I think it’s important to understand the nature of time. That’s because I think it leads to other things. I also think you can gain an understanding of the nature of time by being empirical. For example we use phrases like time flows and time passes, but when you look for the empirical evidence of time flowing or passing, you can’t find any. That’s because there isn’t any. I can hold my hands up a foot apart and show you the gap, the space between them. In this respect I can show you space, so space is empirical. I can also waggle my hands and show you motion, so motion is empirical too.
But I can’t show you time
But I can’t show you time. I can show you a clock, and you might point to the big hand and the little hand and say that’s the time. But what am I really showing you? A box with two moving pointers that go around and around, that’s all. This is the nub of Einstein’s operational definition of time. It’s in his 1905 special relativity paper on the electrodynamics of moving bodies. He talked about trains and clocks, and said this: “Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by “time”. We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, “That train arrives here at 7 o’clock”, I mean something like this: “The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events””. This was in a paper about moving bodies. A train is a moving body, so is the big hand of a clock, and so is the little hand of a clock. And the crucial point is that the time is nothing more than the position of the hands. I know that might sound simplistic, but get your magnifying glass out and take a cold hard look at what clocks do.
What clocks do
Open up a clockwork clock and you’ll find a mainspring and a gear train, with an escapement to keep the gears turning at a constant rate. One of the gears is connected to the big hand, another to the little hand. All the clock is doing, is “clocking up” some kind of regular cyclical internal motion:
Clockwork gif from the Popular Mechanics article Building a Clock by Eric Limer
All clocks do this. It doesn’t matter whether it’s a Victorian pocket watch with a spiral spring and cogs, a quartz wristwatch with a piezoelectric crystal and electronics, or an atomic clock with caesium atoms and microwaves. A clock is some kind of machine which somehow counts or accumulates some kind of regular cyclical internal motion and shows you some kind of cumulative display that you call the time. The gears move so the hands move. Or electrons move and a liquid-crystal display changes. Or something else moves and changes. Whichever way it’s made, a clock is in essence a motion accumulator. It doesn’t literally measure the flow of time. A clock is not some cosmic gas meter. Open up a gas meter and you’ll find gas flowing through it. Open up a clock and you won’t find time flowing through it. All you’ll find is some kind of regular cyclical internal motion. Tick tock, tick tock, the internal mechanism of a clock isn’t called a movement for nothing.
Time does not flow
The notion that time flows is just a figure of speech. Rivers flow, currents flow, blood flows. These things flow because something moves. Water moves, hearts move, people move. The Earth moves, the stars move, the galaxies move. Everything moves, and you can see this motion because light moves to your eye and electrochemical signals move in your nerves and brain. Because photons and electrons and other things move. But you can’t see time flowing. That’s because it doesn’t. Nor can you see it passing. That’s because it doesn’t. The passage of time is just another figure of speech. Footballers pass, buses pass, kidney stones pass. But there is no physical thing called time that actually passes. Instead things move. Things like planets and planes and pendulum clocks.
Time exists like heat exists
That’s not to say that time does not exist. I think it’s best to think of it as something like heat. Heat exists. You know this, especially if you’ve ever burnt your hand on the stove. However heat isn’t fundamental, it’s an emergent property of motion. In a gas the molecules move freely as per the kinetic theory of gases. The temperature of a gas is effectively a measure of the average kinetic energy of its molecules. The faster they move, the hotter the gas:
GNUFDL translational motion gif by Greg L, see the Wikipedia temperature article and Wikipedia Commons
If you examine one molecule, it has no fundamental property of heat or temperature. However if it and the other molecules are moving fast, the gas is hot. This macroscopic property is perfectly real, and it’s why we can cut steel with an oxy-acetylene torch. Time is something similar. Whilst temperature is an average measure of motion, time is a cumulative measure of motion. And time exists like heat exists, because a hundred years t will kill you just as surely as a hundred degrees C.
