09-11-2024
Soumendra Nath Thakur
Discussion Topic: Is Spacetime Curvature the True Cause of Gravitational Lensing?
Dear Mr. André Michaud,
Thank you for your thoughtful reply. Your mention of a "little inconsistency" in my description seems to stem from a different interpretation of the photon's trajectory during its interaction with an external gravitational field. To clarify, there are three main considerations in the photon’s path:
Consideration 1: The Photon’s Initial Straight-Line Trajectory
The photon begins its journey from the source along a straight-line trajectory with velocity c. Here, an initial redshift occurs as the photon loses a slight amount of energy due to gravitational interaction with the source’s gravitational well, resulting in a corresponding increase in wavelength (Δλ>0). This change follows the relationship E = hf = hc/λ, where the energy E and frequency f are inherent to the photon and directly proportional to the wavelength.
Consideration 2: Arc Path and Energy Exchange During Gravitational Bypassing
As the photon approaches and passes an external massive body, it undergoes a temporary arc-shaped deviation in its trajectory due to the external gravitational influence. This interaction involves two phases:
First Half-Arc: A blueshift occurs, corresponding to a wavelength decrease (Δλ<0) as the photon gains energy due to gravitational influence while approaching the massive body.
Second Half-Arc: As the photon moves away, a redshift (Δλ>0) occurs, returning the photon’s wavelength to its original state as it completes the arc and leaves the gravitational field. This reversible shift is due to energy exchange within the field, summarized by E + Eg = E + 0, where Eg represents the energy gained and then lost by the photon within the gravitational arc path.
Consideration 3: Return to Original Straight-Line Trajectory
After exiting the gravitational field, the photon resumes its original straight-line path. At this point, it retains its inherent energy, with any additional energy or momentum imparted by the gravitational field removed. Its wavelength also remains as it was upon entry into the gravitational encounter, indicating no net change in wavelength (Δλ=0) beyond that caused by its initial emission.
Conclusion
Your perception of a "net deflection" and an uncompensated redshift does not account for the full cycle of energy exchange during the photon's passage through the gravitational field. The photon’s wavelength shifts symmetrically—first through blueshift, then redshift—without resulting in a net loss of inherent energy. Consequently, upon exiting the gravitational field, it continues along its original trajectory, undisturbed in frequency and energy.
This balanced interaction negates the need for "expended work" or a net trajectory deflection, aligning with the complete arc-path considerations outlined above. I hope this clarification resolves the apparent inconsistency and aligns our perspectives on the photon’s behaviour in gravitational interactions.
Best Regards,
Soumendra Nath Thakur
#GravitationalLensing
Dear Mr. André Michaud
Thank you for your thoughtful reply. I appreciate the opportunity to clarify my perspective further.
1. First, I reckon that there may have been a slight misinterpretation of my earlier statement: “Your perception of a 'net deflection' and an uncompensated redshift does not account for the full cycle of energy exchange during the photon's passage through the gravitational field.”
The intention behind this statement was to emphasize the photon’s symmetrical energy shifts during its interaction with external gravitational field. Specifically, the photon’s wavelength undergoes a blueshift as it approaches the massive body, followed by a redshift as it moves away. This complete cycle results in no net change in energy or trajectory once the photon exits the external gravitational field. This was also highlighted in the conclusion: “The photon’s wavelength shifts symmetrically—first through blueshift, then redshift—without resulting in a net loss of inherent energy. Consequently, upon exiting the gravitational field, it continues along its original trajectory, undisturbed in frequency and energy.”
2. Regarding the table you provided, titled “Experimental Results on the Deflection of Light”, I must point out that it references deflection observed on Earth due to direct sunlight rather than deflection in an external gravitational field. This does not directly support the discussion concerning the photon's trajectory when interacting with an external gravitational field, such as the one caused by a massive celestial body.
To further clarify my stance on this topic, I would like to offer the following elaboration, which aligns with the core of our discussion:
General Relativity (GR) suggests that massive objects, such as galaxies or galaxy clusters, curve spacetime, causing light to bend as it passes through this curved spacetime. However, this curvature is not uniform throughout space, and regions between massive objects remain flat. When a massive body is present, it bends spacetime, leading to gravitational lensing.
