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Travelling through time...
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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!
VI) 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...