The arrow of time is an abstract thing
But whilst heat really does flow, time doesn’t. There is no river of time flowing from the past to the future. That’s just an abstract concept for which we have no scientific evidence at all. There’s no real direction of time either. Yes, there’s an inevitable sequence to events, because if you don’t move from A to B you can’t move from B to C. But there’s nothing flowing from past events to future events. People talk about the arrow of time which points from the past to the future, and they talk about entropy. But entropy is merely “sameness”, associated with available energy, wherein energy-density tends to even out as we do work. Entropy increases, but the direction of this is as abstract as the direction of cooling in your cup of coffee. You cannot point in this direction, so there is no arrow of statistical mechanics in any real sense. I can point forwards in space, but you can’t point forwards in time. That’s because the future isn’t a place you can point to. It’s a name we use for the state of the universe after everything has moved. Yes, people say motion is a change in position with respect to time. But when you measure the motion of an object, you use a clock, and that clock merely features other things that move. So you end up saying motion is a change in position with respect to some other change of position. That’s circular. So it doesn’t make sense to say you need time to have motion, not when you can see it’s the other way around. Say it how it is: motion is a gradual change in position. Don’t describe something you can see in terms of something you can’t.
Abstraction can get in the way
This is particularly important in physics, where abstraction can get in the way of understanding. Einstein hinted at this in 1908 when he said “since the mathematicians pounced on the relativity theory I no longer understand it myself”. I think he was referring to his former teacher Hermann Minkowski. You’ve doubtless read Minkowski’s Space and Time which starts like this: “The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality”. Minkowski said this in September 1908. In January 1909, less than four months later, he was dead. He was only 45. I think that if he’d lived longer physics would be different today, because I think he would have seen that the union is between space and motion, not between space and time. But we are where we are, and nowadays some physicists talk about Minkowski spacetime as if it’s the black stuff between the stars. It isn’t. It’s a mathematical model that combines space and time into a single “continuum”. It’s a four-dimensional manifold made up of three spatial dimensions plus the time dimension. We can drop one of the spatial dimensions to depict it:
A manifold is a “topological space”. It’s essentially a mathematical map. It maps out the block universe, which is utterly static because it models space at all times. It’s like you film a red ball with an old-style movie camera, then develop the film, then cut it up into individual frames and form them into a stack. There’s a red streak through the stack. This red streak is the ball at all times, but it isn’t moving up the stack. In similar vein there is no motion through the block universe. That means there is no motion in spacetime. The motion of an object through space “over time” is represented by a world line. But the object isn’t moving up its world line. There is no plate-of-the-present moving up the block universe either. And you cannot look up to the clear night sky and point out a world line. Or a light cone. Or a reference frame.
The map is not the territory
All these things are abstract things, not things that exist. When you are trying to understand those things that do exist, it is important to avoid being distracted by the things that do not. Your reference frame is little more than your state of motion through space. When you accelerate we say you change your reference frame, but it’s not like changing your socks. You’re changing your state of motion, and as a result your measurements change. Your measurements of space and time change, and to make sense of that, we refer to special relativity which in turn refers to spacetime. But it is important to be aware of the distinction between space and spacetime. We move through space, but not through spacetime. Spacetime is the map, but the map is not the territory. Ours is a world of space and motion, not some static mathematical manifold of world lines and light cones. A clock doesn’t really measure the distance between two spacetime points, just as it doesn’t really measure the flow of time. It merely clocks up local motion. That’s all there is to it. It’s as simple as that.
That’s not to say special relativity is wrong. It’s right. Time dilation is perfectly real. We have good scientific evidence of that. Clocks go slower when they’re moving fast, for a very simple reason. I think this is best explained using the parallel-mirror light clock, which features a light beam bouncing back and forth between parallel mirrors:
Public domain image by Mdd4696, see the Wikipedia time dilation article
The scenario is that you and I are identical twins, and we each have a parallel-mirror light clock. You stay on Earth whilst I go on a fast out-and-back trip in my gedanken spaceship. After I’ve landed back on Earth we compare clock readings, and we find that my clock went slow compared to yours. That’s easy to understand when you appreciate that my clock reading is just the number of times light bounced back and forth between my parallel mirrors. Yours is the number of times light bounced back and forth between your parallel mirrors. My light moved diagonally whilst yours moved up and down, so my clock reading is less than yours. My local motion was of necessity reduced by my macroscopic motion through space, because the maximum motion is the speed of light c. You could see this if you had a gedanken telescope, and could watch me zooming across the night sky. You’d see my light beam bouncing back and forth between my mirrors, but because you’re panning, you wouldn’t see my light moving in some zigzag fashion. It would look like it was moving straight up and down. Like your own, but slower. It’s slower by something called the Lorentz factor. Amazingly enough, this is derived very simply from Pythagoras’s theorem. Take a look at the simple inference of time dilation due to relative velocity on Wikipedia:
Public domain image by Mdd4696, see the Wikipedia time dilation article
The hypotenuse of a right-angled triangle represents the light path. The base represents my speed v as a fraction of c. The height gives the Lorentz factor, which can be written as √(1 – v²/c²). If I could somehow travel at .99c, the Lorentz factor would be √(1-.99²/1²) = √(1-.98) = √(.02) = .1414, which is a seventh. So my clock clocks up one year while yours clocks up seven. The Lorentz factor is that simple, and it applies to everything because of the wave nature of matter. Robert Close talked about this in the other meaning of special relativity. We can make electrons out of light in pair production, and we can diffract electrons. Remember what Feynman said about around and around, and think of electron spin as light going round a circular path. Then look at it sideways like this: |. Then set it moving so that the circular path looks like a helical path. Sideways on, it would look like this: /\/\/\/\. It’s just like the light bouncing back and forth between the parallel mirrors, and it’s why time dilation applies to electrons and other particles too, and me, and you.
