deBroglie's equation and heavy electrons

Longview,

Below is my calculation of the energy/momentum absorbed from the magnetic
vector potential in a collision between an electron and a positively charged
particle of nearly equal and opposite momenta in an intense current arc
- based on the Feyman reference below ([3] p.21-4 "Two kinds of momentum).

It is just copy of a past posting to Vortex-L. I want to check it again and
revise it with some new data, but time does permit. For simplicity, I
assume spinless particles. Perhaps such collisions occur in arcs, or near
electrodes. The crude Ascii-graphics may have to be viewed with fixed
font-size to appear correctly. It is a bit tedious to read and check:

'Slow' arcing electrons can gain relativistic mass

Widom-Larsen, Brillouin (and some others) propose that electrons acquire
782 KeV mass/energy and overcome the electroweak barrier to combine with
protons, deuterons or tritons to produce low momentum neutrons.

Storms notes [1] that an electron must reach relativistic speeds to gain
782 KeV in a lattice, - seemingly a very tall order, due to collisions.
Others, e.g. Hagelstein, et al[2], doubt that field strengths in LENR
experiments provide this extra energy ("renormalized" mass).

In an arc, colliding electron-proton(deuteron) wave packets pairs are
strongly squeezed together by equal, opposite magnetic forces.

Even when the composite packet has velocity zero (lab frame), the packets
continue absorbing field energy by becoming more oscillatory, localized and
overlapping as spectra shift to high mass/energy eigenstates. In pictures:

TIME Low resolution ASCII graphic of
| e-p collision with (lab) velocity ~ 0
|
V PROTON ELECTRON
| -----> <----- Decreasing
| _____________ _____________ Magnetic
| / \ / \ Vector Potential
| / PROTON \ / ELECTRON \
| / 'p' \ / 'e' \ A
| -------------------+--------------------- ------------->
|
V |\ 'HEAVIER' |
| | \ ELECTRON |
| _____________ | \ /\ |
| | \| \ / \ V
| | | \/ \ /\ /\ |
| | | \/ \/ \ A |
| -------------------+--------------------\ -------> |
| V
| | A-field
| |\ transfering
| | \ | 'HEAVY' momentum
| | \ |\ ELECTRON to e-p pair
| ___________|___\ | \ | |
| | | |\| \|\ |
| | | | | | | |
| | /\| | \ \ \ A |
| -------------/------+-------\-\---------- ---> V
V significant e-p electron wave packet
wave packet overlap becomes squeezed, more
localized, oscillatory,
- spectrum shift to high
mass/energy eigenstates

Electron velocities in arcs are usually far below relativistic, but the arc
magnetic field stores huge energy and momentum that is transferred to/from
colliding particles when the arc current rises, falls, or is interrupted.

To gain 782Kev in energy, an electron can equivalently acquire (see [6])

momentum = 6.3480 * 10^-22 [N*sec] -- where [N] = newtons

The following example shows that this does not require exotic lab equipment.

Assume the electron is in an arc plasma uniformly distributed in a tube
with radius=R, length=10*R, current=I aligned with the z-axis of 3-space.

We want to compute how much field momentum can be transferred to a electron
'e' in a collision at a radial distance 'r' from the tube center.

=============================== x-axis
^ e \ /
| ^ <----- I[Amps] \ /
| | r \ /
2R -------+------------------- <------x----- z-axis
| / \
| / \
v / y-axis
===============================

|<------ L = 10*R ------->|

The (under-utilized) "magnetic vector potential" field (denoted A(r))
depends only on local currents. Very conveniently [3,4] --

q*A(r) = momentum impulse (as a vector) that a charge 'q' at point 'r'
picks up if currents sourcing vector-field 'A' are shut off

By ref[5], near the outer surface of the electron plasma tube (r = R),
the momentum available to electrons, protons, or deuterons is

[e]*|A(R)| = [e] * (u0/4*pi) * ln(2L/R) * I
= (1.6*10^-19 [C]) * (10^-7 [N/Amp^2]) * ln(20) * I
= 4.8 * 10^-26 [C] * [N/Amp^2] * I

So, the minimum current which can provide a colliding electron (at a
radial distance R) in this arc with 782 KeV is

I = {6.348 * 10^-22 [N*sec]} / {4.8 * 10^-26 [C*N/Amp^2]}
= 1.33 * 10^4 [Amp]

-- [e] = electron charge = 1.6*10^-19 [C], [C] = coulomb
u0 = permeability of free space = 4*pi*10^-7 [N/Amp^2]
ln = natural log, ln(20) ~ 3
[Amp] = [C]/[sec]

Much greater arc currents are routinely achieved [7].

NOTES -
1) Only electrons can acquire significant relativistic mass from
a momentum "kick" in arcs due to their small mass.
More massive protons, deuterons or tritons will not gain much mass.

