**Redshift Explained through Gravitational Deflection and Entropy: A Framework of Charge Admittance**

**Abstract**

This paper introduces a novel interpretation of redshift based on the interaction between energy dipoles and gravitational deflections, exploring the role of entropy and energy redistribution in altering the frequency of electromagnetic waves. By analyzing the cumulative effect of gravitational interactions and their irreversible influence on energy dipoles, we propose that redshift may result from permanent wavelength changes due to energy stretching. This challenges the Doppler-based explanation of redshift and offers a new lens through which to understand cosmic redshift and its relationship with the structure of the universe. Implications of this theory suggest that the universe may not require expansion for redshift to occur, offering a static or infinite model of the cosmos.

**Introduction**

The phenomenon of redshift is traditionally attributed to two primary causes: Doppler effects (relating to motion) and gravitational redshift (resulting from energy climbing out of gravitational wells). These explanations, while consistent with many observations, leave some room for alternative theories, especially when considering the irreversible effects of energy interactions with gravitational fields.

This paper introduces a new mechanism: Charge Admittance (CA). We hypothesize that when an energy dipole interacts with a gravitational field, the leading charge of the dipole experiences the gravitational pull slightly earlier than the trailing charge. This differential force stretches the dipole, leading to a permanent increase in wavelength—a redshift from the dipole’s perspective, even though the observer within the gravitational field sees a blueshift.

We aim to incorporate entropy into this explanation, suggesting that the increase in wavelength is an irreversible process, contributing to the arrow of time. Additionally, gravitational interactions cause sideband generation, further altering the photon’s spectral content over time.

**Historical Background**

The classical view of redshift developed from Doppler’s work in the 19th century to Hubble’s law in the 20th century. Redshift is seen as evidence of either relative motion (in the case of Doppler shifts) or the expansion of space itself (in cosmological contexts). The gravitational redshift was later added as a natural consequence of General Relativity, particularly when photons escape strong gravitational fields.

The classical view of redshift developed from Doppler’s work in the 19th century to Hubble’s law in the 20th century. Redshift is seen as evidence of either relative motion (in the case of Doppler shifts) or the expansion of space itself (in cosmological contexts). The gravitational redshift was later added as a natural consequence of General Relativity, particularly when photons escape strong gravitational fields.

In 1868, British astronomer William Huggins determined the velocity of a star moving away from Earth using redshift, and in 1871, optical redshift was confirmed through observations of solar rotation. The early 20th century saw further advancements, with Aristarkh Belopolsky verifying optical redshift in the laboratory.

However, these explanations rely on the assumption that redshift is primarily tied to the relative velocity of galaxies or the expansion of space. We propose to revisit this assumption by examining the microscopic effects of gravitational deflection and entropy, offering an alternative explanation.

**Theoretical Background**

An energy dipole consists of two opposite charges, separated by a finite distance, forming a dipole moment. This dipole travels through space as a propagating electromagnetic wave, where the permittivity (ϵ0ϵ0) and permeability (μ0μ0) fields define the medium’s impedance.

As the dipole moves through a gravitational field, the forces acting on the leading charge differ slightly from those on the trailing charge. This interaction causes a stretching of the dipole, leading to a permanent energy shift that manifests as a redshift.

**Energy Dipole Interaction with Gravitational Fields:**

We describe the forces acting on the dipole using a simplified form of Lorentz force law:

**F⃗ = q(E⃗ _{0}+ΔE⃗) + qv⃗x (B⃗_{0}+ΔB⃗)**

Where:

E⃗_{0} and B⃗_{0}B are the initial electric and magnetic fields, respectively.

ΔE⃗ and ΔB⃗ are the changes in fields due to gravitational interaction (the local impedance gradient).

v⃗ is the velocity of the dipole charges.

**Mathematical Framework**

We begin by exploring the forces acting on the energy dipole as it passes through a gravitational field. Assuming that gravitational forces create a gradient in impedance, we can model the stretching of the dipole.

**Force and Deflection:**

The net change in velocity (Δv⃗ ) due to the asymmetric forces experienced by the dipole is:

**Δv⃗ = ∫ F⃗/m dt**

This deflection alters the dipole’s trajectory and energy distribution. Since the leading charge experiences the force first, it is stretched relative to the trailing charge, leading to an overall stretching effect.

