The Discrepancy Between General Relativity and Observational Findings: Gravitational Lensing.

Soumendra Nath Thakur ₁,₂ Deep Bhattacharjee ₃,₄

29-10-2024

Abstract:

This study investigates gravitational lensing as interpreted through general relativity (GR), which posits that massive celestial bodies induce curvature in spacetime, thereby bending light's path. In regions devoid of massive objects, spacetime remains relatively flat. However, the presence of such bodies disrupts this state, causing downward curvature. While GR suggests that gravity results from this curvature, recent observational experiments indicate that light is predominantly bent due to the curvature of the gravitational field, rather than spacetime itself. This contradiction raises significant questions about the validity of GR in explaining the interaction between light and gravity. This study aims to reconcile these discrepancies, suggesting a revised understanding of gravitational lensing and its underlying mechanisms.

Keywords: General Relativity, Gravitational Lensing, Curvature of Spacetime, Gravitational Field, Light Bending, Observational Experiments, Massive Celestial Bodies, Gravity.

₁ Tagore’s Electronic Lab., West Bengal, India

₃ Integrated Nanoscience Research (QLab), India

₄ Electro – Gravitational Space Propulsion Laboratory, India 

Correspondence:

Corresponding Author₁,₂

₁ postmasterenator@gmail.com

₂ postmasterenator@telitnetwork.in

₃ deepbhattacharjee.ac@gmail.com

₄ Formerly engaged with R&D EGSPL

Declarations:

Funding:

No specific funding was received for this work.

Potential competing interests:

No potential competing interests to declare.

______________________

Introduction:

According to general relativity (GR), massive celestial bodies—such as galaxies or galaxy clusters—create curvature in the fabric of spacetime. In regions devoid of nearby massive objects, such as the vast expanses between galaxy clusters, spacetime remains flat. The introduction of a massive body causes spacetime to curve downward toward it, leading to gravitational lensing, where light's path appears bent.

GR asserts that gravity arises from this curvature of spacetime. The gravitational field can be visualized as mirroring the shape of spacetime curvature, analogous to a globe where the lower half represents spacetime curvature and the upper half symbolizes the gravitational field. However, GR claims that light bends downward along the curvature of spacetime, rather than conforming to an upward curve of the gravitational field.

Contrarily, observational experiments indicate that the bending of light occurs primarily due to the curvature of the gravitational field, challenging the GR interpretation. This study will examine these discrepancies and propose avenues for future research.

Methodology:

This study employs a multi-faceted approach to investigate the discrepancies between GR and observational findings regarding gravitational lensing, encompassing both theoretical analysis and empirical data evaluation:

Theoretical Framework

Literature Review: A thorough review of existing literature on gravitational lensing, GR, and the interaction between light and gravity will be conducted, focusing on seminal works and contemporary studies.

Mathematical Modelling: Theoretical models of gravitational lensing will be developed based on equations derived from GR, including the application of Einstein's field equations to describe how massive celestial bodies influence light's path.

Simulation of Light Paths: Computational simulations will model light trajectories around massive objects according to GR predictions, visually illustrating light bending and facilitating comparison with observational data.

Empirical Analysis

Data Collection: Observational data from astrophysical surveys documenting gravitational lensing events will be collected from sources like the Hubble Space Telescope and ground-based observatories.

Data Analysis: The collected data will be analysed to measure the degree of light bending in various gravitational lensing scenarios, employing statistical methods to assess correlations with GR predictions.

Comparison with Theoretical Predictions: The results will be compared systematically with theoretical predictions, identifying significant discrepancies between observed and predicted light bending.

Synthesis of Findings

Discrepancy Analysis: The identified discrepancies between theoretical predictions and observational findings will be critically examined to understand their implications for GR's validity.

Re-evaluation of Theoretical Models: Based on findings, a re-evaluation of theoretical models used in GR will be conducted, exploring alternative models or modifications that could provide a more accurate representation of observed phenomena.

Implications for Future Research: The study will conclude with recommendations for further observational studies and theoretical investigations to enhance understanding of the complex relationship between light, gravity, and spacetime.

Validation and Peer Review

Peer Review: The results and conclusions will be submitted for peer review to ensure the robustness of findings, integrating feedback to refine the study.

Publication: Upon successful peer review, the study will be published in a relevant scientific journal to disseminate findings and encourage ongoing exploration of gravitational lensing.

Mathematical Presentation:

A photon representing light carries inherent energy denoted as E. As the photon ascends from a gravitational well, it loses part of this energy, resulting in a redshift (Δλ>0). However, the photon's behaviour changes significantly when encountering a strong external gravitational field.

