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STRING
THEORY The Inelegant Universe
by
Miles Mathis
Between
foolish art and foolish science, there may indeed be all
manner of mischievous influence
John
Ruskin
He was one of that
countless and multifarious legion of nondescripts, putrescent
abortions, and uninformed obstinate fools who instantly and
infallibly attach themselves to the most fashionable current
idea, with the immediate effect of vulgarizing it and of turning
into a ridiculous caricature any cause they serve, however
sincerely.
Feodor
Dostoevsky
First posted
September 20, 2005
Readers
coming here from a websearch or from other chapters of mine may
assume I have nothing to say about the math of string theory.
They will assume that since I am neither an insider nor a famous
mathematician, the subtleties of 11dimensional math are beyond
me. And since the first part of this paper attacks the theory and
not the math, many will assume that I am just making a
philosophical critique. They are quite mistaken. In Part II of
this paper I will make a foundational critique of the math,
revealing some astonishing facts that even the princes of the
theory will not want to miss. So if you tend to nod off at any
stretch of sentences that fails to contain a number or a
variable, there is something for you here, too. The big laughs
are in the first part of this paper, but the lasting interest
lies in the last part.
Part
I The Theory
Since
the late 1980s string theory has continued to gain in popularity,
until now it has become a sort of fashion. Brian Greene puts it
this way in his book The Elegant Universe:
[In
1984] there was a pervasive feeling among the older graduate
students that there was little or no future for particle physics.
The standard model was in place and its remarkable success at
predicting outcomes indicated that its verification was merely a
matter of time and details. . . . [Then] the success of Green and
Schwarz finally trickled down even to firstyear graduate
students, and an electrifying sense of being on the inside of a
profound moment in the history of physics displaced the previous
ennui.
Most will find nothing
particularly revealing in this quote, I imagine. No doubt Greene
believes he is just stating a fact, not baring his wicked soul.
But I find in it the entire explanation for the movement in
science in the 20th century. The keyword is "ennui". In
the late 20th century it took a lot to interest the top graduate
students like Brian Greene. They could see no quick road to fame
by studying the boring past. What was wanted was an avant garde
math or theory to latch onto. This is what had made Einstein
famous, and after him Feynman and Hawking and all the rest.
Mathematics had been the key, and it looked to continue to be the
key in the near future. For Brian Greene and the other ambitious
young physicists of our time, the job is not to try to discover
why the old avant garde maths aren't working; no, the job is to
create ever newer avant garde maths that are harder to test. This
will automatically provide fewer empirical contradictions, and
thereby a "stronger theory".
In this paper I
will use The Elegant Universe as my scratching post. I do
this for a number of reasons, but the main reasons are: 1) It is
a recent bestseller and has done as much as any book to
popularize the theory, 2) It describes an almost unbelievably
inelegant universe, 3) It is as transparent as thinnest glass,
setting me up for easy scores on almost every page. As far as the
last reason goes, I will show that it is probably a mistake for
avant garde maths and theories to allow themselves to be
presented to popular audiences, especially if the presentation is
in a clear language. Brian Greene is a good science writer: good
in the sense that a reader can penetrate what he is saying. But
science writers used to understand that obscure theories should
always remain in obscure language. That was the only hope for
them, no matter the audience. An honest presentation of a
dishonest theory is too dangerous. For one thing, it allows other
scientists like me to find the flaws too easily. Fully cloaked in
its armor of equations, it is not so easy to sort out, even for a
mathematician. But stated baldly it becomes a sitting duck.
I find it astonishing that string theory has made it this far.
Greene says that the early years were a bit of a struggle, but I
don't tend to believe it. The fact that a theory that is such a
magnificent mess is on its feet at all is a very bad sign. It
shows the uncritical nature of our milieu, not only in the public
and publishing sector, but at the highest levels. The reason for
this is clear: graduate students like Greene were welltrained in
being uncritical, and they have been for more than half a
century. The old uncritical graduate students are now deans and
department chairs, and they are all very far gone down the road
of nondiscrimination. The list of things they have accepted at
face value is long and shocking. Greene's first five chapters are
a public airing of all the absurd things he has accepted without
much analysis. It is clear that he has accepted them because he
never really cared if they were true or made sense or not. He,
like the others, has from the beginning judged each incoming
piece of information based on its likelihood to add to his
prestige, and anything that was already a settled question could
not help in that area. What he and the other ambitious
theoreticians were looking for all along was the end point. "Get
me to the endpoint as fast as possible." Because then they
could begin making their personal contribution. "Put me as
close to the front of the line as you can, where I can begin
pushing." For these
brightest students, physics was no longer seen as a field they
could add to, it was a field they could trump. Their greatest
goal was to make all of the past immediately obsolete. Basic
physics was digested like a breakfast at the drivethru,
Relativity was duly cut and pasted, and QED was memorized by
rote. All this was done by the age of 24 or 25. Another year of
allnighters provided them with the latest hypermaths and
theories, so that they could immediately begin discussing
tenvector fields with full abandon at the coffeeshop and
braintrust. In this way
science has become just like Modern Art. The contemporary artist
and the contemporary physicist look at the world in much the same
way. The past means nothing. They gravitate to novelty as the
ultimate distinction, in and of itself. They do this because
novelty is the surest guarantee of recognition. The contemporary
artist always has his nose to the wind, sniffing the air for the
next trend. As soon as he gets a whiff of it he is off running.
