A reader has pointed out that The Guardian, a British leftwing daily, is promoting the theory and industry (power plants) based on the "hydrinos" invented by Randell Mills, a Harvardtrained medical doctor, and investigated by a "hardy band of scientists", as the newspaper calls the undereducated or corrupt humans who believe this stuff. Hydrinos are supposed to be small versions of the Hydrogen atom. No muons are involved; indeed, Mills also wants to kill the uncertainty principle. Forget your 143a Quantum Mechanics I as well as billions of experiments that confirm it in detail.
Instead of the muons, the theory underlying Mills' activities is based on the assumption that quantum mechanics should be replaced by the socalled "Grand Unified Theory of classical quantum mechanics"; and that we should also abandon the Big Bang theory. Randell Mills is no small fish among the crackpots. By 2000, he had collected 25 million USD for his "BlackLight Power Inc." company. He has actually built a factory and no doubt, his banking account is much richer today.
How much energy does Mills get, according to his own words? He can get 1000 times more than the conventional fuels, he says. Also, Mills has demonstrated that he is able to multiply "2 times 13.6 electronvolts". He obtained 27.2 electronvolts. He argues that his "catalysts" absorb 27.2 electronvolts from the Hydrogen that is becoming a hydrino.
In 2000, Mills also promised to fill California with hydrino plasma cars. He claimed that he had make breakthroughs in artificial intelligence, cosmology, medicine, and gravitational jujitsu.
50 million dollars or so is a lot of money, and actually there are many other people who earned big amounts of money by promoting the crackpot in his early stages. This list includes John Farrell who was a department chair of a Pennsylvania college when Mills was a student there. You must wonder  how much money did the comrades in The Guardian  especially Alok Jha  receive for this particular article that will undoubtedly attract new money from the undereducated rich people and undereducated managers of various companies? Apparently, this big scale crime is completely legal.
Well, if the flows of tens of millions of dollars are supported by huge amounts of human stupidity, everything is legal. Many people apparently believe that the existence of the 13.6 eV ground state of the Hydrogen atom is just an invention of "big oil energy mafia's scientific inquisition" and others have been convinced that "your chemistry teachers turned out be wrong". It is not hard to make statistics among the blogs writing about the issue to conclude that a vast majority of the people are complete ignorants.
Ask Ethan #89: The Universe’s Dark Ages (Synopsis)

“[I]f there were no light in the universe and therefore no creatures with
eyes, we should never know it was dark. Dark would be without meaning.”
–C.S. Lew...
7 hours ago
snail feedback (18) :
Right On, Lubos! But honestly, the multiple vacua thinking seems to allows for this kinda of thing. What is the Hydrino is a false vaccum state generated by breaking some new spin 0 symmetry, something akin to the inverse of the inflaton. I am, of course, kidding, but I find it ironic that stringvangelist like you don't seem to notice the BILLIONS that SUSY/MTheory as absorbed out of the economy with nary a pennie in return!
Dear Lumos,
I’ve followed the link and read the flatearth paper by Dr Mills on “Maxwell’s Equations and QED: Which is Fact and Which is Fiction”. In his abstract, he falsely ridicules the polarisation of the vacuum around real particle cores. He rightly quotes material saying that QED is a mathematical fiddle, but he ignores the fact that heuristic progress can be made with understanding Feynman’s approach.
To summarise, Mills is wrong to rely on Maxwell’s equations and an extended charge distribution to prevent radiation. The reality is that the QED picture of the electron as pictured by the mainstream is on the right lines but has not gone far enough. Mills’ “classical” treatment is false. On my home page I have extensive material on Maxwell’s equations, which are my speciality. Notice that most of the people who work in this area are crackpots who don’t really know QM, unlike me. I know the facts.
Mills falsely assumes that the charge doesn’t radiate. I’ve shown on Woit’s blog that this is false. QED specifies that forces are due to exchange of radiation, an analogy to classical exchange via the Prevost mechanism of 1792. Since electromagnetic forces are continuously acting, so is the exchange of energy by radiation. This radiation physically causes forces. In this sense it is “classical” but it is not “classical” in the sense that Mills means by “classical” (which to him means electrons which don’t radiate, since he hasn’t wit enough to grasp the fact that if every particle in the universe is doing the same thing, there will be an equilibrium of sorts which prevents net loss due to radiation).
