Why is Newtonian Gravity so accurate?

[geordief]

The concept is apparently flawed and the notion of a force acting at a distance seems to have been distrusted well before General Relativity was formulated but it seems conceivable to me* that without the stupendous advances in technology since then that GR might still be a niche subject since Newtonian gravity did the job so well in the main.

 

So what is it about Newtonian gravity that works so well ? Is it a bit like the difference between Special Relativity and Euclidean geometry: is Newtonian Gravity something of a "special case" of General Relativity?

 

As an afterthought and to acknowledge the weakness of my mathematical skills it is not possible is it that ,if we replace the distance "r squared" in Newtonian Gravity with the "s squared" ** of Special Relativity that we can "tweak" Newtonian Gravity to be something that little bit more accurate ,is it?

 

* obviously I could be way off in my estimate

 

** I mean of course using the "distance " between spacetime events as calculated in the formula s^2 =x^2 +y^2 +z^2 -(ct)^2

[mathematic]

I won't try to address your proposal about using s squared. The main reason Newtonian gravity works so well in general is that things are moving much slower than the speed of gravity, just as Newtonian mechanics works so well because things are moving much more slowly than the speed of light.

[geordief]

That is the first time I have come across the expression "the speed of gravity" . I am aware that there is a speed to the propagation of gravitational waves (c of course);

 

Is that the speed to which you were referring?

Edited April 25, 2016 by geordief

[ajb]

Is it a bit like the difference between Special Relativity and Euclidean geometry: is Newtonian Gravity something of a "special case" of General Relativity?

That is one way of viewing it. We know that general relativity has a Newtonian limit and so for a lot of gravitational phenomena Newtonian gravity will work well.

[elfmotat]

Your intuitions are good. Newtonian gravity can be derived from GR with the assumptions that: 1) gravity is weak, and 2) matter is non-relativistic. In particular you assume that the metric is nearly flat, different only by a small amount [math]|h|\ll 1[/math]:

 

[math]g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}[/math]

 

You plug this into the Einstein Field Equations (making use of the fact that matter is non-relativistic so all but the 00-component of the Stress-Energy Tensor will be zero), and you're left with the differential equation:

 

[math]\nabla^2 h_{00} = -8 \pi G \frac{\rho_E}{c^2} = -8 \pi G \rho_M[/math]

 

where [math]\rho_E[/math] is energy density, which we can replace with mass density [math]\rho_M[/math] because matter is non-relativistic. Note the similarity to the Poisson Equation for Newtonian gravity:

 

[math]\nabla^2 \Phi = 4 \pi G \rho_M[/math]

 

for gravitational potential [math]\Phi[/math]. Indeed we can simply identify [math]h_{00} = -2 \Phi[/math] and they are equivalent. So using only the assumptions that gravity is weak and matter does not move fast, we obtain the fundamental equation of Newtonian gravity from GR. (The inverse-square law can be derived from Poisson's equation.)

 

 

AFAIK your suggestion to replace the denominator of the inverse-square law with the interval (proper distance perhaps?) does not really have any meaningful interpretation.

Edited April 25, 2016 by elfmotat

[Strange]

The other answer is: because it was designed to be.

 

In other words, it was derived from observation and so matches what we observe.

[geordief]

Is it possible to tweak  Newtonian gravity by addressing the problem of it's  speed of propagation? 

I don't think Newton's  msbu1*msub2/r^2 law   took into account the idea that if the Sun's mass  was to somehow disappear in an instant it would take 8 minutes for us to notice the effect.

 

What if Newton's Law of Gravity  had this delay built into it? Would its predictions be any better?

 

I don't  think I am confusing the speed of a gravitational wave  with the speed of  the creation of a gravitational field....or am I? 

 

(Hope I am allowed to necro my own thread  )

 

  

[MigL]

Not sure how you would build in this 'delay' into Newtonian gravity.
And even if it helped account for relativistic effects, it would still only be applicable to nearly flat space-time  (IE weak gravity limit ).

As for the OP, I think Strange hit the nail on the head.
Both are based on experiment/observation; how could they not be.

Edited September 2, 2019 by MigL

[Strange]

There are a set of equations that model gravity by analogy to Maxwell’s equations for electromagnetism (called, not surprisingly, gravitoelectromagnetism). I think the speed of propagation would come out of these. 

They are more complex than Newton’s law (but simpler than GR)

[swansont]

12 hours ago, geordief said:

I don't  think I am confusing the speed of a gravitational wave  with the speed of  the creation of a gravitational field....or am I? 

They are the same: c. Gravity only gets modified if the source is accelerated, and gravitational waves can come from certain accelerations.

Mass doesn’t just appear or disappear, so there is no creation of the field from this effect.

[geordief]

2 minutes ago, swansont said:

They are the same: c. Gravity only gets modified if the source is accelerated, and gravitational waves can come from certain accelerations.

Mass doesn’t just appear or disappear, so there is no creation of the field from this effect.

So a gravitational wave passes through (and combines with?)the pre existing gravitational field.....is it correct to say that a graviton  is theorized to represent an "excitation"  in the gravitational field?

And there is no understanding yet   of the actual mechanism of  the gravitational field actually telling matter how  to move (as per "matter tells space how to bend, while space tells matter how to move") ?

Might there be a signal involved?

[Strange]

1 hour ago, geordief said:

And there is no understanding yet   of the actual mechanism of  the gravitational field actually telling matter how  to move (as per "matter tells space how to bend, while space tells matter how to move") ?

I don't think that is true. The explanation comes down to the geometry of space-time.

As an analogy, imagine two people walking forwards, side by side, on a flat plane. Their paths will remain parallel over time. We can consider the direction they are walking as the "time" dimension (they are moving steadily into the future) and the distance between them as one of the space dimensions.

On the the flat plane, the distance between them doesn't change over time. Now put them on the surface of a sphere (e.g the Earth, so they are walking along lines of longitude towards the North Pole). As they move forwards (in time) they get closer together. No force is acting on them, it is just a consequence of the curved geometry they are travelling in. You can consider them falling towards one another because of the "gravity" of the curved space-time they are in. Another observer might consider there is a force acting on them.

[geordief]

33 minutes ago, Strange said:

I don't think that is true. The explanation comes down to the geometry of space-time.

As an analogy, imagine two people walking forwards, side by side, on a flat plane. Their paths will remain parallel over time. We can consider the direction they are walking as the "time" dimension (they are moving steadily into the future) and the distance between them as one of the space dimensions.

On the the flat plane, the distance between them doesn't change over time. Now put them on the surface of a sphere (e.g the Earth, so they are walking along lines of longitude towards the North Pole). As they move forwards (in time) they get closer together. No force is acting on them, it is just a consequence of the curved geometry they are travelling in. You can consider them falling towards one another because of the "gravity" of the curved space-time they are in. Another observer might consider there is a force acting on them.

I think I should have said "And there is no understanding yet   of the actual mechanism of  the gravitational field actually telling matter how  to move        

matter telling how spacetime curves"

 

That's the case  isn't it? 

[StringJunky]

42 minutes ago, Strange said:

I don't think that is true. The explanation comes down to the geometry of space-time.

As an analogy, imagine two people walking forwards, side by side, on a flat plane. Their paths will remain parallel over time. We can consider the direction they are walking as the "time" dimension (they are moving steadily into the future) and the distance between them as one of the space dimensions.

On the the flat plane, the distance between them doesn't change over time. Now put them on the surface of a sphere (e.g the Earth, so they are walking along lines of longitude towards the North Pole). As they move forwards (in time) they get closer together. No force is acting on them, it is just a consequence of the curved geometry they are travelling in. You can consider them falling towards one another because of the "gravity" of the curved space-time they are in. Another observer might consider there is a force acting on them.

It seems to me gravity could be called 'freefall curvature'.

[Strange]

15 minutes ago, geordief said:

I think I should have said "And there is no understanding yet   of the actual mechanism of  the gravitational field actually telling matter how  to move        

matter telling how spacetime curves"

 

That's the case  isn't it? 

I suppose so. But I have seen one person (much more familiar with GR than me) reply to that with "that is what mass is". Which you might think is a bit of a tautology (like "time is what clocks measure") but things either have to be defined in terms of something else or, ultimately, defined as just being what they are.

[Mordred]

32 minutes ago, geordief said:

I think I should have said "And there is no understanding yet   of the actual mechanism of  the gravitational field actually telling matter how  to move        

matter telling how spacetime curves"

 

That's the case  isn't it? 

Your expression should be mass tells spacetime how to curve. As all forms of energy and matter can contribute to the mass term.

 It would help if you think of mass as resistance to inertia change and curvature as the freefall paths.

 In this you can use parallel laser beams. If you have no curvature the beams are parallel. If you have positive curvature the beams will converge. If negative they diverge.

[StringJunky]

15 minutes ago, Strange said:

I suppose so. But I have seen one person (much more familiar with GR than me) reply to that with "that is what mass is". Which you might think is a bit of a tautology (like "time is what clocks measure") but things either have to be defined in terms of something else or, ultimately, defined as just being what they are.

Some things, like time, seem to be defined by their effect i.e. time affects clocks, or spacetime affects the passage of freefalling objects, which is known as gravity.

 

41 minutes ago, geordief said:

I think I should have said "And there is no understanding yet   of the actual mechanism of  the gravitational field actually telling matter how  to move        

matter telling how spacetime curves"

 

That's the case  isn't it? 

There's the graviton mechanism (to be confirmed) and the spacetime curvature mechanism.

[geordief]

38 minutes ago, StringJunky said:

There's the graviton mechanism (to be confirmed) and the spacetime curvature mechanism.

How might the graviton  allow matter to curve spacetime? Are there rival theories?

Edited September 2, 2019 by geordief

[StringJunky]

3 minutes ago, geordief said:

How might the graviton  allow matter to curve spacetime? Are there rival theories?

I've no idea. i just know the idea exists.

[Mordred]

Gravitons don't create curvature they would if they exist simply act as a mediator much like photons mediate an EM field.

[geordief]

6 minutes ago, Mordred said:

Gravitons don't create curvature they would if they exist simply act as a mediator much like photons mediate an EM field.

So  are there no theories at all as to how matter creates curvature? Might gravitons have any role to play at all?

 

If I am following the em  analogy at all, might we be looking for something like a "gravitational charge"? A gravitational  counterpart to the electron?

Edited September 2, 2019 by geordief

[Strange]

19 minutes ago, geordief said:

So  are there no theories at all as to how matter creates curvature? Might gravitons have any role to play at all?

I think (some of) the various quantum gravity theories might do (things like loop quantum gravity, causal dynamical triangulation, etc.) where space-time emerges from a lower level description, and hence its relationship with mass-energy is explained by that theory. (That is a bit off the top of my head since it is several years since I read much about the subject).

22 minutes ago, geordief said:

If I am following the em  analogy at all, might we be looking for something like a "gravitational charge"? A gravitational  counterpart to the electron?

That is one way of thinking about mass; it is (roughly) analogous to charge.

Why does charge create the electric field that causes a force of attraction? Because that is what "charge" means.

Why does mass create the curvature in the space-time field that causes a force of attraction? Because that is what "mass" means.

[Mordred]

There is no easy explanation for how mass curves spacetime in terms of freefall paths. It takes a considerable amount of study to follow Euler Langrene equations for the path of least action just to get a feel for it. Unless your already familiar with calculus of variations.

In essence at each infinitesimal there is a relation between a particles kinetic energy and the fields potential energy. The path taken at each spacetime coordinate will involve the path with the least action which will equate to the shortest path.

The mass term is synonymous to how strongly particles couple to a field this is true of spacetime as well.

The path of least action also works under Newtonian gravity 

 

 

Edited September 2, 2019 by Mordred

[swansont]

2 hours ago, geordief said:

I think I should have said "And there is no understanding yet   of the actual mechanism of  the gravitational field actually telling matter how  to move        

matter telling how spacetime curves"

 

That's the case  isn't it? 

And if we had that, we wouldn’t know why that mechanism was the one.

It’s turtles all the way down.

[studiot]

Quote

Why is Newtonian Gravity so accurate?

 

Don't forget it is only a small part of a much wider system of (Newtonian) mechanics.