Abstract
We propose a new geometric model to explain the redhead to the red observed from distant celestial objects without invoking cosmic expansion or a gravitational red shift. By examining the angular geometry between the light source, the observer, and a fixed reference point “above” of the observer, we demonstrate how spatial geometry alone can cause an apparent increase in the wavelength of light – a red shift – as a function of the distance. Our model builds triangles with variable angles to illustrate this effect, maintaining a static universe and by attributing the gap towards red to purely geometric phenomena. This approach offers an alternative perspective on cosmological observations and invites to re -examine fundamental hypotheses in cosmology.
1. Introduction
The cosmological red shift is a fundamental observation in astrophysics, indicating that the light of the distant galaxies is moved to the red end of the spectrum. This phenomenon is traditionally attributed to the expansion of the universe, leading to the general acceptance of the Big Bang model. The law of Hubble, which establishes a linear relationship between the gap towards the red of a galaxy and its distance from the earth, was a cornerstone of the concept of an expanding cosmos.
However, alternative models that do not invoke cosmic expansion can provide new information on the structure of the universe and the mechanisms behind the observed phenomena. By exploring different explanations for the red time, we can question existing paradigms and improve our understanding of cosmological principles.
In this article, we propose a geometric approach based on the geometry of the triangle to explain the phenomena of gap towards red in a static universe. By analyzing the angular relationships in a specific geometric configuration involving the light source, the observer and a point of reference “above” the observer, we demonstrate how the geometric effects purely can lead to an apparent increase in the wavelength of light with distance.
2. Geometric framework
Our model is built on three fundamental principles:
1. Static universe
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Assumption: The universe does not develop or contract; Its large -scale structure remains constant over time.
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Involvement: This allows us to assign red difference effects observed to factors other than cosmic expansion.
2. Light propagation in a straight line
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Assumption: Light moves into straight lines through space, unless it is influenced by gravitational fields or other forces.
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Involvement: This simplifies the model with classic Euclidean geometry, making calculations and interpretations simpler.
3. Angular geometry
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Assumption: Redshift occurs due to the geometric configuration between the light source, the observer and a fixed reference point “above” of the observer.
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Involvement: By examining how the angles and lateral lengths of this configuration change with the distance, we can connect these geometric modifications to the movements in the wavelength observed.
3. Red offset mechanism based on triangle
Triangle
We build a right angle triangle to model the geometric relationship between the light source, the observer and a fixed point.
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Peaks::
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S (source): The distant celestial object emitting light.
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O (observer): The location where light is detected (for example, earth).
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P (perpendicular point): A point located at a fixed perpendicular distance \ (h \) “above” of the observer \ (o \), forming a right angle to \ (o \).
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Sides::
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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 \) at point \ (p \).
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\ (L \): the hypotenuse connecting the source \ (s \) to point \ (p \).
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Source angle (\ (\ Theta \))
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Definition: \ (\ theta \) is the angle at the source \ (s \) formed between the sides \ (d \) and \ (l \).
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Behavior with distance: As \ (d \) increases, \ (\ theta \) decreases, which makes the triangle become more elongated.
Wavelength
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Assumption: Lighting on the side \ (l \) corresponds to an effective increase in the length of the path that light moves, influencing the wavelength observed.
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Mechanism: A smaller angle \ (\ theta \) at the source led to a longer hypotenuse \ (l \), which is associated with a stretch of the observed wavelength, resulting in a lag towards red.
4. Mathematical representation
4.1 Triangle relations
For a right angle triangle with the sides \ (h \), \ (d \) and hypotenuse \ (l \):
L = \ sqrt {d ^ 2 + H ^ 2}
\ Theta = \ Arctan \ Left (\ Frac {h} {d} \ right)
4.2 Wave length stretching mechanism
We propose that the wavelength observed \ (\ lambda _ {\ text {obs}} \) is linked to the effective length of the path \ (l \):
\ Lambda _ {\ text {obs}} = \ lambda _ {\ text {emit}} \ left (1 + \ Frac {\ delta l} {l_0}}
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Definitions::
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\ (\ lambda _ {\ text {emit}} \): The wavelength of the light emitted by the source.
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\ (\ Delta L = L – L_0 \): The increase in the length of the hypotenuse in relation to a reference length \ (L_0 \) at a 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 Expression of red shift
The Redshift \ (Z \) is defined as the fractional change in wavelength:
