Blog Ekkehard Friebe

Nachstehend bringe ich einen weiteren Beitrag von Miles Mathis.

Quelle: http://milesmathis.com/death.html

Zitat:

Death by Mathematics
by Miles Mathis 

In the 20th century, physics underwent a transformation. No one would deny that. But normally the transformation is credited to Relativity and Quantum Mechanics. And normally the transformation is seen as a great advance. In this paper I will argue the opposite. The transformation was due more to a transformation in mathematics, and that transformation has been almost wholly deleterious.

This transformation due to mathematics began in the 19th century, but it did not engulf physics until the 20th century. In the 19th century the stage was set: we had several abstract mathematical fields that reached „fruition“, including a math based on action variables and principles, a math based on curved space, a math based on matrices, a math based on tensors, a math based on i, and a math based on infinities.

As I have shown, 19th century mathematics inherited many unsolved problems from the past, including problems from Euclid and Newton. It made no progress in solving these problems because it did not recognize them as problems. It had already given up on foundational questions as „metaphysics“, and it preferred instead to create more and more abstract systems. The more abstract the mathematical system became, the more successful it could be in avoiding foundational questions.

The clearest example of this is the field of applied mathematics based on action variables. For the last hundred years we have heard an ever-increasing level of praise of action variables, culminating in the propaganda of Feynman. But action variables are just an abstraction of Newtonian variables. By abstraction, I mean that they do not add clarity, they cloak disclarity. Newtonian variables were never very rigorously defined, but action variables are very good at hiding Newtonian variables. Action variables do not replace Newtonian variables, as some appear to think. Action variables contain Newtonian variables. Action variables restate Newtonian variables in what is considered to be a more efficient form. But action variables are utterly dependent on Newtonian variables. If it were discovered that Newtonian variables were false, action variables would be, too, by definition. The action concept developed directly out of Newtonian mechanics, and action assumes the absolute validity of Newtonian mechanics. Action does not transcend Newton in any conceivable way, it only compresses his method. Just as velocity is a compression of distance and time, the Lagrangian is a compression of kinetic and potential energy. Each compression is a mathematical abstraction, because the individual variables are no longer expressed singly. They often do not appear in the equations at all. They are included only a parts of greater variables.

From an engineering standpoint, this is a real advance. As long as the greater variables express the changes of the individual variables in the right way, abstract systems like this can save a lot of time. But from a theoretical standpoint, abstract mathematics can be a great danger. Since the individual variables are no longer in the equations, it becomes much more difficult to see when they are being misused. Abstract mathematics must assume that all its original assumptions are applying with each new application, and with many new applications this may not be so. If time and distance are not behaving in normal ways, then the equations have no way of correcting for that, since they don’t have any way to express it. The equations rely on original definitions and assignments, and modern mathematicians and physicists do not usually bother to check to be sure that all these definitions and assignments hold for each new application. They don’t do this for two reasons. One, they often don’t know what the original definitions and assignments were. The mathematical systems are taught as abstract systems, where foundations are considered to be moveable. In the case of the Lagrangian, for instance, we are taught that the variables are general coordinates that we can apply to almost anything. Well, this is true to only a limited degree, and the limits have been ignored. Two, definitions and variable assignments are considered to be metaphysical, and therefore beneath the notice of mathematicians and scientists. Modern scientists cannot be bothered to look at foundational questions, since math is only the equations themselves. If you have mastered the manipulations, you have mastered the math, they think.

To be very clear, it is not action variables I object to. What I object to is their misuse. They are misused when they are applied to systems that do not match the time and distance assignments they were created for. I also object to the implied superiority of action variables. They are very efficient in some uses. But because they are abstract, they are prone to misuse. In this way they are actually inferior. They are inferior because they are less transparent than Newtonian variables. Newtonian variables are not always transparent either, but action variables are always less transparent. Action variables are the first cloaking of physics. And in some cases this cloaking is not an accident. Action variables and the math surrounding action is not always used to generate efficient solutions in familiar situations. It is now often used to blanket over holes in theory or math. Like many other mathematical systems, it is now used to mask purposeful fudges.

The next mathematical system that invaded physics is that of Gauss and Riemann, invading through the door of General Relativity. This was really the first major invasion, and the most important. Up until then, physicists had been wary of allowing mathematicians to define their fields, especially with the new abstract systems. The action principle had not yet invaded physics on a full scale, and would not until the arrival of quantum mechanics. Einstein himself was very wary of abstract math, purposely avoiding it until 1912. Put simply, he „did not trust it.“ But in that year he discovered Gauss, and called on his friend Grossman to help him with the math. A couple of years later Einstein was hired in Berlin, and there he got even better help, from Hilbert and Klein, no less. Einstein had asked the wolf in at the front door.

I don’t think it is an accident or coincidence that the first thing the wolf tried to do is take over the house. Hilbert, after schooling Einstein on all the latest techniques, tried to beat Einstein to the punch by publishing the theory of General Relativity two weeks before him. He didn’t succeed in this dastardly trick, but amazingly history has not held it against him. Einstein quickly forgave him, and now Hilbert is treated as the greatest mathematician of the 20th century. But to me, this incident perfectly presaged the way the 20th century would go. The mathematics department, invited to consult, would see its opportunity to steal the show, and it has since stolen the show. Someone like Feynman could throw barbs at the math department, but this was only misdirection. The top mathematicians could look back over their shoulder in feigned opposition, only because they had already taken over the physics department. Feynman was not smirking at mathematics, he was smirking at mathematicians who were too narrow to crossover and become famous, like he had. It was as if to say, “We now own physics, the queen of the sciences and the modern kingmaker, and you guys prefer to argue over trivialities like Fermat. That will never win you a Nobel Prize or a trip to the White House.”

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Contrary to what we are told, contemporary physics is not booming. It is not very near to omniscience, it is not the crown jewel of anything. In fact, it is near death. It has been damaged by any number of things, only a few of which I have mentioned by name here. But the prime murderer has been abstract mathematics. Physics has succumbed to a suffocation. It is the victim of a strangulation. It is in a not-so-shallow grave, and piled on top of it like dirt are a thousand fields and operators and variables and names and spaces and terms and eigenvalues and dimensions and criteria and functions and coordinates and conjugates and bases and bijective maps and automorphism groups and abelian gauge fields and Dirac spinors and Feynman diagrams so on ad nauseum. The only way the grave could be any deeper and darker, in fact, is if we allowed Deconstruction to dump its transfinite dictionary of onanic terms on top of this one.

The only road out of this grave is to start digging in the upwards direction, clearing away all this schist. The sort of math that physics requires is a math of rigorous definitions and transparent variables, with as little abstraction as possible. We don’t need spaces of infinite dimensions, since we don’t have infinite physical dimensions. We don’t need abstract operators, we need direct representation of motions and entities. Taking the advice of Thoreau, we must „simplify, simplify, simplify.“ That is our only hope of a Unified Field and a mechanical explanation of the universe.

(Zitatende)

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Beste Grüße Ekkehard Friebe