2) The equation for |A(r)| is singular at r=0 (see [5]).
This is not "unphysical" since volume integral is still finite.
It shows that much smaller currents still can produce "heavy electrons"
at the center of current flow, but less frequently.

3) It is not obvious whether inner K-shell electrons of an atom in an
arc can be forced into the nucleus - resulting in "electron capture"

4) Perhaps a similar analysis applies to currents in emulsions of metal
particles in dielectric fluids [8].

REFERENCES -
[1] (p. 29) "A Student’s Guide to Cold Fusion"
http://lenr-canr.org/acrobat/StormsEastudentsg.pdf

[2] "Electron mass shift in nonthermal systems"
http://arxiv.org/pdf/0801.3810.pdf

[3] "Feynman Lectures on Physics" Vol.3, Ch.21 (p.5)
http://www.peaceone.net/basic/Feynman/V3 Ch21.pdf

[4] "On the Definition of 'Hidden' Momentum" (p.10 - note cgs units)
http://hep.princeton.edu/~mcdonald/examples/hiddendef.pdf

[5] UIUC Physics 435 EM Fields & Sources - LECTURE NOTES 16 (p.
http://web.hep.uiuc.edu/home/s…re_Notes/P435_Lect_16.pdf

[6] Accelerating Voltage Calculator
http://www.ou.edu/research/electron/bmz5364/calc-kv.html

[7] "EXPERIMENTAL INVESTIGATION OF THE CURRENT DENSITY AND THE HEAT-FLUX
DENSITY IN THE CATHODE ARC SPOT"
http://www.ifi.unicamp.br/~aruy/publicacoes/PDF/IfZh current density and U.pdf

[8] AMPLIFICATION OF ENERGETIC REACTIONS - Brian Ahern
United States Patent Application 20110233061
http://www.freepatentsonline.com/y2011/0233061.html - EXCERPT:

Comments/criticisms are welcome.

Good questions, Longview

I can only speculate on them.
BTW, I do not claim Hagelstein is wrong - only that (barring any miscalculation of mine) QED/QFT and simple QM analyses seem contradictory.
It's impossible for me to characterize and analyze the very messy physics of (alleged) LENR.
But, here are my best guesses, without guarantees -

1) Possibly the very large electric field gradients involved in plasmon charge foci (colliding e+p) localize e+p pairs so that enough mass/momentum is acquired.
I tried to do some calculations with large numbers of "classical" electrons confined in a steep (2 x 10^11 V/m) electric potential well, but it got too messy.
But, if the effect is real, arcing may only be one route to achieve the reaction.

2) I suppose all of your conjectures could be correct. Only experimentation will reveal which, if any, happen.

3) No idea. An interesting (but probably wrong) possibility, is something like the Branly effect.
For example, see "Cold Fusion And Branly Effect" - http://www.physforum.com/index.php?showtopic=27676
There are more papers on this at the Arxiv.org website.

4) Good question. I have no opinion.

5) Yes. A "classical" electron in a current is coupled to the others by the magnetic vector potential.
Some of the W-L papers use the "Darwin Lagrangian" which gives the coupling terms between electrons explicitly.
In any case, the classical electron does not want to stop during a collision, and borrows energy/momentum from the other electrons to resist stopping
- analogous to the way the atom a the tip of an arrow does from the arrow body.
The Feynman reference presents the math pretty clearly.

6) I do not know if the many arc experiments (e.g., Irion-Wendt) purporting to show transmutations were correctly analyzed.
They should be fairly simple to repeat, but it would take a brave experimentalist to challenge the established beliefs.
One of the papers George Miley co-authors claims some very bizarre effects can occur in intense arcs.

Longview,

I just attempted to post an answer, but somehow it got lost due to my hitting the wrong key.
If it does appear, ignore this one. But, I will condense what I tried to write earlier --

Regarding your question "How would this second momentum fit with deBroglie's equation?" --

It's important to distinguish between a wave packet's group velocity (translational motion) and
its phase velocity. A particle standing still (group velocity = 0) can still possess a spectrum with
high energy/momentum components (i.e., with high "phase velocities") - These have short
deBroglie wavelengths, but when all are superposed, there is no motion.

If I understand the theories correctly, this can occur in (at least) two ways -

First, when a colliding particle borrows energy (via e-m field coupling) from the parallel traveling
particles nearby - analogous to the atom the tip of an arrow.
Or, when a trapped particle is resonantly excited to amplify its high energy spectrum without
causing motion (e.g., see thread "New preprint on D-D LENR in metal deuterides") - analogous to
how water waves in a tank grow when shaken resonantly.

Only speculation. No assertions. Trust only experiments.

Logview,

Difficult questions.

