Archive for September, 2012

Results for relativistic tunneling

Tuesday, September 25th, 2012

Feed: Dr. Myron Evans
Posted on: Tuesday, September 25, 2012 12:32 PM
Author: metric345
Subject: Results for relativistic tunneling

These are important results from Dr Horst Eckardt, they show that the slower the incoming particle the more the tunnelling – so it seems that this is strong evidence for low energy nuclear reaction. The high energies needed for relativistic effects inhibit the quantum tunelling and fusion. I used google keywords “quantum tunnelling of atoms” to find that there is a complete dissertation on the net on the sobject of atomic qunatum tunnelling. I suggest a plot of T against m from the standard equation for transmission, eq. (10) of note 228(12) without relativistic effects, keeping everything constant except m. Loosk as if UFT228 will be a good paper.

228(12).pdf

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Discussion on Note 228(12)

Tuesday, September 25th, 2012

Feed: Dr. Myron Evans
Posted on: Tuesday, September 25, 2012 5:07 AM
Author: metric345
Subject: Discussion on Note 228(12)

Agreed with these remarks, the relativistic theory in essence premultiplies k and kappa by the Lorentz factor gamma and adds a term due to rest energy. Specialists with supercomputers can refine the details of these simple but instructive calculations. So I will now proceed to write up my sections of UFT228.

In a message dated 25/09/2012 10:44:21 GMT Daylight Time, writes:

In eq. (10) the square is missing after the first parenthesis in the denominator.
You have defined kappa with a factor (E-V0). In our considerations we have V0>E for quantum tunneling. Since kappa must be real valued, I used the factor (V0-E) instead. I think that (E-V0) is correct as far as the k vector in the barrier region is considered, and this comes out so from the Schroedinger equation. But for kappa we have

k = i kappa

which reverses the sign of (E-V0).

Horst

Sent: Tue, Sep 25, 2012 11:21 am
Subject: 228(12) : LENR, Relativistic Theory of Quantum Tunnelling

In this case the transmission coefficient is given by eq. (10) and for a given particle mass m, barrier thickness 2a and potential height V sub 0, T can be plotted against the incoming particle velocity v. The new linear equation of relativistic quantum mechanics was used to derive this result. In the hyper relativistic limit:

v goes to c

the following assumption is usually used

gamma m = 1

In the non relativistic limit:

v << c

these equations reduce to the theory already graphed for UFT228. So Horst may like to graph these results as usual and I will proceed to write up UFT228 with co authors Horst Eckardt and Douglas Lindstrom.

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Gamma Ray Production in LENR

Tuesday, September 25th, 2012

Feed: Dr. Myron Evans
Posted on: Tuesday, September 25, 2012 3:38 AM
Author: metric345
Subject: Gamma Ray Production in LENR

These are important remarks. The relativistic theory just sent over can be used to consider the collision of a relativistic electron with a static electron, reprsented very roughly by V sub 0. This could produce gamma rays by annihilation. Usually the particle accelerators consider the collision of an electron with a positron. The most well known products are gamma rays:

e (minus) + e (plus) = 2 gamma

The incoming wave vector k could also be augmented by a quantum of spacetime momentum. In the region

E goes to zero, a goes to zero T goes to one, finite V sub 0

a small amount of spacetime energy might catalyze the nuclear reaction. In general there are quanta of spacetime E and quanta of spacetime p. It could be that the gamma rays are emitted and absorbed again, so are not observed as a product of the reaction. Of course we do not want harmful gamma rays to be emitted by the apparatus.

In a message dated 25/09/2012 09:03:52 GMT Daylight Time:

For further discussion:
At the Zurich conference, Rossi told that gamma rays are a substantial part of the LENR process and transmutation is more a by-product. However such rays are not detected outside the reactor what is a bit surprising. Perhaps an explanation is that these gamma rays are the reaction components from spacetime. Nevertheless, since Hydrogen is involved which is brought in via a special ceramic (my guess), the nuclear process is essential. The catalysing process is unclear and could even consist of the electronic structure of the ceramic. As we have seen from Merzbacher and our results, the transmission coefficient can be enhanced at certain places in the crystal lattice, perhaps at the positions of the Ni nuclei. This would require however that the Ni atoms move from the powder (how they are put in) into the ceramic.

Horst

Sent: Tue, Sep 25, 2012 9:38 am
Subject: Low Energy Nuclear Fusion Reactors (LENR)

Many thanks to Dr Gareth John Evans. I hope that LENR will be developed with the utmost urgency to replace wind turbines. LENR should be used alongside gas and coal until new forms of energy production are ready to come on market.

Excellent new physics that the standard model could never explain. This may be how science progresses but increasingly we must wonder how much has been missed by the old physics with all its flaws. Modern physics was naive and full of errors and misconceptions that resulted at times in nonsense and deflected thought from areas like LENR that are important and useful. Well done both of you – your contributions to natural philosophy are immense.

Subject: Fwd: Transmission plots, E dependence

Co author of UFT288, Horst Eckart, demonstrates in this 3 – D graph the precise condition for low energy nuclear reaction through standard quantum tunnelling through a barrier of width 2a. He shows that when a approaches zero (very thin barrier), the transmission coefficient approaches 100% even when the energy of the incoming particle approaches zero. It quantum tunnels straight through a barrier represented by V sub 0 = 10. This is not possible in classical physics. Contemporary supercomputer code libraries may have programs that could compute this process for two real atoms fusing with each other, i.e. one of them quantum tunnels straight in to the other AT LOW ENERGY. This is of course the simplest first theory of quantum tunnelling, but it gives all the essentials of even the most sophisticated code. The final step for UFT228 is to incorporate relativistic effects.

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228(12) : LENR, Relativistic Theory of Quantum Tunnelling

Tuesday, September 25th, 2012

Feed: Dr. Myron Evans
Posted on: Tuesday, September 25, 2012 3:23 AM
Author: metric345
Subject: 228(12) : LENR, Relativistic Theory of Quantum Tunnelling

In this case the transmission coefficient is given by eq. (10) and for a given particle mass m, barrier thickness 2a and potential height V sub 0, T can be plotted against the incoming particle velocity v. The new linear equation of relativistic quantum mechanics was used to derive this result. In the hyper relativistic limit:

v goes to c

the following assumption is usually used

gamma m = 1

In the non relativistic limit:

v << c

these equations reduce to the theory already graphed for UFT228. So Horst may like to graph these results as usual and I will proceed to write up UFT228 with co authors Horst Eckardt and Douglas Lindstrom.

a228thpapernotes12.pdf

View article…

Low Energy Nuclear Fusion Reactors (LENR)

Tuesday, September 25th, 2012

Feed: Dr. Myron Evans
Posted on: Tuesday, September 25, 2012 1:40 AM
Author: metric345
Subject: Low Energy Nuclear Fusion Reactors (LENR)

Many thanks to Dr Gareth John Evans. I hope that LENR will be developed with the utmost urgency to replace wind turbines. LENR should be used alongside gas and coal until new forms of energy production are ready to come on market.

Excellent new physics that the standard model could never explain. This may be how science progresses but increasingly we must wonder how much has been missed by the old physics with all its flaws. Modern physics was naive and full of errors and misconceptions that resulted at times in nonsense and deflected thought from areas like LENR that are important and useful. Well done both of you – your contributions to natural philosophy are immense.

Subject: Fwd: Transmission plots, E dependence

Co author of UFT288, Horst Eckart, demonstrates in this 3 – D graph the precise condition for low energy nuclear reaction through standard quantum tunnelling through a barrier of width 2a. He shows that when a approaches zero (very thin barrier), the transmission coefficient approaches 100% even when the energy of the incoming particle approaches zero. It quantum tunnels straight through a barrier represented by V sub 0 = 10. This is not possible in classical physics. Contemporary supercomputer code libraries may have programs that could compute this process for two real atoms fusing with each other, i.e. one of them quantum tunnels straight in to the other AT LOW ENERGY. This is of course the simplest first theory of quantum tunnelling, but it gives all the essentials of even the most sophisticated code. The final step for UFT228 is to incorporate relativistic effects.

View article…

Exact Condition for LENR: Transmission plots, E dependence

Tuesday, September 25th, 2012

Feed: Dr. Myron Evans
Posted on: Monday, September 24, 2012 11:36 PM
Author: metric345
Subject: Exact Condition for LENR: Transmission plots, E dependence

Co author of UFT228 (in prep.), Horst Eckart, demonstrates in this 3 – D graph the precise condition for low energy nuclear reaction through standard quantum tunnelling through a barrier of width 2a. He shows that when a approaches zero (very thin barrier), the transmission coefficient approaches 100% even when the energy of the incoming particle approaches zero. It quantum tunnels straight through a barrier represented by V sub 0 = 10. This is not possible in classical physics. Contemporary supercomputer code libraries may have programs that could compute this process for two real atoms fusing with each other, i.e. one of them quantum tunnels straight in to the other AT LOW ENERGY. This is of course the simplest first theory of quantum tunnelling, but it gives all the essentials of even the most sophisticated code. The final step for UFT228 is to incorporate relativistic effects.

View article…

LENR, Further Comments on Quantum Tunnelling (Note 228(6))

Saturday, September 22nd, 2012

Feed: Dr. Myron Evans
Posted on: Saturday, September 22, 2012 10:51 AM
Author: metric345
Subject: LENR, Further Comments on Quantum Tunnelling (Note 228(6))

The results show that:

1) When V = E, x = 0 for all a, and T = 1, there is complete transmission through the barrier.
2) When a approaches zero for finite kappa, then T approaches 1, and there is complete transmission.
3) When kappa approaches zero for finite a, then T approaches 1 and complete transmission.
4) The rate of change of T with x = kappa a is minimized at x = 0.25.

When there is complete transmission, an incoming matter wave of an atom passes right through the barrier (another atom) . Under this condition, fusion has occured in one sense. These results can be refined greatly in several directions in future work. For example the relativistci theory of note 228(7) can be developed. Also, when

dT / dx = 0

there is a maximum, minimum or inflection of T in general. There may be more than one solution to this equation. At x = 0 there is a maximum of T.

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Checking my Hand Calculations in 228(6)

Saturday, September 22nd, 2012

Feed: Dr. Myron Evans
Posted on: Saturday, September 22, 2012 8:02 AM
Author: metric345
Subject: Checking my Hand Calculations in 228(6)

Thanks again to Horst for checking eq. (20) of note 228(6) by computer algebra, the equation is correct. So quantum tunnelling is a far more complicated problem than people might think. It needs computer algebra to find its most basic features.

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LENR, Graphs of the Transmission Coefficient of Standard Quantum Tunnelling

Saturday, September 22nd, 2012

Feed: Dr. Myron Evans
Posted on: Saturday, September 22, 2012 7:58 AM
Author: metric345
Subject: LENR, Graphs of the Transmission Coefficient of Standard Quantum Tunnelling

Many thanks to co author Horst Eckardt for this graph, which shows that the transmission coefficient of standard quantum tunnelling theory is a maximum of one at

x = kappa a = 0

and falls to zero monotonically with increasing x. The function dT / dx goes through a minimum at

x = 0.25

The dT / dx function is exceedingly complicated and has to be evaluated by computer algebra, which also evaluates the complex number algebra. So to maximize the chances of low energy nuclear reactions, the transmission coefficient must be maximized, so kappa must be very low for a given a (thickness of the square well), or a must be very small (thin sample) for a given kappa (the wavenumber inside the square well). It could be that the fused entity is at its most stable condition at the minimum of dT / dx, the point at which the transmission coefficient changes the most slowly with x = kappa a. It was found that Merzbacher’s calculations are correct, (E. Merzbacher, “Quantum Mechanics”, Wiley, second edition), but those of P. W. Atkins for the same problem are wildly erroneous (P. W. Atkins, “Moelcular Quantum Mechanics”, Oxford University Press) due to erroneous alegbra and maybe more errors in concept. The next step is to input spacetime resonant absorption now that the baseline problem has been defined.

228(6).pdf

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228(7) : LENR, Relativistic Theory of Quantum Tunnelling

Saturday, September 22nd, 2012

Feed: Dr. Myron Evans
Posted on: Saturday, September 22, 2012 7:38 AM
Author: metric345
Subject: 228(7) : LENR, Relativistic Theory of Quantum Tunnelling

In this case the trasnmission coefficient is given by eq. (37), with kappa and k defined by eqns. (36) and (33). The new relativistic generalization of the Schroedinger equation is eq. (34).

a228thpapernotes7.pdf

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