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367) Modifying potential energy barriers

Ludwik Kowalski; 5/25/2009
Department of Mathematical Sciences
Montclair State University, Upper Montclair, NJ, 07043

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Introduction
In the abstract submitted for the ICCF15, A. Meulenberg and K.P. Sinha, describe a mechanism by which a coulomb barrier, between two atomic nuclei, can be reduced (in both the height and the length). That would indeed increase the probability of fusion, both cold and hot? I do not understand forces that are said to be responsible for the the reduction of the barrier. One thing is clear; the forces must be attractive.

Figure 1 shows the barrier encountered when two charged particles, for example two protons, approach each other. Only two forces are responsible for the shape of the barrier, the coulomb force and the nuclear force. The nuclear attractive force is zero at distances larger than about 3 fermi; the coulomb repulsive force decreases with the distance according to the 1/r2 law. The maximum potential energy occurs when the magnitudes of two forces are equal. The nuclear force prevails at a very short distances.

Figure 2 shows potential barriers whose shapes are modified by a third force of some kind. The 1/r2 coulomb force is assumed to be the same as for the potential energy in Figure 1. To produce potential barriers shown in Figure 2, the additional force (or forces) must be attractive. Note that the height of the barrier of curve A is the same as the height of the barrier in Figure 1. But the width of the barrier is reduced. In the case of the curve B, on the other hand, both the height and the width are substantially reduced by the presence of the additional attractive force.

The probabilities to penetrate barriers in Figure 2 would certainly be much higher than the probability to penetrate the coulomb barrier in Figure 1. The hight of the horizontal arrow, on the right side of each figure, represents the relative kinetic energy of two particles at a very large distance.

CMNS messages:
There were an interesting exchange of questions and answers, about the M&S theory, at the private Internet list for CMNS researchers. After reading some of them I also posted a comment. I wrote:

“Dear Andrew,
1) I certainly belong to those who are not sufficiently familiar with atomic and solid state physics to actively penetrate your ideas. Please prepare a simplified description; I am probably not the only one CMNS researcher who would appreciate it. More specifically, write an essay for physics teachers, and for their students. I would be 
happy to post it at my CF website.

2) A nuclear coulomb barrier, for example between two protons, can be viewed as a sequence of narrow rectangular barriers (for example 1 F wide each) of different heights. The two protons  would fuse if they were able to penetrate all these rectangular barriers. Heights of narrow barriers are low when protons are far apart; they become higher and higher as the distance, r, decreases, according to Coulomb's 1/r^2 law. But that changes when the distance between two protons becomes smaller than about 2 F. Here the nuclear attractive force starts to compete with the electric repulsive  force. That is why the potential energy of two protons starts to decrease. Yes, I know that most of readers of this message know this. But how can a retired physics teacher resist an opportunity . . . ?

3) Mills is well aware that his theory, if accepted, could become an explanation for some CMNS phenomena. But he decided not to validate the theory in terms of CMNS claims, he decided to validate it by presence of black light (spectral lines in deep UV). I think that this is a smart strategy; no one questions validity of optical spectroscopy. My impression is that his experimental results are reproducible on demand; the debate is only about interpretations.

4) You have a new theory and you want it to be accepted. What would I do in such situation? First I would address theoretical people, specialists in atomic and solid state physics (instead of addressing people like me). That would reassured me that no computational errors were made. Your theory probably makes some predictions that have nothing to with CMNS. I would try to formulate these predictions and would start, if possible, performing validating experiments. Or I would try to convince others that such experiments are worth performing. Validating a theory in terms of experimental results that are not always reproducible is not the most productive strategy.”

And here is Andrew’s reply (also on the CMNS list):

“Based on your comments below (item 1 above) and one that Ed made, I realized that only a few people in CMNS (other than some of the Russians) have any real sense of what is going, or can go on, at all 3 (the solid-state, atomic, and nuclear) levels. Many have little idea about any of them. The fault is not theirs; it is not their field. For those that are in the fields, there is a bigger problem in that they have been improperly taught, or taught the wrong things. I had thought about doing a seminar at ICCF-14 to try to give the experimentalists a "gut feeling" for what is going on. Had I done that, I would have been unable to contribute, as I did, to K.P. Sinha's picture.

With spread sheets, the process you outline in item 2 is almost trivial. I did that the week before the conference in Slide # 16 of the presentation at
http://en.alternapedia.org/wiki/A_model_for_enhanced_fusion_reaction_in_a_solid_matrix_of_metal_deuterides%2C_by_Sinha
to check KP's asymptotic approximation  to obtain a better expression for tunneling thru a thin barrier. While it supports KP's approximation, it is much better and covers the full range of interest. Your example (a picture of many barriers in series) may be the best example for Ed. It intuitively conveys the importance of barrier width. (Good teaching instincts!)

