The Flow of Energy

Scientific Paper
Title	The Flow of Energy
Read in full	Link to paper
Author(s)	Frank J Znidarsic, Glen A Robertson
Keywords	energy, Cold Fusion, speed, LENR, speed of transition, Josephson junction, Planck constant, gravitational anomaly
Published	2011
Journal	Physics Procedia
Volume	20
No. of pages	8
Pages	457-464

Read the full paper here

Abstract

In this paper, the flow of energy in materials is presented as mechanical waves with a distinct velocity or speed of transition. This speed of transition came about through the observations of cold fusion experiments, i.e., Low Energy Nuclear Reactions (LENR) and superconductor gravity experiments, both assumed speculative by mainstream science. In consideration of superconductor junctions, the LENR experiments have a similar speed of transition, which seems to imply that the reactions in the LENR experiment are discrete quantized reactions (energy - burst vs. continuous). Here an attempt is made to quantify this new condition as it applies to electrons; toward the progression of quantized energy flows (discrete energy burst) as a new source of clean energy and force mechanisms (i.e, propulsion).

Overview

Presented at the Space, Propulsion & Energy Sciences International Forum in 2011 and published in Physics Procedia, this paper is the most formal published statement of Frank J Znidarsic's central claim, written with Glen A Robertson: that there exists a characteristic speed of transition V_t ≈ 1.094 × 10⁶ m/s at which energy passes between the electronic and nuclear structures of matter, and that when energy flow reaches this speed it becomes discrete — delivered as a burst rather than a continuous emission — opening the door to phenomena not seen in classical systems.

The authors treat the flow of energy in a material as a mechanical wave: only the energy propagates, the material itself stays near equilibrium, and the wave passes by jumping from particle to particle. The number V_t is not postulated from theory but read off from two experimental programmes that mainstream physics regards as speculative — Low Energy Nuclear Reactions (LENR, or cold fusion) and the superconductor gravity anomaly experiments — where the authors find the same order-of-magnitude velocity appearing independently.

The paper's ambition is then to show that this same velocity is already implicit in ordinary atomic physics. It argues that the Bohr radius, the electron orbital radii, the photoelectric relation and even Planck's constant can be recovered as consequences of a condition in which "the speed of light within the electronic structure of the atom equals the speed of a mechanical wave within its nuclear structure" — an impedance match that permits energy to be exchanged without reflection and so allows the quantum transition to proceed. Modes of differing impedance, they write, "are evanescent and block the flow of energy". This inverts the usual direction of explanation: rather than deriving atomic structure from quantum postulates, the postulates are presented as emerging from a classical wave-matching condition.

The argument

The speed of transition from LENR

The starting observation is that LENR experiments report thermal energy and nuclear transmutations, including of heavy elements, at room-temperature energies of a fraction of an electron volt, where contemporary theory requires millions of electron volts — and with very little or no radiation. The authors suggest such reactions could proceed without radiation "under a condition where the range of the nuclear spin-orbit force is extends through the coulombic barrier", so that cold fusion "may require a radical restructuring of the range and strength of the natural forces".

Taking the reaction domain as r_N of order nanometres and the associated angular frequency as ω_N ~ 10¹³ to 10¹⁴ Hz, the product r_Nω_N gives a transitional speed of order 10⁶ m/s. Written generally,

V_t = (f_c/n_i)(2πn_xr_x) = (n_xr_x/n_iλ_i)c

with the thermal frequency expressed as a fraction 1/n_i of the Compton frequency f_c = 1.236 × 10²⁰ Hz. With r_x ≈ 2r_e this yields V_t ≈ 1.0942 × 10⁶ m/s. In classical mechanics V_t would be infinite, corresponding to n_x ≈ n_i; here it is postulated that when the particle wavelength becomes quantized so must the reaction range, and hence so must the energy flow.

The superconductor analogy

The same number is then obtained from a completely different system. A Josephson junction gap is of order a few nanometres, and the superconductor electron-pair fluctuation time is of order 10⁻¹⁴ s; the product of gap and frequency again gives a separation speed of order 10⁶ m/s — the speed required, on this reading, to release the electron pairing energy and cross the junction. The authors further cite Li and Torr's calculation that the phase velocity of gravitational waves inside any superconducting material would be ~10⁶ m/s, and connect this to the Podkletnov gravitational anomaly experiments of the early 1990s, in which a two-layer high-T_c superconducting disk reportedly produced a local gravitational effect that "seems to violate the conservation laws".

The convergence of these two independent speculative results is the paper's central empirical claim: it "appear[s] to place a minimum velocity with respect to distance and time from which 'free' energy (i.e.; vacuum energy; dark energy or etc.) can be pulled from the subatomic scale (~10⁻⁹ m) interactions".

A mechanical wave in the nucleus

The authors next reconstruct V_t from nuclear parameters. Starting from a harmonic potential energy E = ½K_er_x², they let the electron elastic constant follow from a "maximum electrical charge force" F_max = 29.05 N as K_e = F_max/n_xr_x, and argue that K_e equals the strong-force constant at the point where the expansive electromagnetic force balances the compressive nuclear force. The speed of transition then becomes the product of a harmonic-oscillator frequency and a displacement,

V_t = (λ_i/2π)√(K_i/m_i)

and for a neutron of mass 1.6749 × 10⁻²⁷ kg at a displacement equal to the Fermi spacing r_n = 1.36 × 10⁻¹⁵ m this gives V_t = 1.0932 × 10⁶ m/s — the same value again.

