return to homepage The Disproof of by Miles Mathis
Abstract: Here I will show the mathematical flaws in the Landau equation, proving that the equation is a ghost. Then I will critique David Gross' Nobel Lecture, showing the simple flaw in his derivation of asymptotic freedom. This will bring down two more of the towers of QCD. Most people (even most physicists) don’t know what asymptotic freedom is, but since three men—David Gross, David Politzer and Frank Wilczek—won the Nobel Prize for it in 2004, it is best we give it a look. Asymptotic freedom is said to have revivified or rehabilitated particle physics, bringing it back from an abyss it faced in 1973. That is the year these men did their work, although they waited 31 years for their prizes. This abyss was an abyss in quantum chromodynamics, or the field in physics that deals mostly with quark interactions inside the nucleus. The problem was with the strong force, in which quarks must play their part. The strong force was proposed to overcome the charge force on the positive protons. Protons exist in the nucleus at very close quarters, despite having a strong repulsion. Therefore it was proposed that an opposite force overwhelmed the charge repulsion. This is the strong force. The problem was, to make this strong force work, it had to change very rapidly. That is, it turned on only at nuclear distances, but turned off at the distance of the first orbiting electron. The strong force is an attraction, and we couldn’t have it affecting electrons. Because the field had to change so rapidly (have such high flux), it had to get extremely strong at even smaller distances. Logically, if it got weaker so fast at greater distances, it had to get stronger very fast at smaller distances. In fact, according to the equations, it would approach infinity at the size of the quark. This didn’t work in QCD, since the quarks needed their freedom. They could not be nearly infinitely bound, since this force would not agree with accelerator experiments. Quarks that were infinitely bound could not break up into mesons, for a start. This problem existed for less than a decade before it was said to be solved. It was solved by proposing asymptotic freedom—which is a short way of saying that the math was pushed. Here is how the math was pushed. First, we take the strong force and its flux as given. We have no direct proof of this field—it is only a postulate—but we assume that our assumptions are correct. In order to calculate the flux, we must calculate how the energy of the field approaches the upper limit. This upper limit then becomes an 1/ e = (N/6π^{2}^{2})ln(Λ/m_{R})I won’t bother you with the right side of this equation yet, since the largest problem is on the left side. What we have here is a value for I could begin my critique of all this by reminding my reader that renormalization is heuristics. Even Richard Feynman, the master of renormalization and inventor of much of it, admitted that, calling it hocus-pocus. The renormalized charge here is just a charge that has been pushed to match experiment. But even if we accept that renormalized math is genuine, one of our charge values here must be wrong. In any given experiment, the electron has one and only one charge, so that either Some will say that I have misunderstood the terms. They will say the bare charge In reality, math like this cannot tell us anything about a limit or a pole or a maximum energy. If you subtract an incorrect value for a charge from a correct value for that same charge, the only information you can get is information about your margin of error. You can tell how wrong one of your maths is. But you can’t tell anything about the flux of any field. Landau’s math is complete and utter bollocks, nothing less. As more proof of this, look at the 1 e_{R}/^{2}e = ^{2}e_{R}(N/6π^{2 }^{2})ln(Λ/m_{R})If e_{R}/^{2}e cannot be greater than 1 or less than zero. If N = 4, and we set the value of ^{2}e_{R}at 1, then the natural log of the velocity must have values between 0 and 14.8. With a natural log of 14.8, the velocity would have to have a numerical value of 2.68 million. Lower values for ^{2 }e_{R} will raise the value of the natural log, and therefore the velocity. For instance, if we measure velocity in meters per second, the charge on the electron must be very much smaller than 1. It must be around 10^{2}^{-19}. This increases the natural log to around 10^{20}, making the velocity e^{100000000000000000000}. Let us say the bare charge and effective charge diverge so that one is double the other. This makes the left side ½, which lowers the natural log to 10 Again, my critics will say that I have pulled this velocity out of my hat. Landau’s equation has no velocity in it. He never assigns the maximum momentum Λ to the electron itself, therefore I cannot assign the velocity to the electron. But again, Landau and current theory are wrong. Landau has the electron represented on both sides of the equation, as charges on the left side and as mass on the right side. This means the momentum variable will automatically assign itself to the electron. Landau may mean to assign it to the field or to another entity, but his intentions mean nothing to the numbers. The way the equation is written, that momentum must attach to the electron, giving us a velocity by the equation p = mv, so that p/m must equal v. Since that velocity has a limit, the charges must have limits that Landau and the standard model have never seen. Even some mathematical physicists, using the same tricks as Landau and Gross, have come to the conclusion that something is wrong with the Landau pole. In the late ‘90’s, there was a well-known “Landau pole problem” that made the pages of several journals. In one of them, the physicists claimed that, “A detailed study of the relation between bare and renormalized quantities