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Travelling
through time(3)...
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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.