**Introducing a New Constant ϕ**** in Quantum Admittance: Energy Waves Travel at Any Speed**

## Abstract

This paper introduces a new constant, **ϕ**, within the framework of Quantum Admittance (QA), challenging the traditional understanding of mass-energy equivalence and the assumption that the speed of light (c) is the fundamental constant. We propose that the constant impedance (Z_{0}) provides a more accurate description of the relationship between energy, mass, and time. This shift has profound implications for the understanding of gravity, quantum mechanics, and the fundamental structure of the universe.

## Introduction

The mass-energy equivalence principle, encapsulated by Einstein’s famous equation E=mc^{2}, has long been a cornerstone of modern physics. However, recent developments in quantum mechanics and general relativity expose inconsistencies in how we treat fundamental constants. Specifically, the assumption that the speed of light (c) is universally constant fails to account for phenomena occurring at the boundary conditions of the universe. This paper proposes Z_{0}^{2} as a new constant, derived from the ratio of permittivity (ε_{0}) to permeability (μ_{0}). This new constant offers a revised perspective, challenging traditional views of energy, mass, and gravity.

**Merging Maxwell and Einstein**

**Merging Maxwell and Einstein**We begin by revisiting classical electromagnetism’s relationships, which are foundational to our proposed revision:

Using these relationships, we reframe the mass-energy equation within the context of Quantum Admittance. The speed of light, c^{2}, is dependent on the inverse product of permittivity ε_{0} and permeability μ_{0}.

For electromagnetic waves to propagate, Z_{0} must remain constant. This constancy ensures that the ratio μ_{0}/ε_{0} maintains the 90-degree orthogonal phase relationship necessary for sustained wave behavior, regardless of the values of μ_{0}/ε_{0}. This allows us to calculate the speed c from its maximum at the edges of the vacuum of space or at the surface of a black hole.

Einstein’s Equivalence Equation:

**E = mc ^{2}**

Maxwell’s Impedance of space:

**Z _{0} = √μ_{0}/ε_{0}**

Maxwell’s Speed of energy:

**c ^{2} = 1/μ_{0}ε_{0}**

In classical electrodynamics, Z_{0} is the impedance of free space, and it plays a crucial role in determining the propagation of electromagnetic waves. However, in this new framework, the focus shifts from the impedance to the “viscosity of space,” represented by a new constant, ϕ.

Traditionally, the speed of light c has been treated as a constant, determined by the fixed permittivity ε_{0} and permeability μ_{0} of free space. However, if we consider c^{2} to vary with changing ε_{0} or μ_{0}, the speed of light becomes an evolving parameter rather than a fixed one.

If we consider the speed of light c^{2} to vary with changing permittivity ε_{0}, we can reformulate the speed of energy propagation using the constant ϕ, which embodies the physical essence of Z_{0}, but in the context of evolving space properties:

**c ^{2} = ϕ/ε_{0}2**

Here, ϕ=Z_{0}^{2}, with Z_{0}^{2} representing the specific numerical value derived from the impedance of space.

**Z _{0}^{2} = μ_{0}/ε_{0} ≈376.732Ω2**

Thus, for clarity we make a new constant **ϕ = Z _{0}^{2} ≈ 141,9402**, which we treat as the viscosity constant for the energy lattice.

In this model, **ϕ** defines the energy lattice’s “viscosity,” dictating how energy moves through space. This constant allows the speed of light c to evolve with changing conditions of μ_{0}/ε_{0} while maintaining the essential properties of wave propagation.

The mass-energy equivalence can now be re-expressed using **ϕ** to reflect this evolving nature of space and its energy lattice:

**E = m/ϕε _{0}**

This reformulation links mass and energy to the evolving nature of space through its viscosity, while still retaining the numerical significance of Z_{0}^{2} within the constant **ϕ**. By doing so, we anchor **ϕ** as both a theoretical and numerical foundation for understanding energy propagation in space.

**Conceptual Insights**

**Photon Disturbance and Wave Propagation**

In the Charge Admittance (CA) framework, the propagation of waves is fundamentally tied to the concept of photon disturbances. Each photon, as understood within CA, consists of a charge and anti-charge pair. These opposite charges interact with the surrounding energy field to create a disturbance, manifesting as a wave in the continuum.