Planck's constant as a condition on the speed of transition

The paper's most striking derivation concerns the electron. From the photoelectric effect the transition speed of an emitted photon is V_t ≈ λ_if_i. The capacitance of the transitional state is obtained geometrically, by "letting the area swept out by a light wave equal to its wavelength squared and setting the distance between the peaks in the wave's amplitude equal to one half wavelength", giving C = 2ε₀λ_e and hence C = 2ε₀(V_t/f_e). Substituting into the electrostatic energy E = ½Q²/C and equating with E = hf_e yields

V_t = Q²/(4πε₀ħ) = 1.0938 × 10⁶ m/s

for a single elementary charge — from which the authors conclude that Planck's constant "emerges as a condition on the speed of transition of electrons in a bulk mass", rather than being an independent postulate.

Electron orbital radius

Setting the nuclear mechanical-wave speed equal to the speed of light within the electronic structure gives ω_er_or = V_t. Working the same elastic constant through for the electron reproduces V_t = 1.0938 × 10⁶ m/s, and the authors then note that the combination F_maxr_p/(M_eV_t²) evaluates to 0.529 × 10⁻¹⁰ m — the ground-state radius of hydrogen. The result is that the electron orbital radius r_or ≈ n_e²r_h is a square multiple of the hydrogen ground-state radius, recovering the familiar n² scaling of the Bohr model from the impedance-matching condition.

The de Broglie wave and the transitional frequency

Following de Broglie's derivation of the matter wave from the superposition of the Compton wave and its Doppler-shifted reflection, the authors obtain λ_d = 2πħ/m_iv_i and hence V_t = 2πħf_i/m_iv_i. Combining with the photoelectric result gives a baseline transitional frequency

f_e = (m_e/ħ)(e²/4πε₀)/V_t

which for V_t = 1.0938 × 10⁶ m/s gives f_e = 1.6448 × 10¹⁵ Hz — "which is of the range of the LENR; but about twice that of the gravitational anomaly experiments". Applying the same relation to a bound electron pair returns a junction spacing of 1.33 × 10⁻⁹ m, described as "the ballpark estimate for the Josephson junction gap distance in superconductors".

Conclusion

The authors conclude that at transition speeds at or above ~10⁶ m/s new phenomena can occur, that the agreement between the LENR and gravity-anomaly experiments points to a threshold velocity below which such energy cannot be extracted, and that this understanding "may lead to new sources of clean energy and force mechanisms (i.e; propulsion)".

Assessment

The paper's appeal is the recurrence of one number. The same ~1.09 × 10⁶ m/s is arrived at from the nanometre-scale reaction domain of LENR, from the Josephson junction gap and pair-fluctuation time, from a harmonic-oscillator estimate at nuclear dimensions, and from the photoelectric relation combined with a geometric capacitance — four routes that do not obviously share assumptions. The impedance-matching framing is also a physically natural one: energy transfer between coupled systems really is governed by impedance, and asking what impedance condition permits a quantum transition to complete without reflection is a reasonable question to pose. Recovering the n² scaling of the Bohr radii from that condition is a genuine formal result within the paper's own scheme.

Several difficulties should be recorded plainly.

The empirical foundation is contested. Both anchor experiments are described by the authors themselves as "assumed speculative by mainstream science", and this is understated in one case: the Podkletnov gravity-shielding result has not been independently reproduced, and published replication attempts have reported null results at sensitivities well below the claimed effect. LENR excess-heat and transmutation claims remain unresolved after three decades and are not accepted as established. A quantity inferred from two unreplicated results inherits their uncertainty; if either dataset is wrong, the coincidence that motivates the whole paper dissolves.

Several steps are stipulated rather than derived. The "maximum electrical charge force" F_max = 29.05 N is introduced by name and value without derivation. The capacitance in equation (7) rests on a geometric convention — that a light wave sweeps out an area equal to its wavelength squared, with peak separation of half a wavelength — that is chosen, not obtained. The equality of the electron elastic constant with the strong-force constant is asserted at a balance point rather than computed. Because these choices feed directly into the numerical outputs, the agreement of the outputs is less independent than it appears.

The direction of derivation is questionable in the Planck-constant result. Equation (13) is algebraically the statement V_t = e²/(4πε₀ħ) — which is simply αc, the Bohr orbital velocity — divided by two, obtained by combining the assumed capacitance with the already-known relation E = hf. Read that way, Planck's constant has not "emerged" from anything; it was inserted through the photoelectric relation and then rearranged. Whether the rearrangement constitutes an explanation or a restatement is precisely the point a critical reader must decide.

Finally, the authors record their own mismatch: the derived transitional frequency of 1.6448 × 10¹⁵ Hz is "about twice that of the gravitational anomaly experiments". A factor of two between the two systems the paper is trying to unify is not fatal, but it is unexplained, and the paper leans on order-of-magnitude and "ballpark" agreement in several places where a quantitative theory would want better. The concluding suggestion that "free energy (i.e.; vacuum energy; dark energy or etc.)" can be pulled from subatomic interactions is a considerably stronger claim than anything the preceding sections establish.

See also

• Frank J Znidarsic
• Glen A Robertson
• The Control of the Natural Forces
• Overview of the Control of the Natural Forces
• Cold Fusion
• Louis de Broglie