Summary
We suggest a novel geometric mannequin to clarify the noticed redshift of sunshine from distant celestial objects with out invoking cosmic enlargement or gravitational redshift. By analyzing the angular geometry between the sunshine supply, the observer, and a set reference level “above” the observer, we exhibit how spatial geometry alone can result in an obvious improve within the wavelength of sunshine—a redshift—as a perform of distance. Our mannequin constructs triangles with various angles as an instance this impact, sustaining a static universe and attributing the redshift to purely geometric phenomena. This method affords another perspective on cosmological observations and invitations reconsideration of basic assumptions in cosmology.
1. Introduction
The cosmological redshift is a foundational statement in astrophysics, indicating that gentle from distant galaxies is shifted towards the pink finish of the spectrum. This phenomenon has historically been attributed to the enlargement of the universe, resulting in the widespread acceptance of the Large Bang mannequin. Hubble’s Regulation, which establishes a linear relationship between a galaxy’s redshift and its distance from Earth, has been a cornerstone supporting the idea of an increasing cosmos.
Nonetheless, different fashions that don’t invoke cosmic enlargement can present new insights into the universe’s construction and the mechanisms behind noticed phenomena. By exploring totally different explanations for the redshift, we will problem current paradigms and improve our understanding of cosmological rules.
On this paper, we suggest a geometrical method primarily based on triangle geometry to clarify redshift phenomena inside a static universe. By analyzing the angular relationships in a selected geometric configuration involving the sunshine supply, observer, and a reference level “above” the observer, we exhibit how purely geometric results can result in an obvious improve within the wavelength of sunshine with distance.
2. Geometric Framework
Our mannequin is constructed upon three foundational rules:
1. Static Universe
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Assumption: The universe just isn’t increasing or contracting; its large-scale construction stays fixed over time.
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Implication: This permits us to attribute noticed redshift results to components apart from cosmic enlargement.
2. Straight-Line Gentle Propagation
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Assumption: Gentle travels in straight traces by way of area until influenced by gravitational fields or different forces.
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Implication: This simplifies the mannequin to classical Euclidean geometry, making calculations and interpretations extra simple.
3. Angular Geometry
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Assumption: The redshift arises because of the geometric configuration between the sunshine supply, the observer, and a set reference level “above” the observer.
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Implication: By analyzing how angles and aspect lengths on this configuration change with distance, we will relate these geometric modifications to shifts within the noticed wavelength.
3. Triangle-Based mostly Redshift Mechanism
Triangle Building
We assemble a right-angled triangle to mannequin the geometric relationship between the supply of sunshine, the observer, and a set level.
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Vertices:
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S (Supply): The distant celestial object emitting gentle.
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O (Observer): The situation the place the sunshine is detected (e.g., Earth).
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P (Perpendicular Level): A degree positioned at a set perpendicular distance ( h ) “above” the observer ( O ), forming a proper angle at ( O ).
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Sides:
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( d ): The horizontal distance between the supply ( S ) and the observer ( O ).
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( h ): A set perpendicular distance from the observer ( O ) to level ( P ).
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( L ): The hypotenuse connecting the supply ( S ) to level ( P ).
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Angle on the Supply (( theta ))
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Definition: ( theta ) is the angle on the supply ( S ) fashioned between sides ( d ) and ( L ).
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Conduct with Distance: As ( d ) will increase, ( theta ) decreases, inflicting the triangle to develop into extra elongated.
Impact on Wavelength
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Speculation: The lengthening of aspect ( L ) corresponds to an efficient improve within the path size that gentle travels, influencing the noticed wavelength.
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Mechanism: A smaller angle ( theta ) on the supply results in an extended hypotenuse ( L ), which is related to a stretching of the noticed wavelength, leading to a redshift.
4. Mathematical Illustration
4.1 Triangle Relations
For a right-angled triangle with sides ( h ), ( d ), and hypotenuse ( L ):
L = sqrt{d^2 + h^2}
theta = arctanleft(frac{h}{d}proper)
4.2 Wavelength Stretching Mechanism
We suggest that the noticed wavelength ( lambda_{textual content{obs}} ) is expounded to the efficient path size ( L ):
lambda_{textual content{obs}} = lambda_{textual content{emit}} left(1 + frac{Delta L}{L_0}proper)
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Definitions:
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( lambda_{textual content{emit}} ): The wavelength of sunshine as emitted by the supply.
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( Delta L = L – L_0 ): The rise within the hypotenuse size in comparison with a reference size ( L_0 ) at a reference distance ( d_0 ).
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( L_0 ): The hypotenuse size on the reference distance.
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4.3 Redshift Expression
The redshift ( z ) is outlined because the fractional change in wavelength:
