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Superstrings
This nOde last updated March 9th,
2024 and is permanently morphing...
(first emerged July 31st, 1999)
superstring
(sper-strng) noun
Physics.
A hypothetical particle
consisting of a very short one-dimensional string existing in
ten dimensions.
It is the elementary particle in a theory of space-time
incorporating supersymmetry.
[super(symmetry) +
string.]
- Michio Kaku -
_Visions_
6<-0->4
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However, the quantum
theory stands in sharp contrast to Einstein's general relativity, which postulates an entirely different physical
picture to explain the force of
gravity. Imagine, for the
moment, dropping a heavy shot put on a large bed spread. The
shot put will, of course, sink deeply into the bed spread. Now
imagine shooting a small marble across the bed. Since the bed
is warped, the marble will execute a curved path. However, for
a person viewing the marble from a great distance, it will
appear that the shot put is exerting an invisible "force" on
the marble, forcing it to move in a curved path. In other
words, we can now replace the clumsy concept of a "force" with
the more elegant bending of space itself. We now have an
entirely new definition of a "force." It is nothing but the
byproduct of the warping of space.
In the same way that a
marble moves on a curved bed sheet, the earth moves around
the sun in a
curved path because space-time itself is curved. In this new
picture, gravity is not a "force" but a byproduct of the
warping of space-time. In some sense, gravity does not exist;
what moves the planets and stars is the distortion of space
and
time.
However, the problem which has stubbornly
resisted solution for 50 years is that these two frameworks do
not resemble each other in any way. The quantum theory reduces
"forces" to the exchange of discrete packet of energy or quanta,
while Einstein's theory of gravity, by contrast, explains the
cosmic forces holding the galaxies together by postulating the
smooth deformation of the fabric of space-time. This is
the root of the problem, that the quantum theory and general
relativity have two different physical pictures (packets of
energy versus smooth space-time continuums) and different
mathematics to describe them. All attempts by the greatest minds
of the twentieth century at merging the quantum theory with the
theory of gravity have failed. Unquestionably, the greatest
problem of the century facing physicists today is the
unification of these two physical frameworks into one theory.
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This sad state of affairs can be compared to Mother Nature having two hands, neither of which communicate with the other. Nothing could be more awkward or pathetic than to see someone whose left hand acted in total ignorance of the right hand.
Superstrings
Today, however, many physicists think that we have finally solved this long-standing problem. This theory, which is certainly "crazy enough" to be correct, has astounded the world's physics community. But it has also raised a storm of controversy, with Nobel Prize winners adamantly sitting on opposite sides of the fence.
This is the superstring theory, which postulates that all matter and energy can be reduced to tiny strings of energy vibrating in a 10 dimensional universe. Edward Witten of the Institute for Advanced Study at Princeton, who some claim is the successor to Einstein, has said that superstring theory will dominate the world of physics for the next 50 years, in the same way that the quantum theory has dominated physics for the last 50 years.
As Einstein once said, all great physical theories can be represented by simple pictures. Similarly, superstring theory can be explained visually. Imagine a violin string, for example. Everyone knows that the notes A,B,C, etc. played on a violin string are not fundamental.
The note A is no more
fundamental than the note B. What is fundamental, of course,
is the violin string itself. By studying the vibrations
or harmonics that can
exist on a violin string, one can calculate the infinite
number of possible
frequencies
that can exist.
Similarly, the superstring can also vibrate in different frequencies.
Each frequency, in
turn, corresponds to a sub-atomic particle, or a "quanta."
This explains why there appear to be an infinite number of
particles. According to this theory, our bodies, which are
made of sub-atomic particles, can be described by the
resonances of trillions upon trillions of tiny strings.
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In summary, the "notes" of the superstring are the subatomic particles, the "harmonies" of the superstring are the laws of physics, and the "universe" can be compared to a symphony of vibrating superstrings.
As the string vibrates, however, it causes the surrounding space-time continuum to warp around it. Miraculously enough, a detailed calculation shows that the superstring forces the space-time continuum to be distorted exactly as Einstein originally predicted.
Thus, we now have a
harmonious description which merges the theory of quanta with
the theory of space-time continuum. 10 Dimensional Hyperspace. The
superstring theory represents perhaps the most radical
departure from ordinary physics in decades. But its most
controversial prediction is that the universe originally began
in 10
dimensions.
To its supporters, the prediction of a 10 dimensional universe
has been a conceptual tour de force, introducing a startling,
breath-taking mathematics into the world of physics.
To the critics,
however, the introduction of 10 dimensional hyperspace borders
on science fiction.
To understand these higher dimensions, we remember that it
takes three numbers to locate every object in the universe,
from the tip of your nose to the ends of the universe.
