Gravity force, related Radius, R and g interrelationship , g = GM /R2
Schwarzschild radius, R and light velocity, C relationship, c = GM/R2
From above derivation, The Schwarzschild radius is too tiny that the light velocity is required by a particle to escape from the gravitational field. The R in equ. (above) and (below) both Newtonian gravity and general relativity have an interrelationship. Schwarzschild radius, R of equ. (below), in which dimension becomes too tiny as a result it attains enormous density, time dilutes. As a result gravitational wave velocity attains as the same as light velocity, c.
Recently the electromagnetic spectrum corresponding to the gravitation wave event has been made for gravitation to photon conversion as phenomenological comparison by Tarrant, J., Beck, G. and Colafrancesco, S., 2021. Making light of gravitational-waves. Astroparticle Physics, 128, p.102565
Dear Bablu K. Ghosh,
Your question is quite interesting. This issue is fundamental in understanding the nature of gravitational waves and light waves within both classical mechanics and the framework of General Relativity.
In Newtonian mechanics, the gravitational acceleration at a distance R from a mass M is described by the equation:
g = GM / R²,
where G is the gravitational constant, M is the mass, and R is the radial distance. This equation reflects the instantaneous interaction of gravity, implying that changes in the gravitational field propagate without delay. However, this notion does not align with Einstein’s Special Relativity, which places a limit on the speed of information transfer.
When considering General Relativity, the picture changes significantly. Gravity is no longer a force acting at a distance but rather a manifestation of spacetime curvature caused by mass and energy. In this theory, gravitational waves—disturbances in the curvature of spacetime—propagate at the speed of light. The Schwarzschild radius of a black hole, which sets the boundary where not even light can escape, is given by the formula:
R_s = 2GM / c²,
where R_s is the Schwarzschild radius and c is the speed of light. This shows a profound relationship between gravity and the speed of light. If we solve for c in this equation, we find:
c = √2GM / R_s.
This equation suggests that the escape velocity for any object approaching the Schwarzschild radius is equal to the speed of light. Therefore, the speed of light becomes a natural limit, reinforcing the idea that the propagation of gravitational effects must occur at the same speed.
Empirical evidence further supports this conclusion. The observation of gravitational waves from events such as the GW170817 neutron star merger, accompanied by gamma-ray bursts, has shown that the difference between the speed of gravitational waves and light is extraordinarily small, less than one part in a trillion. This coincidence confirms Einstein’s prediction that gravitational waves travel at the same speed as light.
Additionally, recent work by Tarrant, Beck, and Colafrancesco 2021 delves into the interaction between gravitational and electromagnetic waves. They explore how gravitational events could be linked to photon emission, providing more evidence of the deep relationship between these two fundamental forces.
So the speed of gravity and the speed of light are equivalent because both are constrained by the same universal limit: the speed of information transfer in spacetime. This conclusion is consistent with both theoretical models and observational data, confirming that gravity, like light, propagates at the speed of c.
The thread question
“How speed of gravity and light velocity is the same?”
- is indeed quite interesting, though before it is necessary to answer to “what is the gravity speed?”, since direct experimental measurement of this speed – in contrast to fundamental Nature Electric force case – is practically impossible.
So that can be made only indirectly - studying of some gravitationally coupled systems, and, using some scientifically rational Gravity Force model/theory, where Gravity speed is a parameter, to find this parameter value that fits the model/theory with experimental data.
Really now such system is unique - that is system “Mercury + Sun”, and firstly, describing in his model the Mercury precession shift, the Gravity speed value was obtained by Paul Gerber in 1898, this value agreed with the speed of light with a few % precision.
Further that the Gravity speed is equal [exactly] to the speed of light was postulated in 1916 in the GR, where the Gerber’s result was confirmed.
However in this case the question “so what is the speed of light, why it is as it is, and why it is so universal?” remains.
The last question [which includes the thread question, and quite not only], can be, and is, really rigorously scientifically answered only in framework of the Shevchenko-Tokarevsky’s Planck scale informational physical model, two main papers are
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, and
https://www.researchgate.net/publication/383127718_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics
- where it is rigorously scientifically shown, that everything in Matter, including particles and at least Gravity, Electric, and Nuclear/Strong, Forces’ mediators, are specific disturbances in
the Matter’s ultimate base - the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with (at least) (cτ,X,Y,Z, g,w,e,s,ct), FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP.