I believe that the "qA" term will result in an effective mass increase for conduction
charge (positive or negative) equivalent to the field energy divided by number of
conduction charges - in direct collisions. In the case of a common inductive circuit,
I believe the field energy density is not high, and most field energy is just thermalized
in soft collisions, each of which extracts only a small amount of field energy.
This is all "hand wavey" - only an attempt to look at classical limits.

A particle in a fixed pure momentum state is a standing wave, and its phase velocity
is proportional to its frequency (inversely to its wavelength.) So a particle with
properly phased momenta components can be energetic and still move slowly,
and be highly localized, due to destructive phase interference away from the
average position of its waveform.

I believe that some of the theories could support proton (or other heavy particle)
involvement if they are in trapped in potential wells and acquire energy (i.e., a
dispersed momentum spectrum) via a resonant excitation. I believe that the
thread on Vladimir Vysotskii's theory -
"The Problem of Creating a Universal Theory of LENR Vladimir Vysotskii"
lenr-canr.org/acrobat/VysotskiiVtheproblem.pdf
- proposes this. Only successful, repeatable experiments can confirm.

- A class of relativistically rigid proper clocks -

R C Jennison

Journal of Physics A General Physics 12/1998; 19(12):2249. DOI: 10.1088/0305-4470/19/12/013
ABSTRACT The principles of proper time-keeping are considered and it is noted that an ideal solution may be represented by a system of helical null lines in 4-space. This construction is translated into 3-space and it is shown that it may be interpreted as a self-contained and coherent system of waves having a well defined boundary. These waves benefit the de Broglie components which interfere to form a rotating particle. Three configurations are considered. In each of these the localised wave system has two components of energy, one of which is at rest in the chosen frame and the other is circulating relative to it. These proper clocks appear to have very many of the properties of fundamental particles of matter and yet they are formed from non-particulate waves. It is finally suggested that the de Broglie waves in these particular configurations may be intrinsically of the same substance as electromagnetic waves trapped in an unfamiliar rotating configuration following a cataclismic event which has squeezed the fields together into a condensed, rotating state which is non-linear in its radial geometry and from which they cannot escape. The stable entities are an example of pure non-particulate matter which may also be applicable on a cosmic scale.

- The formation of charge from a travelling electromagnetic wave by reduction of the effective velocity of light to zero -

R C Jennison

Journal of Physics A General Physics 12/1998; 15(2):405. DOI: 10.1088/0305-4470/15/2/013
ABSTRACT An experiment is described in which an electromagnetic wave is retarded in a slow-wave structure and finally brought to rest relative to the laboratory by revolving the structure, in the opposite sense, at the same angular frequency as that of the wave. The static field system forced from the wave may be considered as electric charge having its origin in the distributed wave field.

https://books.google.com.ph/books?id=y8sSFTDkQ20C&lpg=PA310&ots=XYfftFbdO0&dq=jennison</a> phase locked cavities&pg=PA310#v=onepage&q=jennison phase locked cavities&f=false</p><p><br></p><p>
https://books.google.com.ph/books?id=SLm8sXLIO8oC&lpg=PA97&ots=X6n6Xa12C-&dq=jennison phase locked cavities&pg=PA103#v=onepage&q=jennison phase locked cavities&f=false

https://books.google.com.ph/books?id=lA8tgLMRu2kC&lpg=PA173&ots=EPiIn9nj_S&dq=jennison phase locked cavities&pg=PA173#v=onepage&q=jennison phase locked cavities&f=false

https://www.academia.edu/11093…_a_Phase-Locked_Resonator

Quote from Longview

We know that Aharonov-Bohm is relevant because Bohm and Schwinger said so, if I recall that correctly.

Randell Mills has a classical explanation of the purportedly quantum mechanical AB effect in GUTCP.

Í look at GUTCP on my desktop

for a few minutes at a time.. then get some paracetamol- acetaminophen for a headache

Heavy electrons play an important role in Widom-Larsen theory of cold fusion and they're simply normal electrons involving relativistic effects. Dense aether model handles space-time like dynamic foam of density fluctuations of hypothetical ultradense gas, similar to supercritical fluid. Particles which are moving across this foam make that foam temporarily more thick and dense like being surrounded of dense atmosphere or coat of vacuum fluctuations. Quantum mechanics handles this situation by so-called pilot wave concept, i.e. wake wave of vacuum undulated by particle moving through it. You can imagine it like wave formed above fish floating beneath water surface. The space-time deformed by pilot wave gets literally more dense for light waves and thick for particles. Note that pilot wave slows down light and speed of time for particle in motion in exactly the way, that the resulting speed of light would remain invariant - in this way the quantum mechanics plays well with special relativity. In dense aether model the speed dependent component of inertia, i.e. relativistic mass of particle represents simply mass of pilot wave which surrounds it. The faster the particle is moving, the more deformed space-time around it gets, the more dense the pilot wave looks like and the more the vacuum deformed by it adds to the effective mass of particle.