For example, if you want to meet some friends for lunch in Manhattan, you say that you will meet them at the building at the corner of 42nd and 5th Ave, on the 37th floor. It takes two numbers to locate your position on a map, and one number to specify the distance above the map. It thus takes three numbers to specify the location of your lunch. However, the existence of the fourth spatial dimension has been a lively area of debate since the time of the Greeks, who dismissed the possibility of a fourth dimension. Ptolemy, in fact, even gave a "proof" that higher dimensions could not exist. Ptolemy reasoned that only three straight lines can be drawn which are mutually perpendicular to each other (for example, the three perpendicular lines making up a corner of a room.) Since a fourth straight line cannot be drawn which is mutually perpendicular to the other three axes, Ergo!, the fourth dimension cannot exist.
What Ptolemy actually
proved was that it is impossible for us humans to visualize
the fourth dimension. Although computers routinely manipulate
equations in N-dimensional space, we humans are incapable of
visualizing spatial dimensions beyond three. The reason
for this unfortunate accident has to do with biology, rather
than physics. Human evolution
put a premium on being able to visualize objects moving in
three dimensions. There was a selection pressure placed on
humans who could dodge lunging saber tooth tigers or hurl a
spear at a charging mammoth. Since tigers do not attack
us in the fourth dimension, there simply was no advantage in
developing a brain with the ability to visualize objects
moving in four dimensions.
From a mathematical
point of view, however, adding higher dimensions is a distinct
advantage: it allows us to describe more and more forces.
There is more "room" in higher dimensions to insert the electromagnetic
force into the
gravitational
force. (In this picture,
light becomes a vibration in the
fourth dimension.) In other words, adding more dimensions to a
theory always allows us to unify more laws of physics.
A simple analogy may help. The ancients were
once puzzled by the weather.
Why does it get colder as we go north? Why do the winds blow to
the West? What is the origin of the seasons? To the ancients,
these were mysteries that could not be solved. From their
limited perspective, the ancients could never find the solution
to these mysteries. The key to these puzzles, of course,
is to leap into the third dimension, to go up into outer space,
to see that the earth is actually a sphere rotating around a
tilted axis. In one stroke, these mysteries of the weather
become transparent. The seasons, the winds, the temperature
patterns, etc. all become obvious once we leap into the
third
dimension.
Likewise, the superstring is able to
accommodate a large number of forces because it has more "room" in its
equations to do so.
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
rained down on a flat, two-dimensional world, called Flatland, where there lived a
mythical race of beings called Flatlanders. These
Flatlanders were intrigued by the beauty of the fragments, which
could be found scattered all over Flatland. The scientists of
Flatland postulated that these fragments must have come from a
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 many, but certainly not all, of the
fragments together into two chunks. The first chunk was called
the
"quantum," and
the second chunk was called "relativity."
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Although they Flatlanders were rightfully proud of their progress, they were dismayed to find that these two chunks did not fit together. For half a century, the Flatlanders maneuvered these two chunks in all possible ways, and they still did not fit. Finally, some of the younger, more rebellious scientists suggested a heretical solution: perhaps these two chunks could fit together if they were moved in the third dimension.
This immediately set
off the greatest scientific controversy in years. The older
scientists scoffed 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. However, the younger scientists were undaunted. Using pure mathematics, they could show that these two chunks fit together if they were rotated and moved in the third dimension. The younger scientists claimed that the problem was therefore theoretical, rather than experimental. If one could completely solve the equations of the third dimension, then one could, in principle, fit these two chunks completely together and resolve the problem once and for all.
We Are Not Smart Enough
That is also the conclusion of today's superstring enthusiasts, that the fundamental problem is theoretical, not practical. The true problem is to solve the theory completely, and then compare it with present-day experimental data. The problem, therefore, is not in building gigantic atom smashers; the problem is being clever enough to solve the theory.
Edward Witten, impressed by the
vast new areas of mathematics opened up by the superstring
theory, has said that the superstring theory represents "21th
century physics that fell accidentally into the 20th century."
This is because the superstring theory was discovered almost
by accident. By the normal progression of science, we
theoretical physicists might not have discovered the theory
for another century.
The superstring theory may very well be 21st century physics, but the bottleneck has been that 21st century mathematics has not yet been discovered. In other words, although the string equations are perfectly well-defined, no one is smart enough to solve them. This situation is not entirely new to the history of physics.
When Newton first
discovered the universal law of
gravitation at the age of
23, he was unable to solve
his equation because the mathematics of the 17th century was
too primitive. He then labored over the next 20 years to
develop a new mathematical formalism (calculus) which was
powerful enough to solve his universal law of
gravitation. Similarly, the fundamental problem facing
the superstring theory is theoretical. If we could only
sharpen our analytical skills and develop more powerful
mathematical tools, like Newton before us, perhaps we could
solve the theory and end the controversy. Ironically, the
superstring equations stand before us in perfectly
well-defined form, yet we are too primitive to understand why
they work so well and too dim witted to solve them. The search
for the theory of the universe is perhaps finally entering its
last phase, awaiting the birth of a new mathematics powerful
enough to solve it.
Imagine a child gazing at a TV set. The images and stories conveyed on the screen are easily understood by the child, yet the electronic wizardry inside the TV set is beyond the child's ken. We physicists are like this child, gazing in wonder at the mathematical sophistication and elegance of the superstring equations and awed by its power. However, like this child, we do not understand why the superstring theory works.
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