SpaceTime Physics and the Future of Time Travel
By Alex MacLellan
Human beings have always tried to explain the world around them. They have worked to organize it, to measure it, and to understand it. These efforts at understanding such basic concepts as space and time and light have led to many discoveries. In the last one hundred years many changes have been made to how we understand these concepts. You may not be able to move as quickly and easily through time as the hero of H.G. Well's Time Machine, but scientists have been able to understand how certain variables can affect time  to slow it down and speed it up  leading them to believe that it is possible that time travel may become possible. Before looking at time travel, an understanding of the terms and history are required. Space, time, and light have been studied and the definitions have evolved as research has advanced. Looking at these concepts as they have been explained through history will help us understand what may be possible in the future.


Portrait of Euclid 
Over history many people have come up with many different views about what time is and what space is, and how to understand them. Space was defined be Euclid, a Greek mathematician. He was the creator of geometry in 295 B.C.
Geometry explained the visible world of threedimensions. Points on a plane can be located with coordinates. These
coordinates were called the Euclidean coordinate system, but were also sometimes called the Cartesian coordinate
system. Soon after the Euclidean coordinate system was made a rule called the Pythagorean rule that could locate
the distance between any two points in a Euclidean coordinate system graph. The rule said that a simple equation
was all that was needed to find the distance between two points, the equation is:
L_{12}^{2} = (X_{2}  X_{1})^{2} + (Y_{2}  Y_{1})
This original idea of how to understand space leads to many discoveries in the future, like locating points using three points, and then soon on to four.
Isaac Newton created the three basic laws of motion and the law of gravity which governs modern physics today.
All of the physical world became predictable and orderly using his laws. Isaac Newton was used to modeling space
using the Euclidean distance function, but he wanted to also graph time so he created spacetime graphs where distance
was the xaxis and time was the yaxis. This was a revolutionary graph because it showed not only things moving
through space but also through time. Newton said, "Absolute, true, and mathematical time, of itself, and from
its own nature, flows equably, without relation to anything external."


Sir Isaac Newton 
Isaac Newton was right about some of his ideas about time but he was wrong about others. For instance, he said that time is absolute. His theory for this was that if a pulse of light is sent from one place to another, different observers would agree on the time it took for the light to get from one place to the next (since time is absolute), but the two observers would not always agree on the distance the light traveled (since space is not absolute). Since the speed of light is simply the distance divided by time, different observers would measure different speeds of light.
This is where Einstein disagreed with Newton, because in Einstein's relativity all observers must agree on the
speed of light because it never changes. In Einstein's theory, since the two observers don't agree on the distance
the light has traveled, they must disagree on the time it took for the light to go between the two places. The
time taken is the distance the light traveled, which the observers don't agree on, divided by the speed of light,
which they do agree on. In other words, Einstein put an end to the idea that time is absolute. Since time is relative,
space must be relative too.
Einstein came up with a formula for his relative time that has to do with you speed and its effect on time. This
formula is called the time dilation factor. The formula is:
(1  (U/c)^{2})^{1/2} 

Albert Einstein 
The time dilation factor theory says that the faster you go the slower time gets for you, because of the fact that
time is elastic and relative, not constant. "Time is not absolutely defined," said Einstein in his theory
of special relativity. He tried to explain how time and space are connected and that this spacetime could be stretched
and shrunk. The method for stretching and shrinking time is very simple  all you have to do is move very fast.
This theory, called the time dilation factor theory, has been tested many times. One example of a test took place
in 1971 when two physicists, Joe Hafele and Richard Keating, took very accurate atomic clocks and put them in airplanes,
which they then flew around the world. They then compared the readings on the clocks in the planes to an identical
clock on the ground. The results were unmistakable; the clocks in the planes were 59 nanoseconds slower. This was
exactly the difference in time Einstein had predicted in his time dilation factor theory. To figure out how much
slower time will get, you take your speed; divide it by the speed of light, square it, subtract your answer from
one, take the square root, and the result is Einstein's time dilation or slowdown factor.
To understand how this affects time travel a basic knowledge of light and time is needed. The fastest known thing
in the universe can travel 1 meter in 0.000000003335640952 seconds. But what is this fast thing called light? After
years of discussion scientist decided that it is both a particle and a wave. (A good example of why this is, is
a solar pinwheel, where a pinwheeltype thing is held inside a clear vacuum sealed container that resembles a light
bulb, and when it is sunny out the light particlewaves go through the glass and spin the wheel). There are many
theories based around light and its speed. A very well know one is part of Einstein's theory of special relativity
(E=mc²), which basically means that an object with mass will increase in mass as it get closer to the speed
of light, and because of this increasing mass, increasing energy will be needed to speed the object even more.
So the object needs an infinite amount of energy to gain the speed of light and when it reaches this point it will
have an infinite mass, thus creating the "light barrier" where nothing that has mass can reach the speed
of light.
Time as most people know it is constant and never changing, but this is very wrong. Time (according to Einstein)
is relative and elastic, meaning that people are affected by time differently depending on their speed (this theory
allow time travel to seem conceivable). This is called the time dilation or "slowdown" factor. There
are many other affects on time that can allow for time travel, such as gravity. Gravity slows down time. There
have been studies where scientists have tested these slowdown factors of time. An example of this is an experiment
conducted by Harvard University to see if time acted differently at different heights. They found that at the top
of a building time was moving slightly faster than on the ground.
With this basic knowledge of time and light it is easier to understand what a light cone is and how it works. A
light cone is built up of three parts: an event, a future light cone and a past light cone. An event its when something
happens. A future light cone consists of all the paths of light that come from an event and move through time to
the future. A past light cone is made up of all the paths of light that led up to the event.
Professor Stephen Hawking, PhD 

Seeing into the past is not as hard as it may seem to be. All you have to do is look up at the stars on a clear
night. The light from the stars has not reached you so if the stars are millions of years away you could be seeing
millions of years into the past. This is because you are looking at the past light cone of those stars. A past
light cone is everything that happened leading up to an event; a good way to describe this is to think of the sun
going out. If you looked up at the sun at the exact moment it went out you would see the sun as it normally is.
You would be seeing everything leading up to its going out  its past light cone. It would take eight minutes before
the sun's future light cone reaches you, what the sun went through when it went out, the event itself and everything
after it. This future light cone would then become the past light cone because the event already happened eight
minutes ago.
If light cones could be folded over so that the future and past overlapped this could allow for time travel. Einstein's
special relativity does not support this idea because in special relativity light cones are rigid but in general
relativity it could be possible. What makes this possible is the ability for light in the light cones to stray
from the sides of the cones. These sides are called the causal boundaries in the light cones; the only way to stray
light from this casual boundary is to use gravity. Gravity has the ability to warp light. Einstein predicted that
large suns could deflect light around them; soon after this prediction this very phenomenon was observed in 1919
when light from stars could be seen going around a sun during a solar eclipse. This supported Einstein's theory
that light from a light cone could be pulled past the casual boundary if the gravity was strong enough, therefore
the warp of time was possible.
Stephen Hawking has continued and expanded on the work of Einstein. He has tried to explain how the universe works
and has studied the problems of space and time for many years. His work on light cones, black holes, wormholes,
and time travel were are extremely revolutionary. Gravitational lensing, when a light cone of an event is bent
by matter and energy, makes scientists believe that time travel may be possible. The Hubble Space Telescope photograph
of the galaxy cluster, Abell 2218 is an example of gravitational lensing. The cluster is so huge and compact that
light rays passing through it are deflected by its gravitational field. The process magnifies and distorts the
view of objects that lie behind the cluster. This creates arc,s which are the distorted images of galaxies that
are 5 to 10 times farther than the cluster being photographed. The viewer sees multiple flashes of light which
actually come from only a single source, creating a crease or bend. Because light and time can be affected by gravity
and other factors, it may be possible to travel between time episodes.
Overall time, space, light, and spacetime are very complex things to understand but in understanding them things
like time travel could be made possible. Peoples interest and understanding of these topics is ever growing. Soon
we may be able to fully understand the mysteries of space and spacetime.
Bibliography
Davies, Paul. How to Build a Time Machine. New York: Viking Press, 2002.
Hawking, Stephen. A Brief History of Time. New York: Bantam Books, 1996.
Hawking, Stephen. The Universe in a Nutshell. New York: Bantam Books, 2001.
Simmons, John. The Scientific 100: A Ranking of the Most Influential Scientists, Past and Present. New York: Citadel
Press, 1996.
Web Sites
"Time Travel in Flatland?" http://www.theory.caltech.edu/people/patricia/lctoc.html.
May 24, 2002.
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