**Frequency Change (Redshift):**

The energy redistribution within the dipole due to the distortion affects its oscillation frequency. The change in frequency can be expressed as:

**Δf=ΔE/h**

Where:

Δf is the change in frequency.

ΔE is the change in energy due to the interaction with the gradient.

h is Planck’s constant.

When this dipole moves through a region where the permittivity and permeability of the medium change, it experiences differential forces, leading to distortion and deflection.

This equation models how gravitational deflection leads to a permanent redshift, introducing the concept of gravitational entropy—a process that cannot be reversed once the photon has passed the gravitational body.

**Deflection and Sideband Generation:**

In addition to frequency shifts, gravitational interactions may induce sidebands—small shifts in the energy spectrum that accompany the main photon frequency. This would result from slight oscillations or “jitter” in the photon’s path caused by complex gravitational interactions.

Sidebands can be analyzed using Fourier transforms of the energy dipole’s trajectory:

E(t) = ∫_{∞} ^{−∞} E^ (f) e^{i2πft} df

Where small deflections from the gravitational interaction lead to minor frequency components in the signal, producing detectable sidebands.

**Gravitational Redshift, Entropy, and Time’s Arrow:**

The process of gravitational deflection causes a permanent redshift, aligning with the concept of entropy and the arrow of time. Energy passing through a gravitational field experiences an irreversible increase in wavelength, consistent with the second law of thermodynamics. This “time’s arrow” interpretation provides a new framework for understanding redshift as a consequence of the photon’s entropic aging over time.

**Counterintuitive Energy Stretching vs. Observer Compression:**

One of the more intriguing aspects of this theory is the counterintuitive difference between how energy experiences gravitational deflection and how an observer perceives it. As an energy dipole travels through a gravitational field, the differential forces acting on the leading and trailing charges cause the dipole to stretch—resulting in an irreversible increase in its wavelength, which we describe as redshift.

However, an observer situated within the gravitational field sees the energy differently. From the observer’s vantage point, the photon appears blueshifted, not redshifted. This is due to the observer’s position within the deeper gravitational potential, where energy is perceived as being compressed rather than stretched. This paradox occurs because the photon, which is experiencing an increase in wavelength due to the differential forces over its journey, carries the “memory” of its stretching. But to a local observer, the gravitational field appears to concentrate or compress the energy, leading to the apparent blueshift.

This duality underscores a crucial distinction between the intrinsic changes in the energy dipole’s state and the relative perception of energy by an observer within a gravitational well. The energy, in a sense, carries the record of its path and deflections in its wavelength, yet this is only apparent from outside the immediate gravitational influence. Locally, the energy appears blueshifted, but globally—across the entirety of its journey—redshift dominates as the photon moves further away from gravitational sources.

This subtle contradiction between local and global energy dynamics offers new insight into how energy interacts with gravitational fields and supports the broader thesis that redshift is a permanent, entropy-driven process rather than a reversible phenomenon tied solely to relative motion.

**Implications for Cosmology:**

If redshift is primarily driven by cumulative gravitational deflections, the necessity of a cosmological expansion to explain the universe’s redshifted light may be reevaluated. Instead, the redshift could simply be a measure of the distance traveled and the number of gravitational interactions experienced by the photon. This suggests a possible static universe model, where galaxies grow in situ, and energy interactions occur on local scales rather than as a result of universal expansion.

**Conclusion:**

This paper presents an alternative interpretation of redshift, where gravitational deflection and entropy play a central role. Redshift, rather than being the result of the universe’s expansion, could arise from the cumulative effects of local gravitational interactions, stretching the energy dipole over time. This model proposes a static or infinite universe, with redshift as a natural consequence of energy traveling through space.

**Future Work**

Further experimental validation of this theoretical model is necessary. Practical setups to test the deflection and frequency change of energy dipoles in controlled impedance gradients will provide empirical support for the proposed mechanism. Additionally, exploring the implications of this model in astrophysical contexts could offer new insights into observed redshift phenomena.

**References**

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**Planck, M.** (1900). On the Theory of the Energy Distribution Law of the Normal Spectrum.