Why cant special reletivity and Newtonian theory of gravity agree?

[[Nicolette]]

I'm reading A Brief History of Time by Stephen Hawking and he says that "gravitational effects should travel with infinite velocity" if an object is moved and therefore the gravitational force between them is instantly changed. this gravitational force then moves faster than the speed of light, which special relativity argues is impossible for objects of mass.

BUT I'm thinking that yes, if an object is moved instantaneously, as he proposes, the effect of gravitation would appear to be instantaneous, but i would argue, when in nature would an object be moved instantaeously? isn't it more realistic that an object would be moved at a speed slower than the speed of light, and therefore the gravitational attraction would increase at a speed that is slower than the speed of light? consistent with the theory?

is there a simple answer to why gravitational effects are neglected in the special theory of relativity?

 

[malawi_glenn]

Gravitational effects are not neglected, they are not even INCLUDED in special theory of relativity. Special relativity deals with inertial frames moving with constant speed with respect to each other, including gravity = free falling accelerating frames, one need General Relativity.

I think the asnwer is that you have misunderstood the phrases..

he says that "gravitational effects should travel with infinite velocity" if an object is moved and therefore the gravitational force between them is instantly changed. this gravitational force then moves faster than the speed of light, which special relativity argues is impossible for objects of mass."

Then you write:
"if an object is moved instantaneously, as he proposes"

Which is wrong, he only wrote that the object IS moving, and in Newtonian Gravity this change in the gravitational field is then instantaneous. One simple example. Imagine that you are in an entire empty universe except the following two obejcts; you and a star located 9287342897 light years away from you. The star moves away from with speed 100km/s, and in Newtonian mechanics this change in the gravitational potential felt by you from the star is changing instantaneous -> thus the information from the star goes faster than speed of light. Not ok in Special Theory of relativity.

So the fact that everything moves slower than speed of light does not solve anything ;-) the POTENTIAL still changes instantaneously.

 

[[Nicolette]]

thank you i think you cleared up what i misunderstood, but now I am wondering if 'potential' applies because i thought its possible for information to travel faster than the speed of light?

 

[Privalov]

I'm reading A Brief History of Time by Stephen Hawking and he says that "gravitational effects should travel with infinite velocity"

The full quote says:

"Newtonian theory of gravity, which said that objects attracted each other with a force that depended on the distance between them. This meant that if one moved one of the objects, the force on the other one would change instantaneously. Or in other gravitational effects should travel with infinite velocity"

 

[Phrak]

In Newton's theory of gravity, gravitational attraction must occur instantaneously. If this were not so, two masses, constrained to parallel tracks would slow each other down as each is attracted to the past position of the other.

Think of two masses separated by a dumbbell bar moving up the page.

0----------0
^---------^
^---------^
x----------x

Each 0 would be attracted to the other 0, but at the former position, x.

Now bring the masses together into one mass. Each part of the glommed-together mass of an object would slow other parts of the extended mass. Energy would not be conserved.

Special relativity with the requisite speed limit c, and Newtonian gravity are not compatible theories.

 

[malawi_glenn]

thank you i think you cleared up what i misunderstood, but now I am wondering if 'potential' applies because i thought its possible for information to travel faster than the speed of light?

No it is not possible for information to travel faster than the speed of light.

 

[A.T.]

In Newton's theory of gravity, gravitational attraction must occur instantaneously.

What does occur instantaneously, attraction or change of it?

If this were not so, two masses, constrained to parallel tracks would slow each other down as each is attracted to the past position of the other.

Think of two masses separated by a dumbbell bar moving up the page.

0----------0
^---------^
^---------^
x----------x

Each 0 would be attracted to the other 0, but at the former position, x.

Not if the field has a velocity component and moves in the same way, as the source moved when the field was "emitted".

Now bring the masses together into one mass. Each part of the glommed-together mass of an object would slow other parts of the extended mass. Energy would not be conserved.
Special relativity with the requisite speed limit c, and Newtonian gravity are not compatible theories.

Replace your two masses with oppositely charged bodies. Will they slow down each other? I don't think so. Does this mean that the E-field transports information instantaneously? I don't think so.

 

[malawi_glenn]

But Newtons theory of gravity is non-local, the speed of the information is "infinite" or rather it is meaningless to ask what the speed of the information propagation is, a change at position x_1 will affect the field at point x_2 INSTANTANEOUSLY. The field HAS no velocity component in Newtonian Gravity, that is the "problem" with it...

 

[A.T.]

But Newtons theory of gravity is non-local, the speed of the information is "infinite" or rather it is meaningless to ask what the speed of the information propagation is, a change at position x_1 will affect the field at point x_2 INSTANTANEOUSLY. The field HAS no velocity component in Newtonian Gravity, that is the "problem" with it...

I just disagree with Phrak's parallel movement example. If correct, it would imply that any interaction has to be instantaneous, to prevent the two bodies from slowing down or accelerating each other.

 

[Phrak]

Hello, A.T. The problem, when applied to charged bodies came up just a couple weeks ago, here. I believe DaleSpam supplied the answer. The force between two charged objects is treated relativistically. In calculating the direction of the force due to charge, use the Lorentz rotated force.

Which begs the question. Historically, how was this reconciled at the turn of the century, 1900, without relativity?

 

[Naty1]

Historically, how was this reconciled at the turn of the century, 1900,

Likely it was recognized as a problem, like relativity and quantum mechanics contradictions today. Around 1900 Maxwell's equations were LAW (since 1868 I think) but people were still fussing with ether theories...

 

[A.T.]

Which begs the question. Historically, how was this reconciled at the turn of the century, 1900, without relativity?

Galilean Relativity already implies that the field must move with an inertially moving charged particle. If it would stay behind, you could detect the absolute movement of the particle.

But coming back to Newton: If you would replace his instantaneous force by a field with a velocity component (like the E-field) - It would be compatible with the c-limit of SRT and the two masses on parallel tracks would still not accelerate each other. Would this create other problems?

Is it really true that:

In Newton's theory of gravity, gravitational attraction must occur instantaneously.

?

Or is the attraction just instantaneous, because Newton didn't consider the difference between a inertially moving and an accelerated mass?

 

[Naty1]

My answer to

Historically, how was this reconciled at the turn of the century, 1900,

may not have been clear: there was a recognized conflict about that time...it was unresloved.

I happened to find the following in the Elegant Universe, Brian Greene, pg 5:

..As far back as the late 1800's...a conflict concerning the motion of light was recognized...according to Newton's laws of motion if you run fast enough you can catch up with a depating beam of light whereas according to..Maxwell's laws of electromagnetism, you can't...the development of Einsteins special theory immediately set the stage for a second conflict...that no influence nor disturance can travel faster than the speed of light...

 

[Naty1]

In Newton's theory of gravity, gravitational attraction must occur instantaneously.

Or is the attraction just instantaneous, because Newton didn't consider the difference between a inertially moving and an accelerated mass?

I may not grasp some subtley in your comment, but Newton had no idea about the limiting speed of light...so I take the finite speed of light limitation to be the most direct reply...

 

[Naty1]

I believe DaleSpam supplied the answer.

I remember that thread, quite recent...Can anyone find that thread? It was a slick insight.
Part of the reply was this, but I am unsure from who: (a wiki reference)

In a field equation consistent with special relativity, the attraction is always toward the instantaneous position of the sun, not the extrapolated position. When an object is moving at a steady speed, the effect on the orbit is order v2/c2, and the effect preserves energy, and orbits don't decay, they precess. The attraction toward an object moving with a steady velocity is towards its instantaneous position.

and from somewhere in aRxiv:

In particular, as in Maxwell’s theory, if a source abruptly stops moving at a point z(s0), a test particle at position x will continue to accelerate toward the extrapolated position of the source until the time it takes for a signal to propagate from z(s0) to x at light speed.
A similar result can be obtained in general relativity by evaluating the gravitational field of a boosted black hole [16], or more generally by systematically approximating the solution of the two-body problem [

 

[A.T.]

I may not grasp some subtley in your comment, but Newton had no idea about the limiting speed of light...so I take the finite speed of light limitation to be the most direct reply...

I know, and proclaiming the force to be instantaneous was the simplest way to make his theory compatible with Galilean Relativity (= avoid problems like the example by Phrak), so he went with it. I wanted to know, if given the c-limit for information, you could modify his theory to be more like the E-field.

 

[3zy]

Lets some fun

http://sites.google.com/site/lorentzrelativity/

 

[Phrak]

I'm beginning to feel rather foolish. I didn't properly understand your objections, AT. The dumbbell model is a good test model, though.

To be clear about both the context and what is being asked, I think the question currently being asked is:

"Can Newtonian gravity, F = GmMr / r³, be compatible with special relativity, where Newtonian gravitational force is modified to propagate at the speed of light and F becomes a 4-force?

 

[Vanadium 50]

I think you have to do it by coming up with a four-potential to make something Newtonian-like that sort-of works. This will leave you with something like the scalar part of scalar-tensor theory.

 

[atyy]

Historically Nordstrom came up with the first consistent relativistic theory of gravitation, which was based a scalar field. It is ruled out by observation, giving the wrong prediction for perihelion precession.
http://arxiv.org/abs/gr-qc/0611100
http://arxiv.org/abs/gr-qc/0405030

 

[Vanadium 50]

I thought about what you wrote a little more:

"Can Newtonian gravity, F = GmMr / r³, be compatible with special relativity, where Newtonian gravitational force is modified to propagate at the speed of light and F becomes a 4-force?

The answer is "no", of course, since the r's - all the r's, not just the one in the numerator - Lorentz contract, so you have a 4-vector on one side of the equation and something else on the other side.

What you have to do is define a 4-vector so that for a mass at rest, it's $(\phi_0,0,0,0)$. For a moving body, one then transforms this to become $(\phi, \vec{A})$. The force on an object of mass m is therefore given by:

$$F = m(-\nabla \phi - \frac{\partial{\vec{A}}}{\partial t}} + \frac{\vec{v}}{c} \times (\nabla \times \vec{A})} )$$

One then links up this expression with the Newtonian prediction to get $\phi_0$, which is of course GM/r.

What I just wrote down is a relativistically correct theory of gravity. However, it is not a physically correct theory of gravity. This gets the wrong value for the deflection of light in a gravitational field, and it gets the wrong value for the perihelion advance of mercury.

 

[Phrak]

I'm not sure how that all works out. You'd need 4-vectors all around. It might be best to convert F = dP/dt. I don't have a handle on any of it, though.