I don't see the problem with action at distance

[Erland]

Since Newton's times, many people (including Newton himself, I think) have felt dissatisfaction with the theory of gravity because there was no explanation of the cause of gravity and of how it can act at distance. Forces that do not act by direct contact between the objects (for example: I kick a ball and the contact force makes ball move away from my foot) seemed mysteroius to many people.
It is often claimed that Einstein solved this problem when he explained gravity as a consequence of the geometry of spacetime.

I will in no way dispute the correctness of Einstein's General Theory of Relativity, but I never understood the problem with action at distance. For if we think a little, we realize that all forces must act at distance, including direct contact forces! The reason is that there must be a distance between any two objects, including objects which appear to be in direct contact with each other. Two objects cannot occupy exactly the same locations in space.
In the example with me kicking a ball, there must be a distance, albeit very small, between the parts of my foot and the ball that we consider as in direct contact with each other, for otherwise those parts of my foot and the ball would occupy the same location in space, which is imposible. In fact, it is the electric repulsion between the electron clouds in my foot and the ball respectively, that constitutes the apparent contact force, and this replusion acts at a (very small) distance. It is analogous to when we try to bring the north poles of two magnets together with our hands. Then we can feel the magnetic repulsion in our hands and still see that it acts at dustance.

So, since all forces must act at distance, I see no reason that we should be particularly skeptical against Newtonian gravity or electrostatic and magnetic forces acting et distance, etc.

 

[chrisbaird]

The "action at a distance" phrase denotes more than the concept of one object acting on another object far away. It denotes that this action is instantaneous. That is where the problem lies. A cause right here which instantaneously leads to an effect over there breaks that concept of causes and effect, and also allows information to travel faster than the speed of light.

 

[Erland]

The "action at a distance" phrase denotes more than the concept of one object acting on another object far away. It denotes that this action is instantaneous. That is where the problem lies. A cause right here which instantaneously leads to an effect over there breaks that concept of causes and effect, and also allows information to travel faster than the speed of light.

So if Newton had said that the force of gravity doesn't act instantaneously upon distant objects, but propagates with some very high speed, say the speed of light, this would have been considered as less problematic?

 

[chrisbaird]

So if Newton had said that the force of gravity doesn't act instantaneously upon distant objects, but propagates with some very high speed, say the speed of light, this would have been considered as less problematic?

Yes. But that then leads to the question: What is propagating at a very high speed to carry the information out to the planet that it's supposed to feel gravity? At that point, you are taking about an exchange of particles, or waves, or field disturbances between two objects, which isn't really "action at a distance" at all.

 

[DrStupid]

Two objects cannot occupy exactly the same locations in space.

Bosons (including gauge boson) can.

So if Newton had said that the force of gravity doesn't act instantaneously upon distant objects, but propagates with some very high speed, say the speed of light, this would have been considered as less problematic?

No. Instantaneous interactions are problematic in the theory of relativity but not in classical mechanics. Therefore Newton didn't need to make such an assumption. Far from it! He was aware that the gravitational force must act instantaneous because any delay would lead to a violation of the 3rd law and that would be a major problem in both relativity and classical mechanics.

 

[jetwaterluffy]

It is analogous to when we try to bring the north poles of two magnets together with our hands. Then we can feel the magnetic repulsion in our hands and still see that it acts at distance.

This "instant" repulsion is in fact caused by the photons transferring information between the magnets. Photons are also what light is made up of, so go at the speed of light. That is why it is called electromagnetic radiation.

 

[Erland]

Sorry for bumping up this old thread, but I have been thinking of it lately.

Yes. But that then leads to the question: What is propagating at a very high speed to carry the information out to the planet that it's supposed to feel gravity? At that point, you are taking about an exchange of particles, or waves, or field disturbances between two objects, which isn't really "action at a distance" at all.

It might have been a mistake of me to talk about propagation. What if we just say that the action at distance acts with a delay? What if Newton had said something like this:

If a particle with mass m₁ is located at P at t=0 and another particle m₂ is located at Q at t=t₁, and the distance between P and Q is r=ct₁, then the force F=Gm₁m₂/r² directed towards P is acting upon m₂ at t₁.

Here, no propagation is mentioned and the action is at a distance but not instantaneous. Would it still have been considered as problematic in Newton's time and later?

 

[D H]

Would it still have been considered as problematic in Newton's time and later?

Yes. The problem with adding a propagation-based delay to Newtonian gravity is that it results in a law that doesn't agree with observation. A law (a "law" is just an empirical equation) that doesn't agree with observation is not a law of nature.

 

[davenn]

This "instant" repulsion is in fact caused by the photons transferring information between the magnets. Photons are also what light is made up of, so go at the speed of light. That is why it is called electromagnetic radiation.

I would dispute that

its ONLY a magnetic field NOT an electromagnetic field between 2 magnets
it isn't EM radiation. EM radiation is emitted by an accelerating charge. There is
no accelerating charge in a magnet

Dave

 

[Erland]

Yes. The problem with adding a propagation-based delay to Newtonian gravity is that it results in a law that doesn't agree with observation. A law (a "law" is just an empirical equation) that doesn't agree with observation is not a law of nature.

We know that now, of course. But at Newton's time, observations were not precise enough to rule out such a delay (Proof: there is really such a delay, by Relativity Theory). It cannot have been until the early 20th century that it was possible to make such precise observations (since Relativity Theory did not exist before).
So if Newton had suggested such a delay (without mentioning any propagation), none of his contemporaries could say that it was inconsistent with observations.

And I don't think it was the instaneity of the action that was considered problematic, but that is was acting at distance, between objects not in contact with each other.

 

[D H]

We know that now, of course. But at Newton's time, observations were not precise enough to rule out such a delay (Proof: there is really such a delay, by Relativity Theory). It cannot have been until the early 20th century that it was possible to make such precise observations (since Relativity Theory did not exist before).
So if Newton had suggested such a delay (without mentioning any propagation), none of his contemporaries could say that it was inconsistent with observations.

The observations were there to rule out such a delay. Adding any appreciable propagation delay to Newtonian gravity would make the solar system unstable. 100 years after Newton's time, Laplace calculated that if Newtonian gravity did have a finite transmission speed it must be at least 70 million times the speed of light.

There's a whole lot more to general relativity than just the finite speed of gravitation. Gravity isn't even a force in general relativity, making it a bit tough to make a direct comparison. However, it definitely is not just Newtonian gravity plus a finite delay. That's an incorrect view of general relativity, one that is easily put to bed by Laplace's calculation.

And I don't think it was the instaneity of the action that was considered problematic, but that is was acting at distance, between objects not in contact with each other.

Actually, it was both the instantaneous nature of the force plus the fact that the objects weren't in contact that bothered Newton.

 

[Erland]

The observations were there to rule out such a delay. Adding any appreciable propagation delay to Newtonian gravity would make the solar system unstable. 100 years after Newton's time, Laplace calculated that if Newtonian gravity did have a finite transmission speed it must be at least 70 million times the speed of light.

There's a whole lot more to general relativity than just the finite speed of gravitation. Gravity isn't even a force in general relativity, making it a bit tough to make a direct comparison. However, it definitely is not just Newtonian gravity plus a finite delay. That's an incorrect view of general relativity, one that is easily put to bed by Laplace's calculation.

It is true that my knowledge of General Relativity is shallow. But I have a question:

Suppose that the sun, by some strange reason, breaks into two parts, one moving towards Earth at a high speed, and the other one moving away from us. This will of course alter the gravity field in the solar system. Does what you say above mean that we, on the Earth, will be able to measure the change in gravity caused by the break before we can see the break happen in the sky?

 

[king vitamin]

Suppose that the sun, by some strange reason, breaks into two parts, one moving towards Earth at a high speed, and the other one moving away from us. This will of course alter the gravity field in the solar system. Does what you say above mean that we, on the Earth, will be able to measure the change in gravity caused by the break before we can see the break happen in the sky?

No, we would measure the change in the gravitational field at the same time we see it. However, before the sun explodes, the gravitational force always points towards the instantaneous position of the sun, not where it was 8 minutes ago.

The common misconception is that because we do not measure a change in the field until a time r/c later, then all dependence on the source of the field must be at retarded times and positions. I think it might be easiest to think of classical EM. If you take a Coulomb field of a point charge and boost it in a direction, the field will still point toward the instantaneous position of the source. If it helps, imagine that the test particle not only "sees" the source's retarded position, but also the source's retarded velocity, and it "updates" the direction of the field accordingly to try to match the instantaneous position (even if doing so is incorrect because acceleration has occurred in the time in between). Of course, when I say "sees" and "updates" I am using unfounded personification. But Maxwell's equations are a great place to see many of the same effects and are much simpler than GR, so I'd recommend playing with them and the Lienard-Wiechert fields to convince yourself that this all makes sense and is consistent.