Travelling through time...

This page is based on a thesis of three students from the St-Gertrudisinstitute in Landen (B). Although I adapted and added some things myself, the major research is done by them. Please mail me before printing this. To see the non-printable version of these pages, click here

I) Introduction

Before 1905 there wasn't much to say about time. In the 17th century Newton defined time as something that continues, no matter what, without any link with reality and according to its own nature. Everybody believed that time had its influence on the environment, but if you believed that the environment had its influence on time, you really had to be mad! That changed in 1905 with Einstein's special relativity theory, in which he showed that time can be influenced. But this doesn't mean time can be changed in such a way that you can travel to the future or the past. That's what it's all about on this pages: Is it possible to travel through time, and if possible, under which circumstances?
It will become very clear that the speed of light has got a major influence on the possibility of time travelling. An object should move faster than light speed to travel through time. Therefore we use the tunnel effect, an effect in the quantum mechanics. That means that a ray of light or a bundle of electrons that is sent through a certain barrier arrives sooner at the other side of the barrier than if there wasn't a barrier.
If time travelling is possible according to the relativity theory, there will be a lot of other problems. I'm not talking about the technical problems, 'cause that's not what this is about, but I mean the paradoxes. For these problems there is no such thing as a logical explanation, no matter how long you'll search.

II) Relativity

There are 2 sorts of physics: Newton's physics and Einstein's physics. When you use formulas from Newton and formulas from Einstein's physics to calculate a certain physical value, you'll become not the same value. In 'normal' situations these differences are extremely small. But in 'extreme' situations these differences will become very big. For example: someone who's in a train that moves with an incredible high speed (like 10 000 km/second) and who measures the distance between the sleepers of the train, will measure a smaller distance than someone who stands still beside the railway. According to the physics of Newton and our intuition we'd say the distance would remain the same. In 'normal' situations that's correct: measuring in a train that moves at hundreds, thousands or even ten thousands kilometers/hour would make the difference in distance immeasurably small. Newton's laws would certainly do in these situations. But when the speed of the train approaches the speed of light, the difference will become noticeable ('extreme' situations), and we would need Einstein's physics. According to the latest experiments, Einstein's formulas seem to be the right ones.

Einstein's special theory of relativity was finished in 1905. It's based on the constant speed of light and the fact that speed isn't absolute; when a helicopter lifts off you can also assume it's the chopper that stands still and the earth that moves. This theory describes the relation between observation of a certain phenomenon by observers that move with a constant speed related to each other.
The general theory of relativity was finished in 1912, but Einstein couldn't interpret his mathematical reasoning physically. He redeveloped the theory, not only based on mathematics but also on physics, and he ended up with the same result as 3 years earlier. Then he published it. This theory describes on one hand the relation between the observations of the observers that move with an accelerating speed related to each other. On the other hand it's about the influence of gravity on observations and the relation between observations that are done from places where gravity differs. Because a constant speed can be looked at as a speed with acceleration 0, the general theory of gravity includes the special one.

a) Special relativity

The speed of light is constantly independent of the reference system of the observer. It is a limit that can't be exceeded by any kind of matter without transforming to energy. Each measurement of that speed will have the same value, no matter how fast you move. Whether you stand still or move at 50% of light speed, the ray of light will always move at an amazing 299 792,458 km/sec. That sounds strange; we would think when you move at 50% of light speed along the ray of light, the measurement of that speed would be halved. But light speed is a universal constant, as is shown in many experiments. That means that time passes slower when you move than when you stand still. If you move at a low speed, that difference is extremely small. But if you move at light speed itself, time stands still. If you move faster than light speed, you could go back or forward in time because you can arrive somewhere before light does. That means you could travel to the future or the past...

All this can be supported by the calculations of Einstein, but actually we only need the solution.
dt  =  dt' . (1 - v²/c²)1/2      In this formula is * dt  the time that passes when you move at a speed v
'--------------'
"                                       * dt' the time that passes when you stand still
"
this part is called the Lorentz-factor          * c the speed of light
or the time-bending factor by speed
When you're moving, the Lorentzfactor is always smaller than 1, therefore we can conclude that, relatively seen, time passes slower in motion than when you don't move. When we reverse this factor, we can express how many times time passes slower in motion than at rest. The closer you get to light speed, the slower time moves on. When you travel at light speed , you'll get 1-1=0
dt' . 0 = 0 --> time stands still!!!!
Another example: If you travel to a star at 80% of light speed during 10 'earth' years, only 6 years will pass. An observer on earth with a mighty telescope would see you acting in slow-motion.
Nice to know: When a journalist asked Einstein what he would say if the observations would not match with his theory of relativity, he answered: "I would pity the Lord, 'cause the theory is right anyhow."