reveals that the Landau pole lies in a region of parameter space which is made inaccessible by spontaneous chiral symmetry breaking.” Gaps between renormalized values cannot yield energy limits, but Gross took this math of Feynman and Landau as bedrock. He accepted the Landau pole as legitimate, and using this math he calculated a Landau pole for QCD. This pole was way too high, so he needed a fix. He needed to lower that pole by a large margin. How did he do that? Well, with a lot more fudgy equations, of course. But under the equations lay the idea of The idea of color confuses this analysis somewhat, and it is easier to understand screening by looking at the screening in QED. In QED the vacuum is composed of positron-electron virtual pairs. As a real electron interacts with the vacuum, the virtual pair shows its positive face, attracting the electron even more. So in QED, this mechanism is used to explain the opposite phenomenon. In QED, we have screening, and in QCD we have anti-screening. In QED, the electron is attracted to the vacuum itself. This is said to solve other problems I don’t have time to address here. What is wrong with this explanation? Many things. We start with the fact that neither gluons nor quarks have ever been seen, or tracked singly in accelerators. Neither have virtual particles. Nor has color. Color has never even been We also have a bald contradiction and But the basic problem is that we have an equally clear But to be consistent, we must then look at the flux of the anti-screening gluon field. The standard model is sick of this stuff, so it just decides to go virtual at this point, dodging all further questions. But if the flux of the strong force was a problem, the flux of the anti-screening gluon field must be a similar problem. Gluons switch from attractive to repulsive over an even smaller area, so they must have greater flux. Gluons are called gluons because they are the “glue” of the hadrons, and glue is an attraction. But in anti-screening, they switch to repulsive. Therefore, we have a repulsive field underneath the strong force, and this force must have greater flux than the attractive strong force. In which case we need a fix for that also, so that QCD answers this by throwing up its hands and saying, “We are beneath the Planck length now, and we refuse to answer any more questions!” But the problem is not one of size, it is one of logic. QED and QCD keep fixing problems in existing fields and particles by proposing sub-fields and sub-particles. But they try to do this by dodging mechanics. Instead of fixing the mechanical hole in the E/M field, they drive around that hole and build another sub-field. That is, instead of showing how charge is created mechanically, they propose the strong force, to counteract charge. Instead of showing how the strong force is created mechanically, they propose anti-screening, to counteract it. But I have shown that if you build the E/M field with the right mechanics, you don’t need the strong force. And if you have no strong force, you don’t need asymptotic freedom to fix it. If you get your first field right, you don’t need an infinite regression of sub-fields to fix your errors. We don’t need all this illogical math and theory, since we can fix the E/M field with simple and logical postulates. We don’t need to renormalize our equations: we need a theory that gives us normal equations to start with. With these normal equations and postulates, we don’t need an infinite regression of repairs. To be specific, many have interpreted asymptotic freedom as giving us a field like a rubber band, The answer to this question is that the strong force needed to be inverted in order to make it change like the E/M field is changing. The physicists think they are measuring strong forces between quarks, but they are actually measuring stacked spins on the baryon, and gravitational-E/M forces percolating through the spins. They therefore have to invert the flux to make the strong field change like the E/M field. They have to make their theoretical field change like the real field, even though an attractive field cannot possibly increase with distance. There is no strong force, so it has to be reversed. Reversed, it magically has the same flux as the E/M field it inhabits, while having the opposite sign! This gives them a force field that acts non-mechanically and illogically, but it at least allows them to keep their strong force. But, as I hope you can see, it is much simpler to assign the reversed flux to a repulsive E/M field, which it fits. Then you can explain attractions as weaker E/M fields, instead of more powerful strong fields. You don’t need finessed math to explain the inversion of the field, you just need a theoretical clean-up. An asymptotically free strong field mirrors the E/M field because it IS the E/M field. The strong force is just a subset of the Unified Field, and does not exist as a separate or separable field. For instance, in 1964 Vanyashin and Teren’tev calculated the charge renormalization of vector mesons, getting the opposite sign they expected. The field flux was reversed, according to their math. They thought there was something wrong with the math. Quantum physicists now explain the sign with asymptotic freedom. But the real answer is that the vector mesons were not traveling in a field of “strong” vectors or potentials: they were traveling in a field of potentials created by gravity-E/M—a field of real As one final proof against asymptotic freedom, let us look at the math, such as it is. It should be a matter of interest that Gross had published, only a year earlier, and using very similar math, “a proof that no renormalizable field theory that consisted of theories with arbitrary Yukawa, scalar, or Abelian gauge interactions could be asymptotically free.” [Coleman and Gross, 