Abstract
We propose a novel geometric model to explain the observed redshift of light from distant celestial objects without resorting to cosmic expansion or gravitational redshift. By examining the angular geometry between the light source, the observer, and a fixed reference point “above” the observer, we show how spatial geometry can lead to an apparent increase in the wavelength of light—a redshift— as a function of distance. . Our model creates triangles with different angles to describe this effect, maintaining a static universe and relating the redshift to purely geometric phenomena. This approach offers an alternative perspective on cosmological observations and invites reconsideration of fundamental cosmological assumptions.
1. Introduction
Cosmological redshift is a fundamental observation in astrophysics, indicating that light from distant galaxies is shifted toward the red end of the spectrum. This phenomenon has traditionally been attributed to the expansion of the universe, leading to the widespread acceptance of the Big Bang model. Hubble’s Law, which establishes a linear relationship between the redshift of a galaxy and its distance from Earth, has been a cornerstone supporting the concept of an expanding cosmos.
However, alternative models that do not invoke cosmic expansion may provide new insights into the structure of the universe and the mechanisms behind the observed phenomena. By exploring different explanations for redshift, we can challenge current paradigms and improve our understanding of the principles of cosmology.
In this paper, we propose a geometric approach based on triangle geometry to explain redshift phenomena within a static universe. By examining the angular relationships in a particular geometric configuration involving a light source, an observer, and a reference point “above” the observer, we show how this can lead to an apparent increase in the wavelength of light with distance are purely geometric effects.
2. Geometric Framework
Our model is built on three main principles:
1. Static Universe
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Assumption: The universe is neither expanding nor contracting; its large-scale structure remains constant over time.
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Implications: This allows us to attribute observed redshift effects to factors other than cosmic expansion.
2. Straight-Line Light Propagation
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Assumption: Light travels in straight lines through space unless influenced by gravitational fields or other forces.
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Implications: It simplifies the model to classical Euclidean geometry, making calculations and interpretations more straightforward.
3. Angular Geometry
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Assumption: Redshift appears due to the geometric arrangement between the light source, the observer, and a fixed reference point “above” the observer.
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Implications: By examining how the angles and side lengths of this configuration change with distance, we can relate these geometric changes to changes in the observed wavelength.
3. Triangle-Based Redshift Mechanism
Triangle Construction
We construct a right-angled triangle to model the geometric relationship between the light source, the observer, and a fixed point.
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Vertices:
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S (Source): The distant celestial object that emits light.
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O (observer): The location where the light is detected (eg, Earth).
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P (Perpendicular Point): A point located at a fixed perpendicular distance \( h \) “above” the observer \( O \), forming a right angle with \( O \).
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Edges:
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\( d \): The horizontal distance between the source \( S \) and the observer \( O \).
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\( h \): A fixed perpendicular distance from the observer \( O \) to the point \( P \).
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\( L \): The hypotenuse connecting the source \( S \) to the point \( P \).
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Angle at the Origin (\( \theta \))
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Meaning: \( \theta \) is the angle at the origin \( S \) formed between the edges \( d \) and \( L \).
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Behavior with Distance: As \( d \) increases, \( \theta \) decreases, causing the triangle to elongate.
Wavelength Effect
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Hypothesis: Elongation of the edge \( L \) corresponds to an effective increase in the length of the path traveled by the light, which influences the observed wavelength.
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Mechanism: A smaller angle \( \theta \) to the source leads to a longer hypotenuse \( L \), which is associated with a stretching of the observed wavelength, resulting in a redshift.
4. Mathematical Representation
4.1 Triangular Relationship
For a right-angled triangle with sides \( h \), \( d \), and hypotenuse \( L \):
L = \sqrt{d^2 + h^2}
\theta = \arctan\left(\frac{h}{d}\right)
4.2 Mechanism of Wavelength Stretching
We suggest that the observed wavelength \( \lambda_{\text{obs}} \) is related to the effective path length \( L \):
\lambda_{\text{obs}} = \lambda_{\text{emit}} \left(1 + \frac{\Delta L}{L_0}\right)
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Definitions:
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\( \lambda_{\text{emit}} \): The wavelength of light emitted by the source.
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\( \Delta L = L – L_0 \): The increase in the length of the hypotenuse compared to the reference length \( L_0 \) at the reference distance \( d_0 \).
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\( L_0 \): The length of the hypotenuse at the reference distance.
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4.3 Redshift Expression
The redshift \( z \) is defined as the fractional change in wavelength:
