The internal conflicts and spats around the Copenhagen era
have been obscured
by a goldtinted sepia..and dogma.
Change gonna come rather than QM plus ca change
I believe that change is imminent
But the change is not going to be by ethereal SAM
The magnetic forces in the nucleus cannot be wished away like this
"There is only one fundamental force: the electrostatic attraction force that is acting between the proton and the electron.
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We had a long debate about this. (Not sure the debate is over...)
Here is a summary of this put together by Jan Emming (SAM):
Dear AHG members,
- Recently, several papers have been circulating in the Ad Hoc Group relating to the nature and structure of the nucleus. Since nucleons have a magnetic moment, it may reasonably be assumed that currents are involved. The recent paper by Paolo Di Sia: The “Renaissance” in Nuclear Physics: Low-Energy Nuclear Reactions and Transmutations, makes this assumption and calculates the magnetic fields of coupled circulating currents. Their results show that in a close-packed nuclear lattice, valid binding energies and magnetic moments can be obtained by considering the magnetic forces between nucleons.
However, comments by Jean-Luc Paillet, in a December 18, 2018 email to the Ad Hoc group, disputes the validity of the derivation of the magnetic field from electric currents using the Biot-Savart law. Andrew Meulenberg in an email of December 17, 2018 comments that he doesn’t think either that the derivation is correct, even though Di Sia may have the right concept.
In the paper the nucleons are represented as circulating currents; see their Fig. 4 and Fig. 5, below. There are no assumptions as to the nature of the currents; only that they circulate in the two circuits 1 and 2. The author calculates the magnetic field at P2 caused by the current i1 for the two different “phasings,” implying that the currents vary in time.
- Feynman [1] and Griffith [2] both emphasize that Biot-Savart, strictly speaking, only applies to electrostatics. Griffiths states in section 5.2 that Biot Savart applies under the condition of “steady” currents (page 223). This means that the density of the circulating charge at each point must be constant: ∂i/∂t = 0. He also states that the law “represents a suitable approximation as long as the actual fluctuations are remote, or gradual.” However, in this situation, with time-varying fields, that stipulation doesn’t apply: time retardations should be considered. Thus, both Jean-Luc and Andrew are correct in their doubts about using the Biot-Savart law this way. However, there is more to the story.
- This Wikipedia article gives the time-dependent generalized equations of the Biot-Savart law by Jefimenko, but stops short of solving the equations. Griffiths uses a Taylor expansion of the Jefimenko integrals in which the higher order derivatives are ignored. He reaches the surprising conclusion that Biot-Savart can be applied after all, due to the cancellation of two errors in the final equation. In his words on page 451: “the Biot-Savart law holds, with the current evaluated at the non-retarded time. This means that the quasi-static approximation is actually much better than we had any right to expect: the two errors involved (neglecting retardation and dropping the second term in Eq. 10.38) cancel one another, to first order.”
- From the foregoing, it can be concluded that the analysis in the paper by Di Sia, is defensible and that it can be applied to calculate binding energies and magnetic moments to a good approximation. This model of coupled ring currents appears to imply that the nucleus is a resonant system at a specific frequency, continuously exchanging energy between nucleons, manifested as mutual attraction or repulsion. All nucleons in a specific element/isotope accommodate each other, finding a way to resonate together. This also explains that there is a definite limit to adding protons or neutrons to a specific structure: at some point a “dissonant” candidate will not fit in. The analysis by Di Sia is made in the context of the FCC model from Norman Cook. It should also apply to the Structured Atom Model (SAM).
- One important issue/question is whether stability of the nucleus can be explained by EM theory. This model appears to provide the mechanism for that stability. Feynman [1] makes the categorical statement: There are no points of stable equilibrium in any electrostatic field – section 5-2. Since the atom is thought to be a collection of static negative electrons and positive protons, quantum mechanics was needed for stability of the atom. Similarly, for a stable nucleus the strong force was postulated. Thus, the electrostatic repulsion between electronic charges appears to be balanced by the dynamic magnetic attraction in a system of synchronized oscillators. If the wavelength of the current is related to the size of the nucleon, on the order of femtometers, then the frequency of the oscillators would be on the order of 1023 Hz. It appears that there is a direct analogy between the atom and the nucleus, in that both resonate at characteristic frequencies dependent on the number of oscillators/nucleons involved. Of course, the atomic (Rabi) oscillations are in the optical domain, with applications in magnetic resonance, solid state physics and quantum computing, for example. At the nucleon level, the resonances will be in the gamma ray region and any practical applications are way beyond current technology.
- Finally, regarding Bob Cook’s email of February 7, 2019, where he refers to Mac Wheeler’s upcoming presentation to the APS on the synchronization of (biological) oscillators. http://meetings.aps.org/Meeting/MAR19/Session/C56.11 It appears that Mac knows a lot about this subject and his paper should be relevant to the study of the nucleus, in addition to the biological applications mentioned in the thread of that email by Nigel Dyer. Nigel suspects a connection to proton-proton interaction for the synchronization. Could it be that the switching of proteins between two states approximately every 12 minutes, has something to do with the neutron decay time of 14 minutes? I am looking forward to see the text of Mac’s presentation in due time.
References:
[1] Feynman: http://www.feynmanlectures.caltech.edu/II_toc.html
Sections 5-2, 5-4, 14-1, 14-2, 14-5, and 14-7 (Biot-Savart)
[2] Introduction to Electrodynamics, 4th Edition (2017), Cambridge University Press, by David J. Griffiths-Kindle edition.