He is always in a race with time, for it is no longer a matter of
being best, it is a matter of being first. He therefore
congregates with others of his type. They mass at the same
hotspots, antennae erect. The
contemporary scientist is the same. He is a social creature,
always trying to impress. Rigor impresses no one in the modern
world, so he does not even have to fake it. What impresses are
lots of difficult equations, with lots of new variables and
terms. The ultimate distinction is coining new words for the new
math and the new objects. CalabiYau shapes and 3branes and
orbifolding: that is rich beyond anything.
The art departments have long since dismantled the old schedules:
painting and sculpture are passe, studio art a dinosaur, drawing
from the nude a sexist embarrassment. The physics and math
departments will soon follow suit, no doubt. Mechanics and
kinematics will be jettisoned as a theoretical nuisance, a
blockage of creativity. Classical algebra and geometry will
become an elective, taken only by historians and archivists.
Instead, seventh graders will be offered "The Rudiments of
Chaos Theory" and "Fun with Tensors" and "Computer
Modelling with i."
Let me now show you a few
examples of the absurdities that the standard model teaches. I do
this to prove that by accepting these absurdities, it encourages
a proliferation of more such absurdities. It teaches the graduate
students, by example, that mathematical fuzziness pays and that
conceptual rigor does not. Let us start with the "messenger
particle,"^{1} a relatively new beast in the
physical zoo. The messenger particle is a photon that tells
another particle whether it should move away or move near. The
messenger particle was invented to solve the problem of
attraction. At some point it became clear to physicists that
attraction couldn't logically be explained by a trading of
particles. Their old blankets over this problem had begin to wear
thin, so they needed a new concept. Enter the messenger particle.
With the messenger particle, we no longer have to be concerned
with explaining physical interactions mechanically. We don't even
have to imagine that movement away in a field is caused by
bombardment, which was such a simple concept. No, we can now
explain both movement away in a field and movement toward in
field as due to information in a messenger particle. This
simultaneously explains both positive charge and negative charge.
How easy: the photon just tells the particle what to do.
Why did we not think of that before?
Once you accept that quantum particles are on speaking terms,
physics is so much tidier. There is no end to what we can explain
this way. We can have the particles trading recipes, emailing
eachother, SMSing, watching TV. It is a theoretical goldmine.
Gluons, weakgauge bosons, and
gravitons are also messenger particles of their various forces.
The problem of attraction is solved once and for all, for all
possible fields. Gravity is not curved space or a physical force.
It is a commandment.
The next absurdity is one of
Feynman's famous absurdities.^{2} This one
concerns letting an electron going through the twoslit
experiment take all possible (infinite in number) paths
simultaneously and then summing over these paths to find the wave
function. Any idiot can see that this is just a mathematical
consideration and has no physical implications, but Feynman was a
special kind of idiot. He insisted for some reason that the math
was the physics, and all the special idiots since then have taken
his word for it. They love to quote or paraphrase him, as Greene
does, "You must allow nature to dictate what is and what is
not sensible." Which means, "You must allow me
(Feynman) to dictate what is and what is not sensible. I am
smarter than you are and if you don't allow me to dictate to you,
I will browbeat you mercilessly." Even now that Feynman is
long in the grave and incapable of personally browbeating anyone,
the special idiots still quote and paraphrase and bow to his
authority. Feynman himself was bowing to the authority of
Heisenberg and Bohr, who first decided, by fiat, that the math of
quantum mechanics was the physics. Or perhaps he was only
learning from their example. Counterintuitive fiats had made them
famous with all the toadies, why not make a few of his own
counterintuitive fiats and toadies?
Greene tells us outright: "Quantum mechanics requires that
you hold such pedestrian complaints [about things making sense]
in abeyance." What could be more convenient for a scientist?
He is now in the position of a priest. The priests have always
said the same thing to nonbelievers. "You must not expect
it to make sense. You must have faith. Trust the Lord."
Trust Feynman. He is smarter than you and understands what you
should believe. He has filled the blackboards with Hamiltonians
and has cracked safes. He has earned the right to say ridiculous
things, like the Dalai Lama or the Buddha or the President.
This is the most important
thing that string theorists have learned from quantum mechanics:
you do not have to make sense anymore. Any contradiction can be
relabeled a paradox, any infinity can be relabeled an axiom, any
absurdity can be given to Nature herself, who is an absurd
creature, in love with illogic and caprice.
I could go on
indefinitely, listing other absurdities like the Twin Paradox and
the singularity and so on, but I have analyzed these problems
elsewhere in great detail; and besides, you already either accept
them or don't accept them, so that my comments are nearly beside
the point. You won't judge the concepts based on anything I could
say of them, you will only judge me for what I say of them.
