# Thread: instantaneous 'action at a distance' vs. special relativity

1. ## instantaneous 'action at a distance' vs. special relativity

Newton characterized the law of gravity as 'action at a distance" requiring the instantaneous exchange of gravitational forces. In calculating planet trajectories, position etc using Newton's force expression, F = - k m1m2/R^2 the calculations will show a remarkable agreeement with observation.

If one uses a retarded force model the claculation for the positions, trajectories etc will be erroneous.

Relativity theory preclude the motion of matter greater than the speed of light, hence the instantaneous exchanghes of gravitational forces has been discarded by relativity theorists .

The question then, seems to be, if SR s correct and Newton in error, how does SR explain that only using instantaneous force exchanges works for "remarkably accurate" trajectory calculations while retarded force models are not verified by observation? Or said another way is "instantaneous" a true velocity?

2. Wasn't this more or less dealt with in a thread you started a couple of months ago?

3. Originally Posted by przyk
Wasn't this more or less dealt with in a thread you started a couple of months ago?

While this is true, the referenced thread did get a bit off the topic with respect to the question here, in a hypothetical discussion involving speed of light limitations within an otherwise Newtonian model of gravity.

Originally Posted by geistkiesel
Newton characterized the law of gravity as 'action at a distance" requiring the instantaneous exchange of gravitational forces. In calculating planet trajectories, position etc using Newton's force expression, F = - k m1m2/R^2 the calculations will show a remarkable agreeement with observation.

If one uses a retarded force model the claculation for the positions, trajectories etc will be erroneous.

Relativity theory preclude the motion of matter greater than the speed of light, hence the instantaneous exchanghes of gravitational forces has been discarded by relativity theorists .

The question then, seems to be, if SR s correct and Newton in error, how does SR explain that only using instantaneous force exchanges works for "remarkably accurate" trajectory calculations while retarded force models are not verified by observation? Or said another way is "instantaneous" a true velocity?
Something that is often difficult to reconcile about the relationship of the speed of light limitation of information transfer inherent within both special and general relativity and the apparent instantaneous nature of a gravitational field, is that it is a limitation to the speed at which change can occur in the field. The field itself exists as if it were an extension of the center of mass itself.

GR models the effect of a gravitational field as being instantaneous between two objects while it limits any change in a gravitational field to a speed of light delay. This at first seems to be a conflicted statement. One must remember that while Newton imagined that gravitational force was actively transmitted instantaneously between two masses, Einstein envisioned gravity to be manifest as a curvature of space, defined by and proportional to the presence and proximity of mass within space.

Since the transfer of information is limited to the speed of light and the transfer of mass is limited to less than the speed of light, there can be no change in the mass of a gravitational source that exceeds the speed of light. This is true even within GR. However, within the limitations of experience and from our frame of reference any change in the distribution of mass of an astronomical object or collection of objects can result in no change in the gravitational potential as we perceive it.

One way to think about this is that were our sun to instantly collapse into a black hole its gravitational influence on us would not have changed. Only that portion of the field between the sun's initial spherical surface and the surface of the new black hole would have changed.

Both Newton's understanding of gravity and gravity as defined within GR act toward the instantaneous center of mass of the involved gravitational field. It is only changes to that field that are limited to a speed of light delay. For all practical purposes we know of no changes that occur that even begin to approach the speed of light.

(NOTE: Theoretically we should be able to detect some variations in the gravitational potential of very massive binary gravitational sources related to the cyclical change in the distribution of mass from our frame of reference. We have yet to detect the expected gravitational waves from such binary systems.)

4. Originally Posted by geistkiesel
The question then, seems to be, if SR s correct and Newton in error, how does SR explain that only using instantaneous force exchanges works for "remarkably accurate" trajectory calculations while retarded force models are not verified by observation? Or said another way is "instantaneous" a true velocity?
Something I missed in my previous post was that SR deals with the "Relativity" of inertial frames of reference and does so from a frame of reference that is locally flat and essentially consistent with a Newtonian model. It does not deal with or explain gravity.

GR was developed by Einstein specifically to address gravity and involves space and matter or mass in a dynamic relationship, in which space is no longer flat.

The speed of light limitation applies in both SR and GR. Gravity in this case can only be addressed from the perspective of GR.

5. Originally Posted by przyk
Wasn't this more or less dealt with in a thread you started a couple of months ago?

You are absolutely correct. I have started this thread for reasons of a furthr look at the problem.

6. Originally Posted by geistkiesel
Newton characterized the law of gravity as 'action at a distance" requiring the instantaneous exchange of gravitational forces. In calculating planet trajectories, position etc using Newton's force expression, F = - k m1m2/R^2 the calculations will show a remarkable agreeement with observation.
They only show good agreement, not perfect. If you want to hit the Moon with a rocket or put a Satellite into orbit around Titan then they are fine. However, if you care about more precise things like nanosecond timings they are not fine and you need to use relativity.

Newton is very good but only to a point. 'Remarkable' is perhaps over stating it, particularly given the level of precision modern technology allows us to have in our observations.

Originally Posted by geistkiesel
If one uses a retarded force model the claculation for the positions, trajectories etc will be erroneous.
Relativity is not like electromagnetism. In electromagnetism you have advanced and retarded waves which are involved in keeping causality. Relativity doesn't model gravity like that, it is warped space-time not objects within the space-time. Wave fronts do occur in relativity (gravitational waves) but not in the sense of photon exchanges in electromagnetism.

Hence it isn't that unsurprising such attempts at interpreting gravity don't pan out, it isn't just electromagnetism with a few terms changed. This is seen even more starkly when trying to quantise it, where vast and fundamental differences become apparent.

Originally Posted by geistkiesel
The question then, seems to be, if SR s correct and Newton in error, how does SR explain that only using instantaneous force exchanges works for "remarkably accurate" trajectory calculations while retarded force models are not verified by observation? Or said another way is "instantaneous" a true velocity?
General relativity's take on causality is more complex than special relativity's take on it, but it does reduce to it when you phrase things right in particular constructs (ie the use of vierbeins).

The reason why Newton's work is as good as it is can be seen from GR's description. By considering things like weak field approximations, doing perturbative expansions of the GR equations in terms of mass, radius of curvature and $\frac{1}{c}$ you can recover Newton's work as a first approximation to a much more complicated framework. For things in the solar system masses and curvatures aren't too big compared to the speed of light so the terms which come after the first approximation are very very small.

For example, consider the Lorentz factor $\gamma(v) = \left( 1 - \frac{v^{2}}{c^{2}} \right)^{-\frac{1}{2}}$. c ~ 300,000,000 m/s. The speed of Earth's motion about the Sun is around 30,000 m/s. Thus v = 0.0001c. Therefore v/c = 0.0001 << 1. Thus we can expand the Lorentz factor using a Taylor expansion, $\gamma(v) = 1 + \frac{1}{2}\frac{v^{2}}{c^{2}} + \frac{3}{8}\frac{v^{4}}{c^{4}} + \ldots$. Using $\frac{v}{c} = 10^{-4}$ we get $\gamma(v) = 1 + \frac{1}{2}10^{-8} + \frac{3}{8}10^{-16} + \ldots$. So the first correction to a Newtonian point of view is about 100 million times smaller.

Consider what happens if you make c larger. The term v/c gets smaller. As $c \to \infty$ the corrections go to zero. Thus you can view the first term as the infinite speed limit, which is precisely the Newtonian term. That's why Newton's work is pretty good, we only looked at slow moving, relatively small (ie low mass) objects, even the Sun is pretty small on the scale of things.

This is stuff you've been told before. Every time I see a thread of yours I think "Not again...." because you ask the same sorts of questions time and again. You make little to no attempt to understand what you were previously told. Your opening posts are always constructed to highlight some problem you think exists and then close with some semi-rhetorical comment which can be summed up as "Physicists are wrong, I'm right, it's obvious!", except all you've done is shown you haven't paid any attention to what it is you've been talking about. Why don't you just buy yourself a few introductory books on vector calculus, differential equations, linear algebra, Newtonian mechanics and special relativity. Nothing difficult, just simple 1st year stuff, stuff a physics undergrad would cover their first term of university so nothing beyond high school understanding is initially needed. You've clearly got plenty of time on your hands since you bang on about this stuff year after year.

If you're too busy, too lazy or too stupid to do that at least realise that what you bring up always is immediately answered by someone who knows relativity. Your understanding is so poor you aren't challenging anyone (other than people's patience). If you're not going to try to advance your understanding in a constructive manner at least realise these threads are a waste of time, for us and for you.

7. Originally Posted by AlphaNumeric
They only show good agreement, not perfect. If you want to hit the Moon with a rocket or put a Satellite into orbit around Titan then they are fine. However, if you care about more precise things like nanosecond timings they are not fine and you need to use relativity.
if calculating the motion of earth with respect to the sun do you use a retarded force expression presuming the force leaves the sun and reaches earth some 8 minutes later, or when calculating earths motion do you use newton's force expression not amended.?

Newton is very good but only to a point. 'Remarkable' is perhaps over stating it, particularly given the level of precision modern technology allows us to have in our observations.
keeping the conservation restricted to stellar body motion, do you, or does the system you use presume a retarded force in caculatng stellar motion?
Relativity is not like electromagnetism. In electromagnetism you have advanced and retarded waves which are involved in keeping causality. Relativity doesn't model gravity like that, it is warped space-time not objects within the space-time. Wave fronts do occur in relativity (gravitational waves) but not in the sense of photon exchanges in electromagnetism.
Are the gravity waves moving at the speed of light? Have any gravity waves been observed? Has the gravity field been observed?

Hence it isn't that unsurprising such attempts at interpreting gravity don't pan out, it isn't just electromagnetism with a few terms changed. This is seen even more starkly when trying to quantise it, where vast and fundamental differences become apparent.
what experimental results have isolated the 'gravity field' any ?

