David Kolb
Independent Researcher
URTG aligns with observational evidence:
- In this paper we determine if the explanation for the bending of light in the proximity of a massive body by this mathematical framework aligns with observations of light bending near large masses as observed during the 1919 eclipse.
1. Einstein's initial 1911 calculation predicted a deflection angle of 0.875 arcseconds for starlight grazing the Sun's limb. This was based on special relativity and the equivalence principle, but did not account for spacetime curvature.
2. In 1915, after completing his general theory of relativity, Einstein revised his prediction to 1.75 arcseconds - exactly twice the 1911 value. This accounted for the full effects of spacetime curvature.
3. The precise formula Einstein derived for the deflection angle is:
α = 4GM / (c^2 R)
Where:
- G is the gravitational constant
- M is the mass of the Sun
- c is the speed of light
- R is the Sun's radius
4. Plugging in the values known at the time:
- G = 6.67 x 10^-11 m^3 kg^-1 s^-2
- M = 1.99 x 10^30 kg
- c = 3 x 10^8 m/s
- R = 6.96 x 10^8 m
This yields α = 1.75 arcseconds (1.75 x 4.8481 x 10^-6 radians)
5. The 1919 eclipse observations by Eddington and others aimed to measure this 1.75 arcsecond deflection predicted by general relativity, compared to the 0.87 arcsecond "Newtonian" prediction or no deflection at all.
So Einstein's precise predicted value of 1.75 arcseconds for starlight grazing the Sun's limb was derived from his full general relativity equations and the known values for the Sun's mass and radius at the time. This prediction was what the 1919 eclipse expeditions set out to test.
Here are the known values for the Sun's mass and radius at the time of the 1919 solar eclipse:
Sun's Mass:
The mass of the Sun was well-established by 1919. Newton had first estimated the Sun's mass in 1687, and by the late 17th/early 18th century, reasonably accurate estimates were available. The modern value is given as:
1.988 x 10^30 kg
This value would have been known to a good approximation by 1919, likely within a few percent of this figure.
Sun's Radius:
The Sun's radius was also well-known by 1919. The search results provide the following value:
695,700 km
This is very close to the modern accepted value. In 1919, astronomers would have known the Sun's radius to within a small fraction of this value.
Specifically for the 1919 eclipse, the search results provide this value used in the calculations:
Sun Semi-Diameter: 15'46.6"
This angular measurement corresponds closely to the physical radius value given above when viewed from Earth's distance.
These values for the Sun's mass and radius would have been used in Einstein's calculations predicting the deflection of starlight, as well as in the analysis of the eclipse observations to confirm the theory of general relativity.
Based on the provided information and the equations in the Unified Relativistic Gravitational Theories (URTG) framework, let's derive the predictions for light deflection angles, compare them with observed values, and ensure consistency with general relativity.
1. Deriving predictions for light deflection angles:
In URTG, we use the Light Propagation Equation:
dx^μ/dλ = c_c * k^μ(C_μν, ψ)
Where k^μ is a modified null vector determined by the causal structure tensor C_μν and the configuration of field dispositions ψ.
To derive the deflection angle, we consider the Enhanced Space-Mass-Light Interaction Tensor:
S_μν = α(R_μν - 1/2Rg_μν) + κφ²R_μν + β∇_μ∇_νφ + σA_μν + ωM_μν + θC_μν + ηEM(ψ, ∂ψ)
For a spherically symmetric mass like the Sun, we can simplify this to focus on the terms most relevant to gravitational lensing:
S_μν ≈ α(R_μν - 1/2Rg_μν) + ωM_μν + θC_μν + ηEM(ψ, ∂ψ)
The deflection angle α can be approximated as:
α ≈ 4GM / (c_c²R) * (1 + ε)
Where ε is a correction term arising from URTG's modifications to general relativity:
ε ≈ θ * C² + η * EM(ψ, ∂ψ)²
2. Comparing predictions with observed values:
Using the provided values:
G = 6.67 x 10^-11 m^3 kg^-1 s^-2
M = 1.99 x 10^30 kg
c_c = 3 x 10^8 m/s (assuming c_c ≈ c for this calculation)
R = 6.96 x 10^8 m
Plugging these into our equation:
α ≈ 1.75 arcseconds * (1 + ε)
This matches Einstein's prediction from general relativity, with URTG predicting a small correction factor (1 + ε).
3. Consistency with general relativity:
To ensure URTG reproduces the successful predictions of general relativity, we need to show that ε is very small for the scales involved in the solar eclipse experiments.
The magnitude of ε depends on terms in URTG that deviate from general relativity, particularly those involving the causal structure C and the emergent electromagnetic interactions EM(ψ, ∂ψ):
ε ≈ θ * C² + η * EM(ψ, ∂ψ)²
Where θ and η are small coupling constants.
For consistency with observations, we require:
|ε| << 1
Given the 1919 eclipse observations' accuracy, we can set an upper bound:
|ε| < 0.3
4. URTG-specific considerations:
In URTG, gravitational lensing is explained through the relational nature of space and time, the interdependence between mass, motion, and the geometry of space, and emergent electromagnetic interactions. The causal structure tensor C_μν and the configuration of field dispositions ψ play crucial roles in determining light's path.
The Unified Spacetime Interval equation in URTG:
ds² = g_μν dx^μ dx^ν = c²dτ² (1 - 2U/c² - v²/c² - h(φ, ℑ) - k(a) - j(C) - z(EM, ∂ψ/∂τ))
suggests that the effective geometry experienced by light is influenced by additional factors beyond just mass-energy distribution.
URTG reproduces the predictions of general relativity for light deflection to first order, matching the observed value of approximately 1.75 arcseconds for starlight grazing the Sun's limb. It also allows for small corrections that could be detected in more precise measurements, potentially distinguishing URTG from standard general relativity in future experiments.
The framework's emphasis on causal structure, emergent electromagnetic interactions, and the configuration of field dispositions provides a novel perspective on the mechanism of gravitational lensing. Future high-precision experiments could potentially detect these URTG-specific contributions, offering a way to test the theory against standard general relativity.