- Brouwer's "hair ball theorem" does not apply. The bound electron current is not a continuous vector field in the sense of this theorem. It is comprised of independent current loops with different densities and angular momentum vector directions that superimpose on the surface to comprise a continuous uniform current density having identical angular velocity and linear velocity magnitude at each spatial position per mass (charge) density, and the angular momentum projections give rise to all the of phenomenon of electron spin. The analytical and computational results are given in Chp 1:and the uniformity and angular momentum projections of the analytical derivations are numerically proven by the computer program (H Distribution Renderer) posted atOn Oct 21, 2011, at 2:20 PM, wedgevw wrote:--- In SocietyforClassicalPhysics@yahoogroups.com, amack43 <no_reply@...> wrote:It is interesting to me that however much I test Classical Physics' conclusions, nothing so far leaps out as being directly opposed by indisputable evidence...What about the fact as I pointed out in an earlier post, that a continuous nonzero vector field on a sphere violates Brouwer's "Hairy ball theorem".I know John doesn't want to see a big pro and con discussion of it, but it is a well established theorem and directly contradicts the Hydrino model. Doesn't that bother anyone?{Note from John Farrell, Moderator.It doesn’t bother me that someone says that “it (the Hairy Ball Theorem) is well established and directly contradicts the Hydrino model”. In part, I show my ignorance here. First, I don’t understand the Hairy Ball Theorem. Second, I don’t see how it contradicts the hydrino model. Beyond my ignorance, apparent contradictions often offer the opportunity to improve the model. After all, numerous people have told me that there cannot be sub n = 1 states for atomic hydrogen because it violates the Schrodinger equation. Who cares if hydrinos violate the Schrodinger equation? Certainly not me! Mills has the physical evidence that hydrinos exist (EUV spectra, dark matter emissions, NMR signatures, and so on). If this sort of evidence can be contradicted or interpreted in a different fashion, fine, I’ll take a look at it. But the “it violates the Schrodinger equation” routine simply goes in one ear and out the other.Consider the fact that the Big Bang theory maintains that the universe began with a big bang. Most reasonably educated persons realize that the velocity of the particles in the universe would be greatest at the moment of the bang (or very shortly thereafter) and that the velocity of the particles would slow as time goes on (not to mention 14 billion years later!). Now, it turns out that Mills thinks that this theory is incorrect and he shows, with his theory, that the rate of expansion of the universe was zero at the beginning, that the expansion slowly accelerates, reaches a maximum, and after 500 billion years, or so, the rate of expansion returns to zero. He publishes his theory. Later, experiments show that the rate of expansion of the universe is accelerating, not slowing. (I believe it has also been shown that the rate of expansion 14 billion years ago was close to zero but I don’t think there has been agreement on the interpretation of this evidence.) That is, Mills was right. What happens next? Something unbelievable! Before the ink is dry on the report of the accelerating universe, scientists are modifying the big bang theory by calling into existence “dark energy” as an explanation. I don’t blame them for this. Quite the contrary, it is what scientists do! After all, science is not about what we know—science is about what we do not know. But it does seem to me that some scientists ought to be paying a little attention to another scientist (Mills) who has made several startling predictions which have turned out to be correct. Maybe he is just the luckiest guy to come along in a long time. Or, maybe, just maybe, the Schrodinger equation and the Big Bang Theory were “almost” right.It is true—I don’t want to see an extended discussion of the Hairy Ball Theorem. We had a lengthy discussion about the electron-electron repulsion of the “pieces” of matter and charge that comprise the electric currents on the orbitsphere. It was not productive. Clearly, the orbitsphere does not self-explode from such repulsions. I came to two conclusions about those discussions at the time. First, Mills does not simply have a new theory—he is creating a new mechanics—a way of understanding matter and energy and their interactions—mathematically and conceptually. Second, the detractors will eventually recognize that we are beyond the “Aha! Moment” whereby the theory will be shown to be incorrect because of a failure to explain (or in their mind, correctly explain) some phenomenon. There are aspects of Mills’ theory that may be modified but too much has been verified to deny its overall validity.Finally, lest anyone is inclined to misinterpret this note, I am always interested in experimental evidence. To me, experimental evidence always trumps theory (one has to keep in mind, of course, that experiments can be misinterpreted). Fortunately, there have been many great scientists—physicists, chemists, astronomers, biologists, geologists, and so on. They should be forever remembered and cherished for their contributions and creativity. But their equations and ideas are always open to modification. I am certain that Newton, Maxwell, and Einstein would agree.So, if anyone understands the Hairy Ball Theorem chime in. If you have the time to learn about the Hairy Ball Theorem, go right ahead and chime in when you are ready. However, I give one warning. In the Wikipedia explanation of the Hairy Ball Theorem it gives a section on Cyclone Consequence. I give one sentence from that section below:“In a physical sense, this zero-wind point will be the eye of a cyclone or anticyclone. (Like the swirled hairs on the tennis ball, the wind will spiral around this zero-wind point - under our assumptions it cannot flow into or out of the point.) In brief, then, the Hairy Ball Theorem dictates that, given at least some wind on Earth, there must at all times be a cyclone somewhere.”As far as I know, there are times when there is wind on Earth but there is no cyclone. Does this mean that the Hairy Ball Theorem is incorrect? Does this mean that cyclones can be so small that no one knows they are there? Or, am I once again showing my ignorance?}------------------------------------Yahoo! Groups Links<*> To visit your group on the web, go to:<*> Your email settings:Individual Email | Traditional<*> To change settings online go to:(Yahoo! 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- --- In SocietyforClassicalPhysics@yahoogroups.com, "Luke" <luthersetzer@...> wrote:
>

The "Hairy Ball" theorem says you can't have a continuous non-zero vector field on a sphere. It doesn't say you can't have a vector field on a sphere, just that such a vector field must either be discontinuous somewhere or zero somewhere. I assume the principle of superposition is valid, so that at any time and any point on the orbitsphere, you have a resultant vector, yielding a vector field. This represents a problem for the orbitsphere unless one of these three conditions are met:

> --- In SocietyforClassicalPhysics@yahoogroups.com, "wedgevw" <kurtz@> wrote:

>

> << I know John doesn't want to see a big pro and con discussion of it, but it is a well established theorem and directly contradicts the Hydrino model. Doesn't that bother anyone?

>

> {Note from John Farrell, Moderator.

> It doesn't bother me that someone says that "it (the Hairy Ball Theorem) is well established and directly contradicts the Hydrino model." In part, I show my ignorance here. First, I don't understand the Hairy Ball Theorem. Second, I don't see how it contradicts the hydrino model. >>

>

> It is my understanding that the current loops of the orbitsphere act as superconducting currents. One unique and experimentally proven aspect of such currents is that they can physically pass through each other. So the cited theorem would seem to have limits surpassed by the nature of superconductivity. At least, that is how someone who interned at BLP explained it to me.

>

> Luke Setzer

>

1. The principle of superposition somehow doesn't apply. I don't know if Luke's comments above suggest that.

2. It is OK for the vector field to be discontinuous.

3. It is OK for the vector field, and hence the resultant current, to be zero at a point (the location of which may vary with time).

If Dr. Mills would clarify that any one of these three conditions is not a problem, then I will agree that the "Hairy Ball" theorem is not a problem. Otherwise it is.

--Lynn

[Note to the Moderator not meant to be part of the post]: John, thank you for allowing my previous post and, hopefully this one. It will be my last post on this subject. I hope Dr. Mills will respond.

Regarding Wikipedia's comment that there would have to be a cyclone somewhere, that is just silly. Any region(s) of calm air nullify the hypotheses. Also, I don't think this issue is comparable to the question of whether equations such as Maxwell's or Shrodinger's model physical reality accurately or need additional tweaking.

Anyway, all the best to you and yours during the upcoming holiday seasons. - In reply to wedgevw's message of Tue, 01 Nov 2011 18:55:22 -0000:

Hi,

My 2 cents:

I suspect that there are 2 zero points, one representing each magnetic pole of

the atom. I further suspect that these poles are continually randomly shifting,

and over time and many atoms average out to zero. Only in an externally applied

magnetic field do they reveal themselves through alignment with the field.

>

Regards,

>

>

>

>

>--- In SocietyforClassicalPhysics@yahoogroups.com, "Luke" <luthersetzer@...> wrote:

>>

>> --- In SocietyforClassicalPhysics@yahoogroups.com, "wedgevw" <kurtz@> wrote:

>>

>> << I know John doesn't want to see a big pro and con discussion of it, but it is a well established theorem and directly contradicts the Hydrino model. Doesn't that bother anyone?

>>

>> {Note from John Farrell, Moderator.

>> It doesn't bother me that someone says that "it (the Hairy Ball Theorem) is well established and directly contradicts the Hydrino model." In part, I show my ignorance here. First, I don't understand the Hairy Ball Theorem. Second, I don't see how it contradicts the hydrino model. >>

>>

>> It is my understanding that the current loops of the orbitsphere act as superconducting currents. One unique and experimentally proven aspect of such currents is that they can physically pass through each other. So the cited theorem would seem to have limits surpassed by the nature of superconductivity. At least, that is how someone who interned at BLP explained it to me.

>>

>> Luke Setzer

>>

>

>The "Hairy Ball" theorem says you can't have a continuous non-zero vector field on a sphere. It doesn't say you can't have a vector field on a sphere, just that such a vector field must either be discontinuous somewhere or zero somewhere. I assume the principle of superposition is valid, so that at any time and any point on the orbitsphere, you have a resultant vector, yielding a vector field. This represents a problem for the orbitsphere unless one of these three conditions are met:

>

>1. The principle of superposition somehow doesn't apply. I don't know if Luke's comments above suggest that.

>

>2. It is OK for the vector field to be discontinuous.

>

>3. It is OK for the vector field, and hence the resultant current, to be zero at a point (the location of which may vary with time).

>

>If Dr. Mills would clarify that any one of these three conditions is not a problem, then I will agree that the "Hairy Ball" theorem is not a problem. Otherwise it is.

>

>--Lynn

>

>[Note to the Moderator not meant to be part of the post]: John, thank you for allowing my previous post and, hopefully this one. It will be my last post on this subject. I hope Dr. Mills will respond.

>

>Regarding Wikipedia's comment that there would have to be a cyclone somewhere, that is just silly. Any region(s) of calm air nullify the hypotheses. Also, I don't think this issue is comparable to the question of whether equations such as Maxwell's or Shrodinger's model physical reality accurately or need additional tweaking.

>

>Anyway, all the best to you and yours during the upcoming holiday seasons.

>

>

Robin van Spaandonk

http://rvanspaa.freehostia.com/project.html