As the photon approaches a massive body, it undergoes a blueshift (Δλ<0) due to electromagnetic-gravitational interactions, causing it to follow an arc-shaped trajectory. This interaction increases the photon's momentum, described by Δρ=h/Δλ, where h is Planck's constant. Upon completing half of the arc, the blueshift transitions into a redshift (Δλ>0) as the photon begins to lose momentum. This process reflects a symmetrical momentum exchange, where the photon experiences a balanced gain and loss of external energy, preserving symmetry in its overall energy behaviour.

Importantly, while the photon undergoes these changes, its inherent energy remains conserved, except for the loss associated with its initial emission. After bypassing the gravitational field, the photon resumes its original trajectory, continuing unaffected by further gravitational influences.

Discussion:

This study delves into the intricacies of gravitational lensing through the lens of GR. The fundamental premise of GR posits that massive celestial bodies create curvature in spacetime, influencing the trajectory of nearby light. However, observational experiments suggest that light is predominantly bent due to the gravitational field's curvature, rather than the curvature of spacetime itself. This distinction raises significant questions regarding the current understanding of gravity and its relationship with light.

While GR leads to the visualization of the gravitational field as mirroring spacetime curvature, this model may not encapsulate the complexities observed in actual experiments. The discrepancy between GR's predictions and observational data necessitates a re-evaluation of gravitational lensing and the underlying mechanics of light propagation in gravitational fields. This misalignment challenges the validity of GR, signalling the potential need for alternative models or modifications that could more accurately describe the observed interactions between light and massive celestial bodies.

Moving forward, this study advocates for a comprehensive approach that bridges the gap between GR's theoretical framework and empirical observations. It emphasizes the importance of conducting further studies to clarify light's interaction with gravitational fields and ascertain whether modifications to existing models are warranted. Such investigations could lead to novel insights into the dynamics of light, gravity, and spacetime, ultimately refining our understanding of the cosmos.

Conclusion:

The principles of GR assert that massive celestial bodies create curvature in spacetime, which affects the path of light. When massive bodies are present, spacetime bends downward, leading to gravitational lensing, where light's path appears to follow this curvature.

However, observational experiments challenge this interpretation, demonstrating that light is primarily bent due to the curvature of the gravitational field, not the curvature of spacetime. This discrepancy suggests that the current understanding of light's interaction with gravity may require re-evaluation. Consequently, the validation of GR based on these experiments is called into question, indicating that the relationship between light, gravity, and spacetime may be more complex than GR predicts.

References:

[1] Relativity: the Special and General Theory by Albert Einstein. (2023, May 2). Project Gutenberg. 

https://www.gutenberg.org/ebooks/30155 

[2] Thakur, S. N., & Bhattacharjee, D. (2023b). Phase Shift and Infinitesimal Wave Energy Loss Equations. Preprints.Org (MDPI). https://doi.org/10.20944/preprints202309.1831.v1

[3] Thakur, S. N. & Tagore’s Electronic Lab. (2024). Photon Interactions with External Gravitational Fields: True Cause of Gravitational Lensing. preprints.org (MDPI - Publisher of Open Access Journals), 202410.2121/v1. https://doi.org/10.20944/preprints202410.2121.v1

[4] Thakur, S. N. (2024). Photon Energy and Redshift Analysis in Galactic Measurements: A Refined Approach. ResearchGate, https://www.researchgate.net/publication/385250383

[5] Direct influence of gravitational field on object motion invalidates spacetime distortion. (n.d.). https://easychair.org/publications/preprint/bGq2

[6] Thakur, S. N. (2023). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature. Definitions. https://doi.org/10.32388/81iiae

[7] Thakur, S. N. (2024). Distinguishing Photon Interactions: Source Well vs. External Fields. Qeios. https://doi.org/10.32388/mhabs9

[8] Thakur, S. N., Bhattacharjee, D., & Frederick, O. (2023). Photon Interactions in Gravity and Antigravity: Conservation, Dark Energy, and Redshift Effects. Preprints.Org. https://doi.org/10.20944/preprints202309.2086.v1

[9] Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints.org (MDPI). https://doi.org/10.20944/preprints202409.1190.v2

[10] Thakur, S. N., Samal, P., & Bhattacharjee, D. (2023). Relativistic effects on phaseshift in frequencies invalidate time dilation II. TechRxiv. https://doi.org/10.36227/techrxiv.22492066.v2

#GeneralRelativity, #GravitationalLensing, #CurvatureofSpacetime, #GravitationalField, #LightBending, #ObservationalExperiments, #MassiveCelestialBodies, #Gravity

We Are Already Traveling Through Time: The Redundant Quest for a New Time Machine.