Therefore, let me proceed to critique string theory, a theory
that is not yet set in stone, even for the toadiest.
String theory begins by defining a string. In most instances a
string is a onedimensional loop, we are told. String theory is
famous for its everincreasing number of required dimensions, so
that you would think that the theorists would have a pretty tight
idea of what a dimension is. But if you think this you would be
wrong. String theory is about math, not about concepts, and these
brilliant mathematicians don't have a very clear idea what a
dimension is or what a onedimensional "thing" would
be. In math, a onedimensional thing is a line. It always has
been, since the time of Euclid, and that has not changed
recently. A zerodimensional thing is a point, a two dimensional
thing is a plane, and a threedimensional thing is a cube or
sphere or whatnot. But all of these things are mathematical
abstractions. They don't exist and can't exist. Of all these
mathematical things, only the threedimensional things have a
potential existence, and then only if you add time. There is a
very simple reason for this that has nothing to do with gods or
turning on the universe or anything else esoteric or
metaphysical. Points, lines and planes cannot exist because they
do not have any physical extension. A plane disappears in the z
direction, a line disappears in the x and y direction, and a
point disappears in all three directions. In mathematical terms,
it means that the variable or field has hit a limit—a zero or
infinity—at this point in the equations, making existence
impossible. Physicists used to
understand simple concepts like this, but no more. Even
mathematicians don't appear to understand them. These concepts
just get in the way until some selfdescribed genius somewhere
finds a clever way around them, and we aren't bothered with them
anymore. After that we are allowed to propose the existence of
mathematical objects and no one blinks an eye. But it remains a
(perhaps unpleasant) fact that a line cannot exist. Even in pure
math, a "onedimensional loop" cannot exist. A
onedimensional loop is false even as a mathematical abstraction.
Why? Because a loop curves. Any curve is no longer
onedimensional. A curve is twodimensional, by definition.
Greene and his heroes imagine
that because you can, in a pinch, express a position on a curve
with one variable, that it is a onedimensional object. But it
isn't. Greene proves this when he begins talking about his
gardenhose world, where the position of a bug on the hose can be
expressed with two variables. He then admits in an endnote that
if the garden hose has an interior, we must have more dimensions.
But when, in a physical situation, is it possible to imagine a
garden hose, no matter how tiny, with no interior? It is not
possible and his "twodimensional" garden hose, if
physical, must have three dimensions.
Greene makes the current confusion even more apparent when he
begins increasing the Type IIA coupling constant.^{3}
This allows strings to expand into two and threedimensional
objects. He says that the twodimensional string is like a
bicycle tire and the threedimensional object is like a donut. So
Greene thinks there is a dimensional difference between a
bicycle tire and a donut! If a bicycle tire is not solid rubber
through and through, then the third dimension has disappeared? We
should at least have to suck the space out of it with some kind
of space vacuum, right?
String theory is such a godawful
mess right from the first concept that it is painful to go on.
But I will. Once we have our impossible onedimensional loops, we
are to imagine that they are vibrating. To vibrate in the right
way for the theory, they must be strung very, very, very tight.
Now, a sensible person would already have several foundational
questions. First of all, why are they vibrating? Second, why are
some vibrating one way and some vibrating another way? Third,
what causes the tension? The
first concept, basic vibration, we can give them. Vibration is
far from being a basic motion, but there has to be some first
cause, and so we will allow one unexplainable motion as first
cause. But the difference in different vibrations cannot be
uncaused. We cannot allow it to be a postulate. Different
vibrations should have different mechanical causes. If one string
is vibrating in a different way from another, there must be a
reason. String theorists have already told us that strings are
not made up of subparticles; they are absolutely indivisible.
They should therefore be undifferentiated. Ultimate strings that
are indivisible should act the same in the same circumstances. If
they act differently, then the circumstances must differ. But we
are not told what these different circumstances are. The vast
variation in behavior is just another postulate.
Besides, even if we admitted the impossible—that a
onedimensional loop could exist—once you give it a vibration
it automatically gains a dimension. All you have to do is look at
the direction it is postulated to vibrate in. Does it vibrate
lengthwise? Of course not. How could it? It is undifferentiated
lengthwise, meaning that it is not made up of subparticles. There
is no way a pulse could travel lengthwise in a string that was
not divisible. So the theorists propose sideways vibrations, of
different sizes and wavelengths. In technical terms, we are
talking about transverse waves, not longitudinal waves. A
transverse wave will automatically push the string into a second
dimension. So all talk of onedimensional strings is a wash from
the beginning, for two fundamental reasons, not one.
This brings us to another question: is it even possible for a
onedimensional string to vibrate sideways? I have reminded the
reader that a longitudinal wave is impossible to imagine without
some subdivision of the string. There has to be some sort of
longitudinal variation to propose compression; but this variation
is not possible without subdivision. In the end this is because
without subdivision you cannot insert any space into the string.
You need space in between the particles making up the string in
order to propose variation in compression. But a closer analysis
shows the same problem with transverse waves on a onedimensional
string. How is a onedimensional string bendable without some
"give" between particles making up the string? If the
string is absolutely indivisible and undifferentiated, then it is
not clear that we can bend it. A bend would occur at the bond
between particles, in a macroscopic string. In a stringtheory
string, there is no bond between particles, since there are no
particles making up the string. Bending or vibrating a
stringtheory string is like proposing to bend or vibrate a cube
or a cone or a sphere. If our fundamental particle were any of
these instead of the string, you would laugh if someone proposed
that it bent. Imagine a cube bending. How would a fundamental,
undifferentiated cube bend? Or a fundamental, undifferentiated
sphere? But bending a fundamental, undifferentiated string is
just as silly. It is just another postulate that is impossible to
explain or justify. Likewise,
tension is a pretty complex concept. It is not a fundamental
motion or event. In fact, tension is a force. But string theory
is supposed to be explaining the four fundamental forces, not
creating more. What causes the tension? How is it possible to
have a tension across an undifferentiated ultimate string? How is
it possible to have tension in a closed loop, unless that loop is
being expanded by some outside force? None of this is explained.
Tension is just an assumption, another axiom.
After a first reading, I had already discovered that string
theory has more basic postulates than any theory I had ever seen
or imagined. To any logical person from past centuries, string
theory would look like a comedy of errors. Newton has been all
but laughed at by string theorists for not giving a mechanical
explanation of force at a distance. But these theorists are in no
position to throw stones. Newton would look at string theory and
say something like, "Well, of course, if you are allowed to
make enough unprovable assumptions at the beginning, you can
formulate a theory to contain anything. Especially if you are
allowed to beg the question so egregiously. String theory is the
attempt to unify the four basic force fields. To do this it
creates, as a postulate, a huge force of uncaused tension. Then
it adds to that a basic 'particle' that can morph into anything,
just by changing its 'tune.' All these morphs are uncaused and
act as further postulates—as postulates they do not require
proof or any justification. Then, whenever the math stops
spitting out numbers they want, they postulate new branes,
donuts, tubes, threeholed buttons, frisbees, and anything else
that tickles their fancy. None of these new objects has to be
justified beyond the fact that they needed them to fill a hole in
the math. 'It fit the hole, therefore it must be real!' Then,
when the going gets really tough, they add a new dimension.
Mtheory gives them the 11th dimension, and why stop there? I
predict that, like Feynman, they will finally understand that the
sky is the limit. Why not predict an infinite number of curled up
dimensions, sum over them in some fudgy way, and achieve any
answer you like, to fit any occasion. Only then will the madness
come to its illogical end."
This is the basic technique of string theory: if you run into
some deadend at any point in the math, transport that deadend
back to the string. For example, perhaps you find the need for a
new particle but your math at that level of size or theory does
not allow it. Well, simply make it another axiom of string
theory. Postulate that your basic string takes that shape under
the circumstances you have discovered, and your work is done. In
this way, every conceivable problem can be collected at the
foundational level and made into an axiom. Since you don't have
to prove axioms, you will never be pestered to supply a proof or
explain anything. All problems can be collected, reinserted at
the axiomatic level, and treated ever after as assumptions. In
this way string theory really is the perfect theory. Using this
technique, nothing is beyond mathematical expression.
String
theory is actually even more inelegant than QED, and QED is not
exactly a poster child for elegance or simplicity. Greene tells
us that string theory was invented to simplify the huge number of
"elementary" particles in QED, as well as to combine
QED and Relativity. But he seems oblivious to the fact that
string theory has a recordsetting number of axioms and an
everincreasing number of vibrations, dimensions, blobs, branes,
and jellies. The only object not yet incorporated into string
theory is the mosscovered threehandled family gradunza. It also
has a truly impressive number of manufactured manipulations, such
as the set of instructions for orbifolding a CalabiYau shape or
the tearing of space in a flop transition. These manipulations
come provided with no theory, and are basically added to the list
of postulates: postulate #89,041—we can floptear an
orbifolded 3brane goofus as long as we can say afterwards that
the math made us do it (and provide a sexy little
computergenerated diagram).
Another of the inelegances
of string theory is the required energy of a string. The
unbelievable amount of tension [10^{39} tons] on a single
string gives it a mass of some 10^{19} protons. This is
about the mass of a grain of dust. The theorists need all this
force on the string since they have gathered all the other forces
here at the axiomatic level. This has the added benefit, they
think, of making the mass too great to be discovered in an
accelerator. Unfortunately, the mass is so huge that it should
make the string discoverable by macroscopic means. I might
suggest a sieve. Seriously though, the theorists admit that "all
but a few of the vibrational patterns will correspond to
extremely heavy particles," meaning particles many times
heavier than a grain of dust.^{4} It is hard to believe
that masses of this sort floating around are undetectable. Greene
says that they are unlikely because "such superheavy
particles are usually unstable."^{5} It is
interesting to note that string theory never says why all such
superheavy particles should be unstable. In fact, there is no
theoretical reason they all should be. It is another postulate:
postulate #76,904—superheavy particles are all unstable
because if they weren't we might be able to find one. The
instability is another axiomatic convenience of the theory.
But let us reverse for just a
moment. The tension is even harder to believe than the mass. Try
imagining putting a thousand trillion trillion trillion tons of
tension on a grain of dust. Talk about tensile strength. Talk
about potential energy. And you thought the atom had a lot of
stored up energy. What a bomb you could make out of one string!
Get one little string to relax for a moment, and you could blow
up the entire galaxy. I suspect someone may have miscalculated by
a teeny bit. You will say, “C'mon, a whole galaxy? Isn't that
hyperbole?” No, 10^{39} tons is actually more than the
weight of 2 trillion suns, which would be four Milky Way
galaxies. All that tension on one string.
Here's another
inelegance. In a subchapter ironically entitled, "The More
Precise Answer,"^{6} Greene develops this idea: the
"violent quantum jitters" can be quieted by imagining a
collision of point particles as a collision of strings instead.
One string represents an electron, say, and the other a positron.
The two strings join for a moment as a string that represents a
photon and then reseparate as two new strings. The reason this
is an improvement, we are told, has to do with Relativity. Greene
uses his two observers George and Gracie (the Burns and Allen
ghosts are due massive apologies for being brought into this
mess, I think) to "slice" his strings into different
events. George sees the strings meeting at one time and Gracie
see the meeting at another time. Among all possible observers the
meeting point will be smeared out over some time. This smearing
calms the quantum jitters.
This is among the most dishonest uses of Relativity and
diagramming I have ever seen. In order for his argument to work,
Greene has to diagram the strings as threedimensional objects.
For it is not the length of the strings that causes the
Relativistic difference in his argument, it is the thickness. But
he began the subchapter by admitting that the strings were
onedimensional. He brags that onedimensional strings can do
what zerodimensional points cannot. Remember that strings have
only a length dimension. They have no thickness. As a matter of
width or thickness or radius, they act just like points. They
have zero radial dimension. This means that Greene's Relativistic
slicing is flat wrong. His diagrams are a big fat lie, since they
cause you to visualize something that cannot be happening. His
words are saying one thing and his diagrams are saying the
opposite. If the strings are onedimensional lines, then the fork
where they meet will also be onedimensional. If you slice it at
a dt, then the fork will be in the same exact place for all
viewers. String theory adds absolutely nothing to QED or the
point problem. It simply adds another layer of lies to cover it
up.
Part
II The Math
As
promised, I will now critique the math of string theory. String
theory has, in the last six or seven years, graduated into
Mtheory, an 11dimensional math that attempts to join together
the six major 10dimensional string theories. Mtheory has 10
space dimensions and one time dimension, we are told. It is in
this matter of dimensions that I have a bombshell to drop. All
the extradimensional theories that have been proposed since the
time of Kaluza in 1919 have contained a basic misunderstanding of
the dimensions they described. No one has seen this before
now, but the added dimensions, whether they are Kaluza's one
extra dimension or Mtheory's seven extra dimensions, are all
time dimensions. To
understand why this must be the case, we must go back to the
basic calculus. All the higher maths that are used by string
theory are based on the calculus. Calculus itself is a math that
is based on comparing rates of change. My long paper on the
calculus makes this crystal clear, but it has always been
understood in some form or another. Velocity is a rate of change
of distance and acceleration is a rate of change of velocity.
That is why velocity is the first derivative of distance and
acceleration is the second. I showed that you can also find third
and fourth derivatives of distance, and so on. The third
derivative is a change in acceleration and the fourth derivative
is a change in that change. These multiple accelerations can
really happen: they are physical. I also showed that you could
write a velocity in one of two ways, either of which was
mathematically acceptable: Δx/Δt or ΔΔx. Likewise,
acceleration can be written as Δx/Δt^{2} or ΔΔΔx. A
seconddegree acceleration can be written Δx/Δt^{3} or
ΔΔΔΔx, and so on. You can
see that even here there is some sort of mathematical equivalence
between x and t. Einstein showed us that this equivalence goes
far beyond anything Newton could have imagined, but even in
Newton's calculus equations, there was a hidden equivalence. The
variables Δx and Δt are the inverse of eachother, in some
sense. In the equations above, the x goes in the numerator when
the t goes in the denominator. This is because, as variables,
they always change in inverse proportion, even when no
transformational changes are involved. Remember that Einstein
showed that as time dilated, length contracted. One gets bigger
as the other gets smaller. This is clear in the transform
equations of Special Relativity, and it is clear in the equations
above as well. A Δx in the numerator is, in some very important
sense, the same as a Δt in the denominator.
