Remember my friend, Al, who insisted that nickel-cadmium
batteries should not show a memory effect? Well, Brian just
called my attention to a Business Week quoting good old Al in
an article on nickel-zinc and other batteries. Al brought the
article to lunch last week and pointed out, I think correctly, that
one of the numbers in the table on the first page of the article was
in error. (For those who saw the article, we think 50 cycles
would have to be 500 cycles to be consistent with the
calculations.) Now to something really weird.
Having had the temerity a couple weeks ago to expound on black
holes, I thought to myself why not go whole hog and write about
the “theory of everything”. For me to do this shows real
Chutzpah inasmuch as my facility with mathematics these days is
limited pretty much to whatever is programmed into my pocket
calculator. Last year, my granddaughter called me about a 4th
grade homework problem requiring her to find the square root of
a number. I was embarrassed by the fact that, in spite of having
had courses in advanced calculus, differential equations and
statistical mechanics, I could not come up with a method for
doing the problem. In fact, it was my wife who suggested that I
consult the encyclopedia, which did indeed contain the answer.
However, the method suggested was totally foreign to me and I
was not comfortable with it. Then it turned out that the teacher
herself did not know how to solve the problem!
Now that I”ve confessed my ineptitude, let”s delve into what must
be some of the most complicated mathematics around. This is
the mathematics of strings. You might say,”Gee, a string doesn”t
seem complicated to me!” But these aren”t your normal
shoestrings. For one thing they”re vibrating and, even more
interesting, they”re only about a zillionth of an inch long! What”s
a zillionth of an inch? For our purposes, an inch divided by
10,000,000,000,000,000,000,000,000,000,000,000 (if I haven”t
lost count, there should be about 34 zeros). Now that”s tiny! If
those out-of-this-world string theorists are right, the whole
universe, you included, may be composed of these tiny little
critters. And be careful, there may be a string theorist living near
you! Universities are fighting to hire them away from each other
and a meeting on strings may draw over 400 attendees. Much of
what follows is based on an article by Gary Taubes, my favorite
science writer, in the July 23rd issue of Science and on
information gleaned from various websites. It might help if you
read my earlier column on black holes from the archives before
continuing.
For the bulk of the 20th century, Einstein”s theories and quantum
mechanics have existed as separate theories which describe in a
beautiful fashion the way our universe works. As we”ve
discussed here earlier, Einstein”s general theory describes gravity
and such things as black holes, bending of light, etc. On the
other hand, quantum mechanics describes what goes on at the
atomic level and smaller and explains, for example, how the
silicon chip works. Quantum mechanics also introduced
uncertainty into the picture by setting limits on our knowledge of
the positions and velocities of particles. Indeed, Einstein
apparently was never happy with this aspect of quantum
mechanics, as expressed in his famous quote “I cannot believe
that God would choose to play dice with the universe.”
Even so, Einstein”s so-called “special” theory of relativity was
incorporated later into quantum mechanics to expand the scope
of the theory. With many embellishments and contributions
from great minds, “The Standard Model” emerged which
describes all kinds of interactions and forces such as
electromagnetism and the forces at nuclear levels. But, lest you
get too impressed by these high falutin” theorists, the Standard
Model needs some 17 parameters that have to be measured by
experiments. Cynics among the scientific community might call
these “fudge factors”. That is, you can “fudge” the different
parameters, giving them different values until the theory agrees
with your experiments.
Unfortunately, The Standard Model can”t deal with one force and
that”s gravity. So, what we have are two beautiful theories, one
explaining gravity, the other just about everything else. For
decades, this inability of the two approaches to mesh smoothly
into each other has driven the theorists to find a Holy Grail, a
“theory of everything”. From the mathematical standpoint, a
problem with the other theories, especially when you try to mesh
them, is that infinities keep popping up. Infinities are not easy
things to swallow. This is where strings MAY be the answer.
Our strings, as we have seen above, are the teeniest little things
ever imagined. There certainly is no hope that anyone will ever
be able to see a string, even with the most powerful microscopes
imaginable. In one sense, this makes it great for the string
theorists since nobody can ever see whether strings really exist!
On the other hand, it also means that it”s very hard to make any
predictions from the theory that can be tested in the real world.