Woit a while back blogged that he thought the ultimate laws will be very simple, even more simple than “classical physics”. This is sustained by the facts, which contradict Mills, who is basically doing for QED what Ptolemy did for ancient cosmology, against Aristarchus’ solar system. If the British Government is funding Mills’ horseshit, I give up on physics. However, some of his chemical epicycles may predict the same as standard quantum mechanics, so it is not all going to be completely wrong (just as the epicycles in the earthcentred universe model allowed fairly accurate calculations and predictions to be made). Consider what Feynman rightly says:
Feynman said, in his 1964 Cornell lectures (broadcast on BBC2 in 1965 and published in his book Character of Physical Law, pp. 1713):
'The inexperienced, and crackpots, and people like that, make guesses that are simple, but [with extensive knowledge of the actual facts rather than speculative theories of physics] you can immediately see that they are wrong, so that does not count. ... There will be a degeneration of ideas, just like the degeneration that great explorers feel is occurring when tourists begin moving i on a territory.'
On page 38 of this book, Feynman has a diagram which looks basically like this: >E S<, where E is earth and S is sun. The arrows show the push that causes gravity. This is the LeSage gravity scheme, which I now find Feynman also discusses (without the diagram) in his full Lectures on Physics. He concludes that the mechanism in its form as of 1964 contradicted the noether relativity model and could not make any valid predictions, but finishes off by saying (p. 39):
“'Well,' you say, 'it was a good one, and I got rid of the mathematics for a while. Maybe I could invent a better one.' Maybe you can, because nobody knows the ultimate. But up to today [1964], from the time of Newton, no one has invented another theoretical description of the mathematical machinery behind this law which does not either say the same thing over again, or make the mathematics harder, or predict some wrong phenomena. So there is no model of the theory of gravitation today, other the mathematical form.”
Does this mean Feynman is after physical mechanism, or is happy with the mathematical model? The answer is there on page 578:
“It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities. But ... it is not good to be too prejudiced about these things. “
Best wishes,
Nigel
I do not believe in this hydrino stuff but as I said I will believe it when I see commercial products made of hydrino widely available on the market. That's a findamental difference from Lubos, who believe that consistency with existing theory is much more important than any experimental verification.
My attitude is after all, any existing theory, no matter how solid they seem to be, can be brought to challenge, as long as you can should experimental data, and your data can stand up for scrutiny. The most rigorous scrutiny of experimental result would be the production of commercial products. With billions of computer chips produced based on the theory of QM, you have to believe QM at least for the part that's responsible for solid state devices.
But Big Bang and all it's so called experimental verifications does NOT stand up to careful scrutinies. We will discuss it another time. QM, on another hand, does not seen to be a complete or final theory, nor is it even compatible with the universe we know so far.
Any one who has ever solved a Schrodinger Equation, knows that the wave function either terminates some where, where you place a theoretical "rigid wall" that the wave can not penetrate. Or, absent the rigid walls, the wave will extend to infinity, decaying exponentially when the energy level is negative, or extends as nonedecaying plane wave when the energy level is positive.
However, the universe is neither ininite in size, nor does it contain any rigid wall at its boundary or any where. So the boundary condition of the universe is one that the Schrodinger Equation really do not know how to deal with.
We do not have a QM theory that is compatible with any cosmology we know so far. And that brings us back to the fundamental problem that QM, which computer chips are based on, and GR, which the cosmological models are based on, are incompatible. Both have problems and both needs modification in the correct TOE.
Quantoken
Dear Quantoken,
I don't agree totally where you said: "With billions of computer chips produced based on the theory of QM, you have to believe QM at least for the part that's responsible for solid state devices.
"But Big Bang and all it's so called experimental verifications does NOT stand up to careful scrutinies."
I can't believe that you believe QM made computers. Computers and IC's were developed into successful, real products by people like Dr Arnold Lynch and Ivor Catt, who did not use QM. I'm a fan of QM for chemistry and nuclear physics like alpha decay (quantum tunnelling), but it isn't true semiconductors came from QM. The Cat's whisker was the first semiconductor and was used 20 years before Schroedinger. You find that QM provided ad hoc explanations for semiconductor theory, not a prediction or a recipe for making the technology.