I had not intendede to engage in a senseless argument with you , but since you insist, please consider the following and respond with rationally forumlated English.

Transponder A and B separated by a constant distance throughout emit and receive EM pulses . Each event (emission and absorption) are recorded at the transponder emitting or receiving the pulse. Similarly the times of receipt and emission are embedded in the signal.

The pulse leaves A at A0, when the B clock is Bu, (unknown).

The pulse arrives at B at Bu + B1 (the total is determined) when the A clock
is A2 + B1.

The pulse is directed back to A from B at Bu + B1 and arrives at A at A2 at which time the B clock is Bu + A2 (all individual terms are not known but the total is measured recorded) and is designated X1.

The pulse then leaves A at A2 arriving at B at Bu + A2 + B1 (the total is recorded). and is designated X2.

The whole experiment requires recording of 4 events A -> B -> A->B.

Using the data collected at the A and B transponders, and subtracting,
X2 – X1 = Bu + A2 + B1 – (Bu +A2) = B1 .

This effectively synchronizes the two clocks.

.he Transponders have been used daily for years in air traffic control systems and were adopted here hypothetically for this thought experiment. Emission and absorption times are recorded and embedded in the pulse signal.

I trust the simplicity of this little thought experiment doesn't jam that which you probably consider a 'mind'.

8. Originally Posted by geistkiesel
if calculating the motion of earth with respect to the sun do you use a retarded force expression presuming the force leaves the sun and reaches earth some 8 minutes later, or when calculating earths motion do you use newton's force expression not amended.?
If you just want an approximate idea then you use the instantaneous Newtonian force expression. If you want a more accurate one then you would proceed in the same manner as is done for calculating the motion of Mercury, since the problem is identical.

You compute the relevant equations of motion for the Schwarzchild metric space-time and work out the motion of the Earth in terms of a geodesic. This doesn't require you to do the whole advanced/retarded wave problem but it still includes the finite speed of gravitational disturbance propagation.
Originally Posted by geistkiesel
keeping the conservation restricted to stellar body motion, do you, or does the system you use presume a retarded force in caculatng stellar motion?
Relativity doesn't directly use the same approach as say electromagnetism.

Originally Posted by geistkiesel
Are the gravity waves moving at the speed of light? Have any gravity waves been observed? Has the gravity field been observed?
Gravitational waves move at light speed. Their effect has been observed in neutron binary systems and their orbital decays are in precise agreement with the predictions of GR. It won the Nobel Prize a few years back. Direct observation is extremely difficult but experiments arre currently running. As for a gravitational field being observed we see gravity's effects so yes.

Originally Posted by geistkiesel
what experimental results have isolated the 'gravity field' any ?
Are you referring to single quanta of gravity or something else? We observe the force, yes.

Originally Posted by geistkiesel
I had not intendede to engage in a senseless argument with you , but since you insist, please consider the following and respond with rationally forumlated English.
I like how you demand I reply with 'rationally formulated English' (the irony being you didn't formulate the sentence coherently) but you have made it clear you have no intention of learning any physics relevant to this discussion. Why should I be nice and rational when you won't be?

Originally Posted by geistkiesel
Transponder A and B separated by a constant distance throughout emit and receive EM pulses . Each event (emission and absorption) are recorded at the transponder emitting or receiving the pulse. Similarly the times of receipt and emission are embedded in the signal.

The pulse leaves A at A0, when the B clock is Bu, (unknown).

The pulse arrives at B at Bu + B1 (the total is determined) when the A clock
is A2 + B1.

The pulse is directed back to A from B at Bu + B1 and arrives at A at A2 at which time the B clock is Bu + A2 (all individual terms are not known but the total is measured recorded) and is designated X1.

The pulse then leaves A at A2 arriving at B at Bu + A2 + B1 (the total is recorded). and is designated X2.

The whole experiment requires recording of 4 events A -> B -> A->B.

Using the data collected at the A and B transponders, and subtracting,
X2 – X1 = Bu + A2 + B1 – (Bu +A2) = B1 .

This effectively synchronizes the two clocks.

.he Transponders have been used daily for years in air traffic control systems and were adopted here hypothetically for this thought experiment. Emission and absorption times are recorded and embedded in the pulse signal.

I trust the simplicity of this little thought experiment doesn't jam that which you probably consider a 'mind'.
What do you want me to say? You haven't actually formalised anything, you've just claimed you get synchronisation. Do you? Can you show it mathematically? You talk about times but times are frame dependent so the question is whose point of view are you using? Are you talking about actual air traffic systems? The nanosecond discrepancies due to relativity will not be relevant to air traffic controllers.

Rather than inventing your own poorly formalised scenario why don't you read up on how the GPS network does it. Learn the basic mathematics behind it, think about iit and then come back with any specific issues you have. If you make it clear you've made an effort to understand the system then people will be happy to help but if you just don't bother and whine then don't expect people to play nice.

Try meeting people half way and you'll find they are a lot nicer. If instead you make it clear you don't have any intention of learning, no matter how many times you're walked through it, don't blame others.

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