In fact, physically, gravitational lensing is the real cause of the curvature of spacetime.

As strange as it sounds, there is a continuum of the matter field as the basic structure and gravity is just an emergence from it. Light-like pilot wave bundles define all separations as null geodesics. Heavier particles fall "down" in that buoyancy as their own geodesics, settling on trajectories as gradient 4-densities.

Gravitational lensing is the direct observation of the curvature of space-time.

Julius Chuhwak Matthew

I thank you for your intelligent answer, however, I wonder who has observed the curvature of space-time? Can you shed some light on this question with proper references?

Regards

Soumendra

Esa Säkkinen

"In fact, physically, gravitational lensing is the real cause of the curvature of spacetime." Why this statement is not scientific but an authoritarian statement?

How can I accept that the 'physical curvature of spacetime' is scientifically credible, unless this statement forces me to accept the preconceived notion. I wonder.

Soumendra Nath Thakur

Because it works. GR leaves open the possibility of interpreting the curvature only as a description, but my research shows that it is a physical structure.

https://www.researchgate.net/post/How-can-we-calculate-the-energy-density-of-the-gravitational-field#view=6719c5f4251d59a42e09284e/9/7

Read the dark matter calculations on page 9.

Dear Mr. Preston Guynn Mr. Esa Säkkinen and Mr. Julius Chuhwak Matthew

This discussion addresses the question, "Is Spacetime Curvature the True Cause of Gravitational Lensing?" and critically examines the conventional explanation, which attributes gravitational lensing to spacetime curvature. Instead, it proposes an alternative perspective in which gravitational lensing results from momentum exchange between photons and external gravitational fields. This conclusion is supported by analysing symmetrical photon behaviours, such as energy gain (blueshift) and loss (redshift) near massive objects, which reveal the actual mechanisms driving gravitational lensing—distinct from the spacetime curvature model proposed by general relativity. This discourse aims to refine our theoretical understanding of the fundamental interactions between light and gravity.

The scientific foundation of this perspective, as articulated in the study "Photon Interactions with External Gravitational Fields: True Cause of Gravitational Lensing," rests on established quantum and classical mechanics principles—specifically, Planck’s energy-frequency relation E=hf and the photon momentum-wavelength relation ρ=h/λ. These equations illustrate how photons experience symmetrical energy shifts (blueshift and redshift) through gravitational interactions, offering a basis for lensing that preserves inherent photon energy and frames gravitational influence as an external, rather than intrinsic, interaction.

Together, these equations suggest that momentum exchange between photons and gravitational fields effectively account for lensing effects. The study’s analyses of photon energy conservation and symmetrical behaviour near massive bodies provide an alternative mechanism for gravitational lensing, distinct from the spacetime curvature paradigm and posing a potential challenge to conventional interpretations. This discourse thus emphasizes momentum exchange over relativistic spacetime curvature, aligning with the defined scope and goals outlined in the initial discussion.

For a comprehensive exploration of this study, please refer to the full text at Preprint Photon Interactions with External Gravitational Fields: True...

Data Photon Energy and Redshift Analysis in Galactic Measurements...

Warm regards,

Soumendra Nath Thakur

Soumendra Nath Thakur

To the best of my knowledge, the very first to observationally verify this space-time curvature was Sir. Arthur Eddington. Sir. Arthur was intrigued on how stellar masses curve the fabric of space-time, the work published by Einstein some years earlier. In summary, Sir. Arthur's experiment challenged general relativity (Einstein) and this was the same experiment that became the backbone to the concept of space-time curvature.

References:

(1) doi: 10.1098/rsta.1920.0009 (very detailed) and;

(2) Experimental evidence for general relativity by Sidney Perkowitz (on Britannica): This provides a coincised summary.

I hope this little info was helpful and provided clarity...

Julius Chuhwak Matthew,

Thank you for your contributions to the discussion. However, I find that the information you've provided is not directly relevant to the primary objective of our inquiry. Our focus is on the question, "Is Spacetime Curvature the True Cause of Gravitational Lensing?" This discussion posits that gravitational lensing results from momentum exchange between photons and external gravitational fields.

Thus, we aim to reach a reasonable consensus regarding the validity of these findings.

Best regards,

Soumendra Nath Thakur

The very space-time concept has been shown to be baseless in the scientific research paper 'Experimental & Theoretical Evidence of Fallacy of Space-time Concept and Actual State of Existence of Physical Universe' which is published in peer-reviewed journal namely Indian Journal of Science and Technology at www.indjst.org.

Soumendra Nath Thakur

Dear Sumendra

Your description is absolutely correct, except for a little inconsistency with regard to your last comment: " After bypassing the gravitational field, the photon resumes its original trajectory ..."

Remember what you wrote previously: "This shift occurs as a result of electromagnetic-gravitational interaction, causing the photon to follow an arc-shaped trajectory. "

So, there will be a net deflection of the photon trajectory, that requires some of its energy to be expended as work to account for this net deflection of its trajectory, resulting in an uncompensated red shift of its frequency.

If interested, this is analyzed in Section 17.9 of this paper:

Article De Broglie’s Double-Particle Photon (Expanded republication PI)

Dear All,

The very space-time concept has been shown to be baseless in the paper published in peer-reviewed journal tittled Experimental and Theoretical Evidence of Fallacy of Space-time Concept and Actual State of Existence of the Physical Universe and there is a standing open challenge to the Einstein's paradigm since last twelve years. Thus the very curvature of space-time is simply rubbish. Read following passage.

Einstein's Theories of relativity lead to Big Bang Theory whereas under Big Bang paradigm there is absolutely no possibility of existence of the Creator for following reasons.

1. Philosophically for existence; it has to be some substance (visible, invisible, perceivable or not perceivable) and this applies to the Creator also. Substances occupy space but there is absolutely no space for the Creator to exist at the time of Big Bang & before.

2. Four things came out of Big Bang namely space, time, matter & light/radiation. We cannot look for eternal Creator in space & time as both had the beginning; secondly humans are in a position to produce all types of light/radiation and something which humans can produce could not be the Creator and since matter is made up of electrons, protons & neutrons these too could not be the Creator.

However Theories of Relativity & Big Bang Theory including Cosmic Inflation has been mathematically, theoretically & experimentally proved as baseless in the published papers "Experimental & Theoretical Evidences of Fallacy of Space-time Concept and Actual State of Existence of the Physical Universe" and "Foundation of Theory of Everything; Non-living Things and Living Things'' which are available at the journal site at www.indjst.org.

There is a standing open challenge to the Einstein's paradigm since last twelve years though some physicists tried to accept the challenge but failed. The open challenge is based on the scientific research papers published in peer-reviewed journals which could be seen on General Science Journal, Natural Philosophers Database erstwhile World Science Database, ResearchGate, SlideShare, viXra and Academia.edu in my profile.

Present so called main-stream physics is obsolete and all the universities and research institutions can no more deceive the people and governments for imparting the wrong knowledge and waste public money in research.There are alternative theories which includes the existence of aether which has been shown to be existing through published papers by me on which further research needs to be done.

With Regards

Mohammad Shafiq Khan

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 (Δλ0) 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

FYI Deep Bhattacharjee

Soumendra Nath Thakur

Dear Sumendra

You wrote: "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."

I clearly understand the logic of what you explain, and agree with most of your reasoning.

But my perception of a net deflection of the photon trajectories and of an uncompensated redshift does account for the proven deflection of the trajectories of all photons passing close to the mass of the sun that were confirmed numerous times in multiple observations of this phenomenon during solar eclipses.

See table attached of the list of these observations that were carried out between 1919 and 1973 from Page 194 of book "Gravitation and Spacetime" by Ohanian and Ruffini.

The blueshift related increase in energy is effectively totally compensated by the real exact total loss of this energy at any equivalent distance on the outward leg of the encounter "whichever direction the mass that the photons would have moved away into".

But the net change in direction according to the 2nd principle of thermodynamics is impossible to explain other than by some corresponding expenditure energy. The only possible source of this energy is the energy of the photon itself, This explains why the net energy of the outgoing photon is slightly redshifted after each such encounter event.

The formulation of the 2nd principle of thermodynamics is that the state of an isolated system cannot be changed without an increase in entropy, meaning that "no change in the state of motion of photons (here the change in direction of photons in the mass-photon isolated system) can occur without some expenditure of the photon's energy as work.

Best Regards, André

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 (Δλ0), 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

Soumendra Nath Thakur

Dear Sumendra

As you wish, but the light deflection experiments were not as you quote " I must point out that it references deflection observed on Earth due to direct sunlight rather than deflection in an external gravitational field.".

They were not observation of direct sunlight since they were carried out during full eclipses of the Sun by the Moon. They were the observed deflection of the trajectories of starlight grazing the mass of the sun on their way to us, that is, within the external gravitational field of the Sun, and very close to its mass.

I suggest that you become acquainted with the text accompanying this table in the previously cited reference work, which is probably available from your institution's library.

Dear Mr. André Michaud

Your statement, "since they were carried out during full eclipses of the Sun by the Moon. They were the observed deflection of the trajectories of starlight grazing the mass of the sun on their way to us, that is, within the external gravitational field of the Sun, and very close to its mass." observationally aligns with the following mentioned phenomenon. Whereas, GR asserts that light bends along the curvature of spacetime itself, where the gravitational field mirrors this curvature. In contrast, observational experiments suggest that light bending is primarily due to the curvature of the gravitational field itself, rather than spacetime.

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 (Δλ0) 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.

However, GR asserts that light bends along the curvature of spacetime itself, where the gravitational field mirrors this curvature. In contrast, observational experiments suggest that light bending is primarily due to the curvature of the gravitational field itself, rather than spacetime. This discrepancy challenges GR's interpretation and suggests the need for a re-evaluation of theoretical models.

This study critically analyses the discrepancies between GR’s predictions and experimental observations. The findings suggest that while GR visualizes the gravitational field as mirroring spacetime curvature, this model does not fully capture the complexities of actual light-gravity interactions observed in experiments. Therefore, a re-examination of gravitational lensing and the underlying mechanisms of light propagation is necessary.

Conclusion:

GR posits that gravitational lensing occurs due to spacetime curvature, but experimental data suggest that the bending of light is primarily driven by the curvature of the gravitational field. This misalignment calls into question the validity of GR in explaining light’s interaction with gravity, suggesting that the relationship between light, gravity, and spacetime may require further exploration and modification. The study advocates for alternative models that could more accurately explain the observed phenomena, paving the way for future research into the mechanics of gravitational lensing.

Soumendra Nath Thakur

Dear Sumendra

You wrote: " GR asserts that light bends along the curvature of spacetime itself, where the gravitational field mirrors this curvature. In contrast, observational experiments suggest that light bending is primarily due to the curvature of the gravitational field itself, rather than spacetime."

Of course, but Einstein's spacetime curvature is only an idealized geometric representation of the real gravitational gradient of the Sun, so they are not in conflict really. 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, in short, it is part of his personal worldview, that a lot of theoreticians took for the real thing.

What is real is the gravitational intensity gradient centered on the Sun, not Einstein's idealized mental representation of it.

All participants of this discussion,

Before you discuss the curvature of space-time you have to be absolutely sure that space is not absolute and in view of fact that space has been shown to be filled with aether the question of space being not absolute does not arise. The existence of aether as proposed by Clerk Maxwell has been confirmed in the paper published in a peer-reviewed journal tittled Michelson -Morley Experiment; A Misconceived and Misinterpreted Experiment. Thus the very concept of space-time curvature is irrelevant and the very discussion about it is simply wastage of time and instead of that you should discuss the alternative theory to the Big Bang Theory which has been proposed in my papers.

With Regards

Mohammad Shafiq Khan

Writer Scientist and Philosopher.

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

Dear Mohammad Shafiq Khan ,

Thank you for your reply and the points you have raised. However, I believe that there is some misalignment with the core focus of the current discussion.

The discussion on gravitational lensing, as described, specifically questions the conventional understanding that gravitational lensing arises solely due to spacetime curvature, as proposed by General Relativity (GR). Instead, it explores an alternative perspective, suggesting that gravitational lensing could be explained primarily through the momentum exchange between photons and external gravitational fields, and this leads to a re-evaluation of how light interacts with gravity. The core aim is to explore the role of momentum transfer, such as energy gain (blueshift) and loss (redshift) of photons around massive objects, and to consider how this might open the door to models such as quantum gravity or flat spacetime theories.

In this context, the discussion does not intend to delve into the nature of space or its possible absolute nature. Therefore, the introduction of the "aether" and the question of whether space is absolute or not is tangential to the topic at hand.

Your assertion regarding the aether and the interpretation of space does not directly contribute to the primary question under consideration, which is about the nature of gravitational lensing and its potential explanations beyond spacetime curvature. The focus here is on the physical mechanisms by which photons interact with gravitational fields, and the suggestion is that gravitational lensing may result from these interactions rather than an abstract curvature of spacetime.

While your contributions are valuable in their own right, they do not address the specific framework and approach being discussed here. The introduction of aether and discussions on the absoluteness of space, while important in other contexts, do not directly relate to the momentum exchange mechanism for gravitational lensing as outlined in the original discussion.

I hope this clarifies the purpose and direction of the discussion.

Best regards,

Soumendra Nath Thakur

Soumendra Nath Thakur

The so called gravitational lensing is the natural & direct phenomenon once we accept the existence of aether and its study under the baseless space-time curvature is simple wastage of time and efforts which will lead us to nowhere. The question of bending of the light when it passing near stars is an evidence of aether rather than validity of general relativity. There are several aspects in research in physics which need to be altogether changed to arrive at the truth especially in cosmology. My point of commenting on this domain was to make the participants aware that main-stream physicists are hiding the factual position on everything and wasting the time of researchers and students.

Soumendra Nath Thakur

Dear Sumendra

Please do not "Mr." me. Just referring to me as André is fine already. I am all in for informal conversations.

From your last post, I see that you have an open mind and are in process of finetuning your worldview with possible new added information that seems to make sense to you.

So I will carefully answer your comments to the info I provided already, that raised further interrogations on your part.

To your comment: "(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."

Actually, given that the spacetime curvature is Einstein's mental worldview idealized interpretation of the intensity gradient of the gravitational field of the masses whose maximum intensity would be located at their center-of-presence, an intensity omnidirectionally decreasing as a function of the inverse square of the distance from this idealized center-of-presence, then yes, I do think and assert that this intensity gradient of the gravitational field of a mass has to be the only responsible physical factor involved in deflecting close by flying photons.

Note that we are all like Einstein with respect to worldviews. We all develop a personal idealized worldview more or less close to physical reality, depending on the amount of info that we each gather, trust or distrust, and integrate about it, and to the extent that we each reverse engineer the characteristics of issues that we personally have no direct info about.

About your comment relative to the inverse square law: "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."

Absolutely correct… but not only.

Coulomb experimentally confirmed in 1784 the same interaction law of a force proportional to the inverse square of the distance separating point-like behaving charges that Newton had previously confirmed one hundred years before in 1687 in his famous work Philosophiæ Naturalis Principia Mathematica as applying between astronomical masses from his analysis of Johannes Kepler's third law that "the cube of the mean radius of a planetary orbit in the solar system is proportional to the square of the orbiting body's period", that Kepler empirically established in 1618 from the data carefully collected over many years by Tycho Brahe about the observable planetary orbits in the solar system.

Given that we know now that all masses are made of "almost empty" atoms, all of which are made of only charged elementary particles located at relatively far distances from each other at the subatomic level, (this latter point was not entirely clarified when Einstein conceived of his curved spacetime curvature), then this inverse square law has been repeatedly confirmed to systematically apply between all point-like behaving charged elementary particles, of which all macroscopic masses are made.

If interested, the final article of my analysis of the subatomic level puts in perspective the major historical steps of the evolution of our comprehension of gravitation with references to the historical formal sources, most of which are directly available on the net, because they all are now in the public domain. Here is a link to this final analysis:

Article From E=mc2 in normal space to E=m0cIcK in the complex config...

You wrote: " 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."

Yes. In fact, Newton offered no explanation as to what set astronomical masses in motion in the first place. In Newtonian mechanics, all masses are assumed at rest and having to be set in motion by some initial impulse. No trace in Newton mechanics of what could have set the planets in motion to then stabilize in their stable orbits about the sun.

In Einstein's GR, all astronomical masses are also assumed to be intrinsically inert, but his spacetime curvature now proposes such an explanation to what could have set planets in motion to start with, simply by moving down the curvature of the spacetime fabric of some other body. The idea was ingenious, but it still is an idealized characteristic of Einstein's idealized worldview. Also analyzed in the previously linked paper.

You wrote: " 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."

Yes. The concept of "force" does not exist in GR. Replaced by inertial motion in the spacetime curvature. This concept however leads at the limit to mathematical singularities that cannot exist for elementary electromagnetic particles at the subatomic level (also analyzed in the above referred paper), from which the concept of black holes is emergent.

But I assure you that all calculations that take into account the electromagnetic characteristics of the electron, particularly its confirmed increasing mass with velocity, that Einstein and the whole community left behind in 1907 due to uncertainty about their applicability to macroscopic masses, account even better than GR for the observed behavior of all macroscopic bodies.

Best Regards, André