Dr Arnold Lynch, who corresponded with me from 972003 and died in Jan this year, was taught about electron theory by JJ Thomson. He was an experimentalist and electronics engineer and designed part of the first successful digital computer, which used VALVES or as you Americans say VACUUM TUBES. It was called Colossus and cracked German codes, helping the war in Europe. At the same time Lynch was doing that, Catt was a kid in Singapore when the Japanese invaded. He got into electronics because his dad was in the RAF specialising in electronics.
He showed the interconnection of logic and crosstalk problems, see
Catt home page
Notice I've written loads of articles in Electronics World mag about all this, sorting out Catt's theory with help from Dr Lynch and from Dr Walton (a former physics professor). But it is all ignored as crackpot, even though Catt's Kernal machine computer is a better more reliable bet than the similar but less reliable idea being touted in the November 2005 issue of Scientific American. Catt's computer has amazine implications for situations where physical reality can be represented physically as an array by the processor array of the kernel machine: so it can predict more reliably tornadoes, hurricanes, plus prevent air traffic control disasters including terrorism using planes. Notice that the big bang is dismissed irrationally, see Feynman gravity home page
For background on explosion dynamics coverups see How about understanding explosions before dealing with the big bang and gravity? Or is real physics too arcane?
The rest of your comments I agree with.
Best wishes,
Nigel
Feynman gravity blog
Catt had a scholarship to Cambridge, but did electronic engineering, and he writes:
"I entered the computer industry when I joined Ferranti (now ICL) in West Gorton, Manchester, in 1959. I worked on the SIRIUS computer. When the memory was increased from 1,000 words to a maximum of 10,000 words in increments of 3,000 by the addition of three freestanding cabinets, there was trouble when the logic signals from the central processor to freestanding cabinets were all crowded together in a cableform 3 yards long. ... Sirius was the first transistorised machine, and mutual inductance would not have been significant in previous thermionic valve machines...
"In 1964 I went to Motorola to research into the problem of interconnecting very fast (1 ns) logic gates ... we delivered a working partially populated prototype high speed memory of 64 words, 8 bits/word, 20 ns access time. ... I developed theories to use in my work, which are outlined in my IEEE Dec 1967 article (EC16, n6) ... In late 1975, Dr David Walton became acquainted ... I said that a high capacitance capacitor was merely a low capacitance capacitor with more added. Walton then suggested a capacitor was a transmission line. Malcolm Davidson ... said that an RC waveform [Maxwell's continuous "extra current" for the capacitor, the only original insight Maxwell made to EM] should be ... built up from little steps, illustrating the validity of the transmission line model for a capacitor [charging/discharging]. (This model was later published in Wireless World in Dec 78.)"
 Ivor Catt, "Electromagnetic Theory Volume 2", St Albans, 1980, pp. 20715.
I completely agree with Lubos on this one. Indeed Randall Mills tried to recruit me and Fred Alan Wolf into his scam over ten years ago. We refused. To this day I am still bombarded with idiots telling me I am wrong about Mills. It is alleged that Mills has "four exCIA" people on his board. I have not confirmed this rumor.
There is a serious theory by the late J.P. Vigier that is similar to the hydrinos but it is based on real quantum theory in the Bohm interpretation with a spatially extended electron. Maric and Dragic in Beograd were testing it 6 years ago. I can dredge up references if there is an interest.
Are hydrinos thinkable? Is Lubos Motl wrong?
Was I wrong?
Remember Lubos Motl's analysis of hydrinos http://motls.blogspot.com/2005/11/hydrinos.html and Lubos is both a string theorist and a Harvard Man! ;)
On string theory see
http://www.fourmilab.ch/fourmilog/archives/Monthly/2006/200606.html
http://www.fourmilab.ch/fourmilog/archives/Monthly/2006/200603.html
See Robert Laughlin's "A Different Universe" for the history of the Hall effects.