The twins paradox
This is why if you and I were identical twins and I take the fast out-and-back trip through space, I come back younger than you. But note that this scenario isn’t the twins paradox. That’s where you and I pass each other in space, and you look through your telescope to see my time going slower than yours, and I look through my telescope to see your time going slower than mine. People think this is a paradox, but it isn’t. When we’re separated by distance I look smaller than you and you look smaller than me. But we know about perspective, so we don’t shout paradox! Nor should we when we’re separated by motion, and my time looks slower than yours and yours looks slower than mine. It’s just another type of perspective. Time is relative because motion is relative. Your time is your cumulative measure of local motion. So when you move relative to me, your time is relative to mine.
The time dimension is not the same as the spatial dimensions
This is why the time dimension can be likened to the spatial dimensions. However it’s important to note that it isn’t exactly the same. In special relativity it’s distinguished by a minus sign in the t term in the spacetime interval. This is written as ds² = -cdt² + dx² + dy² + dz², and it is said to be invariant. It’s the same for both my parallel-mirror clock and yours, because our light-path lengths are the same. The time dimension is also different because time is a dimension in the sense of measure, not in the sense of freedom of movement. It’s a measure of how much local motion occurred inside our clocks, nothing more. Hence I can hop forward a metre but you can’t hop forwards a second. Because you can’t move through a measure of motion. That’s why you can’t move through time. You can’t move through spacetime either, because there is no motion in spacetime. Some say you can’t move at all, which is what eternalism says. The opposite view is presentism, which is more in line with Einstein’s 1905 operational definition. It’s also in line with his 1949 view. Palle Yourgrau wrote about that in A World without Time: The Forgotten Legacy of Godel and Einstein. It’s an interesting book. It even mentions time travel.
Time travel is science fiction
Talking of which, I love films like Timescape, 12 Monkeys, and Déjà vu. They feature time travel, as do many more. I love them even though I know that time travel is science fiction. I love them even though I know why time travel is science fiction, and why time travel to the past is out of the question. It isn’t because of the grandfather paradox or the chronology protection conjecture. It’s because we don’t even travel to the future. Travelling to the future is just another figure of speech. Yes, you may have seen Stephen Hawking saying you can travel to the future on a superfast train:
But you aren’t really travelling to the future. Instead you’re affected like the parallel-mirror light clock. As the train speeds up, the local rate of motion in your body and brain has to reduce. If it didn’t, adding your local motion to the train motion would mean the total motion exceeds the speed of light. That can’t happen because of the wave nature of matter. So you’re time dilated, that’s real enough. But you aren’t travelling to the future, any more than I am sitting in my chair. I’m not travelling to the future at one second per second, and you aren’t travelling to the future at seven seconds per second. You’re just living your life in slow motion for a while. And whilst you’re doing that, I can watch you every inch of the way. You can look out the window and watch me every inch of the way too. You don’t disappear up some time tunnel to start living your life in the middle of next week. You’re living your life in slow motion so you effectively fast-forward through the week. Like bullet time in reverse. Then when you step off the train it’s me who meets you at the station. I don’t miss you by a week. You slowed down your time by slowing down your local motion, that’s all.