The Widom-Larsen theory thus considers, that the electrons are moving fast, so that they get heavy. These heavy electrons, i.e. electrons of high relativistic mass also play a role in many chemical and physical properties of heavy elements, the atoms of which are so large, that the electrons in outer orbital shells are forced to revolve them at high speed. Because such an electrons are thus more massive, their orbitals get shrunken, which brings a number of anomalies into periodic table of elements..

Quote

Possibly related to this, an examination of "heavy electron" theory, will show that generally mass variation for electrons or "effective electrons" is vectorial, that is an increased effective mass in one direction is accompanied by decreases in at least one of the other spatial dimensions.

If we take a look at pilot wave, we realize that it deforms vacuum only in direction of particle actual motion, that means that in another directions the vacuum remains relatively flat. The perceived/observed inertia of electrons would thus correspond the deform of vacuum observed from particular direction. The effective mass of electron doesn't decrease in perpendicular directions - except the fact, that increased vacuum density makes the rest mass of electron relatively lower as a whole. What de-Broglie wave affects instead is the projection of particle spin into direction of particle motion: the half-integer spin of electron changes gradually into integer spin of boson - in another words, the fast moving particle gets widespread and it gradually changes into a charge wave.

Quote

Can we argue that it is nearly the same mass gain, for modest velocities as a percent of C (electron at say 10%, or ~0.5% mass increase and proton at way under 0.01% or ~zero mass increase) likely to be seen in many CF / LENR experiments often involving very short range accelerations?

Yep, any acceleration of particle ads another undulation to its pilot wave - actually the more, the higher derivatives of motion gets. In my theory the cold fusion results from Astroblaster effect during sharp collisions of multiple atoms along single line, during which the orbitals at the place of collision get literally shaken and their electrons gain high relativistic mass for a brief moment of time.

Quote from Zephir_AWT

If we take a look at pilot wave, we realize that it deforms vacuum only in direction of particle actual motion, that means that in another directions the vacuum remains relatively flat. The perceived/observed inertia of electrons would thus correspond the deform of vacuum observed from particular direction. The effective mass of electron doesn't decrease in perpendicular directions - except the fact, that increased vacuum density makes the rest mass of electron relatively lower as a whole. What de-Broglie wave affects instead is the projection of particle spin into direction of particle motion: the half-integer spin of electron changes gradually into integer spin of boson - in another words, the fast moving particle gets widespread and it gradually changes into a charge wave.

Yep, any acceleration of particle ads another undulation to its pilot wave - actually the more, the higher derivatives of motion gets. In my theory the cold fusion results from Astroblaster effect during sharp collisions of multiple atoms along single line, during which the orbitals at the place of collision get literally shaken and their electrons gain high relativistic mass for a brief moment of time.

Dear Zephir,

Could your model be related with polaritron plasmons and latest Google patent explanation ?

Quote from Zephir_AWT

..heavy elements, the atoms of which are so large, that the electrons in outer orbital shells are forced to revolve them at high speed.

Quote from Zephir_AWT

These heavy electrons, i.e. electrons of high relativistic mass also play a role in many chemical and physical properties of heavy elements, the atoms of which are so large, that the electrons in outer orbital shells are forced to revolve them at high speed. Because such an electrons are thus more massive, their orbitals get shrunken, which brings a number of anomalies into periodic table of elements..

This "electrons in outer orbital shells..." is nonsense - may be a typo: "inner shell orbits are supposed to move faster. But calculations show that there is no classic correlation between relativistic mass increase due to higher speed in deeper nuclear orbits. The main reason is that inner electrons move on SO(4) orbits and not on classical ones...

Even worse: If you look at e.g. gold then you cannot see inner electrons on orbits anymore. One more modeling challenge.

Only free electrons acquire classic relativistic mass but these certainly play no direct role in LENR. But they could provide the oscillating fields we need.

Quote

" is nonsense - may be a typo: "inner shell orbits are supposed to move faster

Of course I do many typos, but according to Kepler law the electrons should move the faster, the father from atom nuclei are.

This is also why the relativist mass affects gold but not lightweight atoms.

Quote from Zephir_AWT

according to Kepler law

Kepler's law may not be tested on orbital electrons..

Mills has a whole lot to say about outer orbital electrons

however inner electrons in the K shell he hardly mentions

especially not for atoms like gold. palladium unfortunately..

since these may be operational in LENR.

GUTCP has severe limitations

Quote from Zephir_AWT

Of course I do many typos, but according to Kepler

Which Keppler?? Outer planets must move slower...Newton laws...

You're right, I got it opposite - relativistic effects shrink central orbitals of atom and they leave just outer electrons unaffected. Thank for correction.