Why is this important? It is important because what all the big
maths of Maxwell's equations, General Relativity, Quantum
Mechanics, Kaluza's fivedimensional theory, string theory, and
Mtheory all do is express fields. All these fields are force
fields and force fields are based on some acceleration. By the
old equation F = ma, if you have a force you have an
acceleration. The reason that Kaluza's fifth dimension helped so
much at first is that it allowed the expression of both
the gravitational field and the electromagnetic field, the only
two of the major four that were known at the time. Using the
vector fields as they have been defined since the end of the 19th
century, the fourvector field could contain only one
acceleration. If you tried to express two acceleration fields
simultaneously, you got too many (often implicit) time variables
showing up in denominators and the equations started imploding.
The calculus, as it has been used historically, couldn't flatten
out all the accelerations fast enough for the math to make sense
of them. What Kaluza did is push the time variable out of the
denominator and switch it into another x variable in the
numerator, just as I did above. Minowski's new math allowed him
to do this without anyone seeing what was really going on.
String theory and Mtheory continue to pursue this method. They
have two new fields to express, so they have (at least) two new
time variables to transport into the numerators of their math.
Every time you insert a new variable, you insert a new field.
Since they insert the field in the numerator as another
xvariable, they assume that it is another space field. But it
isn't. It is a transported time variable.
Readers will no doubt be reeling at this information. It was
difficult enough to imagine extra space dimensions, most of them
curled up like little pillbugs. But how do we make sense out of
eight simultaneous time dimensions? It is actually a lot easier
than you think, since, once understood, it is easy to visualize.
It doesn't take any leaps of faith or warnings that "you
can't possibly diagram this, but you must accept it anyway."
To show this, I will use the visualization I used in my calculus
paper. Let us say you are at the airport, walking along normally.
In addition, let us say that you are walking in a perfectly
straight line and that your stride is perfect. Each step is the
same as every other step. You therefore have a constant velocity,
and your stride is, in a sense, measuring off the ground. If you
are very retentive, you might even be counting as you walk: 1, 2,
3, 4, and so on. Well then, let us give you a watch, too. Some
Swissquartz stunner than never misses a beat. So time, the
retentive soandso that he is, is also counting off his numbers:
1, 2, 3, 4 and so on. Next you come to a moving sidewalk. You
step on and for one interval you are accelerated. It is not an
instantaneous interval, since some amount of time passes between
your initial speed and your final speed. But there is an
acceleration over only one interval. It stops at the end of that
interval and you have a new constant velocity, a velocity found
by adding your own velocity and the velocity of the sidewalk.
Since there was an
acceleration over that interval, then by the standard way of
expressing acceleration, we how have a t^{2} in the
denominator: a = Δx/Δt^{2}. As we know, that can also
be written a = Δx/Δt/Δt. Either way we have a second time
variable. Therefore we might say that we have a second time field
and a second time dimension. Now, we must study that interval.
What happened over that interval? Did you step into another
dimension? Did another dimension open up under you? In a very
limited sense, yes. That interval is a sort of subinterval to
the ones you were measuring off with your feet and your watch.
But it is not mysterious in any way. It is not curled up
anywhere. In fact, you can measure both time dimensions with your
watch. That is why we usually just square the time dimension. It
is a second measurement over the same interval. If the two time
dimensions weren't directly related, we obviously couldn't square
them. We would have to call them Δt_{1} and Δt_{2}
or something, and keep them separate.
What I mean when I say that we are measuring two things
simultaneously is that we are measuring how far the sidewalk goes
in Δt and how far the walker goes in Δt. An acceleration is
these two velocities measured over the same interval. So you can
see that what we really have is two Δx's and one Δt. But since,
in the real world of airports and things like that, we measure
strides and lengths on sidewalks with the same measuring rods, it
is easier to write the equation with one Δx and two Δt's.
Therefore, we get the equation a = Δx/Δt^{2}.
All this is very elementary, of course. But everyone seems to
have lost sight of it at this late date in history. Because what
it means, especially when you have a math that is expressed by a
lot of superscripted dx's, is that those dx's are not mysterious
extra space dimensions, they are equivalent to velocities being
measured simultaneously to achieve complex accelerations. These
complex accelerations express the meeting of multiple fields over
the same (perhaps infinitesimal) interval.
To see this even more clearly, let us say that our man on the
moving sidewalk hits yet another field. When he first stepped
onto the sidewalk, we might say that he passed through a
oneinterval field. Well, if we are mischievous, we can plaster
that interval with so many fields it will make the man's head
spin. We can move him sideways, up, down, or we can spin him any
number of revolutions we like. And we can do them all at once.
Again, not all at an instant, but all over the same finite
interval. Every time we add a motion, whether is a linear motion
or a spin, we have hit him with another force. We have also hit
him with another variable. We have also hit him with another
field. We have also hit him with another dimension. We have done
a finite number of things to him during a finite time. Therefore
we have created a oneinterval field of multiple forces and
dimensions. Stated in this
way, there is nothing mysterious about it at all. When we add a
dimension, all we have to do is add another Δx to the numerator
or another Δt to the denominator (but not both). But none of
these extra dimensions is strange or difficult to imagine. We
have just imagined it, physically. We could also draw it and
diagram it. All we need is tracing paper and overlays. Nothing is
curled up. Nothing is unexpressed, nothing only comes out at
night.
An 11dimensional math can be expressed using all
the ridiculous equations of Mtheory, where supercomputers are
wasted just storing the postulates. Or you can express it like
this: A = Δx, Δy, Δz/ Δt^{8}.
A perceptive reader may say, "Wait, didn't you just say that
we could express a new field or force by either a new space
variable in the numerator or a new time variable in the
denominator? If this is true, then why can't Mtheory call all
the new dimensions space dimensions if it wants to?" Well,
it can, but it has to be very careful what this implies. I have
shown how multiple time dimensions are really a rather simple
idea, with no mystery involved. Likewise, seven new space
dimensions, correctly interpreted, are also not mysterious or
esoteric or difficult to understand at all. A new dimension is a
new force applied over a finite interval. If this force is
continuous, then it causes a continuous field. By continuous
field I mean a field that spreads across an extended set of
intervals, not just one interval. Over one interval, a force
causes a velocity. Over an extended set of intervals, a
continuous force causes a continuous acceleration. We have known
this for a long time. But what all this means is that the new
dimension is not a new direction in space. Every time we add a
new dimension to our math, it does not mean that a new,
autonomous xvariable has been invented, going off in some
strange new path, like the path of i or the path of a
curled up pillbug. It just means that we have a new velocity
happening simultaneously to all our other velocities over the
interval in question. This velocity does not have to have a
direction in space all to itself. It does not have to be at a
right angle to all previous dimensions. There is nothing to say
that forces cannot overlap, or that directions cannot overlap or
that times and subtimes cannot superimpose. In fact, they must
superimpose. When we create these largedimensional maths, we are
doing so precisely to ask how the various accelerations and
forces superimpose. That is what we are seeking. We are seeking
the total field at dt, and that total field is a superposition of
all the velocities caused by all the force fields present at that
interval.
There are two basic and separate ways to
"unify" the four known forces and all the spins. One is
to find a math that contains them all. The other is to show how
one force field is equivalent to another field, thereby
simplifying our equations. If we can show that the same basic
motion causes two separate fields, we will have unified those two
fields. String theory attempts to unify in both ways, but does
neither. It tries to unify all fields by expressing them as
various vibrations of an ultimate particle, but this part of the
theory is just gibberish, as I have shown. It also tries to
contain all the fields using a multidimensional math, and in
this it has made one tiny step in the right direction. If the
dimensions are interpreted in the way I have interpreted them
above, then they start to make some sense. The first step toward
the mathematical expression of a unified total field is to add up
all the accelerations and to express them as separate dimensions.
But I think it is clear from my airport sidewalk example that a
completely successful math must, in the end, recognize the
ultimate equivalence of all the time variables. The man in the
airport could measure all the various velocities with the same
watch, and so can the scientist computing the unified field. When
physics understands how all these fields superimpose, it will be
able to simplify its equations back down to x. y, z, t. It can do
this because all the t's are equivalent. Once again, the total
physical field, in the presence of eight degrees of linear and
angular acceleration, would be A = Δx, Δy, Δz/Δt^{8}.
That is (a maximum of) 8 fields, but only 4 dimensions^{7}.
Some will complain that all
the time variables can't be equivalent due to Relativity. But I
refer them to my airport example once more. In that example we
are studying the field over one interval. In all the maths that
are based on the calculus, including tensor calculus and the math
of Mtheory, we would make that interval an infinitesimal
interval or dt. Relativity can't find any variance at dt or dx,
for the very simple reason that the observer cannot be any
distance away from the phenomena at dx, dt. Notice that in the
airport example we have the walker measuring himself using his
own watch. He is therefore at no distance from the event and the
speed of light has nothing to do with it. The time variables must
be equivalent, both physically and definitionally.
A
reader will have one final question: why Δt^{8}? Might
that be telling us something fundamental about the number of real
accelerations that exist in the universe? Meaning, if
fivedimensional math was used for gravity and electromagnetism,
then shouldn't the (limited) success of 11dimensional math be
telling us we have 8 fundamental accelerations going on
simultaneously, and therefore 8 fundamental force fields?
Maybe. It is possible that we can get to 11 dimensions by adding
spin as a dimension wherever we find it. The spin of the electron
may be caused by one separate force and the spin of the quark may
be caused by another, and so on. Or, some of the accelerations we
already know about may be second or thirddegree accelerations.
No one has ever considered the possibility that the strong force
or E/M may be Δx/Δt^{3} instead of Δx/Δt^{2}.
But before we run off pellmell in search of some giant equations
to express this, I think we should back up a bit and reassess the
entire road to how we got here. In this paper I have shown that
string theory is criminally confused about almost everything.