Your item 4 is important, but has problems. The theoreticians all are generally too busy with their own theories to do more than provide a cursory analysis of someone else's. This is the role of critics. It is a necessary and useful one - but can be abused. As an experimentalist, with instincts, I try to use the theory as a tool to guide work. It has to be understood first. So I have been working with KP (as a critic and student) to understand it and hopefully translate it for other experimentalists.

I had thought that looking for other applications of the model would be like trying to get green paint to perform photosynthesis. However, that is not a positive attitude. Your suggestion is a good one. And, if we don't look, we won't find another application. On the other hand, concepts that can be translated into improved heat or other LENR consequences (like the laser beat frequencies to stimulate specific phonon modes) could be just as useful. KP has an idea that we'll try to patent here in India this summer.

Another important point is the desired goal. If we are trying to convince the unbelievers, anything may be a waste of time. If we are trying to help the present experimenters (the ones most likely to listen to us), then writing for the CMNS site and ICCF conferences could be the most productive.

Back to item 1:  Your suggestion of a tutorial essay (with lots of pictures) on your website is worth the effort. But I'll try it in a series. The first stage might be a questionnaire to determine where people are in their ideas about the atomic ground state (and at the same time give them a picture of the various ideas being tossed about). If you know of any (physics?) students who might be interested in analyzing the response, that would be helpful. (My own students - bright engineering undergraduates -are working on presentations to the International Astronautics Congress in Korea right after ICCF-15. My interest in alternative energies is very broad.)

It is clear that Ed does not have what I consider to be the correct picture of the ground state. (However, it is close to the one that I held for 40 years and only modified in the last decade.) I would start a new thread for that study. A later essay (at a much higher level) is actually covered in a second abstract for ICCF-15 (CHARACTERISTIC FREQUENCIES IN CMNS) and included below.

In another message Andrew wrote that he is going to survey the list, in order to determine our level of exposure to modern physics. That will probably confirm what I think; most of us had very little exposure to QM. That is why I suggested that the theory should be discussed among theoretical people, preferably experts in atomic and solid state physics. What follows will be a description of my attempts to understand the M&S theory.

More messages were posted on CMNS list

1) The following message was posted on the CMNS list when I was composing the above. Responding to Andrew Meulenber, Ed Storms wrote: “While I agree, being able to use the same vocabulary is important, I don't think this is the major problem with having a theory about CF accepted. Two other issues I think are more important. The first is that every proposer of a theory passionately believes that they are right and everyone who does not accept the idea is wrong. The second issue is that assumptions are always made that frequently are hidden or not acknowledged as being assumptions. These two issues make acceptable by an objective and independent observer rather difficult, even after the vocabulary is understood.  

The solution to the first problem is for the proposer to realize that many ways to view reality are equally correct and equally wrong, including their own, with debate being the only path to deciding which is which. The solution to the second problem is to clearly state what is assumed and what has clear experimental evidence. I agree, all theories contain assumptions, specially early in their history.  So, having assumptions is not bad. Failure to acknowledge them is the problem.  When you say that people do not understand quantum mechanics, part of this apparent ignorance is a failure to accept some of its assumptions.  

This rejection of assumptions is compounded by the need to explain the concepts with simplified diagrams and models, which in themselves contain assumptions.  If we are to make any progress, we need to clearly understand where assumptions end and where reality begins. This is a difficult task, but can only be solved by not taking a dogmatic approach to the process.  Your willingness to openly discuss your theory is unique in the field and shows that you understand these issues.”

2) Responding to the above, I wrote: “It is clear that M&S agree that two deuterons have a negligible probability to fuse at room temperatures. Kinetic energies of individual ions are fractions eV while the coulomb barrier, preventing fusion of two hydrogen ions, is close to one MeV (and higher for heavier ions). But two ions in a solid matter, for example in palladium, are not alone. They are surrounded by zillions of atoms. Kinetic energy of random oscillatory motion of each Pd atom, in a lattice, is very small (typically 0.04 eV). But, according to M&S, these atoms can be made to act in unison. Suppose that a line of ten million of atoms collides with another line of ten million of atoms (the motion is confined to a single dimension). The kinetic energy of relative motion becomes 0.8 MeV (2*106*0.04 eV).

The probability to penetrate the coulomb barrier, for two ions pushed toward each other by surrounding atoms, becomes much higher than for two independent ions.  The basic assumption of M&S theory is that lines of atoms can act collectively, as described above. Is this an assumption or is it a logical (mathematical) consequence of well known theories?  My theoretical background is not sufficient to answer this question.”

3) Ed responded: “I agree, Ludwik, this is one part of the mechanism. My issue is one of magnitude. While this mechanism can be imagined to occur, does it have enough energy to cause a nuclear reaction and under what very unusual conditions? These questions, which are important to the idea being accepted, are not answered by Andrew.”

Yes, the probability that such lines of atoms are formed might be much smaller than the probability of penetrating a coulomb barrier when the available kinetic energy is one eV. This mechanism does not involve changes in height or width of the coulomb barrier. The only difference in my Figure 1 (see above) is that the horizontal arrow would be higher than where it is for relative kinetic energies below one eV. (Note that the arrows in my figures are at the hypothetical 1 MeV level.)

Another proposed mechanism has to do with existence of particles called “lohons.” In one of his explanations, Andrew wrote: “Electron pairing is another critical feature of the model. Each of a pair of electrons in an s orbital is less tightly bound to its nucleus than is a single electron in the same orbital. Nevertheless, with an external E field (phonon, optical, etc.) and the proper configuration (e.i., the nuclei are much closer than their equilibrium positions), it is more likely that two electrons bound to two nuclei will find themselves together on the same nucleus at the same time rather than one on each of the nuclei. This ‘polarization’ of the electron pair about the converging nuclear pair means that the nuclear repulsion is overcome until the nuclei get very close. This is an actual ‘attraction.’ It is greater than just a strong-screening effect.”

Taking this justification for granted, I want to emphasize the word “attraction.” An attractive force between two approaching positive ions, no matter what its nature is, would cause a change in the shape of the potential barrier. Will the change be as strong as illustrated in my figures (see above)? I am not able to answer this question. Andrew also wrote: “Lochons may not exist (continuously) except during the near-approach of nuclei in the optical-phonon mode.” What determines time of their existence? I wish I knew how to answer this kind of questions.

4) Michel Jullian asked: “Dear Andrew, can your alternative theory predict the next decimal places for the electron's intrinsic magnetic moment (presently 12 or so) _before_ they are experimentally determined, as QED has been doing for about 60 years? See http://cerncourier.com/cws/article/cern/29724 for the latest I believe (2006) experimental refinement of the value.”

5) John Fisher wrote: “My view of the language of physics is very simple. I fully and unconditionally accept quantum mechanics as a thoroughly and quantitatively verified theory that applies on both the nuclear scale and the cosmic scale. In my view a theory that contradicts quantum mechanics disqualifies itself for consideration. It is wrong from the start. . . . .”

6) . . . wrote: “Dear John, . . . . ”

7) I asked Andrew Meulenberg for a short essay on the new theory, for the benefit of general readers. Here is what he wrote.

“Title of the essay?

Etc. etc.



What follows was posted on the CMNS list, on 5/27/2009

Ludwik,
Since it may be a while before I get to write the essay, I'll put some comments out that might be useful.
_ _ _ _
Re: 367 --- You have my permission to include this material in your website.
also --- "A. Meulenberg and K.P. Sinha, describe a mechanism by which a coulomb barrier, between two atomic nuclei, can be reduced (in both the height and the length)" This pertains to what was already presented at ICCF-14 and subsequently at http://en.alternapedia.org/wiki/A_model_for_enhanced_fusion_reaction_in_a_solid_matrix_of_metal_deuterides%2C_by_Sinha
The abstracts for ICCF-15 cover the next step, which is the fusion process itself, including the alternative pathways from the excited 4He (= 4He*) down to the ground state. This process assumes the barrier is penetrated and then "explains" and is the basis for many of the "strange" things seen in LENR.
More corrections/suggestions for 367 all the way at the end (below).
_ _ _ _
Before I get back to Ed's questions, I wanted to address your comments, because they can be very helpful to all that are interested (and to you and Ed in particular). Your analysis (below) of KP's model was a good starting point.

Conceptually, your description of the collective action is correct up to the point of tens of millions acting in unison. I would recommend that everyone in CMNS read at least the introductory paragraphs of http://en.wikipedia.org/wiki/Phonon .  They provide the basic vocabulary essential to understanding any collision process in H (or D) loaded crystals. The article gets dense very quickly after the introduction, so you might skip down to the Acoustic and Optical Phonons section just for those definitions.

The first figure in the article is an animation that describes standard collective longitudinal motions of atoms in the crystal. Notice that, in specific modes, the atoms may “collide” with their neighbors twice every cycle. This is standard solid-state physics with nothing new.
1. Your point of the 1e6 atoms would indicate that crystals were very large. (At first, I defensively thought you were mocking the concept.) In practice, strings of 10 - 100 atoms may be sufficient to achieve the purpose.
2. The purpose of the phonon assist is not to attain energies sufficient to surmount the Coulomb barrier. It is to orient the deuterons and produce a collective motion that allows a high “collision” rate.
3. The collision rate is important in the overall probability of tunneling through the barrier.
4. But, the orientation of the deuteron motion in the lattice is critical to the charge state of the deuterium. Lattice oscillations have been found to make H- and H+ more likely than H (because the oscillations can create fields that attract and repel charge). If such charge oscillations are in phase with the collision mode, then an optical-phonon mode results. (This is similar to the well-known modes found in ionic crystals. The assumption that this observed mechanism also happens in PdD is to be validated. The atoms in ionic crystals are normally charged; but, in this model, the charges are field induced.) 
5. In an optical-phonon mode, the H- and H+ ions are dynamically forced together in the Pd lattice until they “see” each other's charge through the Pd electron charge field. At that point, there is no Coulomb repulsion between nuclei. There is the Coulomb attraction between oppositely-charged ions (but still screened by the Pd electrons).
6. Once the attraction between the oppositely-charged ions becomes significant, it leaves the phonon resonance and the process enters a new regime.
This brief story is only the solid-state beginning of the model (which itself only proceeds up to the nucleus) outlined in http://en.alternapedia.org/wiki/A_model_for_enhanced_fusion_reaction_in_a_solid_matrix_of_metal_deuterides%2C_by_Sinha The next step in the presented model is into the realm of atomic and molecular physics, where it is necessary to determine the appropriate electron orbital radii (as a function of inter-nuclear distances for a 1-dimensional collision) and the point at which the Coulomb attraction changes into a highly-screened Coulomb repulsion.
Andrew M.
_______________________________________
On Mon, May 25, 2009 at 8:42 PM, Ludwik Kowalski <kowalskil@mail.montclair.edu> wrote:
...
= = = = = = = = = = = = = = = = = = = =
Here is how I understand the proposed M&S theory.
 
It is clear that M&S agree that two deuterons have a negligible probability to fuse at room temperatures. Kinetic energies of individual ions are fractions eV while the coulomb barrier, preventing fusion of two hydrogen ions, is close to one MeV (and higher for heavier ions). But two ions in a solid matter, for example in palladium, are not alone. They are surrounded by zillions of atoms. Kinetic energy of random oscillatory motion of each Pd atom, in a lattice, is very small (typically 0.04 eV). But, according to M&S, these atoms can be made to act in unison. Suppose that a line of one million of atoms collides with another line of one million of atoms (the motion is confined to a single dimension). The kinetic energy of relative motion becomes 0.8 MeV (2*10^6*0.04 eV). The probability to penetrate the coulomb barrier, for two ions pushed toward each other by surrounding atoms, becomes much higher than for two independent ions. 
 
The basic assumption of M&S theory is that lines of atoms can act collectively, as described above. Is this an assumption or is it a logical (mathematical) consequence of well known theories?  My theoretical background is not sufficient to answer this question.  
Ludwik
_________________________
Additional comments on 367:
1. Your figure 1:  The energy level pk might be considered to be at the 250 keV level. For interstitial deuterons (even with phonon assist) would be at the eV level (rather than the 100 keV of your figure). To put that on your figures, you have to go out more than 3 decades beyond your value. A log-log plot is the only way to give perspective. If you are writing for readers who are not familiar with that display, then additional (or different) figures might be required to properly convey the magnitude of the problem (and the reason why nuclear physicists reject the possibility of cold fusion).
2. Your figure 2:  The concepts are good. However, if we could shrink the barrier width into the fermi range, the search would be over. If we could reproducibly get it into the mid 100 fm range, I think that marketable products would be available shortly thereafter.


Appended on 5/27/2009
The Sinha-Meulenberg theory was not the only one that was discussed on the CMNS list during the last several days. Another theory was presented by Dean Sinclair. Here is how it was introduced. On May 26 Dean posted this message:

“I've shared a document with you called "OLD DATA/NEW MODEL":

http://docs.google.com/Doc?id=dcb2474d_233q69gfghq&invite=325886566

It's not an attachment -- it's stored online at Google Docs. To open this document, just click the link above.
---
All of you are very busy, but I'd like to request a favor. I need some "peer review, " feed back on something which I have been working on for about five years.

I didn't set out to try to do what Einstein wanted to do, just started to following a line of logic. However, I came up with a deceptively simple, but, to me logical little model which seems to unify a lot of ideas.

I don't know whether, in my doteage, I have morphed into a legitimate scientific theorist, or whether the things that I hae come up with are the crackpot nonsense of a senile, old man, which seems to be the general concensus of my family....

The link included is to a brief article summarizing some of my ideas; and, as this note is being sent to "collaborators." it is presumend that you can comment right into the article.

It would be much appreciated if you-all could take a few minutes of your time to check this out. If the ideas are valid, they should be prertinent in some way to cmns.“


Responding to the above, I wrote: “In the linked-above article, you wrote: ‘. . . An alternative, almost totally reversed, interpretation goes something like this:  The Michelson-Morley Experiment defined the maximum speed at which information is carried in the 'Aether,' whatever it may be. It, also, showed that the 'Aether' can act as if it were a solid, carrying the transverse wave disturbances which we understand as 'light.' . . . ‘

1) Aether was believed to be a substance present in air (where their interferometer was located), in stars, interplanetary space, soil, volcanic lava, etc. Temperatures of these substances are very different. You are saying that aether is at a triple point (that is at  a well defined temperature and pressure).  If aether is a substance that is always at its triple point, as you claim, then how can it be in thermal equilibrium with substances whose temperatures are so different?

2) What kind of experiment would demonstrate existence of aether? Yes, I know that only scientists need experiments. Validity of a mathematical  theorem does not depend on experiments; it depends on correctness of logical conclusions (derived from accepted axioms, and from already-proved theorems).

3) Unless redefined, the term ‘solid’ refers to a collection of atoms. From what kind of atoms is your solid aether made? How do these atoms interact with each other? How do they interact with atoms of other substances?”

Responding to the above Dean wrote:”The Aether, Substance of Existence, as I envision i would not be exactly as was envisioned  by the old timers but woild be a basic subsance, at this point undefined, which is a basic "filer of all spaee"  such that all actions and reaction within that existenfe can be considered as if thaat substance were tautomatically compensating towanrd a situation of equilibrating motion throughout.  A substance tending toward a triple point seems to be the best analogy which Iknow of....”

Referring to an earlier message, in which Sinclair was describing neutrons as unions of electrons and protons, Ed Storms wrote: “Dean, neutron formation is possible but it takes 0.78 MeV to do the job. The mass of the neutron is that much heavier than a proton + electron. You have to supply this extra mass as energy.  Even if something else converts into a neutron, this conversion has to be exothermic, i.e. energy is given off. This energy should be visible as some kind of radiation. Nevertheless, if you propose the existence of an undetected particle that occasionally converts into a neutron, you are opening a can of worms bigger than CF.  If CF is to be understood, we need to keep the number of strange assumptions to a minimum.”

Responding to the above, Dean Sinclair wrote a long message (in green below). Ed Storm responded with comments inserted into what was posted by Dean (see in red below) by quoting dean

I know, Ed, we have to keep the, as you put it, strange assumptions to a minimum.  The problem that I'm having with all of this is that, more and more, I seem to be coming to the conclusion that much of what we have so blithely taken as "fact" for a long time is based on what, if we looked more closely would be very strange assumptions coming in some cases from the use of circularly defined or undefined terms and concepts. (Mass and Energy are good examples.  Energy moves Mass Mass and Energy are somehow intercovertible, etc. Really, if we look closely we don't know what we are talking about.)...

All of nuclear physics is based on the idea of E=mc2.  In addition, the energy given off by all nuclear reactions agree very exactly with the mass change. This idea is not even worth debating.  The masses and energy simply have to add up.


For instance, we assume that the electron and anti-electron "annihilate" to pure energy.  We also say that if an amount of energy equal to the amount of annihilation energy be in contact with matter, somehow w3 can get pair production, which is, logically, the reverse of annihilation. We apparently know that prior to a "annihilation" the electron and anti-electron can associate for a period of time.  This implies that "annihilation" probably requires an exact orientation of the two. It is known that the two, electron and anti-electron are "complementary particles, "  there is some very old data which can be interpreted to say that they qualify very nicely as the halves of a split oscillator.    Annihilation and pair production , even the annular radiation noted on '"annihilation" suggest that the two processes are inverses. That pair production is the splitting of an oscillator, annihilation the rejoining of halves of an oscillator.   The problem. of course, is that no-one has been able to isolate the oscillator, or, for that matter, apparently even suggested that one may exist. ( I probably wouldn't be thinking this way myself had I not been through Radar School a little over a half century ago. )

The point I'm trying to make is it seems a far less strange assumption to me to rationalize  annihilation and pair production as  reversal processes dealing with a neutral , probably ubiquitous pulsating oscillator of the same "Mass" (internal vibrational -rotational motion content) as either the electron or positron , which has gone undetected.   Similarly, it makes more sense to me for this same unit to be deformable to a neutron than for an electron  and proton to some how get lined up then given a push by "energy"  (Which we don't really know any really good definition for) so as to join them together as a neutron.,( and give them just the right amount of push for their coordination to be perfect.)     It makes more sense to me for the neutron to arise from the same source, by a slightly different mechanism, as do an electron and positron by "pair production.."

Positron production is a fact of nature. The positron is antimatter that annihilates when it comes in contact with matter to give two gamma rays equal in energy to the mass  that was lost. This is observed fact. We can speculate all day why or how this happens. However, I don't think this helps to achieve an understanding CF.

Yes, I know, what I"m saying is that much of what we consider as fact and many of our assumptions on which we work may be sheer Bull, misapprehensions that some how have a Small grain of "truth."  It' s awfully hard to say, "Lets go back to the drawing board when we have years of study invested in memorization of certain ideas. Our mentors taught them to us as facts and we accepted them.   It's very hard to let go and look at some of the assumptions critically to decide what are strange assumptions and which are simply looking at old assumptions to see if. though they be not strange they are misleading......

You need to be careful where you pick your fights. I suggest it is not worth trying to overturn a huge data set that shows the E=mc2 relationship just to explain CF by a theory based largely on imagination.

In other words, to me, by assuming an unrecognized, rather ubiquitous neutral entity, as the unit involved in a number of different processes, I find, at least to me, a better explanation  than the current non-explanations usually involving, energy and mass defect values, when we usually do not operate with any really clear definition of either energy or mass.

The relationship between energy and mass is extremely well established. This would become obvious when you study the field of nuclear chemistry.

Oh, yes, the conversion of the postulated oscillator to a neutron would not be exothermic so as to emit radiation. Just maybe that "Can of Worms" needs to be opened to understand "CF. "

One of the problems with many attempts at creating a theory is the willingness to ignore what is known and is well established in other fields. I don't think it is useful to start from scratch and propose ideas that have no experimental support at all just because the CF effect is odd.  I think that certain well established ideas need to be used as building blocks of any theory. Two basic ideas that should be accepted without argument are the reality of E=mc2 and the Second Law of Thermodynamics. These two basic conditions automatically eliminate many proposed theories.  The question then becomes, where do we go next to find the mechanism?

I agree with Ed; this kind of speculations will not help us to understand CMNS. Explaining one mystery by another mystery is not desirable. I already wrote about this in

http://pages.csam.montclair.edu/~kowalski/cf/363alchemy.html

And here is another meaasage from Dean, also posted on the CMNS list.

“I'll make one last comment.   The two gamma rays given off are in opposite directions.  Now a point radiator radiates in all directions. A single annular radiation hitting two detectors spaced at 180 degrees would be read as two gamma rays at opposite directions.   Hence the two times the mass.....  There is actually only one wave disturbance. I defefer to your advanced knowledge of the theory of nuclear physics. However, I doubt that you ever studied any electronics or radio theory.....I doubt also that you will ever consider me other than an uneducated crackpot.... Oh, well.

Oh, yes, whence commeth the derivation of the idea that E=mc2 ? By integrating the fact that energy is the integral of momentum, hence E=p^2=(m^2v^2)/2, evaluating this at "c" one could argue that E=(m^2c^2)/2  rather than mv^2.”

Appended on May 31, 2009
A message from Ed Storm:
Dean, you miss the important point. Ideas must be tested by comparing them to well established understanding, which has nothing to do with being a crackpot. If you have an idea that conflicts with well established understanding you either need to abandoned it or show why it is a better idea than what is known.  Of course, you must first know what is known.  As for radio theory, I have some knowledge of this subject and it does not apply to the situation when antimatter annihilates.  This process creates energy and momentum that must be conserved. This can only be done by two particles of photon energy going in opposite directions. This situation never comes up in radio theory.  The equation E-mc2 was derived by Einstein and others before and since. It is a basic and well supported law of nature.

There were other messages on the subject. Responding to one of them, I wrote: “The Golden Age of CMNS might be approaching. Suppose that at least five of us confirm reality of Oriani-type tracks. independently. (Unfortunately there are only two participants in the Curie Project so far.) This would be ideal time for making verifiable predictions based on mathematical calculations. Starting with Oriani protocol, experimentalists would be able to test theoretical predictions, changing one parameter at a time. Please use your favorable tool and tell us what effect would a parameter have on the observed track density. The obvious parameters are:

a) The cathode material (for example, replacing Ni by Pt, Ag, etc.)
b) Distance between the cathode and the CR-39 chip protected by the mylar film c) Distance between the two electrodes
d) Initial electric current (to remain nearly constant)
e) Initial concentration of the electrolyte (also to remain nearly constant)
f) Kind of electrolyte, for example, NaCl instead of Li2SO4
g) External magnetic field, as in SPAWAR experiments
h) Effect of illumination (darkness versus day light, or versus a laser light).

What other parameters are worth mentioning? I wrote it hoping that omeone else will join The Curie Project.

Appended on 6/21/2009

1) Several messages, posted yesterday and today, are worth showing. Before doing this, let me say that, according to Randell L. Mills, hydrogen atoms can exist in the energy states described by fractional quantum numbers, such as 1/2, 1/3, 1/4, etc. Such atoms were named hydrinos. Mill’s theory conflicts with generally accepted quantum mechanics. According to that theory, quantum numbers can only be integers, such as 1, 2, 3, etc. The quantum number n=1 refers the lowest possible energy state of any atom. The average distance between an electron and proton, in a hydrino, is expected to be considerably smaller than in an ordinary hydrogen atom. For more details, see

http://en.wikipedia.org/wiki/Blacklight_Power

and other Internet references.
Ignoring earlier messages, let me quote the one posted by Akito Takahashi.