The stasis box
It’s not unlike those films or TV programs such as a kind of stopwatch where the protagonist has a device that can stop time. If you look carefully, you’ll notice that what the device really does, is stop motion. One such device is the stasis box. When I put you inside, everything stops. Electromagnetic waves don’t propagate, electrochemical signals don’t travel in your nerves and brain, and electrons don’t move. So you can’t see, you can’t hear, and you can’t even think. Hence when I open the door a week later, to you it’s like I opened the door just as soon as I closed it. It would feel like you’d “travelled” to the future in an instant. But you didn’t move, you were totally motionless. Instead everything else moved. Yes, the stasis box is science fiction too, but don’t forget that we can freeze embryos today. Someday we’ll perhaps be able to freeze an adult and thaw him out with no damage and no loss of memory:
Cryogenic vats image from the Cryonics Institute
Then you could “travel to the future” by stepping into a glorified freezer. But you aren’t really travelling to the future. The freezer is like the stasis box, but it works at the biochemical level rather than the subatomic level. Either way, you aren’t moving. Instead everything else is. The crucial point is that there isn’t really any travelling forward through time. There is no way you can move to get to next week. The Earth turns seven times, then it’s next week come what may. There’s nothing you can do about it, whether you’re sitting on the superfast train or in your armchair at home. You can’t travel to the future just as you can’t climb to a higher temperature. There is no cosmic rewind button. And there is no way you can move such that all other things not only move back to where they were, but never moved at all.
Closed time-like curves do not permit time travel
So don’t think that closed time-like curves permit time travel. Because they don’t. Because spacetime models space at all times. So there is no motion through spacetime. So there is no motion along a world line. So there is no motion around a world line that curves full circle. See A World Without Time again. See page 142 where Palle Yourgrau says Wheeler conflated a circle with a cycle:
Fair use excerpt from Palle Yourgrau’s A World Without Time : The Forgotten Legacy of Gödel and Einstein
He’s right. If your world line was a 24-hour closed time-like curve, it wouldn’t be time travel, and it wouldn’t be Groundhog Day either. It would be more like Mayfly Day. You hatch from an egg, you live, you lay that egg, you die. You live only once, for 24 hours only, and yours is a life without cause and effect. That isn’t like the real world at all.
Wormholes are science fiction
In addition, don’t think that you can travel through time by going through a wormhole. Yes, some physicists talk about traversable wormholes, and say you can use wormholes for time travel. Others say they’re associated with black holes, and say all you need is some negative energy, and you’ve got yourself an Einstein-Rosen bridge:
The trouble is that there is no negative energy, just as there are no negative pencils. There are no Einstein-Rosen bridges either. If you’ve ever read Einstein and Rosen’s 1935 paper you’ll know it’s about the particle problem in the theory of general relativity. They talked about a mathematical representation of space wherein a particle is represented by a bridge connecting two sheets. It isn’t anything to do with the popscience wormholes you read about today. They grew out of David Finkelstein’s 1958 paper past-future asymmetry of the gravitational field of a point particle. He was talking about point particles and antiparticles, and saying an antiparticle was some kind of white hole, which it isn’t.
There is no time travel
Bear all this in mind next time you read some book by some celebrity physicist claiming that backward time travel is governed by the laws of quantum gravity. Because it isn’t. Ditto if you see some celebrity physicist waxing lyrical on the Discovery Channel about how to build a time machine. Because you can’t. Because time dilation is a reduced rate of local motion, and things can’t go slower than stopped. Which means that there is no need for any chronology protection conjecture, and no need to worry about the grandfather paradox. Because motion is motion whichever way it goes, and there is no such thing as negative motion, just are there are no pencils that are less than zero inches long. You can’t travel back in time, or forwards, because time is merely a measure of motion, and motion is travel, and you can’t travel through travel. All you can do is step into that glorified freezer or slow your life down some other way, then wait for the world to change.
Why clocks go slower
You might feel a little sad that time travel is science fiction. But there’s something that more than makes up for it. Something that’s glistening down there in the smouldering ruins of the TARDIS. Something shiny. Pick it up and dust it off, and you find it’s a key. A golden key. It’s the key that opens all the doors in physics, and it’s this: clocks don’t go slow because time goes slow. It might not seem like much, but it is. That’s because it applies to all types of clocks, including optical clocks. Think on this: if your clockwork clock was going slow, and I told you it was because time was going slow inside that clock, you’d laugh in my face. Because you know full well that if your clockwork clock was going slow, it’s because the clockwork was going slow. In similar vein an optical clock doesn’t go slower when its lower because time is going slower inside it. It goes slower for another reason entirely.