What is the Speed of Gravity

My question is simple. If the equations which govern General Relativity, the deceptively simple looking field equations, can be reduced to Newtonian dynamics where the speed of gravitation is less than the speed of light, and they work because they are transformations of the accepted equations, do we say that the speed of gravity is at or near that of light?

I understand that fundamentally the field equations are intended to have the speed of gravity equal to that of light or near it. Yet there is no definitive speed of gravity which has been proven as rigorously as the speed of light has been studied. I’m only aware of one study which looked at a quasar in line to be lensed by Jupiter and it gave a reading between close to and almost but not quite the speed of light, but that’s still a window rather than a definite quantity.

At the end of the day it is simple to process gravity as a force in mathematical terms, yet famously the exact constant of that force remains elusive. It is known to be approximately the inverse square of the distance between two objects as a vector equation, yet how much the exact force of gravity is pushing or pulling an object isn’t known.

Naturally this is solved by General Relativity which would say gravity is doing neither pushing or pulling, an object hurtling through space has it’s own inertia to do that already. There the speed of gravity is tantamount to instantaneous and would be more about size and speed of the relative objects in a curved spacetime rather than a question of how long does it take to feel the effect of gravity from one point to another. That isn’t my question though. Since the gravitational constant is so hard to pin down does that imply the force is dynamic, that it is better described by an kind of evolutionary value metric beyond the obvious mass/distance relationship?

This isn’t some kind of end around argument for MoND, rather an open question of interpretation. If Einstein can be reduced to Newton, is it not at least possible that gravity is a force that propagates at a variable sub light frequency rather than a fixed frame rate? It certainly seems like the equations already exist which could transform either way.

This derivative variability in the velocity of gravity wouldn’t solve the dark matter problem since all we are talking about are Newtonian equations derived from the field equations giving identical results. This wouldn’t be changing anything, it would just be looking at the problem of describing gravity from another angle. If gravity was a force that wouldn’t invalidate the observation of spatial curvature or gravitational lenses, but neither do those observations mean gravity itself isn’t a force, they simply represent a physical phenomenon no one had noticed before.

So yes, I would be curious to hear why the speed of gravity must be the speed of light, had it been proven empirically through experimentation or is there some subtle aspect in the math which holds the clue? If we can construct equations that can describe the solar system that are literally equivalent to those of General Relativity and they show gravity at less the C, how do we then prove the speed of gravity is moving at C? Doesn’t that violate our equations we derived from the very equations that assume that it does?

So yeah, I guess I’m curious…what exactly is the speed of gravity?

In Newtonian physics, gravity is seen as instantaneous. No matter how far apart objects are, a change in one will instantly result in the change in the other through gravitation.

But this is not what we’ve observed and measured. (And would actually cause a whole host of other problems as we scale out to the entire universe).

Gravity travels at the speed of light. But it’s important to note that c (the speed of light) actually has nothing to do with light. It’s really just the fastest that anything can happen/propagate in nature (in a vacuum). Since light travels at this speed, and it was the first thing we discovered to travel at this speed, we colloquially still call it “the speed of light”.

We know gravity (gravitational wave) travels at this maximum speed because we’ve observed it. Which supports the math of relativity that said gravity must travel at this speed. In fact, gravity actually travels through space better than light because it propagates through space-time without a care to its curvature. Whereas light has to follow that curvature. So, in the recent kilonova, the gravitational waves were detected a couple of seconds before the first light (gamma rays) were detected because the light had to take the longer curved path to us.

I guess my view of physics is that light is the lag or delay of kinetic energy being transferred between different objects with mass. Assuming that’s true, we’d know that the fastest we can transfer energy between different objects to be a maximum of ‘c’.

Someone could then make the argument that ‘c’ implies a maximum on the rate of change in any system. And since Einstein theorized in special relativity that gravity is simply the warpage of space and time (which seems to make a lot of sense to me), the speed at which space changes would have a theoretical limit at less than ‘c’, but not ‘c’.

I say not at ‘c’ because space relates objects with mass and relativity says that mass can not change at a rate of ‘c’ without ceasing to exist; if you did, your time would essentially stop compared to everything else in the universe that would go through infinite time. I am skeptical that universal constants, such as ‘c’, are always the same everywhere in the universe or that the vacuum of space is empty and not filled with some kind of ether that could be hard to interact with and then relatively motionless. We still don’t know why matter can be created and destroyed, while conserving energy or why quarks can lose their mass and disappear and then reappear again somewhere else. Or even what a ‘charge’ means other than to describe repulsion and attraction.

But so I’d say less than ‘c’, but not at ‘c’.

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The instantaneous action of gravity over distance is a fundamental assumption that I believe should be looked at a little more closely. Especially in the context of clear math that demonstrates if it moves at less than c it can transform directly into the field equations and give the same results and predictions. In general relativity it is important to remember that gravity waves are not gravitational but buckles is spacetime resulting from highly energetic events and gravity isn’t transactional between the two bodies but rather with the effects of their energy on spacetime. If gravity as we experience it really is only inertial motion the effect isn’t traveling between the bodies, when you enter the reference frame you enter it instantly and feel the effect because the space is bent where you are already. It would have been well beyond the technological capability of his time for Newton to really test the speed of gravity as a force between objects yet we have run with this assumption for almost 300 years.

The answer to the question has already been hinted at by wiegabo. See the paper;

Multi-messenger Observations of a Binary Neutron Star Merger

The EM radiation from the neutron star merger arrived 1.7s after the GW. Near as makes no difference, that shows that the speed of gravity = c.

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There is one cool article that I was stumbled across on my Feedly feed. It’s from, again me off the topic, but it may contain some crumbs lead toward some more basic blunders. This is link to relativity comprehensive text in programming field that may sparkle ‘out of the box’ thinking. Functional vs declarative is what may lead us back right to plausible railway of we-are-heading-the-right-way.

Talking in declarative way may be the blunder we are doing cos setting up the stage was maybe off-the-track and so. For example the one Newton meter is the force needed to lift one unit up on one meter. This claim is correct until we conduct the testing on solid ground. In other words any gas giant and non solid in universe can’t support the same theory without having different results. Einstein was wise and has introduced the term ‘relativism’ into physics. Wise one. Same as W. Heisenberg was wisely skipped the form “… and given area” for defining uncertainty of particle. Maybe micro gravity that goes into account to light dual property/nature.

Ishkoday was mentioned that even if we take into account dark matter…

… so it is obvious that declarative way of vise one must have some bugs from the elementary level of education. In not saying that everything is wrong but maybe everything we knows in not that much precisely defined on functional levels.

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This has sparked some lively debate, that’s good to see. Here is what makes sense to me. If Einstein’s field equations can be transformed into Newtonian physics it means gravity as a force can make the same predictions as relativity. The critical difference being rather than an instantaneous force irrespective of distance it is treated as a decelerating force with respect to distance. The most fascinating aspect of this reality to me is that Milgrom’s law is derived as a consequence. After all if gravity is a decelerating force not only is it getting weaker it’s taking longer to affect you making it seem weaker than it should be thus allowing you to orbit faster at greater distances without simply flying away. What does that mean? The short version is it is possible to create a Newtonian universe that exactly matches the predictions of general relativity, and works better to predict the large scale structure of the universe without dark matter up to the size of a galaxy. If the only difference is rather than as an instantaneous force between objects it diminishes speed with distance and this is one hundred percent mathematically demonstrable, isn’t it at least maybe potentially possible…?

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If the only difference is rather than as an instantaneous force between objects it diminishes speed with distance and this is one hundred percent mathematically demonstrable, isn’t it at least maybe potentially possible…?

It would appear not. See the paper I linked. Speed of gravity = c. Near as makes no difference. Any hypothesis that relies on gravity not travelling at c is therefore refuted. There would appear to be no room for argument.

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I am jumping in rather late and without reading all earlier posts, but as I have thought about the speed of gravity for some time, I though it worth mentioning that finite speed of gravity is incompatible with energy conservation. This is easily revealed by simple vector analysis of the two body system with two equal masses orbiting. Finite gravity speed results in acceleration.

I have not seen a convincing experimental demonstration that gravity speed is finite.

A mathematician I know once told me Einstein tried to put a speed limit on gravity but that it was very hard to do, which caused him to look at the problem another way which led him toward the path to General Relativity. Which of course does exactly that by eliminating the need for vector equations and setting the speed of all interactions to C. However I still wonder if that intial instinct was correct because MoND works so well and the effect of weaker gravity is the same as gravity that takes longer to get there…

At the risk of repeating myself - there is no argument to be had here! Did you miss the paper I linked? The binary neutron star merger killed all theories that rely on gravity propagating instantaneously. Or at anything other than c. That is why the gravitational waves and the EM signature were detected at the same time (near as makes no difference). Had gravity been instantaneous, we would be sitting around for ~ 130 million years waiting for the EM signature! We aren’t. We didn’t. Ergo, instantaneous gravity, and any theories that rely upon it, are history. Dead. Brutally and pitilessly murdered;

Troubled Times for Alternatives to Einstein’s Theory of Gravity

I agree the major problem with Newtonian mechanics is the instantaneous propagation of gravity, I would take it further and say describing gravity as a force with a speed limit shouldn’t be completely disregarded in favor of inertia alone…

So you agree that MOND is dead? Like I said - no more word salad. Yes?

Perhaps, but we shouldn’t consider a theory dead when it works and we don’t know why. It really shouldn’t work at all but it does and between the Hubble tension and the apparent failure of dark matter to explain our observations it is looking like it’s not out yet. The current thinking is rather than dead what MOND likely needs is a relativistic parent theory to bring it more in line with the mainstream.