Years have been wasted chasing curled up dimensions that don't
even exist. There are no CalabiYau shapes clinging to the
corners of x, y, z. The orbifolding and all the rest was just
mental masturbation. The string theorists have invented shapes
and folds and histories and ancestries for these pillbugs nesting
in the crannies, and now they find they are completely
uninfested. Like some nefarious chemical company, they have
soaked the foundations of the communal house in order to roust
out the bugs, and now we find that we are all poisoned.
I think it is time to declare that string theory is worthy of a
Superfund site and move into a new house. In this house our first
order of business is in truly understanding the physical heritage
that has come down to us. I have shown in my various papers that
there is plenty of work to do in this regard. All the misguided
theorists of the past century have quite simply been wrong when
they stated, with maximum hubris, that classical and quantum
physics was over. Neither classical nor quantum physics is
anywhere near finished. We have only touched the surface, even
regarding linear maths and "poolball" mechanics. Post
quantum theories, whatever they are, will never be possible until
QED is corrected and filled out. And QED will never be corrected
and filled out until some of the elementary concepts I have spent
such a vast amount of time exploring are better understood. Until
we understand how our maths are working we can never hope to
understand how the universe is working. And this is only the
beginning. Velocity, acceleration, circular motion, rate of
change, and many other basic physical concepts are not understood
to this day. All our physical "knowledge" is dominated
by heuristics. Whether we are studying quantum interaction,
orbits, or cosmological origins, our equations are overwhelmed by
nescience. The best thing to do in this situation is admit the
fact and get to work. A primary
piece of this work will be in reestablishing QED without the
point particle. One of the only places I agree with string theory
is in its critique of the point particle. Quantum math was never
able to express its field using an extended particle. String
theory realized the problem here and the need to correct it, but
it only corrected it by burying it below the Planck limit where
no one can see it. In this way the point is given extension, but
the extension is only another postulate. Postulate #5 or so: the
loop has extension but it is so small that 1) it can't be
detected physically, 2) it can't be detected mathematically.
Therefore we can fudge over it by misusing the calculus for the
millionth time. To my mind this is not a great advance over QED.
The only solution is to return to the beginning of QED and start
over. We have a lot of very useful heuristics that we can use to
guide us, and lots of experimental data. But the math needs a
thorough cleaning. The place to begin is in a better
understanding of the calculus. Establishing the calculus on the
constant differential instead of the diminishing differential
will change every physical and mathematical concept of the last
300 years, and will impact all our theories of motion, force, and
action. Only once we have rebuilt the old theories from the
ground up can we begin counting the force fields and dimensions
we will need for a unified math. We may find that we need 11
dimensions. But we may not. We may find that the house looks very
different after we have cleared away all the garbage.
Part III
Conclusion
I
will end by analyzing a short quote by David Gross, which I also
steal from Greene's book. "It used to be that as we were
climbing the mountain of nature the experimentalists would lead
the way. We lazy theorists would lag behind. . . . We all long
for the return of those days. But we theorists might have to take
the lead. This is a much more lonely enterprise."^{8}
You can almost hear the violins. Those poor putupon theorists,
saving us from the past, leading us bravely into the future. I am
not an experimentalist, but when I read this quote my eyes rolled
so far back in my head I nearly broke into St. Vitus' dance. The
dishonesty literally pours off the page. The string theorist
pretending to be an unwilling leader, a humble servant. When in
fact he is little more than a shallow revolutionary, a completely
monomaniacal, delusional person who has convinced himself that by
hoodwinking us he has done us some great favor. Salesmanship
posing as magnanimity. I think
you can tell by the tone of this paper that I am angry at string
theory, and I don't deny it. The last century would try any
honest person's patience, in any number of fields. In my opinion
we are past the point of a mild rebuke. The physics department
needs a good kick in the pants, and the math department too. Both
have degenerated nearly past the point of recognition, and they
might as well join up with the art department and begin putting
on Daliesque plays and masked balls. I had hoped that QED would
someday develop some humility and that we, as physicists, would
get back to work. That we would recognize the huge gaps in our
theories, going all the way back to Euclid, and make some effort
to fill them. Instead young physicists have continued to learn
all the wrong lessons from the recent past and to fail to learn
the mostneeded lessons. What they have taken from QED is only
its Berkeleyan idealism and its intellectual dishonesty. They
have remained buried so far under their esoteric maths that they
cannot see daylight. And they have continued to dig. They are now
at a depth that apparently precludes all cries of logic, all
ropes of humility, all ladders of embarrassment. It seems likely
that they will continue to dig until the air runs out. Or until
they hit the baby black hole at the center of the earth, and the
selfcreated chasm at the center of their own theory sucks them
into a wellearned hell.
^{1}The
Elegant Universe, p. 123. ^{2}Ibid,
p. 111. ^{3}Ibid,
p. 311. ^{4}Ibid,
p. 151. ^{5}Ibid,
p. 152. ^{6}Ibid,
p. 158. ^{7}In
fact, it is only three dimensions, since time is operationally
just a second measurement of one of the others. See my paper on
time for a clarification of this
assertion. ^{8}The
Elegant Universe, p. 214.
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