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This paper develops the quantum branch of the Temporal Theory of the Universe (TTU), showing that temporal gradients (∇T) directly affect the probability of low-energy quantum tunneling. When a particle enters a region of slower time flow, its effective kinetic energy rises by E₍grad₎ = η ∇T, lowering the Coulomb barrier and enhancing tunneling according to a modified Gamow factor. The work introduces the Temporal Tunneling Equation (TTE), which quantitatively links macroscopic time-field variations with microscopic quantum behavior. Numerical estimates suggest that gradients ∇T ≈ 10⁻¹⁹ - 10⁻²⁰ s/m can reduce the potential barrier by about 10⁻³ eV, sufficient to explain neutron anomalies observed in metal-hydride systems at cryogenic temperatures. The paper defines the physical meaning of the coupling coefficient η and coherence parameter γ, proposes laboratory methods to detect ∇T, and outlines prospects for temporal engineering-the deliberate control of time gradients to influence quantum and nuclear processes. | ||
Theory of Low-Temperature Quantum Tunneling
Lemeshko Andriy
Doctor of Philosophy, Associate Professor
Taras Shevchenko National University of Kyiv, Ukraine
ORCID: 0000-0001-8003-3168
Abstract
This paper develops the quantum branch of the Temporal Theory of the Universe (TTU), demonstrating how temporal gradients (T) influence the probability of low-energy quantum tunneling.
When a particle or nucleus enters a region of slower time flow, its effective kinetic energy increases by Egrad = T, reducing the Coulomb barrier and enhancing tunneling according to a modified Gamow factor.
The model introduces the Temporal Tunneling Equation (TTE), quantitatively connecting macroscopic temporal fields with microscopic quantum events.
Numerical estimates indicate that gradients T - 10 10« s/m lower the effective barrier by - 10 eV, sufficient to explain anomalous neutron emissions in metalhydride systems at cryogenic temperatures.
The work refines key parameters the temporal-energy coupling and coherence parameter and outlines realistic mechanisms for generating T in laboratory and plasma environments.
These results extend TTU into the quantum domain, establishing time-gradient physics as a testable bridge between relativity, condensed-matter, and nuclear phenomena.
Keywords: temporal gradients, TTU, quantum tunneling, cold fusion, temporal field, modified Gamow factor, temporal engineering
1 Introduction: From TTU to Quantum Mechanics
Conventional quantum mechanics treats tunneling as a purely probabilistic process determined by barrier height V and particle energy E.
Yet multiple reports of low-temperature fusion and anomalous neutron emission suggest the presence of additional, non-thermal activation channels.
The Temporal Theory of the Universe postulates that variations in the local rate of time flow, (x,t) = dT/dt, create real conservative forces capable of modifying microscopic dynamics.
When applied to tunneling systems, this framework predicts an additional energy term linked to the temporal gradient T, producing measurable deviations from classical tunneling probabilities.
2 Theoretical Foundation
The TTU force law defines the interaction of matter with a non-uniform temporal field:
= m c« ln
where is the local rate of time flow.
Integration along the tunneling path yields an incremental energy proportional to T:
Egrad = T
Here is the coupling coefficient between temporal-field variation and particle energy (J"s/m).
This leads to an effective potential:
Veff = V Egrad
A positive T (slower internal time) lowers Veff and increases transmission probability.
The dynamics of the temporal field follow from a Lagrangian density
= ()« «,
where represents the stiffness of time (resistance to rapid variation) and defines its coupling to matter.
The ratio / sets the propagation length of temporal perturbations effectively a permeability of time.
3 The Temporal Tunneling Equation (TTE)
The transmission probability through a potential barrier of width d and height Veff is
P exp [ -( (2m / «) " (V (E + T)) ) / (1 + T) ]
where
m particle mass,
reduced Planck constant,
temporal energy-coupling coefficient,
temporal coherence parameter.
As T 0 and T 0, the expression reduces to the classical Gamow factor.
The denominator (1 + T) captures how temporal decoherence suppresses tunneling enhancement.
4 Physical Interpretation of and
Temporal Energy Coupling Coefficient
The parameter links the spatial gradient of time to energy gain:
Egrad = T.
Dimensional analysis (J"s/m) implies - / , where = c is the temporal Compton length of the particle.
Thus scales inversely with mass:
- / (m c).
Heavier particles experience smaller coupling, while light particles (e.g., electrons) are more sensitive to T.
Temporal Coherence Parameter
quantifies the interaction between temporal fluctuations T and the phase stability of the wavefunction.
It can be related to the coherence lifetime _c of the tunneling state:
- 1 / _c.
Large corresponds to rapid decoherence (short _c), while small preserves temporal coherence and amplifies tunneling probability.
This makes an experimentally observable property, measurable through phase-noise spectra or interferometric linewidths.
5 Numerical Estimates
Process | T (s/m) | Egrad (eV) | P / P (increase) |
|---|---|---|---|
DD fusion in Pd lattice | 10 | 10 | - 10 increase |
DT fusion | 10« | 10 | - 10« increase |
Electron tunneling (Josephson) | 10 | 10 | phase drift detectable |
For - / (m c) - 10« J"s/m and T - 10 s/m,
the effective barrier reduction V - 10 eV is sufficient to enhance tunneling by several orders of magnitude without thermal activation.
6 Experimental Proposals
6.1 Mechanisms for Generating T
Observable temporal gradients can emerge from stress, electromagnetic, or thermodynamic asymmetries:
MetalHydride Systems: T arises from intense lattice-stress gradients during hydrogen loading / deloading.
Cryogenic Plasma: magnetic-field gradients (analogous to the Schiff effect) produce differential time-flow zones.
Superconducting Loops: resonant AC fields create oscillating T patterns, measurable via phase-locked detectors.
6.2 Measurement Strategies
(a) Correlate neutron bursts with optical-clock phase drift near Pd targets: / - / 10 10.
(b) Use trapped-ion spectroscopy to detect Egrad - 10 eV via line shifts.
(c) Apply quantum-clock interferometry to observe phase lags from controlled T fields.
7 Discussion
7.1 Possible Objections and Limitations
Critics may attribute neutron or spectral anomalies to local heating, impurity reactions, or stochastic field effects.
However, TTU-based experiments seek direct correlation between neutron yield and optical-clock phase drift.
A statistically significant / neutron correlation would rule out purely thermal mechanisms.
Nonetheless, environmental noise and systematic uncertainties remain major challenges for early verification.
7.2 Interpretational Implications
Temporal gradients act as hidden energy channels linking macroscopic field structure and microscopic quantum events.
This provides a coherent explanation for:
Enhanced neutron production in metalhydride experiments,
Temperature-independent activation phenomena,
Analogous effects in superconducting tunneling and Josephson junctions.
The TTE thus serves as a quantitative bridge between temporal-field physics and quantum dynamics.
8 Conclusion and Outlook
Temporal gradients modify quantum barriers through the energy term Egrad = T, reducing Veff and enhancing tunneling probabilities by orders of magnitude.
The parameters and now possess clear physical meaning respectively mass-dependent coupling and temporal-coherence lifetime enabling direct experimental determination.
Future tests combining optical-clock metrology and neutron spectroscopy can verify or falsify this mechanism.
Confirmation of the Temporal Tunneling Equation (TTE) would not only clarify anomalous low-temperature fusion but open a new discipline temporal engineering where controlled gradients of time are used to manipulate nuclear reactions and quantum states.
TTU thus offers both a unifying theoretical vision and a technological pathway for 21st-century physics.
References
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