this in mind, try to figure out an area of human endeavor that wouldn't be profoundly altered by time phones. You could call yourself in the future and find out who your spouse is going to be; heck, you might be getting birthday cards from them already from your future. If anything is invented at any point in the future, plans can be faxed back to the first point where they can be manufactured. Indeed, plenty of "inventions" that no one invented will be faxed back, causing themselves...

The Triumph of the Whiny

It's impossible to imagine what such a society would look like; all we can really do is name some things it wouldn't have. One interesting thing to note is that the more picky you are, the better things are likely to work out for you. Think of someone you know who is miserable without the very best - if they had a time phone, they'd always get it. Someone who's willing to settle for "pretty good" will certainly get at least that, but has no guarantee of anything more...

Low Availability - The Eternal Dictatorship

If time machines or time phones are rare and difficult to get hold of, what you get is an eternal, unbreakable dictatorship. Think about it - whoever gets time travel first will have an incredible advantage over everyone else. If anyone conspires against them, the "time lords" will know about it, perhaps even before the conspirators know that they'll be part of an opposition.

Indeed, the first message from the time phone or the first visitor might be, "Okay, here's how you took over the world. First, blackmail these people with this information. Also, invest in these stocks then, and sell them at such-and-such time. Eliminate these people, here's where they will be..."

Imagine trying to fight someone who knows, better than you do, exactly what you are going to do. And they know you will lose. After all, they can ask themselves in the future exactly how they beat you. If you had succeeded, they'd never have taken over the world to begin with, right? (Note the problem with verb tenses in English again.)

The only variable here is the amount of bandwidth. If the channel is low-bandwidth, only the absolutely critical information needed to stop the opposition will be sent, and you'll have some freedom of action. The less of a threat you are, the less interference you'll suffer. As the bandwidth increases, progressively smaller threats are dealt with.

High Availability, Low Bandwidth

So long as access to time travel is spread over a wide enough number of people, a dictatorship is unlikely. There might still be a differential between the time travel "haves" and "have-nots", but the authority would presumably be spread out a little more.

But if the bandwidth is low, again, the time machines will primarily be used to preclude emergencies. Disasters like airplane crashes and train wrecks will be avoided. Oil spills won't happen - drunk captains will be reported ahead of time and relieved of duty. Political assassination and major terrorism will be nearly impossible; again, the authorities might know about a terrorist operation before the perpetrators dream it up.

As the bandwidth increases, smaller and smaller annoyances get taken care of. Individual car crashes are prevented; Savings and Loan crises are averted; traffic jams are smoothed out; sequels like "Mannequin II" are kept out of production. In the limit we reach the "High Availability, High Bandwidth" case above.

Some Examples of Different Models in Books and Movies