To model the bending of light in a flat Earth scenario covered by a dome using the principles of gravitational lensing, Snell’s law refraction, and wave diffraction, we can explore various configurations and interactions of light with the medium. Here is a detailed analysis of how these phenomena can explain the observed light paths:
Model used https://walterbislin.journalofgeocentriccosmology.org
1. Snell’s Law Refraction
Setup:
Assume the dome has a gradient of refractive indices that varies smoothly from the top to the bottom. The sun’s light enters the dome at a certain angle, refracts at the interface between the air and the dome material, and then refracts again when exiting.
Mathematical Framework:
Snell’s Law: n1 * sin(theta1) = n2 * sin(theta2). If the dome has layers with varying refractive indices n(z) where z is the height, the path of light will continuously bend as it travels through the dome.
Application:
Light entering from above the dome (positioned outside) will bend toward the normal as it enters a denser medium and away from the normal as it exits. Multiple domes or layers can create more complex paths, with each interface bending the light further.
2. Gravitational Lensing
Setup:
Assume there is a massive object either within or beneath the dome that creates a gravitational field strong enough to bend light.
Mathematical Framework:
Einstein’s General Relativity: The deflection angle alpha of light passing near a mass M is given by alpha approximately equal to (4 * G * M) / (c^2 * b), where G is the gravitational constant, M is the mass, c is the speed of light, and b is the impact parameter (closest approach).
Application:
Light passing near this massive object will bend towards it, creating an apparent shift in position. This can create multiple images of the sun or other celestial objects depending on the alignment.
3. Wave Diffraction
Setup:
Consider the dome surface or multiple layers as having structures (like apertures or slits) that cause diffraction.
Mathematical Framework:
Diffraction is described by the Huygens-Fresnel principle and can be quantified using the equations for single-slit or multi-slit diffraction. For a slit width a and light of wavelength lambda, the diffraction angle theta is given by a * sin(theta) = m * lambda, where m is an integer (order of the diffraction).
Application:
Light interacting with fine structures on or within the dome will spread out and bend around these structures, leading to complex light paths. This could explain unexpected light bending, creating multiple apparent positions for the sun or other light sources.
Combined Model
To achieve the bending observed in the image:
- Layered Dome with Varying Refractive Index: A dome with a gradient of refractive indices can bend light gradually, making celestial objects appear displaced from their actual positions.
- Gravitational Effects: If a hypothetical massive object (like a concentrated mass under the dome) is present, it would further bend the light paths.
- Diffraction Effects: Structures within the dome could cause diffraction, adding complexity to the light paths.
Step-by-Step Explanation:
- Initial Refraction: Light from the sun enters the dome at a specific angle. The initial refraction occurs at the air-dome interface, bending towards the normal.
- Layered Refraction: As light travels through layers with varying refractive indices, it bends continuously, changing its trajectory smoothly.
- Gravitational Influence: If a massive object is present beneath the dome, light passing near it would bend further due to gravitational lensing.
- Exit Refraction: When light exits the dome, it bends away from the normal, contributing to the apparent shift.
- Diffraction: As light interacts with fine structures or apertures within the dome, it diffracts, spreading out and bending in additional directions.
By combining these effects, we can model the observed bending of light paths in the image, where the sun’s apparent position is shifted due to the complex interplay of refraction, gravitational lensing, and diffraction within the dome.
4. The 24-Hour Antarctic Sun Phenomenon
To theoretically explain the phenomenon of a 24-hour Antarctic sun within the framework of a flat Earth model covered by a dome, we need to delve deeper into the combined effects of refraction, gravitational lensing, and wave diffraction. These principles can collectively create the conditions necessary for continuous daylight in the Antarctic region.
Assumptions and Setup
- Flat Earth Model: The Earth is depicted as a flat plane with the Antarctic region at its periphery.
- Dome Structure: A dome, potentially with multiple layers or gradients of refractive indices, covers the flat Earth.
- Sun’s Path: The sun moves in a circular path above the plane, with its height and azimuth varying throughout the day.
- Layered and Multi-Dome Configuration: The dome consists of layers with varying refractive indices or multiple domes stacked concentrically, each contributing to the bending of light.
Mechanisms Involved
- Snell’s Law Refraction
- Setup: As sunlight enters the dome, it refracts at the air-dome interface. The refractive index gradient within the dome bends the light continuously.
- Mathematical Framework: Using Snell’s Law, n1 * sin(theta1) = n2 * sin(theta2), where the refractive indices vary with height n(z).
- Application: This continuous bending ensures that sunlight, even when the sun is geometrically below the horizon, is refracted back towards the Antarctic region.
- Gravitational Lensing
- Setup: Assume the presence of a hypothetical massive object beneath or within the dome, generating a gravitational field strong enough to bend light.
- Mathematical Framework: Using the deflection angle formula alpha = (4 * G * M) / (c^2 * b), where G is the gravitational constant, M is the mass, c is the speed of light, and b is the impact parameter.
- Application: The gravitational field bends light around the periphery of the flat Earth, making the sun visible even when it would otherwise set.
- Wave Diffraction
- Setup: The dome’s surface or internal layers have structures that cause diffraction, such as apertures or slits.
- Mathematical Framework: Using the diffraction equation a * sin(theta) = m * lambda, where a is the slit width, lambda is the wavelength, and m is the diffraction order.
- Application: Diffraction spreads sunlight around obstacles and edges within the dome, ensuring it reaches the Antarctic region continuously.
Combined Effects for 24-Hour Sunlight
- Layered Refraction: The gradient in the dome’s refractive index bends sunlight to follow a curved path. During the Antarctic summer, the sun’s position and the dome’s refraction ensure that light is always bent towards the Antarctic region, even at geometrical night.
- Gravitational Influence: The hypothetical massive object creates a lensing effect, bending light further around the flat Earth’s edges. This effect can create overlapping images of the sun, contributing to continuous daylight.
- Diffraction Patterns: Structures within the dome cause light to spread through diffraction, filling gaps and smoothing out the light distribution. This ensures that the Antarctic region receives a consistent amount of sunlight.
Example Calculation
- Refraction Angles:
- Calculate the angles of refraction using Snell’s Law at various interfaces within the dome, considering a gradient refractive index n(z).
- Example: If n1 = 1 (air), n2 = 1.5 (dome material), theta1 = 45 degrees, then theta2 = arcsin((n1/n2) * sin(theta1)).
- Gravitational Deflection:
- Using alpha = (4 * G * M) / (c^2 * b), determine the deflection angle for light passing near the massive object.
- Example: For M = 5 x 10^24 kg, b = 10^6 m, alpha = (4 * 6.674 x 10^-11 * 5 x 10^24) / ((3 x 10^8)^2 * 10^6).
- Diffraction Angles:
- Calculate diffraction angles using a * sin(theta) = m * lambda for different slit widths and light wavelengths.
- Example: If a = 0.01 m, lambda = 500 nm, m = 1, then theta = arcsin(m * lambda / a).
By combining these principles, we can create a model where the sun’s light is continuously bent and spread, ensuring that the Antarctic region experiences 24-hour daylight. This approach leverages the complex interplay of refraction, gravitational lensing, and diffraction within the dome to simulate the observed phenomenon in a flat Earth model.