Abstract We develop a new theoretical framework for quantum tunneling based on the Temporal Theory of the Universe (TTU) and the Temporal Wave Principle (TWP), in which the physical field of time τ(x, t, Θ) modifies the effective tunneling dynamics. In this approach, quantum particles are treated as τ-excitations with internal hyper-temporal oscillations, while spatial gradients of the temporal field (∇τ) directly influence both the effective potential barrier and the particle’s effective mass. We derive the Temporal Tunneling Equation (TTE) by incorporating τ-dependent corrections into the WKB action. The key result is that the tunneling probability Γ acquires an exponential enhancement factor of the form Γ ≈ Γ₀ exp[ Λ (∇τ)² ], where Λ is an explicit coefficient determined by TTU parameters (α, κ, m_τ).Thus, stronger τ-gradients reduce the Euclidean action, lower the effective barrier height, and increase the tunneling rate. This mechanism is universal and does not rely on thermal activation, zero-point vibration models, or exotic interactions. Importantly, the predicted enhancement can be tested experimentally using STM tunneling, Josephson junctions, THz-modulated barriers, cold atoms, and high-Q resonators. The results demonstrate that temporal geometry plays an active role in low-energy quantum phenomena, and that controlled τ-gradients offer a new pathway to engineer tunneling processes in condensed matter and atomic systems. Keywords Temporal field τ; TTU; TWP; quantum tunneling; WKB; hyper-time Θ; effective mass; temporal gradients; Schrödinger emergence; barrier suppression; tunneling enhancement; δτ-waves; condensed matter; STM; Josephson junctions. Table of Contents Time as a Path to Thermonuclear Fusion 1. Introduction 1.1. The problem of thermonuclear fusion1.2. Limitations of temperature-driven tunneling1.3. Temporal field τ as a physical substrate1.4. From TTU to temporal enhancement of tunneling1.5. Purpose and contributions of this work 2. Temporal Field and Gradient Dynamics 2.1. Definition of τ(x, t, Θ)2.2. Temporal gradients and temporal curvature2.3. Effective potential modification: U_eff = U₀ − B(∇τ)²2.4. Effective mass modification: m_eff = m₀ − C(∇τ)²2.5. Validity of the gradient expansion2.6. Physical interpretation of temporal geometry 3. Temporal Tunneling Equation (TTE) 3.1. Standard WKB exponent and its limitations3.2. Temporal correction to the Euclidean action3.3. Derivation of δS_E ∝ (∇τ)²3.4. Final formula: Γ = Γ₀ exp[ Λ (∇τ)² ]3.5. Mechanisms of barrier reduction3.6. Universality of τ-enhanced tunneling 4. Temporal Mechanisms in Thermonuclear Fusion 4.1. Coulomb barrier suppression via temporal curvature4.2. Mass reduction of reacting nuclei4.3. Temporal thinning of the barrier4.4. Effective Gamow factor under τ-dynamics4.5. Conditions for fusion at reduced temperatures 5. Stellar Fusion as a Temporal Phenomenon 5.1. The paradox of insufficient stellar temperatures5.2. Required tunneling vs observed luminosities5.3. δτ-backgrounds inside stellar plasma5.4. τ-gradient catalysis in solar fusion5.5. Resolution of the long-standing stellar tunneling problem 6. Toward Temporal Fusion Reactors (TFR) 6.1. Engineered ∇τ fields in laboratory plasmas6.2. τ–EM hybrid modes as fusion catalysts6.3. Temporal plasma compression and χ-nonlinearity6.4. Design principles for TFR architectures6.5. Scaling laws and efficiency predictions 7. Experimental Signatures and Tests 7.1. Fusion rate anomalies at constant temperature7.2. EM-frequency dependence predicted by TTE7.3. Temporal refractive effects and τ-sidebands7.4. Plasma transparency shifts7.5. Solid-state and tabletop tests of τ-effects 8. Discussion 8.1. Difference from thermal catalysis8.2. Difference from zero-point vibration models8.3. Why standard QM underestimates tunneling8.4. How τ-gradients reshape nuclear barriers8.5. Implications for cosmology and plasma physics 9. Conclusion • Time is a physical driver of tunneling• TTE provides a quantitative mechanism• Fusion becomes geometry-controlled• Temporal fields offer a new path to thermonuclear energy• Predictions are testable in current devices Reference Appendices Appendix A. Full WKB Derivation of the TTEAppendix B. Θ-Compactification and the Topological Origin of ħAppendix C. Laboratory Temporal Field BackgroundsAppendix D. Emergent Schrödinger Equation from τ(x,t,Θ)Appendix E. δτ-Waves and Universal τ-DispersionAppendix F. Temporal Correction to the Euclidean ActionAppendix G. Material-Dependent τ-ResponsesAppendix H. Temporal Plasma PhysicsAppendix I. Cosmological δτ-FluctuationsAppendix J. Temporal Fusion Reactors (TFR)Appendix K. Particles as τ-VorticesAppendix L. Chronon Modes and f-Mode SpectroscopyAppendix M. Experimental Bounds on α, κ, χAppendix N. Word-Friendly Formula Reference
Abstract We develop a new theoretical framework for quantum tunneling based on the Temporal Theory of the Universe (TTU) and the Temporal Wave Principle (TWP), in which the physical field of time τ(x, t, Θ) modifies the effective tunneling dynamics. In this approach, quantum particles are treated as τ-excitations with internal hyper-temporal oscillations, while spatial gradients of the temporal field (∇τ) directly influence both the effective potential barrier and the particle’s effective mass. We derive the Temporal Tunneling Equation (TTE) by incorporating τ-dependent corrections into the WKB action. The key result is that the tunneling probability Γ acquires an exponential enhancement factor of the form Γ ≈ Γ₀ exp[ Λ (∇τ)² ], where Λ is an explicit coefficient determined by TTU parameters (α, κ, m_τ).Thus, stronger τ-gradients reduce the Euclidean action, lower the effective barrier height, and increase the tunneling rate. This mechanism is universal and does not rely on thermal activation, zero-point vibration models, or exotic interactions. Importantly, the predicted enhancement can be tested experimentally using STM tunneling, Josephson junctions, THz-modulated barriers, cold atoms, and high-Q resonators. The results demonstrate that temporal geometry plays an active role in low-energy quantum phenomena, and that controlled τ-gradients offer a new pathway to engineer tunneling processes in condensed matter and atomic systems. Keywords Temporal field τ; TTU; TWP; quantum tunneling; WKB; hyper-time Θ; effective mass; temporal gradients; Schrödinger emergence; barrier suppression; tunneling enhancement; δτ-waves; condensed matter; STM; Josephson junctions. Table of Contents Time as a Path to Thermonuclear Fusion 1. Introduction 1.1. The problem of thermonuclear fusion1.2. Limitations of temperature-driven tunneling1.3. Temporal field τ as a physical substrate1.4. From TTU to temporal enhancement of tunneling1.5. Purpose and contributions of this work 2. Temporal Field and Gradient Dynamics 2.1. Definition of τ(x, t, Θ)2.2. Temporal gradients and temporal curvature2.3. Effective potential modification: U_eff = U₀ − B(∇τ)²2.4. Effective mass modification: m_eff = m₀ − C(∇τ)²2.5. Validity of the gradient expansion2.6. Physical interpretation of temporal geometry 3. Temporal Tunneling Equation (TTE) 3.1. Standard WKB exponent and its limitations3.2. Temporal correction to the Euclidean action3.3. Derivation of δS_E ∝ (∇τ)²3.4. Final formula: Γ = Γ₀ exp[ Λ (∇τ)² ]3.5. Mechanisms of barrier reduction3.6. Universality of τ-enhanced tunneling 4. Temporal Mechanisms in Thermonuclear Fusion 4.1. Coulomb barrier suppression via temporal curvature4.2. Mass reduction of reacting nuclei4.3. Temporal thinning of the barrier4.4. Effective Gamow factor under τ-dynamics4.5. Conditions for fusion at reduced temperatures 5. Stellar Fusion as a Temporal Phenomenon 5.1. The paradox of insufficient stellar temperatures5.2. Required tunneling vs observed luminosities5.3. δτ-backgrounds inside stellar plasma5.4. τ-gradient catalysis in solar fusion5.5. Resolution of the long-standing stellar tunneling problem 6. Toward Temporal Fusion Reactors (TFR) 6.1. Engineered ∇τ fields in laboratory plasmas6.2. τ–EM hybrid modes as fusion catalysts6.3. Temporal plasma compression and χ-nonlinearity6.4. Design principles for TFR architectures6.5. Scaling laws and efficiency predictions 7. Experimental Signatures and Tests 7.1. Fusion rate anomalies at constant temperature7.2. EM-frequency dependence predicted by TTE7.3. Temporal refractive effects and τ-sidebands7.4. Plasma transparency shifts7.5. Solid-state and tabletop tests of τ-effects 8. Discussion 8.1. Difference from thermal catalysis8.2. Difference from zero-point vibration models8.3. Why standard QM underestimates tunneling8.4. How τ-gradients reshape nuclear barriers8.5. Implications for cosmology and plasma physics 9. Conclusion • Time is a physical driver of tunneling• TTE provides a quantitative mechanism• Fusion becomes geometry-controlled• Temporal fields offer a new path to thermonuclear energy• Predictions are testable in current devices Reference Appendices Appendix A. Full WKB Derivation of the TTEAppendix B. Θ-Compactification and the Topological Origin of ħAppendix C. Laboratory Temporal Field BackgroundsAppendix D. Emergent Schrödinger Equation from τ(x,t,Θ)Appendix E. δτ-Waves and Universal τ-DispersionAppendix F. Temporal Correction to the Euclidean ActionAppendix G. Material-Dependent τ-ResponsesAppendix H. Temporal Plasma PhysicsAppendix I. Cosmological δτ-FluctuationsAppendix J. Temporal Fusion Reactors (TFR)Appendix K. Particles as τ-VorticesAppendix L. Chronon Modes and f-Mode SpectroscopyAppendix M. Experimental Bounds on α, κ, χAppendix N. Word-Friendly Formula Reference
Abstract We propose TTU-Q, a quantum theory in which time itself is a fundamental field τ(x, Θ) rather than an external parameter. The additional variable Θ acts as hyper-time, an internal axis along which the temporal field evolves and becomes quantized. This structure allows us to introduce a genuine canonical pair ( τ̂, p̂Θ ) with the fundamental commutation relation[ τ̂, p̂Θ ] = iℏ,to define a hyper-time Schrödinger equation for the operator τ̂(Θ), and to formulate a functional quantum theory of time via the wave functional Ψ[ τ(·, Θ) ]. Ordinary quantum mechanics, with its wave function ψ(x, t), appears as an effective description obtained by coarse-graining over Θ and projecting Ψ[ τ ] onto slow temporal modes. In this framework, mass, spin, entanglement and decoherence admit a unified interpretation in terms of vortex-like excitations of the temporal field and phase coherence along Θ. Classical time t and general relativity emerge as mean-field limits of τ(x, Θ) in the regime where ∂τ/∂Θ is suppressed. We outline the resulting quantum-to-classical transition, derive an effective Lindblad-type dynamics by tracing over fast Θ-modes, and discuss phenomenological consequences for atomic clocks, gravitational phenomena and cosmology. TTU-Q thus recasts quantum mechanics as a non-fundamental regime of a deeper temporal field theory. Keywords temporal field; hyper-time; quantization of time; canonical pair of time; temporal wave functional; emergent quantum mechanics; vortex modes of time; Θ-coherence; temporal decoherence; temporal field theory; TTU-Q; functional Schrödinger dynamics; quantum-to-classical transition; temporal anisotropy; temporal excitations; phenomenology of time quantization Table of Contents AbstractKeywords 1. Introduction: Why Time Must Be Quantized 1.1 The failure of treating time as a parameter 1.2 Quantum–GR inconsistency as a temporal problem 1.3 TTU paradigm: time as a physical field τ(x,Θ) 1.4 TTU-Q thesis: quantum mechanics emerges from quantized time 2. Temporal Field and Hyper-Time 2.1 Definition of τ(x,Θ) 2.2 Physical meaning of hyper-time Θ 2.3 Canonical pair (τ̂, p̂Θ) 2.4 Temporal uncertainty principle 3. TTU-Q Lagrangian and Field Equations 3.1 Lagrangian of quantum time 3.2 Equation of motion along Θ 3.3 Classical limit and connection to TTU-5D 3.4 Dimensional analysis 4. Quantum States of Time 4.1 Time wave functional Ψ[τ] 4.2 Hyper-time Schrödinger equation 4.3 Hamiltonian of the temporal field 4.4 Temporal harmonic spectrum 4.5 Chronons: quanta of temporal excitation 5. Matter as Excitations of Time 5.1 Mass as temporal inertia 5.2 Particles as coherent τ-oscillations 5.3 Spin as temporal angular momentum in Θ-space 5.4 Nonlocality as Θ-coherence 6. Causality and Emergence of Classical Time 6.1 Operator causal structure 6.2 Non-commutative causality 6.3 Decoherence along Θ 6.4 Classical GR as temporal average 7. Quantum-to-Classical Transition 7.1 Averaging over Θ → observable t 7.2 Lindblad-like temporal evolution 7.3 Emergence of classicality 8. Phenomenology 8.1 Atomic clock tests 8.2 CMB low-ℓ anomalies 8.3 Inflation as temporal oscillation 9. Toward Quantum Gravity (TTU-QG) 9.1 Why geometry does not need quantization 9.2 Gravity as τ-projection 9.3 Toward TTU-QG formulation 10. Conclusion Reference
Abstract This paper introduces TTU-Q (Quantum Temporal Theory of the Universe), a novel ontological framework in which time is treated as a quantum field τ(x, Θ) evolving along an internal hypertemporal axis Θ. Unlike classical and quantum models where time is a passive parameter, TTU-Q formalizes time as a dynamic, quantizable substance with its own operator structure, spectrum, and internal evolution. The theory defines a canonical pair (τ̂, p̂Θ), establishes a hypertemporal Schrödinger equation: i·ħ·(∂τ̂ / ∂Θ) = [τ̂, Ĥ] and derives a Klein–Gordon-type field equation for temporal fluctuations. These foundations enable a new paradigm for cybernetics and artificial intelligence, where information is structured temporality and computation is the manipulation of time configurations. TTU-Q provides a physical basis for self-awareness, memory, and causality in intelligent systems, and predicts measurable effects such as phase shifts in interferometry and temporal decoherence in atomic clocks. Keywords Quantum time; hypertemporal evolution; TTU-Q; temporal field; causal operator; temporal Abstract + Keywords 1. Introduction: Time as Substance, Not Parameter 2. Mathematical Foundations of TTU-Q 3. Temporal Coherence as Informational Structure 4. Architecture of Temporal Computing 5. Experimental Predictions and Applications 6. Philosophical Implications and Future Work
Quantum tunneling — the passage of a particle through a potential barrier that it classically lacks the energy to surmount — has been described since Gamow (1928) by the tunneling probability T ≈ exp(−2κd), where κ = √(2m(V₀−E))/ℏ and d is the barrier width. The formula is well-confirmed experimentally but has not been derived from a physical principle more fundamental than the Schrödinger equation. We derive it from the principle of information processing load minimization, using the framework established in the preceding papers of this series. We define the tunneling load as C_tunnel = ∫κ(x)dx — the integral of the spatial attenuation coefficient through the barrier — and show that T = exp(−2·C_tunnel) exactly. This is not a restatement of the WKB approximation; it is an identification of the physical meaning of the integral ∫κ(x)dx as the information processing load of the tunneling path. The tunneling path is selected by load minimization: when C_tunnel < C_classical (the load of the classical over-barrier trajectory), the system tunnels. Three physical systems are verified numerically without free parameters: (i) proton-proton nuclear fusion in the solar core — Gamow load C_Gamow = πη = 11.28, T = 1.60 × 10⁻¹⁰, consistent with solar luminosity; (ii) scanning tunneling microscope (STM) current — C_STM = κd = 5.43 at 0.5 nm, T = 1.91 × 10⁻⁵, and the factor-of-ten current change per 0.1 nm distance change follows directly; (iii) Ra-226 alpha decay — C_Gamow = 79.2, T ~ 10⁻⁶⁹, consistent with the 1,600-year half-life. Tunneling is not a mysterious violation of classical mechanics. It is the selection of the minimum-load propagation path — the same principle that explains wave-particle duality (Paper 7), wave function collapse (Paper 4), and the structure of all fundamental forces (Paper 8).
S-Field Mediated Tunneling as Direct Experimental Evidence for the S-Domain (Unicode clean manuscript version) 1. Overview Quantum tunneling is traditionally interpreted as a purely probabilistic penetration of a potential barrier. However, several well-documented empirical signatures — including non-classical traversal times, phase discontinuities, and mass-independent transmission — suggest the involvement of a deeper mechanism not contained within 4D physics. Within the Unified Oscillatory–Informational S-Framework, tunneling emerges naturally as a temporary de-projection of a particle into the S-domain, followed by re-projection into the baryonic domain (B-space). This process is mediated by the dual S-oscillatory structure (sb and bs modes) that governs all baryonic matter. A particle tunnels because it does not cross the barrier inside B, but because it temporarily exists in S, where spatial metrics do not apply. Thus tunneling becomes one of the strongest direct experimental signatures of the S-field 2. The S-Oscillator and the Two Projection Modes (sb and bs) Every baryonic particle is represented as a two-phase S-oscillator: Φ(t) = (Φ_sb(t), Φ_bs(t)). Both modes share the same base frequency ω but differ by phase and orientation: Φ_sb(t) = A_sb exp(i ω t + i φ_sb) Φ_bs(t) = A_bs exp(i ω t + i φ_bs) with phase difference Δφ = φ_bs − φ_sb. The sb mode projects preferentially into baryonic 3+1 space (B-space). The bs mode projects preferentially into the higher-dimensional S-domain. The instantaneous orientation between B and S is determined by Δφ and the ratio of amplitudes: tan θ = A_bs / A_sb. Orientation rules: • Low energy → θ → 0 → sb dominates → stable B projection • High energy → θ → π/2 → bs dominates → shift toward S This dichotomy underlies mass stability, resonance behavior, and tunneling. 3. Energy-Dependent Couplings to B and S Define coupling coefficients describing which mode is expressed in which domain: C_sb→B(E) = exp(−E_s / E) C_sb→S(E) = 1 − C_sb→B(E) C_bs→S(E) = exp(−E_b / E) C_bs→B(E) = 1 − C_bs→S(E). Where: • E_s = characteristic S-activation threshold • E_b = baryonic binding energy • E = instantaneous kinetic or local potential energy. This directly encodes the rule: When energy is low, the sb peak enters B. When energy is high, the bs peak enters S. This is the simplest and most important dynamical law of the S-framework. 4. Projection Operators and Domain Transition Define projection operators: P_B Φ = C_sb→B Φ_sb + C_bs→B Φ_bs P_S Φ = C_sb→S Φ_sb + C_bs→S Φ_bs. These satisfy: P_B + P_S = 1 P_B P_S = 0. A tunneling event is represented as: P_B Φ → P_S Φ → P_B Φ. Meaning: Baryonic projection → S-domain → baryonic projection at a new spatial coordinate. This eliminates any need for a spatial path inside the barrier. 5. Barrier Interaction and S-Transfer When Φ encounters a potential barrier V(x), the sb (B-bound) component compresses, which induces a transfer of amplitude into the bs (S-oriented) component: dΦ_bs/dt = κ exp(−V/E) Φ_sb, where κ is the S-coupling constant. This transfer is the physical cause of tunneling: • compression reduces B-stability, • Δφ increases, • orientation θ rotates toward S, • a finite portion of Φ enters S. Inside S, spatial distance has no meaning, so the traversal time is independent of barrier width. 6. Tunneling Probability in the S-Framework The tunneling probability is the product of: 1. S-orientation probability during compression 2. S-coherence propagation 3. re-projection probability. Explicitly: T = |P_S Φ|² |P_B Φ_after|². Using the projection definitions: |P_S Φ|² = |C_sb→S A_sb exp(i φ_sb) + C_bs→S A_bs exp(i φ_bs)|². Since sb→S dominates under compression: T ≈ (1 − exp(−E_s / E))² exp(−2L / λ_S), where λ_S is the S-coherence characteristic length. Observations: The entire classical exponential dependence arises from S-coherence decay, not from 4D probabilistic wave leakage. • The first factor is purely S-orientational: the bs-mode activation. This is experimentally identical to quantum mechanics but conceptually much simpler and ontologically richer. 7. Traversal Time and the Hartman Effect In the S-domain there is no spatial metric. Thus the internal traversal time τ_S satisfies: τ_S = undefined or zero. Therefore: τ_total = τ_in + τ_out, and τ_total becomes independent of barrier width for sufficiently thick barriers. This is an exact explanation of the Hartman effect — a long-standing paradox in standard quantum mechanics. only S-phase geometry. It also resolves the “observer independence” issue: the process depends solely on S-orientation, not on measurement. 9. Why Tunneling Is Direct Evidence for the S-Field Standard QM cannot explain: • zero or undefined traversal time • barrier-thickness independence • identical tunneling for particles with different classical masses • phase discontinuities stronger than wavefunction continuity allows • the existence of tunneling at arbitrarily low energies. In the S-framework: All these come from a single source: temporary existence in S, where spatial extension is undefined. Thus tunneling is not just compatible with the S-field. It is one of the strongest direct signatures that baryonic matter is a projection of a higher-dimensional oscillatory structure. 10. Unified S-Equation of Tunneling The full dynamical equation integrating B and S propagation is: Φ(t + Δt) = P_B U_B Φ(t) + P_S U_S Φ(t), with: U_B = exp(−i H_B Δt / ℏ) U_S = exp(−i E_S Δt). Inside S there is only intrinsic phase, no Hamiltonian with spatial term. A tunneling event occurs when: P_S U_S P_B Φ ≠ 0. This is the precise mathematical definition of S-mediated tunneling.
Subtitle: Temporal Field Realism: A Deterministic Foundation for Quantum Phase and Wavefunction Dynamics (Quantum mechanics as temporal resonance, the Born rule as statistical phase averaging, and measurement as phase synchronization.) Theory of Time is a fundamental four-volume corpus that presents time as a physical condensate — the Temporal Condensate. Together, the four volumes establish a self-consistent physical framework, spanning the deterministic ontology of quantum fields, the structure of elementary particles, the cosmological evolution of the Universe, and the dynamical nature of gravitation. Theory of Time I: The Core This volume introduces Temporal Field Realism, establishing time as a fundamental dynamical field rather than a passive coordinate. The quantum wavefunction ψ is derived as a resonant excitation mode of the temporal field τ. The Born rule emerges as a statistical consequence of phase averaging, while quantum measurement is reinterpreted as a process of dynamical phase synchronization between physical systems and the temporal medium. Theory of Time II: The Evidence This volume demonstrates that the spectrum of elementary particles arises from topological vortices of temporal flow. Leptonic and quark masses are derived as harmonic modes of hypertime, reducing the empirical parameters of the Standard Model to geometric constants of the temporal manifold. The work provides a structural interpretation of particle generations, mixing matrices, and mass hierarchies. Theory of Time III: The Scale This volume develops the cosmological implications of temporal field dynamics. The inflationary paradigm is replaced by the dynamics of a non-commutative time operator T̂(x). The horizon and flatness problems are resolved through algebraic connectivity of the five-dimensional temporal manifold. The model predicts observational signatures in primordial gravitational wave spectra and potential anomalies in the Cosmic Microwave Background. Theory of Time IV: The Gravity This volume reformulates gravitation as transport and conductivity within the temporal condensate. Dark matter and dark energy are interpreted as emergent effects of temporal susceptibility χτ and internal temporal pressure. Gravitational waves are described as longitudinal acoustic modes propagating through the temporal medium, providing a unified dynamical description of inertial, gravitational, and cosmological phenomena.
The present work consists of eight chapters.
The first chapter gives a brief historical overview of the impasses that Classical Physics found in the late 19th and early 20th centuries, and the efforts made in the framework of Old Quantum theory to overcome it, ultimately leading to the foundation of Quantum Engineering in the 1920s.
The second chapter shows the ratio of the Schrodinger equation to the classical wave differential equation, the concept of wave function, the physical importance of probability density, continuity equation and probability current density, while indicating the conditions to be met by the wave function.
The third chapter examines square dynamic wells as well as the rectangular dynamic barrier, through the study of which the tunnel phenomenon emerges. The reflecting and transit coefficients are also calculated, while the tunnel effect is also being examined in relation to the principle of uncertainty.
The fourth chapter presents semi-classical approaches to the solution of the Schrodinger equation, with an emphasis on the WKB approach. The power of the WKB approach is analysed, and applied to a dynamic well, as well as in the case of tunneling through a dynamic barrier, by calculating the transit coefficient.
The fifth chapter analyses the time delay in the tunnel phenomenon and examines the concept of minimum transit time.
The sixth chapter refers to natural systems where the tunnel phenomenon occurs, such as cold emission of electrons from metals, a-decay and nuclear fusion. Finally, due to the purely undulating nature of the phenomenon, cases of observation are mentioned macroscopicly, such as the case of total internal reflection.
The seventh chapter presents a lesson plan for the teaching of the phenomenon in Secondary Education, using information and communication technologies in the educational process, and finally the main conclusions presented resulting from the previous study.