The key to understanding this interaction lies in the role of the characteristic impedance of space, Z0^{2}. As long as this impedance remains constant, the charge and anti-charge pair are perpetually attracted towards each other. This attraction ensures that the energy of the wave is entirely contained within the photon disturbance itself. The wave does not radiate energy outward, nor does it experience deflection, because the energy remains confined by the interaction between the charges.

This is a significant departure from traditional wave propagation models where energy can radiate or dissipate depending on the medium. In CA, the constant **ϕ** guarantees that the wave maintains its integrity, and energy is neither radiated nor lost as long as the impedance remains unchanged.

This interaction is not merely a theoretical construct but serves as a **proof** of the CA photon hypothesis: photon disturbances generate waves due to the interplay of charge and anti-charge under the constraint of **ϕ**. This constant ensures that the energy dynamics of the wave remain internal and self-contained, thereby preventing the outward radiation of energy. A change in impedance, however, would disrupt this equilibrium, allowing for radiation or deflection to occur.

By maintaining the constant ratio **ϕ**, the CA framework explains wave propagation in a manner that integrates both the electromagnetic properties of space and the energy dynamics of photons, providing a unified view of how energy disturbances propagate without loss.

**Charge and Anti-Charge Interaction and Non-Radiation in the Energy Continuum**

In the Charge Admittance (CA) framework, the relationship between charge and anti-charge is governed by the characteristic impedance of space, **ϕ**, which remains constant regardless of variations in the density of the energy continuum. Whether in free space or regions with varying permittivity (ε_{0}) and permeability (μ_{0}), as long as the ratio **ϕ** is maintained, the interaction between charge and anti-charge remains purely attractive. This means that the charges are not deflected outward, and their acceleration is fully contained within the energy disturbance of the wave itself, preventing any radiation of energy. In other words, under conditions where the impedance of space remains constant, the energy of the wave remains self-contained, with no loss through radiation. Only when the impedance changes—when there is a mismatch in the **ϕ** ratio—does the system allow for energy to be radiated or deflected. This insight highlights the critical role of impedance in the propagation of energy disturbances and suggests that the radiation of energy occurs only when the speed of energy is altered due to changes in the impedance of the medium.

**Dynamic Nature of a Variable c**

Unlike the fixed speed of light c, the introduction of **ϕ** allows for a more flexible interpretation of electromagnetic phenomena. This flexibility accommodates the evolving nature of electromagnetic fields across varying regions of space-time, enabling consideration of phase shifts that may occur at critical boundary conditions.

**Implications for Energy-Mass Interactions**

Understanding the ratio μ_{0}/ε_{0} can elucidate how electromagnetic energy behaves under diverse conditions. This understanding is crucial for examining phenomena like resonance, impedance matching, and energy transformation at various limits.

**Boundary Conditions**

The role of the ratio μ_{0}/ε_{0} highlights how electromagnetic wave propagation influences energy-mass relationships. This perspective may provide valuable insights into the quantum behavior of electromagnetic interactions.

**Energy Conservation Through Impedance Matching**

In such scenarios, the constancy of the impedance of space Z_{0} acts like a “matching condition,” ensuring that no energy is lost in the propagation. This is analogous to an electrical system, where if the load impedance matches the source impedance, power transfer occurs efficiently without loss.

In such scenarios, the constancy of the impedance of space Z_{0} acts like a “matching condition,” ensuring that no energy is lost in the propagation. This is analogous to an electrical system, where if the load impedance matches the source impedance, power transfer occurs efficiently without loss.

**Why Does the Constancy of Z _{0} Matter?**

The ratio Z_{0}=E/H defines the relationship between the electric and magnetic fields in the wave. For wave propagation to remain undisturbed, the balance between these fields must be preserved. Variations in μ0 o ε0 could disrupt this balance, leading to reflection, absorption, or scattering of the wave unless Z_{0} remains constant.

In idealized, lossless propagation (e.g., in a vacuum), the constancy of Z_{0} ensures that the wave maintains its energy as it moves through space, without dissipation.

