A Theory Of Everything?
Page 6
PARABLE OF THE GEMSTONE
To understand the intense controversy surrounding superstring theory,
think of the following parable. Imagine that, at the beginning of time,
there was once a beautiful, glittering gemstone. Its perfect symmetries
and harmonies were a sight to behold. However, it possessed a tiny flaw
and became unstable, eventually exploding into thousands of tiny pieces.
Imagine that the fragments of the gemstone then rained down on Flatland.
These Flatlanders were intrigued by the beauty of the fragments, which
could be found scattered all over their world. The scientists of
Flatland concluded that these fragments must have come from a single
crystal of unimaginable beauty that shattered in a titanic Big Bang.
They then decided to embark upon a noble quest, to reassemble all these
pieces of the gemstone.
After 2,000 years of labor by the finest minds of Flatland, they were
finally able to fit only a few of the fragments together. Many
Flatlanders began to think that these pieces could never be reassembled.
Finally, some of the younger, more rebellious scientists suggested a
heretical solution: perhaps these chunks could fit together if they were
moved "up" in the third dimension.
This immediately set off the greatest scientific controversy in years.
The older scientists scorned at this idea, because they didn't believe
in the unseen third dimension. "What you can't measure doesn't exist,"
they declared. Furthermore, even if the third dimension existed, one
could calculate that the energy necessary to move the pieces up off
Flatland would exceed all the energy available in Flatland. Thus, it was
an untestable theory, the critics shouted, and hence not a theory at
all.
However, the younger scientists were undaunted. Using pure mathematics,
they could show that every one of these pieces fit together perfectly if
they were assembled in the unseen third dimension. The younger
scientists claimed that the problem was therefore theoretical, rather
than experimental, even if it can never be tested.
And so the controversy rages, both in Flatland as well as in our own
three dimensional world.
"THE MIND OF GOD"
In conclusion, the theory of higher dimensions has set off perhaps the
most delicious, lively debate in theoretical physics in generations.
Although the existence of these higher dimensions cannot be verified by
any experiment on this planet, it has already sparked an avalanche of
papers in the leading research institutes around the world. Although the
mathematics required to find the unique solution has soared to dizzying
heights, physicists around the world are confident that the unique
solution will eventually be found.
Nobel laureate Steven Weinberg, in his book Dreams of a Final Theory,
holds out for the exciting possibility of attaining the Final Theory. He
writes, "How strange it would be if the final theory were to be
discovered in our lifetimes! The discovery of the final laws of nature
will mark a discontinuity in human intellectual history, the sharpest
that has occurred since the beginning of modern science in the
seventeenth century."
Cosmologist Steven Hawking, who closes his book A Brief History of Time
on this theory, has written, "...if we do discover a complete theory, it
should in time be understandable in broad principle by everyone, not
just a few scientists. Then we shall all, philosophers, scientists, and
just ordinary people, be able to take part in the discussion of the
question of why it is that we and the universe exist. If we find the
answer to that, it would be the ultimate triumph of human reason - for
then we would know the mind of God."
Perhaps one day one of the readers of this article may gaze into a pond
and notice the carp swimming on the bottom, beneath the lilies. Perhaps
the reader will be inspired to investigate the theory of higher
dimensions and complete the quest for the Theory of the Universe.
THE PHYSICS OF TIME TRAVEL
In H.G. Wells' novel, The Time Machine, our protagonist jumped into a
special chair with blinking lights, spun a few dials, and found himself
catapulted several hundred thousand years into the future, where England
has long disappeared and is now inhabited by strange creatures called
the Morlocks and Eloi.
That may have made great fiction, but physicists have always scoffed at
the idea of time travel, considering it to be the realm of cranks,
mystics, and charlatans, and with good reason. However, rather
remarkable advances in quantum gravity are reviv- ing the theory; it has
now become fair game for theoretical physicists writing in the pages of
Physical Review magazine.
One stubborn problem with time travel is that it is riddled with several
types of paradoxes. For example, there is the para- dox of the man with
no parents, i.e. what happens when you go back in time and kill your
parents before you are born? Question: if your parents died before you
were born, then how could you have been born to kill them in the first
place?
There is also the paradox of the man with no past. For example, let's
say that a young inventor is trying futilely to build a time machine in
his garage. Suddenly, an elderly man appears from nowhere and gives the
youth the secret of building a time machine. The young man then becomes
enormously rich playing the stock market, race tracks, and sporting
events because he knows the future. Then, as an old man, he decides to
make his final trip back to the past and give the secret of time travel
to his youthful self. Question: where did the idea of the time machine
come from?
There is also the paradox of the man who is own mother. (My apologies to
Heinlein.) "Jane" is left at an orphanage as a foundling. When "Jane" is
a teenager, she falls in love with a drifter, who abandons her but
leaves her pregnant. Then disaster strikes. She almost dies giving birth
to a baby girl, who is then mysteriously kidnapped. The doctors find
that Jane is bleeding badly, but, oddly enough, has both sex organs. So,
to save her life, the doctors convert "Jane" to "Jim."
"Jim" subsequently becomes a roaring drunk, until he meets a friendly
bartender (actually a time traveler in disguise) who wisks "Jim" back
way into the past. "Jim" meets a beautiful teenage girl, accidentally
gets her pregnant with a baby girl. Out of guilt, he kidnaps the baby
girl and drops her off at the orphanage. Later, "Jim" joins the time
travelers corps, leads a distinguished life, and has one last dream: to
disguise himself as a bartender to meet a certain drunk named "Jim" in
the past. Question: who is "Jane's" mother, father, brother, sister,
grand- father, grandmother, and grandchild?
Not surprisingly, time travel has always been considered impossible.
After all, Newton believed that time was like an arrow; once fired, it
soared in a straight, undeviating line. One second on the earth was one
second on Mars. Clocks scattered throughout the universe beat at the
same rate.
Einstein gave us a much more radical picture. According to Einstein,
time was more like a river, which meandered around stars and galaxies,
speeding up and slowing down as it passed around mas- sive bodies. One
second on the earth was Not one second on Mars. Clocks scattered
throughout the universe beat to their own dis- tant drummer.
However, before Einstein died, he was faced with an embar- rassing
problem. Einstein's neighbor at Princeton, Kurt Goedel, perhaps the
greatest mathematical logician of the past 500 years, found a new
solution to Einstein's own equations which allowed for time travel!
The "river of time" now had whirlpools in which time could wrap itself
into a circle. Goedel's solution was quite ingenious: it postulated a
universe filled with a rotating fluid. Anyone walking along the
direction of rotation would find themselves back at the starting point,
but backwards in time!
In his memoirs, Einstein wrote that he was disturbed that his equations
contained solutions that allowed for time travel. But he finally
concluded: the universe does not rotate, it ex- pands (i.e. as in the
Big Bang theory) and hence Goedel's solu- tion could be thrown out for
"physical reasons." (Apparently, if the Big Bang was rotating, then time
travel would be possible throughout the universe!)
Then in 1963, Roy Kerr, a New Zealand mathematician, found a solution of
Einstein's equations for a rotating black hole, which had bizarre
properties. The black hole would not collapse to a point (as previously
thought) but into a spinning ring (of neu- trons). The ring would be
circulating so rapidly that centrifugal force would keep the ring from
collapsing under gravity.
The ring, in turn, acts like the Looking Glass of Alice. Anyone walking
through the ring would not die, but could pass through the ring into an
alternate universe.
Since then, hundreds of other "wormhole" solutions have been found to
Einstein's equations. These wormholes connect not only two regions of
space (hence the name) but also two regions of time as well. In
principle, they can be used as time machines.
Recently, attempts to add the quantum theory to gravity (and hence
create a "theory of everything") have given us some insight into the
paradox problem. In the quantum theory, we can have multiple states of
any object. For example, an electron can exist simultaneously in
different orbits (a fact which is responsible for giving us the laws of
chemistry). Similarly, Schrodinger's famous cat can exist simultaneously
in two possible states: dead and alive. So by going back in time and
altering the past, we merely create a parallel universe. So we are
changing someone ELSE's past by saving, say, Abraham Lincoln from being
assassinated at the Ford Theater, but our Lincoln is still dead. In this
way, the river of time forks into two separate rivers.
But does this mean that we will be able to jump into H.G. Wells'
machine, spin a dial, and soar several hundred thousand years into
England's future?
No. There are a number of difficult hurdles to overcome.
First, the main problem is one of energy. In the same way that a car
needs gasoline, a time machine needs to have fabulous amounts of energy.
One either has to harness the power of a star, or to find something
called "exotic" matter (whtime machine needs to have fabulous amounts of
energy. One either has to harness the power of a star, or to find
something called "exotic" matter (which falls up, rather than down) or
find a source of negative energy. (Physicists once thought that negative
energy was impossible. But tiny amounts of negative energy have been
experimentally verified for something called the Casimir effect.
Then there is the problem of stability. The Kerr black hole, for
example, may be unstable if one falls through it. Similarly, quantum
effects may build up and destroy the wormhole before you enter it.
Unfortunately, our mathematics is not powerful enough to answer the
question of stability because you need a "theory of everything" which
combines both quantum forces and gravity. At present, superstring theory
is the leading candidate for such a theory (in fact, it is the ONLY
candidate; it really has no rivals at all). But superstring theory,
which happens to be my specialty, is still to difficult to solve
completely. The theory is well-defined, but no one on earth is smart
enough to solve it.
Interestingly enough, Stephen Hawking once opposed the idea of time
travel. He even claimed he had "empirical" evidence against it. If time
travel existed, he said, then we would have been visited by tourists
from the future. Since we see no tour- ists from the future, ergo: time
travel is not possible.
Because of the enormous amount of work done by theoretical physicists
within the last 5 years or so, Hawking has since changed his mind, and
now believes that time travel is possible (although not necessarily
practical). (Furthermore, perhaps we are simply not very interesting to
these tourists from the future. Anyone who can harness the power of a
star would consider us to be very primitive. Imagine your friends coming
across an ant hill. Would they bend down to the ants and give them
trinkets, books, medicine, and power? Or would some of your friends have
the strange urge to step on a few of them?)
In conclusion, don't turn someone away who knocks at your door one day
and claims to be your future great-great-great grandchild. They may be
right.
Sheila Na Gig
Send e-mail to mapona@yahoo.com
Copyright © 1999 Sheila Na Gig.
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