1973.] No one had shown this proof was wrong, but nonetheless Gross could see that the need in quantum physics for asymptotic freedom was greater than the need for proofs against it. QCD wanted asymptotic freedom, and Gross planned to supply it. He would change his course in any way required in order to supply it. If Abelian gauge theories were necessarily non-asymptotically free, he would pursue non-Abelian gauge theories. But all this talk of gauge theories is misdirection, as Gross proves in his Nobel Lecture, where he supplies “the arithmetic”: The contribution to Gross then tacks on the formula for the beta function of the non-Abelian gauge theory, but that is just window dressing. You can see that he has already given us the math and the explanation, with simple arithmetic! To begin with, notice the odd language here after the math. “In any case, the upshot is. . . .” I was struck by that the first time I read it. “In any case” is not applicable here, since Gross is not supposed to be giving us an example or a suggestion, he is giving us famous math. It is highly irregular to follow a mathematical proof with “in any case,” as if all this is perhaps beside the point. “The upshot is” is also odd phrasing. We find nothing else like it in this lecture. As one would expect with a Nobel Lecture, this paper is not breezy and informal. It appears that Gross is subconsciously attempting to hurry us past this math, and trying not to put too much emphasis on it. Why? Because he has just told two whopping lies and put them in full view. He is afraid someone might notice this, but he can’t help but tell the lies anyway. Both lies happen to reside in the sentence immediately preceding “In any case.” The first lie is the last equation. The second lie is that the “minus sign arises because quarks are fermions.” I would hurry past that, too, if I were Gross. The whole proof relies on it, and it is known historically that he and his colleagues changed the sign right at the end. At first they had the “wrong” sign, and then they changed it. This is a well-known part of the story, since Politzer claims to have gotten it right the first time (and claims special recognition for that). But we are dealing with spins and charges here, as you see. The final equations are 11/3 This is crucial, since that minus sign decides, by itself, the asymptotic freedom of the field. It has to be the opposite sign of the gluons, so that the anti-screening of the gluons can counteract the screening of the quarks. If both signs are the same, we have no anti-screening and no freedom. Gross himself has proved my point, in his own Nobel Lecture. As I have said before, physicists don’t know when to shut up. It was a magnificent blunder for Gross to publish this simple math, since it put the lie in high focus. It would have been much better for him to continue to hide behind the beta function and the gauge fields, which provided some cover. But his Prize made him overconfident. Like a criminal who has dug up the loot after three decades, Gross couldn’t help bragging. He has unmasked himself. As a closer, I will draw your attention to the fact that people are now being given Nobel Prizes in physics without doing any physics. As I have proved, what Gross, Wilczek and Politzer did was bad math, not physics. Physics is supposed to be “physical,” which means material and mechanical. Non-mechanical theories and mathematics are not physical. Virtual particles are not physical: if they were, there would be no need to call them “virtual.” The Landau pole is not physical, since it is found by applying a mathematical margin of error to a problem, and claiming to have developed a number that can be applied to a momentum. But a momentum cannot be derived from a margin of error. That is like saying that you can manufacture a leprechaun from a bag of leap-years. It is mathematical alchemy of the most ridiculous sort. Not only did these guys fail to do any physics, they failed to do any real math. They did only ghost-physics and ghost-math. They created a problem with ugly math, defined it with uglier math, and solved it with even uglier math. Ironically, each math created more problems than it solved. Math and science are supposed to solve problems, but ghost-math and ghost physics do the opposite. Each ghost spawns at least two more ghosts. This is great for job-creation, but terrible for anyone who desires a meaningful or physical explanation. The 2008 Nobel Prize for physics was awarded to three more physicists working on basically the same problem. Yoichiro Nambu, Makoto Kobayashi, and Toshihide Maskawa won for their work on spontaneously broken symmetry. In my paper on QCD, I show that spontaneously broken symmetry is more awful theory and math, so the prize is once again being awarded to fake physicists. Since there are no quarks, giving prizes to quark physicists is like giving prizes to fairy spotters. Also take note that the Nobel physics committee can't seem to find any real physicists to honor. Although physics is an astonishingly broad field, it appears to be winding down. The Nobel Committee keeps returning to the same narrow sub-field, and we may assume that this is because that sub-field, QCD, has benefitted from the most promotion in the past several decades. As with Hollywood, physics is now mainly PR, and the Nobel Prize is simply the capstone in the long public relations campaign, the Oscar of physics.
^{1Göckeler et. al., arXiv:hep-th/9712244v1
2See my paper on screening.
3http://pr.caltech.edu/periodicals/CaltechNews/articles/v38/asymptotic.html
}
If this paper was useful to you in any way, please consider donating a dollar (or more) to the SAVE THE ARTISTS FOUNDATION. This will allow me to continue writing these "unpublishable" things. Don't be confused by paying Melisa Smith--that is just one of my many |