There is something called the quantum Hall effect with integer quantum numbers. Then they discovered the unexpected fractional quantum Hall effect. Is this analogy a good one or is it stupid? http://www.pha.jhu.edu/~qiuym/qhe/qhe.html
Marchese starts with
En =  13.598ev/n^2
Where n is the principal quantum number
n = N + L, n = 1, 2, 3,
L = 0,1, ... n1
N  1 is the number of nodes in the radial wave function.
L is the orbital angular momentum also an integer.
Therefore n = fraction is complete nonsense.
However
13.598 ev =  (Reduced Mass)(Charge)^4/2h^2
So if for example
n = 1/7
That's the wrong way to look at it!
We do not allow h to change.
What if the effective charge is "fractional"?
Well suppose the charge e
e > xe
En > En' = (Reduced Mass)x^4(Charge)^4/h^2n^2 = (Reduced Mass)(Charge)^4/h^2n^2/x^4
n' = n/x^2
So now maybe we are cooking?
It's not important that the effective charge be a simple fraction BTW. All that is important is that x < 1 from some kind of plasma screening effect perhaps since there is an electric permittivity in the denominator as well.
En = 13.598 ev/n^2 =  (Reduced Mass)(Charge)^4/(permittivity)2h^2n^2
I have not had time to think deeply about this, but there may be a connection to the fractional quantum Hall effect, fractional quantum statistics and 2D anyons in surface plasma oscillations? Too soon to know if this crazy intuition is crazy enough to be interesting. WYSIWYG. Prior to this moment these halfbaked thoughts did not exist on this planet.
On Jun 8, 2006, at 6:39 PM, Jack Sarfatti wrote:
Correction he does mention "hydrinos"  am reading it now.
On Jun 8, 2006, at 6:33 PM, Jack Sarfatti wrote:
Marchese and his team have impressive credentials. He has a Princeton Ph.D. However so far I see nothing in his final Phase I report that requires the "hydrinos" of Randall Mills.
http://users.rowan.edu/~marchese/finalniac.pdf
As far as Marchese is concerned one must be completely pragmatic and look at the complicated phenomenon bearing in mind the warnings of Stanford's Robert Laughlin in "A Different Universe."
Rowan was launched with a $100 million grant.
Typo correction, that should be x > 1.
On Jun 8, 2006, at 8:38 PM, art wagner wrote:
Jack, of possible interest: http://xxx.lanl.gov/abs/physics/0507193
Yes, interesting paper but it does not explain Marchese's data I suspect.
J.P. Vigier got hydrinos in NR QM with a spatiallyextended electron as a Bohm hidden variable.
In my theory the Bohm hidden variable microgeon electron's shell of charge is stabilized by an inner core of negative zero point vacuum energy with positive pressure and w = 1. When you hit the electron hard enough it appears to shrink to a point parton from the huge spacewarp induced by the inner ZPF core corresponding to an effective shortrange Salam G* maybe 10^40G. This also can be thought of as a string because of blackholestring duality, but the string is 10^13 cm that shrinks to 10^16 cm for small impact parameters and there is no hierarchy problem. Not sure if this will really work but it's interesting. The old hadronic string theory is brought back and it applies to leptons as well as quarks  the spin 2 is Salam's old fgravity in new clothing.
More details on my theory can be found at
http://www.authorhouse.com/BookStore/ItemDetail.aspx?bookid=23999
There are a lot of other interesting true stories there as well.
Of course the plasma screening scale is probably much larger than the size of the atom so that if there is a real effect here it must involve vacuum polarization. Simplest explanation is that there is no real hydrino effect here. :)
On Jun 9, 2006, at 5:06 AM, Marchese, Anthony J. wrote:
Jack,
Thank you for your interest in my work. As background, my project was funded by NASA to evaluate the propulsion potential of the resonant transfer plasmas reported by Mills. I did not evaluate the theoretical aspect of his work nor am I qualified to do so since I am an aerospace engineer, not a physicist.
I would be as surprised as anybody if his theory turns out to be valid. But, his experimental work has been published in some top peer reviewed journals, and the results show some interesting nonequilibrium plasmas.
Regards,
Anthony

Anthony J. Marchese, Ph.D.
http://users.rowan.edu/~marchese
Thanks, that's exactly what I suspected. Good luck with your interesting experiments. There was similar work going on in Beograd in 2000 by Maric & Dragic, but I think they used a plasma pinch effect as well. Creon Levit at NASA is familiar with the details. I can get more details for you if you like. The Beograd work is based on a real quantum theory by the late JeanPierre Vigier. I suppose Mills hired some competent experimentalists with his $25 million. :)
On Jun 9, 2006, at 3:21 PM, Paul Zielinski wrote:
So Marchese and his team of investigators believe that Mills has discovered a "real effect". Marchese also confirms that Blacklight's experimental work on plasmas has been published in peerreviewed journals. He also confirms that Mills has working prototypes.
JS: That's right. But wait I am not agreeing to "over unity" claims and neither is Marchese.
PZ: At the same time, Marchese is not taking any definite position on the relationship between Mills' theoretical model, based on classically nonradiating bound electron charge distributions, and the experimental results.
JS: Of course not, he's a Princeton man! So it's Harvard (Lubos Motl) vs Princeton with me (Cornell) in the middle.
PZ: You in the middle? You were with Motl.
JS: On the "theory" only. Marchese, Sarfatti & Motl are all in essential agreement that, perhaps like string theory ;), Mills's "theory" is "not even wrong" (Pauli). Motl, being a string theorist "of the most bigoted kind" (W.S. Gilbert's remark about "Methodists"in "Gondoliers"). Motl has said nothing about Marchese's experiment. A string theorist from Harvard dare not argue with a Princeton Ph.D. engineer on practical matters  right? Remember Feynman's "A beautiful theory is often slain by an ugly fact." (paraphrase)
PZ: Jack, I was in the middle. Now you've moved to the middle under my prompting!
JS: Don't steal Ron Stahl's thunder. I think he first mentioned Marchese not you? Also, remember JeanPierre Vigier's theory and the MaricDragic experiments in Beograd have been on my back burner all along. My point with Stahl is that in science it's not enough to be right, one must be right for the right reasons. Randall Mills's "theory" is the "wrong reasons" for sure. Lisa Randall's hyperspace little black holes may be a test of string theory?
"Fight fiercely Harvard" Tom Lehrer
"Don't send my boy to Princeton,the dying mother said." Cornell football song
"Onward Christian Soldiers ..." Dan Smith
http://stardrive.org/cartoon/dan.html
PZ: Obviously an interesting question for further investigation is whether the [deleted] hypothetical subRydberg hydrino term structures supposedly predicted by Mill's theory really do exist, whichever theory might eventually be invoked in order to explain them.
JS: That's right. Vigier's theory is plausible for this. I also raised some new considerations that may be relevant I am not sure, i.e. whilst the principal quantum number n remains an integer, there is some new kind of charge antiscreening effect on scale of a fraction of an Angstrom  unlikely but maybe.
PZ: I'm sure there are all kinds of possible explanations if such states really do exist.
JS:
Nothing so far in Marchese's data requires "hydrinos" as far as I can tell right now. Or, most likely, what Marchese sees has nothing to do with "hydrinos"  this is a complex phenomenon remember.
PZ: I think the evidence claimed for hydrinos goes well beyond these plasmas. I think Mills et al. have published spectroscopic evidence?
JS: I strongly doubt that. Can you be specific? If so, I am a Monkey's Uncle and will eat my hat if David Williams sends me one made out of hemp! :) See Robert Laughlin "A Different Universe" directly addresses this kind of issue!
PZ: OK.
R. Mills "hydrinos" vs J.P. Vigier's "tight atomic states"
On Jun 10, 2006, at 2:13 PM, Paul Zielinski wrote:
"A normalized stationary QM *probability* distribution  psi (r)  ^2, multiplied by e, is not the same as a stationary charge distribution rho(r). To get a *physical* explanation of stationary states, we have to decide whether the atomic electron is actually smeared out in space, or is still a point particle. Quantum mechanics doesn't tell us. All we can really say here is that in QM there is insufficient information contained in the atomic energy eigenfunctions to attribute a single definite location to the electron in any of those states. At any given time, that is."
JS: Bohm explains all this properly in "The Undivided Universe" with Basil Hiley. In Bohm's hidden variable theory the atomic electron is a point particle in a nonlocal quantum potential in addition to the classical potential. The electron has a definite classical trajectory! In J.P. Vigier's extension, the electron is spatially extended and this gives "hydrinos" (not same as Mills).
PZ: "Exactly. This is precisely the general direction taken by Mills, and as far as I can see his "orbitsphere" model is not so different from Vigier's."
JS: No Paul it's completely different! No comparison! Randall Mills seems to have the old Schrodinger idea of the smeared charge over the atomic orbital. This is not what Bohm has. Bohm has a point particle in a quantum potential that is significant in the support of the atomic orbital. Randall Mills has nothing like a quantum potential. Note, to do photons requires a SUPERQuantum Potential. The configuration & phase spaces of a classical field are infinite dimensional. The configuration space & phase spaces of the single electron are finite dimensional. Use Wigner phase space density.
PZ: "The key to Mill's approach is the use of a classical set of boundary conditions on the Fourier components of the EM field to ensure nonradiation in stationary states."
JS: That is a CLASSICAL EM FIELD without any Super Quantum Potential  in Mills's not even wrong parody of a theory.
PZ: "There is no question that certain dynamic charge distributions classically don't radiate. Precise classical conditions for radiation were investigated by Haus in
H. A. Haus, 'On the Radiation from Point Charges', Am. Journ. Phys. 54, 1126 (1986)."
JS: So what? This is not relevant. How does Mills explain physically observed effects of coherent superpositions of atomic energy eigenstates?
PZ: "Very good question!"
JS: How does he explain the quantum jump with the release of a photon?
PZ: "How does anyone explain it?"
JS: Bohm explains it in Undivided Universe.
2.5 & 5.3 & 5.6
PZ: "For Bohr, quantum jumps were an *inscrutable mystery*: You know: "Whereof one cannot speak...." (Wittgenstein)."
...
JS: Can you follow Randall Mills? If so, explain to us, thanks.
PZ: "I'm reading one of his technical papers, which seems to explain his basic views on the QM model of the hydrogen atom in a reasonably coherent way:
http://www.blacklightpower.com/theory/theorypapers/
Exact_Solutions_120_Electron_Atoms_102804.pdf
So far it doesn't come over as 'crackpottery'. I'll let you know what I find out."
JS: We are waiting. Also, here is typocorrected 2nd draft on the
Necessity and uniqueness of the asymptotic boundary conditions for atomic orbital bound states:
Paul, you seem to have garbled scattering states of positive energy with bound states of negative energy in a potential (only NRQM for now). When the total energy E is negative and there is a potential well, there are classical mechanical turning points where the kinetic energy is negative, so that its square root that controls the radial spatial dependence is imaginary would go imaginary. These are the classically forbidden regions where the radial wave must decay exponentially. Therefore you are completely wrong about your statement that the bound state boundary conditions are adhoc.
PZ: "I'm quite familiar with Bohm's textbook, among many others. So your basic argument here is that the solutions themselves automatically fix the boundary conditions, rather than the other way round?! Is this really what you wanted to say? That the exponential form of the radial eigensolutions for the Coulomb potential at large separation themselves fix asymptotic boundary conditions on
the hydrogen wave functions, forcing the radial probability density to go to zero at infinity? As opposed to such boundary conditions being *imposed* on the general solutions of the Schroedinger equation in order to determine the energy eigensolutions of the equation?"
JS: Yes, that is basically the fact. If a state is "bound" by definition it has a support in a limited region of space  hence the spatial boundary conditions that the state be small at large distances are part of the very definition of the concept. Therefore, you look for a globally selfconsistent Ansatz  and it's quite obvious as the details below clearly prove.
Look at Bohm p. 334 eq. (3)
The radial eq. for hydrogen for Swaves
d^2gl(r)/dr^2 + (2m/h^2)[E  V(r) ( h^2/2mr^2)l(l + 1)]gl(r) = 0
In the classically forbidden region V(r) > E and both V(r) & E are negative. In the classically allowed region E > V(r) and both are negative.
E = K + V
K = kinetic energy
E < 0 for a bound state in NRQM
V < 0 for a bound state in NRQM
Consequently in the classically allowed region K > 0 and in the classically forbidden region K < 0. Now for l = 0 Sstate for simplicity, the general radial solution ~ e^i(2mK/h^2)^1/2r.
Note that K/h has dimensions 1/time.
m/h has dimensions (time)/(length)^2
Therefore the argument of the exponential is dimensionless as it must be for mathematical consistency.
In the classically allowed region K > 0.
Radial function oscillates in space.
In the classically forbidden region K < 0.
Radial function decays in space.
The boundary condition is implicit in the dynamics here!
Obviously the exponentially growing piece is zero for a bound state.
You do not have overwhelming probability to find the electron at infinity if it is in a bound state  obviously. There is nothing adhoc here.
Memorandum for the Record
Subject: Will hydrinos make us independent of foreign oil?
On Jun 10, 2006, at 2:15 PM, Paul Zielinski wrote:
Naudt took the hydrino hypothesis seriously enough to try to explain it using the KG
equation, and wrote a paper on it. That's the point.
Of course his *explanation* is completely different from Mills'  but the existence of
"hydrino" states is not in question.
Z.
Jack Sarfatti wrote:
No it does not explain Mills at all. It's an interesting paper with nothing to do with the details of Mills' allegations. If Vigier is correct the hydrinos, if there, are not relativistic corrections, but are finite size corrections.
On Jun 9, 2006, at 7:29 PM, Paul Zielinski wrote:
Here's an arXiv paper by J. Naudts ("On the hydrino state of the relativistic hydrogen atom") that explains Mills' hydrino states using the KleinGordon equation:
http://arxiv.org/abs/physics/0507193
Z.
No Paul, you miss the key point. Naudts does not, as I recall, get the same quantitative spectrum of fractional principal quantum numbers n for hydrogen alleged by Randall Mills. I doubt that J. P. Vigier's NRQM with Bohmian hidden variable spatially extended microgeon electron gets same spectrum as Mills.
In any case, as a matter of logic and math, I doubt that n can be a fraction unless there is something like, analogous to, the 2D Anyon trick with magnetic flux strings attaching to electric charges in the plasma. I don't see how anything this can happen in Marchese's experiment as yet. Anyons are strictly properties of 2Dim electron gases in perpendicular magnetic fields. Maric and Dragic in Beograd have a magnetic plasma pinch BTW. However, I don't see how this could possibly affect the bound atomic electrons in the hydrogen?
Marchese mentions "nonBoltzmann" populations in the ultrabroadened hydrogen lines. Anyons have fractional quantum statistics and, as I recall, can go from boson to Boltzmann to fermion continuously as the magnetic flux is changed. But I do not see how something like a fractional quantum Hall effect (FQHE) can happen in the plasma unless there is some kind of strong coupling between the ionized plasma electrons and their atomic orbital electron bound state partners? This seems unlikely. But maybe there is another effect here analogous to FQHE if there is a strong plasma pinch magnetic field that couples to the magnetic moment of the atomic orbital electrons?
Will a plasma pinch induce a phase transition of atomic electrons in unionized hydrogen into a 2D anyon phase?
Can we have a 3D quasianyon if part of the time the electron is free and another part of the time the electron is bound so that its effective bound charge is a fraction of e? You can also have fractional orbital angular momentum L and since the principal quantum number is
n = (Number of radial nodes) + 1 + L
If you can make L a fraction, then n is also a fraction.
If somehow you can freeze out one dimension of space for the "atom" maybe in a strong magnetic plasma pinch so that the atomic hydrogen electrons are squeezed into planar Larmor orbits with magnetic flux tubes sticking to them? If the magnetic pinch field is very strong in the final moments then the magnetic moments of the orbital motions should all align with the magnetic field, so that in effect the bound atomic electrons will only be free to orbit in the planes perpendicular to the ultra strong pinch for a short burst of power to a hydrino state?
Fractional quantum statistics ("nonBoltzmann" reported by Marchese) are inherent in the kinematics of 2 + 1 dim NRQM.
On Jun 10, 2006, at 9:03 PM, Jack Sarfatti wrote:
Hydrogen atoms are 3D spatial objects. We can imagine making anyonic 2D spatial analogs of 3D atoms with nanotechnology.
Spin is quantized in 3D space, but it can be a continuous real number in 2D space with fractional quantum statistics intermediate between boson and fermion. Fractionally electrically charged magnetic vortices in some Higgs models are anyons. Can anyons be created in a plasma with a magnetic pinch? Can a magnetic flux tube attach to a bound electron in hydrogen? Ionized plasma has free electrons and atomic ions. What does this have to do with neutral hydrogen mixed in with this ionized plasma?
OK suppose the electron is in a coherent superposition of a free ionized unbound state and a bound state?
e> = abound> + bfree>
Will the effective charge of the bound hydronic electron then be a^2e. Now imagine that the magnetic flux tube attaches to the electron.
e,magnetic flux> = (abound> + bfree>)magnetic flux>
> (abound>magnetic flux> + bfree>magnetic flux'>
Is the emergent collective object an anyon?
Will this affect the atomic spectra when we couple this state to the photon field?
Marchese starts with
En =  13.598ev/n^2
Where n is the principal quantum number
n = N + L, n = 1, 2, 3,
L = 0,1, ... n1
N  1 is the number of nodes in the radial wave function.
L is the orbital angular momentum also an integer.
Therefore n = fraction is complete nonsense.
However
13.598 ev =  (Reduced Mass)(Charge)^4/2h^2
So if for example
n = 1/7
That's the wrong way to look at it!
We do not allow h to change.
What if the effective charge is "fractional"?
Well suppose the charge e
e > xe
En > En' = (Reduced Mass)x^4(Charge)^4/h^2n^2 = (Reduced Mass) (Charge)^4/(h^2n^2/x^4)
n' = n/x^2
So now maybe we are cooking?
It's not important that the effective charge be a simple fraction BTW. All that is important is that x > 1 from some kind of plasma antiscreening effect perhaps since there is an electric permittivity in the denominator as well.
En = 13.598 ev/n^2 =  (Reduced Mass)(Charge)^4/(permittivity) 2h^2n^2
I have not had time to think deeply about this, but there may be a connection to the fractional quantum Hall effect, fractional quantum statistics and 2D anyons in surface plasma oscillations? Too soon to know if this crazy intuition is crazy enough to be interesting. WYSIWYG. Prior to this moment these halfbaked thoughts did not exist on this planet.
I have been reading "Quantum fields in curved space" by Birrell & Davies as well as Frank Wilczek's "Fractional Statistics and Anyonic Superconductivity."
The quantization of gauge forces, EM, weak & strong is not simple (gaugefixing terms + ghosts) and curved spacetime demands the addition of the 3D+1 cousins to 2D+1 anyons called "ghosts" i.e. fermionic spin 0 scalar fields that violate the spinstatistics connection in a direct physical way not found in globally flat quantum field theory. This is related to the fact you can subtract out zero point energy ZPE in flat QFT, but not in curved QFT  a great error Puthoff makes BTW violating the equivalence principle. It's the strong direct curving of spacetime by ZPE that enables the metric engineering of warp and wormhole. Therefore, Hal & Co. (Eric Davis etal) have literally thrown the baby out with the bathwater.
More on this anon. p. 88 Birrell & Davies eqs. 3.192  3.195
Note that anyons have fractional quantum statistics as well as fractional angular momentum and are 2D spatial structures. What anyons and ghosts have in common are new forms of quantum statistics.
Anyons may be a boundary of ghosts in the sense of the world hologram  this is less than halfbaked at the moment.
"the vacuum polarization cloud ... attaches magnetic flux to charges, and electric charge to flux points in general transmuting the statistics of both ... a vortex carrying the fundamental flux unit 2pi/e acquires fractional electric charge e/2. It also has a total angular momentum 1/4 + integer, and obeys halffermi statistics." Wilczek p. 48
The traditional spinstatistics connection has no fractional anyonic statistics and demands that spin 0 scalars be bosons not fermions. Violate this and get signal nonlocality punching through event and particle horizon barriers as well as unstable vacuums. Well that's a clue!
Ordinary 3D fermions & bosons come from the permutation group. 2D anyons come from the braid group and something called ChernSimons theory. We're getting there. ;)
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