Soumendra Nath Thakur

28-10-2924

We are, in fact, continuously moving through time. This inherent progression renders the idea of inventing a "new" time machine both unnecessary and impossible. Every machine that facilitates motion—whether it's a car, a plane, or even our own footsteps—moves us through time as well as space. In this sense, all motion-related devices are already time machines, enabling us to travel forward in time naturally. Therefore, the pursuit of a separate or unique "time machine" overlooks the reality that our passage through time is a fundamental, ongoing aspect of existence, inseparable from any form of movement.

Universal Expansion is the Receding of Galaxies, Not Space Itself:

Soumendra Nath Thakur

28-10-2924

I see many posts on the expansion of the universe but those posts read like that of someone inspired by a childlike curiosity about the universe, yet lacking a commitment to rigorously studying science and mathematics.

Unfortunately, these posts convey several inaccuracies, largely rooted in a relativistic bias. Observational evidence suggests that dark energy exerts a repulsive effect, opposite to the attractive force of gravity. This repulsion causes isolated galaxies and galactic clusters to move toward the universe's edges, increasing the distance—and thus the space—between these structures. Although this process makes it appear as though the universe is expanding, it does not imply that space within the universe is expanding.

To clarify, we can observe that space within gravitationally bound systems, such as galaxies, remains unaffected by this expansion. The spatial structure within any galaxy, anchored by its central gravitational forces, does not expand. This phenomenon is feasible only if space itself is not expanding; if the entirety of universal space were expanding, we would see expansion occurring universally, including within each galaxy. However, this is not supported by observational data.

In summary, these posts incorrectly imply that space itself is expanding, a misconception driven by relativistic interpretations that treat space-time as a fundamental entity. This overlooks the concept that time emerges as a result of existential events, rather than as an inherent dimension.

#Expansion #UniversalExpansion #expansionofspace

A Supplementary resource (2) for ‘Phase Shift and Infinitesimal Wave Energy Loss Equations'.

Proportional Relationships in Oscillatory Wave Dynamics: Time Shifts and Energy Changes

Soumendra Nath Thakur

28-10-2024

Description: 

This study explores the mathematical relationships between phase shifts in oscillatory wave frequencies and their corresponding time periods and energy changes. The time period associated with a 1° phase shift, denoted as T(deg), is defined as the inverse of the product of 360 and the original frequency f₀. This period is directly proportional to the infinitesimal time shift Δt when f₀ remains constant. Additionally, the change in energy ΔE is expressed as the product of Planck’s constant h, the original frequency f₀, and the infinitesimal time shift Δt, establishing that ΔE is proportional to f₀ and inversely related to Δt. Furthermore, the study presents how the infinitesimal time shift Δtₓ associated with an x° phase shift is directly proportional to x under constant frequency conditions. This paper concludes with key proportional relationships that facilitate a deeper understanding of the dynamics within oscillatory wave systems.

Keywords: Oscillatory waves, phase shift, time period, energy change, Planck's constant, frequency, mathematical relationships, wave dynamics.

Equation Relationship:

Derivation: 

T(deg) = (1/360f₀) = Δt 

The time period corresponding to a 1° phase shift in the wave’s oscillatory frequency, denoted as the time period per degree T(deg), is defined as the inverse of the product of 360 and the wave’s original frequency f₀. This period T(deg) also represents the infinitesimal time shift Δt associated with a 1° phase shift. Consequently, when the wave's original frequency f₀ remains constant, T(deg) is directly proportional to Δt. Thus, T(deg)∝Δt when f₀ is constant.

ΔE = hf₀Δt 

The change in energy, ΔE, is given by the product of Planck’s constant h, the original frequency of the oscillatory wave f₀, and the infinitesimal time shift Δt associated with a 1° phase shift in the wave’s frequency. This relationship implies that ΔE is proportional to the original frequency f₀, and, in turn, f₀ is inversely proportional to the infinitesimal time shift Δt. Therefore, ΔE∝f₀ and f₀∝1/Δ.

Δtₓ = x(1/360f₀) 

The infinitesimal time shift, Δtₓ, associated with an x° phase shift in the wave's oscillatory frequency, is given by the product of the phase shift angle x and the inverse of the product of 360 and the original frequency f₀. This indicates that Δtₓ is directly proportional to the phase shift angle x when the original frequency f₀ remains constant. Therefore, Δtₓ ∝ x when f₀ is constant.