b) General relativity

In this theory gravity has got an important influence. We will use the 'equivalent principle' here. This principle equals acceleration to gravity. That might sound strange, but it can be cleared out with one simple example. When you sit in a box that falls down to the earth, you fall with an acceleration of 9,81 m/s². In the box you don't move, you float. Now when your box is far away of all star systems in space, and some kind of alien (just a way of explaining!!!) pulls your box at an acceleration of 9,81 m/s², you can think you're just falling to the earth, it's exactly the same. The alien exercises the same power on you by acceleration than the earth does by gravity. Therefore, in this principle, acceleration equals gravity. All what will be written about gravity can also be interpreted for acceleration. Gravity has got it's influence on light, time and space.

Gravity deflecting light is not so difficult to understand. An example is easily found: in space, the mass of, for instance, Mars deflects the light of a shining star. Gravity influencing time and space is a little bit more difficult to understand. But if you look in the previous paragraph, things will get more clear. Gravity equals acceleration, and we already know that acceleration = 0 influences time (special relativity). I'll explain everything using Einstein's thoughts.
Assume there's a rotating disc somewhere in space, far away from all gravity fields. Our reference system is not rotating, and the middle of the disc is not rotating. We call this system C. We choose as a second reference system C' the disc itself. So in the second reference system the disc doesn't move at all. Now we put three clocks (that tick exactly with the same speed in the same circumstances) and three sticks (that are exactly of same length in the same circumstances) on different places: in the middle of the disc (clock 1 and stick 1), on the edge of the disc (clock 2 and stick 2) and on the outside of the disc (clock 3 and stick 3). Clock 1, stick 1, clock 3 and stick 3 don't move in C. Clock 1, stick 1, clock 2 and stick 2 don't move in C'. Because clock 1 and clock 3 don't move in C, they tick exactly with the same speed. Clock 2 moves in C with acceleration = 0 (not speed = 0!!) and can be placed under special relativity. So this clock ticks slower than clock 1 and 3.
Clock 1 and clock 2 don't tick with the same speed. That's strange, because they're in the same reference system C'. This can only be explained by the fact that clock 1 and clock 2 are not influenced in the same way by the field of gravity caused by the rotation of the disk. The gravity of clock 1 is 0, and the gravity of clock 2 is at maximum.
The same story with the sticks; stick 1 has got the same length as stick 3 because they don't move in C. Stick 2 moves at a certain speed with acceleration = 0 in C and is shorter than 3 or 1. Stick 1 and stick 2 are in the same reference system C', but not of the same length because the disc rotates. It's only the gravitation of the disc that can do this, so gravity bends time and space.

c) Time-bending factor by gravity

We'll calculate this factor now on the surface of the earth:
(1- (2 f M) / (c² r))1/2
= (1- (2 . 6,67.10-11 . 5,96.1024) / (299792458² . 6,36.106))1/2 = (1 - 1,39.10-7)1/2 = 0,9999999305 (= almost 1)
Because the time-bending factor on the surface of the earth is almost 1, time on earth passes almost as slow/fast as on places where no gravitation field exists. When we look at the formula for the time-bending factor by gravity, we notice that it becomes smaller when M is bigger or r is smaller. If M becomes that big and/or r that small, the time-bending factor would be = 0. So seen from the outside, it appears that time stands still. Someone in such a place would probably become mad (if possible there to live), because he would see time pass infinitely fast on the outside of his place (where there 's NO infinite gravity).

An application of this is a black hole. To explain this, we first need to introduce a new word: the radius of Schwarzschild or the horizon of a black hole. This is the distance between the places where the speed to escape the black hole is just a little bit higher than light speed, and the middle of the black hole. A body that is on the inside of the radius of Schwarzschild can never escape from the black hole, because it would need a speed higher than c to do that, and a body can never move faster than light speed. Now we need to think in four dimensions. It's impossible for humans to think in four dimensions, but there's a way to overcome that problem. Space is bended, so think of our solar system as an enormous trampoline in which the sun lies in the middle. The heavier the sun, the deeper the hole in the trampoline, the harder objects get attracted. Well, suppose there's a black hole lying in the trampoline. It's a very deep, small hole (big mass, small radius). The closer you get to the hole, the steeper the inclination. Time passes slower on places where gravity is bigger (M bigger and/or radius smaller --> time-bending factor smaller --> time slower), so where the hole in the trampoline is steeper. The steeper, the slower time. So the closer you get to a black hole, the slower time passes. On the radius of Schwarzschild the inclination is 90°, so time stands still there. It could be possible that, under certain circumstances, when you get even closer to the middle and you passed the radius of Schwarzschild, the inclination would be bigger than 90° and so, somehow, make it possible to travel through time.
In reality you can never pass the radius of Schwarzschild. If you would come that close to a black hole, you would be attracted with an enormous power and you'd be resolved molecularly. However, the image of your body would be seen forever on the edge of the black hole by an outsider, 'cause on the radius of Schwarzschild time stands still. Although you're resolved a long time ago, your image stays forever in the radius of Schwarzschild!
This means we can look at ourselves in another way. Because time-bending is caused by gravity, we could see ourselves as time travellers. After all we are in the gravitation field of the earth. It's easy for us to travel to the future, it happens all the time! Going back in the past is a little bit more difficult....

III) On the other side of light

In the previous chapters we assumed that no matter can move faster than light speed. But in fact, all these theories don't exclude such particles. Because they're  not discovered yet, they remain strictly hypothetical, but we can try to reason with those particles, called tachyons.
Suppose we've made a tachyonsgun that fires at a target with a speed of 2c. Let's call the moment of firing G1 and the moment of hitting the target G2. Observer 1, who doesn't move, sees the gun firing and then the bullet hitting the target (G1,G2). Observer 2, who travels at 50% of light speed in the same direction as the bullet, sees departure and arrival happen at the same moment (G1=G2). Observer 3, who travels at 80% of light speed in the same direction as the bullet notices that the bullet moves from the target to the gun (G2,G1)! So we can conclude that when a speed, bigger than c is permitted, in certain reference systems these fast particles can travel back in time, relative to normal physical processes.
When tachyons exist, we can send messages back in time. Another example: Sean leaves at 10 am at 80% of light speed while Jodie stays at home. At noon, exactly at 12 am Jodie sends a message by using tachyons at 4c. Sean receives the message at 12.30 am earth time, but for him, it's 11.30 am. Only 1 1/2 h (3/2h = 12/8h) passed because of the time-bending factor of 0,6. According to Sean there's a distance of 0,8 . 1 1/2h = 1,2 light hours between him and Jodie. When Sean answers with a signal that travels at 4c in his reference system without delay, then the signal will do 22 1/2 minutes  (3/8 hour) on that trip. The total travel time of the first and second signal together have taken 15/8 (12/8 + 3/8) hour according to him. We need to use the time-bending factor to calculate Jodie's feeling of time: 15/8h . 0,6 = 9/8h. On earth it's 11.07 1/2 am, that's 52 1/2 minutes before the departure of the original signal! So if tachyons exist and we could manipulate them, we could send messages to the past, but not persons, 'cause the matter we're made of can't travel faster than light.