**Relation to Electrons in Quantum Systems**

In quantum systems, the concept of quantized energy levels plays a similar role in preventing energy loss, as discussed earlier. However, in the classical and quantum fields, the constancy of certain fundamental quantities (Z_{0} in electromagnetic waves or energy quantization in electron orbitals) ensures that energy is conserved over time without spontaneous dissipation.

## Implications

The introduction of **ϕ** presents a novel framework for understanding deeper connections between energy and gravity. Traditionally, the speed of light (c) is treated as the universal constant governing massless particles, however **ϕ** opens new avenues for exploring how energy density influences gravitational interactions and cosmic phenomena. This framework could shed light on enigmas like dark matter, dark energy, and the unification of quantum mechanics with general relativity.

If the permittivity ε_{0} and permeability μ_{0} vary inversely to maintain a constant **ϕ**, the wave propagation remains lossless. This is because the energy distribution between the electric and magnetic fields remains balanced.

Changes in ε_{0} and μ_{0} could occur, for example, in different regions of space or near extreme gravitational or quantum conditions (e.g., near black holes or in highly exotic media). But as long as the product maintains a stable impedance Z_{0}, energy conservation holds.

Additionally, **ϕ** may have significant implications for edge conditions—where energy forms or disintegrates. It could help explain inconsistencies in general relativity, particularly through the phase shifts at these boundary conditions, enhancing our understanding of quantum disambiguation and wave function collapse.

## Experimental Considerations

In order to empirically verify **ϕε _{0}** role, a variety of experimental approaches are proposed. These include:

Investigating phase transitions in quantum states: Experiments focused on phase shifts at the quantum level, particularly wave function collapse, could shed light on **ϕε _{0}** role in energy transformation.

Examining gravitational anomalies: Observations of regions exhibiting unexplained gravitational behavior, such as near black holes or at cosmological scales, may provide evidence supporting the **ϕε _{0}** -based framework.

Testing in Particle Accelerators: Investigating high-energy environments (e.g., in particle accelerators) could explore whether could explore whether ** ** influences mass-energy conversions, particularly during particle creation and annihilation events.

## Future Directions

The introduction of **ϕε _{0}** raises critical questions about the nature of energy, mass, and their interaction with space-time. Future research should explore:

How **ϕε _{0}** interacts with other fundamental constants, including the Planck constant, and its potential to unify gravity with quantum mechanics.

The behavior of **ϕε _{0}** across different regimes of energy and matter to uncover a more comprehensive and unified theory of the universe.

**Theoretical Development**

Further develop the implications of introducing **ϕε _{0}** to see how it modifies existing frameworks and whether it leads to new predictions or insights.

**Experimental Validation**

Consider potential experimental setups or observations that could validate or challenge the predictions made by your revised mass-energy relationship.

**Interconnections with Quantum Mechanics**

Investigate how **ϕε _{0}** relates to concepts in quantum mechanics, particularly regarding wave-particle duality and field interactions.

## Conclusion

This paper proposes a paradigm shift in mass-energy equivalence through the introduction of **ϕε _{0}**, derived from the ratio μ

_{0}/ε

_{0}. By challenging the traditional role of the speed of light as the defining constant of physics,

**ϕε** offers a new avenue for understanding the interplay between energy, mass, and gravity. We hope this perspective will inspire further theoretical and experimental investigation, leading to new insights into the fundamental workings of our universe.

_{0}## References

Einstein, A. (1905). “Does the Inertia of a Body Depend Upon Its Energy Content?”. Annalen der Physik, 18: 639–641

Maxwell, J. C. (1865). “A Dynamical Theory of the Electromagnetic Field”. Philosophical Transactions of the Royal Society of London.

Jackson, J. D. (1998). Classical Electrodynamics (3rd ed.). John Wiley & Sons.

Penrose, R. (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage Books

Feynman, R. P. (1964). The Feynman Lectures on Physics. Addison-Wesley.

Thorne, K. S. (1994). Black Holes and Time Warps: Einstein’s Outrageous Legacy. W.W. Norton & Company.

Planck, M. (1900). “On an Improvement of Wien’s Equation for the Spectrum”. Verhandlungen der Deutschen Physikalischen Gesellschaft.