At that all disturbances constantly and always move in the utmost universal [and observable by humans and in mainstream physics as the Matter’s spacetime] “kinematical” 4D space with metrics (cτ,X,Y,Z) with 4D velocities that have identical absolute values c=lP/tP.
The above Forces’ mediators and particles “photons” and “gravitons” move only in the 3DXYZ space with the above “c” value, which is well measured and is called “speed of light”
More see the linked papers, SS posts in, say, https://www.researchgate.net/post/The_origin_of_Lorentz_transforms/5 pages 3,5,6,7,8, and, say,
https://www.researchgate.net/post/NO47What_is_Force_a_Field_Where_is_the_Force_Field_How_does_it_appear_Is_the_Force_Field_a_Regulating_Effect_of_the_Energy-Momentum_Field/2, pages 1,2
- are relevant to this thread question.
Cheers
...the speed of gravity and the speed of light are the same? Who told you that? The speed of gravity and the speed of light are the same only at the surface of a gravitating nucleon, and at a distance from it the speed of gravity decreases and what is called "free fall acceleration" appears. And there are obvious reasons for this. But this is not the place for learning. Read "fresh" scientific literature.
Light (electromagnetic radiation) and gravity do not travel at the same speed. They are different natural phenomena caused by different sources. Electromagnetic radiation, directly related to the movement of electrons from one orbit of an atom to another, propagates in a vacuum at the speed of light c. Quanta of light (photons) are conventionally called massless particles, since their rest mass is zero: they have only relativistic mass (mass of motion). Gravitational radiation is associated with the spatio-temporal structure of bodies with non-zero rest mass m0. To get closer to understanding the physical nature of the gravitational field, it is necessary to turn to GTR. Its mathematical apparatus allows us to closely approach ways of solving the problem of the movement of material bodies in gravitational fields, including teleportation (instantaneous movement). A physical observer with a material rest mass cannot yet even overcome the light barrier (i.e. exceed the speed of light), much less instantly teleport from one point in space to another. But he can carefully analyze works that talk about the conditions under which the proper time for a physical observer is the same as for the observed object, even if it is located far from the observer. And this is precisely what means the instantaneous connection of the observer with the observed objects, i.e. the existence of long-range action.
In the 1970s, the Pulkovo astronomer N. A. Kozyrev conducted a series of astronomical observations of distant objects (stars, globular star clusters in the constellations Aquarius and Hercules, the Andromeda galaxy) with the sole purpose of proving the existence of instantaneous communication between objects in the Universe, i.e. long-range action. Kozyrev proved through observations of celestial objects that the receiving device (a specially converted reflecting telescope) records three positions of the observed object: past, present and future. n this case, the past and future images of the object are located symmetrically relative to the central (true) image. Calculations confirmed that the positions of the two extreme images exactly coincide with the positions of the observed objects in the past and future relative to the moment of observation (present). All three images had a negentropic (structure-restoring) effect on the receiving device. To explain these results, we turn to the theory of physical observable quantities in GTR, formulated by the cosmologist A. L. Zelmanov.
According to this theory, the elementary interval of observed time dτ for a real observer depends on the magnitude of the three-dimensional gravitational potential and the scalar product of the rotation speed of the three-dimensional space of the observer's reference and the speed of translational motion of the observer's reference frame. If the sum of these quantities is equal to the square of the speed of light, then time stops for the observer. This means that the observer and the observed object (the central image), despite the distance separating them, are at the same moment in time. Kozyrev called the two images of the object, located to the left and right of the central one, the past and future images of the observed object.
To create a clearer picture of what was happening, Kozyrev proposed to imagine each four-dimensional point in space-time as a rotating gyroscope, simultaneously moving in three-dimensional space. This model is quite applicable for describing an elementary four-dimensional vector in the space-time of general relativity, describing the distance between two infinitely close points. It follows that the rate of time for an observer is determined by: 1) the gravitational effect of the potential at the observation point; 2) the combined effect of the rotational speed of the reference frame v_i and the speed of its translational motion. If there is no rotation or the vectors of rotational velocity and translational motion are orthogonal to each other, then only the gravitational potential affects the frame of reference. In this case, time stops for the observer, as, for example, on the surface of the Schwarzschild sphere. If the reference frame rotates, then the speed of the reference body and the direction of its rotation make their positive or negative contribution to the magnitude of the rotation speed. And since the overwhelming majority of celestial bodies rotate both around their axes and around the central objects that attract them, then the picture of the world proposed by Kozyrev as a set of different-sized gyroscopes is entirely consistent with modern ideas about the structure of the Universe.
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