“Dear Ed, Tom, Andrew and all, “The most essential problem in CMNS/CF/LENR study is how the nuclear energy (mass defect by deuteron fusion, or nuclear reactions) of He-4 production is transferred to thermal energy (of lattice vibration of reactor matter), without neutron and hard gamma-ray emission; that is yet to be solved. Many colleagues are trying to answer, although the hurdle is so high.   For experimentalists, the mass-defect (nuclear excited energy) should be shared to outgoing particles to conserve the system energy and momentum (namely kinematics). Outgoing particles can be alpha-particles, other charged particles, neutrons, hard gamma-rays and low energy photons (characteristic X-rays, soft X-rays and visible light or IR, UV photons), to conserve the system momentum (probably of many body system). Experimentalists should search all the possibilities, taking the spectra (specific energy values) of particles as key information.

  As a material for our further studies and debates, I summarized and edited some of discussions in the previous cmns-google-group discussions (see attached file: Essential Problem Heat vs He4). I hope we will find the truth someday. . . .

  2) Ed Storms responded: “Since I have made an effort to comment on other people's theories, let me throw out some ideas of my own.  I propose that any theory must explain the following and this must be done using as few assumptions as possible.

****1> The rarity of the effect and its association with certain conditions related to atomic structure and composition, including operating in living organisms.
****2>. The ability to initiate several different kinds of nuclear reactions with different reaction products, including fusion fission and transmutation.
****3>. The absence of significant energetic radiation.
****4> The ability to produce helium+heat at levels that exceed 10^12 reactions/sec.

I suggest that the Mills hydrino theory can form the basis for an explanation of CF that satisfies all of these requirements.  I will assume you have a basic knowledge of this model.

(a). The hydrino requires the presence of certain catalysis to form. These catalyst are rare because the required element must have a special chemical form.  
(b). Once the electron in H(D) has dropped to an orbit near the nucleus, by release of energy to the catalyst, the assembly ceases to have an effective nuclear charge, much like a neutron. This makes any kind of nuclear reaction possible, which unlike a neutron, does not add an electron to the reaction event. 
(c) The hydrino can condense into clusters, which also do not have an effective charge, hence can enter the nucleus of an atom to produce the Iwamura effects.  When a member of the cluster fuses, the resulting energy is shared between all members of the cluster. Consequently, the primary radiation consists mainly of low energy deuterons or protons and electrons, with secondary X-radiation. Alpha radiation is only seen when the cluster is small, otherwise its energy is too small to be detected.
(d) The reaction rate is controlled only by how fast hydrinos can form and condense into clusters.
(e) These hydrinos can form in any material containing the required catalyst and enough H or D, thus explaining the effects seen by Oriani using liquids and the ability of living organisms to support such reactions.

Of course, this model can be refined to account for many more observed details, but this requires more assumptions.  This model is particularly convenient because Mills has provided much of the experimental evidence for the initial assumption, i.e. the reality of the hydrino.  Most other theories have to start from scratch to justify their initial assumption.  So, what do you think of this idea?”

3) Responding to this, Akito Takahashi wrote: “Dear Ed and all, “[As far as I know], Hydrino” cannot exist unless we deny the quantum mechanics which is proven very true by undeniable microscopic data of nature greatly accumulated up to now in atomic and nuclear physics, nano-material science, etc. We need to avoid such ideas that basically are in contradiction to established physics. However, your trigger would be useful for group discussions.”

4) Another message from Ed Storms: “Dear Akito, I agree, you raise a complaint leveled at the hydrino idea. However, Mills has proposed ways to get around this criticism. In addition, his observations make a good case for the existence of something that has the characteristics of the hydrino.   In fact, cold fusion is, its self,  in contradiction to established physics. Consequently, I think we are not in a position to make this argument about Mills. ;-)

5) Scott Little responded: “IMHO, there's no getting around the conflict between hydrinos and QM.  According to QM, the H atom (in the ground state) is the lowest possible energy configuration for an electron and a proton.....that's why it's so marvelously stable (13 billion years and counting)!  The reason the energy goes up if you force the electron close to the proton is something called "Schroedinger pressure", which arises directly from the Uncertainty Principle, specifically dxdp >= hbar/2.  As the electron is confined closer to the proton, dx goes down so dp (momentum) goes up and so goes its kinetic energy.

  It really doesn't matter what Mills thinks about QM, it is undeniably one of the most successful theories ever devised in physics.  It is simply impossible to say that one of its basic building blocks, the Uncertainty Principle, is wrong.”

6) Another researcher mentioned that cold fusion (lattice assisted nuclear reactions) is consistent with existing science. What he probably had in mind was that the energy to overcome the coulomb barrier is provided by a large number of atoms in a crystal. That idea, by the way, already expressed by Andrew Meulenberg, prompted me to start composing this unit. He is working on a paper which will probably be published this year.

Appended on 6/22/2009

8) Elaborating on what he wrote yesterday, Ed Storms continues: "

Dear Scott and Akito, OK, lets explore the issue you raise. Mills agrees that quantum rules determine behavior at and above the conventional lowest level.  The lowest level exists because energy cannot be released as photons to allow the electron to go to a lower level. At this point, we all are in agreement. Now Mills assumes that another mechanism exists that can remove energy from the electron, resulting in an orbit that is closer to the nucleus. The issue is not a violation of quantum rules,  but is whether a new mechanism is possible that does not involve emission of a photon. This transition would be rare, but would have occurred everywhere over cosmic time. Consequently, Mills proposes hydrinos exist in outer space, but are invisible because they do not absorb or give off phonons, in other words are "dark matter".   The only issue is whether such a state can exist, not whether quantum rules are being violated.  We know that quantum rules are constantly being expanded without the need to throw out the whole system.  Nevertheless, I and other people acknowledge that some of the conclusions provided by Mills based on his observations do not make logical sense, but may not be essentially wrong.  Consequently, I think it is premature to debate the details or reject the basic idea. The main issue is whether an electron can, in fact, enter stable orbits close enough to the nucleus to offset the nuclear charge. Indeed, Mills might be exploring only one of several mechanisms that could cause this to happen.

What is the evidence? First, you need to know that Mills is using only protium. Therefore, fusion is not possible, although some of the effects might be caused by transmutation. Mills is silent on this possibility.

Mills predicts that helium atoms and oxygen in H2O are suitable catalysts. He mixes these gases with H2 and subjects the mixture to RF or microwave discharge. He observes that the hydrogen has acquired high energy, much more than can be accounted for by any normal process.  When Ar, Ne, Kr are used, which are not catalysts for the process, the "hot" hydrogen does not form. To him, this shows that the predictions of his theory are consistent with observation.  In addition, UV radiation is produced having wavelengths that his model is able to predict. In addition, he predicts that NaH is a suitable catalyst and is now developing a commercial energy generator based on this observation, which has been replicated in other laboratories.  The theory and the experimental observations are well described on the www.blackpower.com website. I suggest you read the papers rather than arguing from ignorance, a complaint we have directed toward skeptics of cold fusion.
I might add, that Mills has a 50,000 square foot laboratory in NJ that is funded by people who believe his claims because they have studied his experimental results.  This success in funding is more than we can claim for CF. He has a model that is successfully guiding his research, which is also more than we can say for CF.  I suggest this work needs to be given an objective evaluation. It might not be completely correct or complete, but it might provide a path to a better understanding.

9) Scott Little disagrees. Here is his reply:“I'm not in agreement.  According to QM, there is no lower level...the ground state of the H atom is the lowest energy state for an electron and a proton.  One datum supporting this prediction is the fact that the rest mass (i.e. total energy) of the neutron is considerably higher than the rest mass of the H atom.

(a) [You wrote:] “Now Mills assumes that another mechanism exists that can remove energy from the electron, resulting in an orbit that is closer to the nucleus.” No, according to QM, you have to add energy to the electron to make it move closer to the nucleus.

(b) [You wrote:] “The issue is not a violation of quantum rules, but is whether a new mechanism is possible that does not involve emission of a photon.” I'm sorry, that's not correct.  Mills' hypothesis...that hydrinos can exist....requires a severe violation of quantum rules...the very same rules that have enjoyed unprecedented success these past ~80 years in predicting the outcome of numerous atomic-scale experiments.

(c) [You wrote:] “ . . . The theory and the experimental observations are well described on the www.blackpower.com website.  I suggest you read the papers rather than arguing from ignorance, a complaint we have directed toward skeptics of cold fusion.”

In this case, my ignorance is mostly due to my native reserve of that plentiful substance....:)  I've read lots of Mills' papers and spent many months trying (in vain) to replicate some of his experiments.  I've also consulted with an expert in QM, who assures me that Mills' theoretical arguments are incoherent.   I wish I could make that judgement myself but I can't.   Very few physicists actually understand QM at the level necessary to evaluate Mills' work.
 
(d) [You wrote:] “I might add, that Mills has a 50,000 square foot laboratory in NJ that is funded by people who believe his  claims because they have studied his experimental results. ”

All we can really conclude from Mills' impressive physical plant is that he is very good at convincing people to give him money.  That does not necessarily validate his physics.
 
Yes, his list of publications is impressive.  Yes, he seems to have found lots and lots of corroborative evidence for the existence of hydrinos.  But experimental results can be misleading and misinterpreted, especially when you are searching for support for your pet theory.   Combine that uncertainty with the fact that hydrinos DO require violation of QM's basic principles and I conclude that he must be mistaken about hydrinos.

10) From my own subsequent comment: . . . Suppose that very deep UV photons are reproducible on demand, as claimed by Mills. The next question would be about a mechanism by which they are produced. Knowing that they are not emitted by hydrogen atoms (that would contradict a theory that has been validated so many times) one has no choice but to say that they are emitted by something else. What can it be? If one explanation is not acceptable than we should be looking for another.

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