But there is another feature of these strings that really boggles
the brain, at least my brain, already boggled to saturation! It
seems that these strings can only operate in 10 dimensions. In
fact, there is a so-called M theory that operates in 11 dimensions.
Now, I don”t know about you, but the difference between 10 and
11 is pretty small potatoes after making the jump to 10! Let”s
back up and try to make sense of all these dimensions. To begin,
Einstein taught all of us that we live in spacetime, that is, we all
trace out our lives in 3-dimensional space. As you get up from
your chair and go the bathroom, time ticks away and you”ve
carved out a little path in spacetime in 4 dimensions, three of
space and one of time. So, whether we”ve thought about it or not,
we”re all quite comfortable living in 4 dimensions. Those high
speed photographs of a runner in motion or a curve ball coming
in to home plate illustrate an object”s path in spacetime. The
painter has to deal with the challenge of capturing the depth of 3-
dimensional objects or scenes on a 2-dimensional canvas. The
holographic security feature on your credit card accomplishes the
same task quite remarkably.
So, we deal with our spacetime dimensions, generally without
giving them a second thought. But, 6 more dimensions? To deal
with this concept let”s go into reverse. Say you have a long piece
of rope in your hand. You know its length and you can also see
and measure its thickness or diameter. You can empathize with
the rope as a 3 dimensional object. Now suppose it”s a magic
rope and starts to fly away from you. Pretty quickly, it”s become
less 3-dimensional as you lose a sense of depth and to you it just
has a length and a width. Even farther away it shrinks down so
much in width that you can only identify its length and it”s a 1-
dimensional line. It”s kind of like the other two dimensions have
curled up; they”re there but you can”t see them.
Have you anticipated the next step? Our savvy string theorists
say that the reason we think we live in a 4-dimensional world is
that the other 6 or 7 dimensions are curled up like in a little ball
so tiny that we can”t see them. Pretty slick, huh? It”s at least a
concept that I can live with since there are so many things that
are invisible to us until we use our magnifiers of various types. I
may be nanve, but I assume that if we could shrink ourselves
down to a zillionth of an inch we would experience these extra
dimensions as being perfectly normal features of our lives.
This is well and good but why should we be interested at all in
this string stuff. It turns out that the mathematics for certain
string theories spits out gravity as a natural consequence of the
theory. Indeed, a “graviton” emerges as just a string that has
curled itself into a little circle. This graviton presumably would
be the thing that carries the force of gravity between objects and
keeps all of us firmly rooted to this rapidly moving and spinning
earth. In the unlikely event that a string theorist reads this
column, please let me know if I”ve made any wrong conclusions
here.
At any rate, string theory not only deals with these little strings
but also comes up with “D-branes”. I gather that a 2-brane
would be like an ordinary 2-dimensional membrane, sort of like a
sheet of paper (neglecting its thickness). These D-branes can be
strings (I guess 1-branes?) or multidimensional branes.
Whatever they are, strings and branes can curl up, wrap
themselves around the curled dimensions, sort of like doughnuts.
What”s really exciting is that they can form black holes by piling
a bunch of these things together. OK, these black holes aren”t
real. They”re so-called “gedanken” black holes. Gedanken is a
German word commonly used to describe a “thought”
experiment, object or calculation. So, what the string people find
is that when they pile up these branes and strings in their
theories, their equations give them objects which would trap light
and have event horizons just like real black holes.
When they carry their calculations to extremes, for example, by
making the temperature absolute zero (as cold as you can get),
they find the behavior of their black holes is precisely that
predicted by such theorists as our friend Stephen Hawking. His
calculations start with Einstein”s general relativity theory, with
no mention of strings. Could this then be the long sought Holy
Grail, the theory of everything? This is only a glimpse of the
rich tapestry being woven by the string theorists and even they
appear to have no idea how it”s all going to end up. Will
fundamental particles such as electrons turn out to be strings or
branes or collections of them vibrating in at different frequencies
or manners? The whole concept of these strings has no
fundamental basis for its existence but the mathematics in the
hands of highly skilled practitioners has led to startling results.
The future ruminations of these string theorists in our simple 4-
dimensional spacetime could lead to the theory of everything or
to the theory of nothing (except for some stupid little strings).
The 21st century should provide the answer.
Allen F. Bortrum