The photon’s path can be divided into three phases:
Initial Straight-Line Trajectory: The photon begins its journey from the source along a straight path, traveling at speed c. As the photon moves away from the source’s gravitational well, it undergoes a slight redshift, resulting in a small increase in wavelength (Δλ>0).
Interaction with External Massive Body: As the photon approaches the external massive body, it temporarily experiences a blueshift (Δλ<0) while moving toward the body. Upon passing the body, the photon begins to move away and experiences a redshift (Δλ>0), returning to its original wavelength. This reversible shift is due to the energy gained and subsequently lost by the photon as it moves through the gravitational field. The photon’s inherent energy drives its straight-line path, but the gravitational field temporarily alters its trajectory in an arc-like fashion. Once the photon completes this interaction, it resumes its original straight path, with no net change in wavelength (Δλ=0).
Return to Original Trajectory: After passing the gravitational influence of the external body, the photon returns to its original straight-line trajectory, retaining its inherent energy and wavelength.
However, General Relativity asserts that light bends along the curvature of spacetime itself. In contrast, observational experiments suggest that the bending of light is primarily caused by the curvature of the gravitational field, rather than the curvature of spacetime itself. This discrepancy indicates a potential misalignment between theoretical predictions and experimental observations, calling for a re-evaluation of the models explaining gravitational lensing.
This study critically examines the differences between GR's predictions and experimental results. The findings suggest that the bending of light is more accurately explained by the curvature of the gravitational field rather than the warping of spacetime, as proposed by GR. This raises questions about the sufficiency of GR in explaining light's interaction with gravity and indicates a need for alternative models.
Conclusion:
While GR asserts that gravitational lensing is the result of spacetime curvature, experimental data suggest that the bending of light is primarily due to the curvature of the gravitational field. This misalignment challenges GR’s interpretation and calls for further exploration and refinement of theoretical models. I advocate for alternative approaches that could more accurately explain the observed phenomena and encourage continued research into the mechanisms of gravitational lensing.
Best regards,
Soumendra Nath Thakur
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Dear Mr. André Michaud,
Thank you for your insights.
This discussion aims to clarify whether spacetime curvature, as posited by General Relativity (GR), is indeed the true cause of gravitational lensing, or if another explanation better aligns with observational data.
GR describes gravitational lensing as resulting from spacetime curvature induced by massive objects, which alters the path of light passing near them. However, interpretative evidence from observational and experimental data suggests that light bending might instead be driven primarily by the gravitational field’s own curvature—essentially, the real, physical gradient of gravitational intensity—rather than an abstract curvature of spacetime. This perspective challenges the idea that spacetime curvature is necessarily the sole or primary cause of lensing.
By contrast, your response suggests that GR’s spacetime model might represent an idealized, geometric interpretation of a more fundamental physical reality rooted in the gravitational field's structure.
(1) However, your response does not conclude that spacetime curvature is entirely irrelevant to lensing, nor does it definitively assert that the gravitational field alone is responsible.
Moreover, regarding your statement, “The gravitational intensity gradient as a function of the inverse square law of the distances is the real thing, and Einstein's spacetime curvature is its geometric mental representation of it,” I would like to clarify that the inverse square law is indeed a concept rooted in classical mechanics, originally articulated by Newton. It describes how the gravitational force between two masses diminishes with the square of the distance between them, and in this framework, the gravitational force is seen as acting at a distance.
In contrast, Einstein's General Relativity (GR) describes gravity not as a force but as the curvature of spacetime caused by the presence of mass and energy. While the inverse square law applies well in Newtonian mechanics and serves as an approximation in weak-field regimes in GR, the concept of spacetime curvature in GR offers a deeper, more comprehensive explanation of gravitational phenomena, especially in stronger gravitational fields.
(2) In this sense, the inverse square law can be viewed as a classical, Newtonian approximation of the more complex curvature-based understanding of gravity provided by General Relativity. GR’s spacetime curvature, then, provides a more generalized framework that goes beyond the limitations of the inverse square law, especially when considering more extreme conditions such as near black holes or in cosmological contexts.
Therefore, while the inverse square law provides an accurate description in many practical situations, it is one aspect of a broader, classical gravitational theory.
Einstein’s spacetime curvature, as an idealized geometric representation, serves to explain gravitational interactions in a more generalized manner, complementing the classical understanding rather than replacing it.
Best regards,
Soumendra Nath Thakur
