Exploring the Cosmos: A Novel Geometric Approach to Understanding Cosmological Redshift in a Static Universe

In this article, we introduce an innovative geometric model that explains the redshift of light observed from distant celestial bodies without relying on the concepts of cosmic expansion or gravitational redshift. By focusing on the angular relationships among the light source, the observer, and a fixed reference point “above” the observer, we illustrate how spatial geometry can account for an apparent increase in light wavelength, or redshift, as distance increases. Our model employs triangles with varying angles to demonstrate this effect while upholding the notion of a static universe. This alternative perspective challenges conventional cosmological assumptions and encourages a re-evaluation of our understanding of the universe.

The cosmological redshift is a pivotal observation in astrophysics, revealing that light from faraway galaxies shifts toward the red end of the spectrum. Traditionally, this phenomenon has been attributed to the universe’s expansion, forming the foundation of the widely accepted Big Bang model. Hubble’s Law, which describes a linear relationship between a galaxy’s redshift and its distance from Earth, reinforces the idea of an expanding cosmos. However, exploring alternative explanations for redshift can provide valuable insights into the universe’s structure and the mechanisms that underlie these observed phenomena. This paper proposes a geometric approach based on triangle geometry to elucidate redshift phenomena within a static universe. By scrutinizing the angular relationships in a specific geometric configuration involving the light source, the observer, and a fixed reference point positioned “above” the observer, we reveal how geometric effects can lead to an apparent increase in light wavelength with distance.

Our model is based on three key principles. First, we assume a static universe, meaning that it neither expands nor contracts; its large-scale structure remains constant over time. This assumption allows us to attribute the observed redshift effects to factors other than cosmic expansion. Second, we posit that light travels in straight lines through space unless influenced by gravitational fields or other forces, which simplifies our model to classical Euclidean geometry. This simplification facilitates straightforward calculations and interpretations. Finally, we suggest that the redshift arises from the geometric configuration between the light source, the observer, and a fixed reference point above the observer. By examining how angles and side lengths in this configuration change with distance, we can correlate these geometric alterations to shifts in the observed wavelength.

To further elucidate this relationship, we present mathematical expressions that govern the triangle’s properties. In our right-angled triangle, the relationship between the sides can be described by the equation L = √(d² + h²). Additionally, the angle θ can be calculated using the arctangent function as θ = arctan(h/d). We propose that the observed wavelength, denoted as λ_obs, is related to the effective path length L through a proportional relationship: λ_obs = λ_emit (1 + ΔL/L₀), where λ_emit represents the wavelength of light emitted by the source, ΔL indicates the increase in hypotenuse length compared to a reference length L₀ at a specific reference distance d₀. Consequently, the redshift z is defined as the fractional change in wavelength, allowing us to express it mathematically.

In summary, our geometric model presents a compelling alternative explanation for the observed redshift of light from distant celestial objects, challenging the long-standing belief in an expanding universe. By emphasizing the role of angular geometry and static conditions, we offer a fresh perspective on cosmological observations. As we continue to explore the intricacies of our universe, such alternative models may enrich our understanding and invite further investigation into the fundamental principles of cosmology. This approach not only stimulates intellectual curiosity but also encourages scientists and enthusiasts alike to reconsider the assumptions that have shaped our current understanding of the cosmos.