IV) Wormholes

The most interesting theories about time travelling have something to do with wormholes. I'll explain it to you by using a simple example. Imagine the world of a 2-dimensional sort of worms. They live at the surface of a huge apple they call the 'appleworld'. Because they have 2 dimensions theirselves, they assume their world to be 2-dimensional too. They can't imagine 3 dimensions. Now there's one weird worm, Oswald, that's got very weird ideas. All the others laugh when they see Oswald, 'cause he pretends that their world is bended into another 3th dimension that no one can feel. Oswald wants to prove he's right and begins his journey. After a long time, he arrives at the same place he started from. This proves the existing of the bended 3th dimension. But Oswald doesn't stop by this idea, he says there's a shorter way than following the 2-dimensonal tour and he eats a hole through the apple. These routes are the so called 'wormholes'.
We can be compared to that worms. We know 3 dimensions and a 4th temporal dimension. So we could travel through the 4th dimension using a shorter way.
Because we can't imagine 4 dimensions, we drop one and we use a piece of bended paper. The 2 dimensions of the paper present the 3 dimensions we know, and it is bended into the 3th dimension (representing the 4th dimension). The tunnel shows a shorter way through the wormhole. It's not that easy to travel through a wormhole, because big wormholes don't just arise out of nothing. They're the result of an enormous gravity, and that's the result of a huge concentration of energy, for example a black hole. In the early 1930's, Albert Einstein and Nathan Rosen discovered that the gravity hole, in which the middle of the black hole lies should be bottomless, and that it should lead to another, hypothetical universe or another part of this time-universe. Such a hole is called an Einstein-Rosen bridge or a wormhole. However, some problems rise when we think of using such a wormhole. In the middle of a black hole gravity is that big that it would tear apart every space ship. Wormholes could be very unstable; the presence of a space ship could be enough to make the wormhole collapse. You also need to go faster than light if you want to reach the other side, 'cause the speed you need to escape a black hole is bigger than light speed. And as a last problem, time passes slower in a wormhole and stands still right in the middle of it. It would take infinite time to travel through the wormhole. So it seems the wormhole isn't made for travelling through time...unless Carl Sagan appears.
In 1985 Carl Sagan sent a manuscript of his book (about alien civilization) to Kip Thorne and Michael Morris, scientists at the California Institute of Technology. He also put a letter with it in which he asked if they knew a way to travel along huge distances faster than light without breaking the light barrier. Thorne was very interested and started to find a way. They wanted to prepare a fast journey for an astronaut, without him getting torn apart or destroyed by a collapsing wormhole. They didn't think about the energy that could be necessary or if the technical knowledge was existing. They just thought about the theoretical possibility. They reached a solution very soon: the wormhole could even be used for time travelling. It would be as comfortable as flying with an aeroplane, the wormhole can't collapse, a journey would take 200 days, maybe less. The only problem was that building such a wormhole isn't possible yet with the science and techniques of today. But there are two ways....
One way is making the wormhole out of almost nothing. If we would observe a small part of the universe, we could see that space looks a lot like a turbulent ocean. That's because of the fluctuations of gravity, that make the space-bending vary. At a level of 10-35 m (or 1020 times smaller than the nucleus of an atom) those fluctuations make arise small, short-living wormholes. Some scientists believe it could be possible to enlarge such wormholes.
Another way uses magnetism. According to general relativity everything that's got energy can bend space, so a magnetic field can too. Claudio Maccone claims it's possible to make a wormhole out of a magnetic field. But for a wormhole with diameter 1 m we need a magnetic field of 1018 tesla, and now we can only make magnetic fields of 10 tesla.
Then some common problems arise. How to protect the wormhole from collapsing? In the middle of a wormhole we need to place a 'rare' matter, consisting out of negative energy and negative mass. Before you start laughing I want you to notice that not a single theory excludes the existence of such matter. In 1948 the Dutch scientist Henrik Casimir proved the existence of negative energy and the possibility to create and to measure it. However, the negative mass for a 1 m-wormhole would be minus 1 time the positive mass of Jupiter (about -1,90 . 1027 kg)!
In spite of all these problems it is possible for a far developed civilization to create such a wormhole and  travel through time. However, the technical level to do this is very high.

V) The tunnel effect

Two professors, not related to each other, claim that they have sent a wave with a speed faster than light. According to Raymond Chiao from the university of Berkeley, who claims to have reached a speed of 1,7c it's impossible to send some information with the signal. Gunter Nimtz of the university of Koln (Germany) says his wave travelled at 4,7c and carried Mozart 40. The question here is not if it's possible to send something with that wave, it's interesting to know that something (an electro-magnetic wave) can move faster than light. If such a signal is able to do it under certain circumstances, maybe an object or a person can too. And maybe that object or that person can travel in time... Chiao and Nimtz call it the 'tunnelling' of an electro-magnetic signal. It comes down to sending an electro-magnetic signal through a special wave conductor.
Although some scientists are sceptical about the results of these professors, nobody has proven their wrong yet. Whether they're right or wrong, when it could be technically possible to travel through time or send messages at a higher speed than c, some terrible problems would arise: the paradoxes!

In this chapter we assume that time travelling is possible.

a) The trick with grandma

What about this paradox? Neve travels back in time, at least 1 year before the birth of her parents. There she kills her biological grandma. No grandma means that she was never born and she could never return to kill her biological grandma. This is a paradox because the present is determined by the past. Changing the past means you change the present.
But what if a time travel doesn't change the past, but perfects it. For example: Kevin travels back to the past, at least 1 year before his birth. He meets his mother, young and very attractive, falls in love, marries her and they get children. Years after that his son disappears, travels back in time to meet his mother,... Here the past perfects the present. At the birth of Kevin's son, we've got 2 identical persons, genetically and identical in mind. They only differ in age.
Another example of time travelling completing the past: A young ambitious, not successful inventor is working in his basement. Suddenly a rich, old man appears out of nothing and hands him over some papers with plans for a time machine. Then he disappears. The young man starts building and gets very rich. On a certain day he travels back in time and hands the plans over. You could think:"Ok, what's the problem  here?" Well, where does the knowledge come from to build such a time machine? Not the young inventor and not the old man have discovered how to build a time machine. Did this knowledge appear out of nothing?

b) Self-generating...

And now last but not least: a huge paradox. In 1966 Jennifer, a girl of 16, meets a vagabond, Roger, along the road. They start talking, and after a while Jennifer seems to be pregnant. Roger disappears without her knowing his name. Nine months later, due to complications with the birth, Jennifer needs to change sex. Her child is also robbed from the hospital. Twenty years later Jennifer, now known as Roger, is poor and survives as vagabond. In 1986 in a bar, after a couple of drinks, Roger does his story to the bartender. This one has got an interesting proposition: he gives him the opportunity to travel back in time and take revenge on the vagabond that made him/her pregnant. Therefore he has to join the secret organization of time travellers. Roger accepts, but when he arrives in 1966, he meets a girl, Jennifer. He makes her pregnant, doesn't find the vagabond and begins a bar. He joins the secret organization of time travellers and talks to the vagabond in 1986. The bartender disappears and travels to 9 months after 1966 to steal Jennifer's child, a girl, out of the hospital so Jennifer doesn't have to raise it on her own.  He brings her 16 years back in time, to 1950, where he leaves her in an orphanage.
A lovely paradox, because Jennifer is her own mother, father, grandma, grandpa, son, daughter, grandson and granddaughter. If we ask: Where does Jennifer come from, we see that this paradox is an excellent example of how time travelling doesn't change the past, but completes it. It's interesting to notice that even time travelling can't prevent you from dying and getting born. Jennifer gets born, and she dies as Roger, but she's captured in a vicious circle.

c) Solutions

In the last 3 paradoxes we've mentioned the idea that time travelling completes the past. When a time traveller can return to the past to exterminate an animal species to change the evolution, then he'll be disappointed. He'll change nothing in the present, he actually made sure that nothing changed. The exterminating of the animal species has created the right biological circumstances to produce the present (from which the time traveller came). The return in time has completed the past (and the present), the journey was already written in the past.
Which paradox is right and which is wrong? We'll need the so called 'world lines' (lines that explain the relation between the 3 dimensions and the 4th dimension, time) here. A property of a world line is that it doesn't just rise out of nothing. The world line of a human being is the gathering of the world lines of the particles what that human being is made of. A second property is that a world line can't be broken. When a man dies, his world line splits into the millions of world lines of particles out of which he consists. When we look at the trick with grandma we see it's impossible. When Neve kills her grandma, she would never have been born, the particles out of which she's made would never have been joined together to make her. Her world line appears out of nothing, and that's not allowed. Neve can't change the past. In the paradoxes about Kevin, the inventor and Jennifer their world lines form a loop. Their world line never rises out of nothing and is never broken. Time travellers complete their past and their journeys are completely 'legal'.

d) Parallel universe

What if parallel universes exist and are spontaneously created? What if, on a certain moment, an exact copy of the universe is created? This has got to do with quantum physics and is a little bit too difficult to explain (or to understand, I don't know it myself!). But it might be possible that both universes 'go separate ways' on a certain moment. The paradoxes would disappear if we accept this theory. When Neve returns in time an exact copy of the world of her grandmother's created on the moment she arrives. The place where she arrives is not her past and the grandma she's trying to kill is not her grandmother, but it's the fake world (copy-world) and the copy-grandmother. When she kills that woman, she doesn't kill her grandmother, so the paradox is gone. Neve can mess around as much as she likes, nothing will change the 'real' past or present.

VII) Conclusion

What can we do with time? Because it seems as if 1 of our biggest certainties has disappeared from our lives. The relativity of time has helped us on one hand with certain problems, but on the other hand it created even more problems. After all, everything started with Einstein by saying that time is relative.
Is light speed really the maximum limit for all sorts of matter, or do some particles that can travel faster than light exist? And what is the influence on their experience of time? Will time travelling become possible, and what with those paradoxes? The wormholes are a good chance to help, but there's a big difference between theory and the practical use.
Let's remember what Stephen Hawking once said: "If time travelling will be possible, why haven't we seen a lot of tourists from the future yet?" Will the earth be destroyed before discovering the secrets of time travelling? Will those secrets ever be clear to anyone, or is that just a dream? Can we ever reach enough energy to enlarge a wormhole and travel through it? Or has time travelling been invented in the future, but is the theory of parallel universes right, so we just see no consequences of it?
All the answers just lay in the future...

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