Conclusion:

The time period corresponding to a 1° phase shift in the wave's oscillatory frequency is proportional to the infinitesimal time shift associated with that phase shift, provided the original frequency of the wave remains constant. Additionally, the change in energy is proportional to the original frequency of the oscillatory wave, which is inversely related to the infinitesimal time shift associated with a 1° phase shift. Furthermore, the infinitesimal time shift associated with an x° phase shift in the wave's oscillatory frequency is directly proportional to the phase shift angle x when the original frequency is constant.

• T(deg) ∝ Δt when f₀ is constant.

• ΔE ∝ f₀, f₀ ∝ 1/Δt.

• Δtₓ ∝ x when f₀ is constant.

List of Denotations for Mathematical Terms:

• f₀ or fᴢₑᵣₒ: The original or initial frequency of the oscillatory wave, representing the base frequency at which the wave oscillates.

• h: Planck’s constant, a fundamental physical constant that relates the energy of a photon to its frequency.

• T(deg) or T𝑑𝑒𝑔: The time period corresponding to a 1° phase shift in the wave's oscillatory frequency, indicating the time required for this phase shift.

• x: The phase shift angle in degrees, used to denote a specific phase shift other than 1°, which affects the time increment proportionally.

• ΔE or δE: The change in energy, calculated as the product of Planck’s constant h, the initial frequency f₀, and the infinitesimal time shift Δt.  

• Δt or δt: The infinitesimal time shift (or time distortion) associated with a 1° phase shift in the wave's oscillatory frequency, representing the time increment for a very small phase shift in the oscillation.

• Δtₓ or δtₓ: The infinitesimal time shift (or time distortion) associated with an x° phase shift in the wave's oscillatory frequency, representing the cumulative time increment for a specified phase shift angle x.

Derivation Analysis:

1. Statement 1:

T(deg) = (1/360f₀) = Δt

This equation implies that T(deg), which might represent a time period defined in terms of degrees, is inversely proportional to f₀ (frequency). When f₀ is constant, T(deg) is directly proportional to Δt, which is confirmed by the relationship:

T(deg) ∝ Δt when f₀ is constant.

2. Energy Relationship:

ΔE = hf₀Δt 

Here, ΔE is proportional to the product of f₀ and Δt, not to each variable independently. This means: 

• ΔE depends on the combined effect of f₀ and Δt.

• If f₀ and Δt vary in inverse proportion (i.e., f₀ ∝ 1/Δ), ΔE remains consistent with expected physical behaviour (where higher frequencies correspond to shorter time intervals and vice versa).

3. Frequency-Time Relation:

f₀ ∝ 1/Δt 

This relationship aligns with physical intuition that as frequency f₀ increases, the time interval Δt decreases proportionally. This inverse relationship is essential for the consistency of the expression:

ΔE ∝ f₀, f₀ ∝ 1/Δt. 

4. Scaled Time Interval Δtₓ:

Δtₓ = x (1/360f₀) 

When f₀ is constant, Δtₓ is directly proportional to x, confirming that:

Δtₓ ∝ x when f₀ is constant

Conclusion:

Each statement logically follows from the previous ones, given the inverse relationship f₀ ∝ 1/Δt and the fact that ΔE depends on the product hf₀Δt rather than independently on f₀ or Δt. Thus, the presentation is mathematically consistent, aligning with the physical interpretation that higher frequencies correlate with shorter time intervals.

Interpreting Negative Mass in Quantum Gravity and the Role of Planck Scale in Virtual Particles:

Soumendra Nath Thakur 

27-10-2024

The question of negative mass or negative effective mass, potentially applicable to virtual particles at the quantum level, emerges in the context of Claudia de Rham's radical new theory of gravity.

In my interpretation, this consideration suggests that observable matter—including dark matter—possesses positive mass. We assess this positive mass through baryonic objects and visible energy, as well as the gravitational influence of dark matter on luminous matter. This framework aligns with classical mechanics, where gravity is regarded as an attractive force, or with extended classical mechanics, which also treats gravity as a force.

Conversely, virtual matter may exhibit negative mass, as seen in assessments of dark energy or "invisible energy." This negative mass is responsible for the repulsive force, or "anti-gravity," resulting from a negative effective or apparent mass, as suggested by observational findings and extended classical mechanics.

My interpretation draws on Planck scale concepts, including Planck length, Planck frequency, and Planck time. Since anything above the Planck scale is imperceptible to us and the frequency of any existence ultimately surpasses the Planck frequency, virtual particles likely exist beyond this threshold, suggesting that virtual particles may exhibit extreme gravitational effects.

#virtualparticle #NegativeMass #gravityasforce #antigravity #extendedclassicalmechanics #gravity