Dumb questions on gravity.

[JohnB]

Right, I was taught in school that Newtonian gravity works on the M1M2/DD formula and I accept that as true.

 

However it was pointed out to me recently that this requires instantaneous action at a distance. Assuming that is impossible then when considering the Earth/Sun system the Earth is not attracted to where the Sun is, but where it was 8 minutes ago and vice versa. Similarly when considering entire Galaxies the Milky Way is not attracted to Andromeda, but to the point where Andromeda was some 2 million years ago.

 

Question 1. Doesn't that muck up calculations? Or doesn't it make a difference?

 

Following on from this. If two bodies are without relative motion the M1M2/DD applies because the system is constant. Now we accelerate one of the objects.

 

Question 2. How do we handle the transition from "constant" gravity to "lagged" gravity? Or isn't it a big enough effect to make a real difference in most cases? Or is that what defines the difference between Newtonian and Relativistic physics?

 

As a thought experiment.

 

If we had one object that is "orbiting" another. We then accelerate the orbiting object, also applying force to prevent it from leaving its "orbit". We would reach the situation where the actual position of the orbiting object was nowhere near the point that the central object is attracted to. I'm lousy with diagrams but if we were looking down on such a system and the "orbit " was anticlockwise and we mark the directions as North, South, East and West. Could we not finish up where the orbiting object was physically at the "South" position while due to lag the central object is reacting gravitationally to when the orbiter was in the "North" position?

 

Whether gravitons or spacetime deformation, presumably you could eventually have the "orbiter" actually catching up to it's own "wake" at some point. My brain hurts just trying to picture that situation.

[lemur]

This is an interesting perspective and one that could have implications for explaining the relationship between electromagnetism and light, imo. If an object accelerates toward the sun, it would experience graviton blue-shift, right? If it accelerates away from the sun, it would be red-shift? The blue-shift may be able to build up to the point of creating a gravity-wave, just as a descending electron could build up to create a photon-emission. There must be some reason why a number of EM or gravitational waves compressing 'spill over' into a moving wave that transports that energy at C. How could the orbiter ever catch up to its own wake if the wake was moving at C? Wouldn't the distance between the orbiter and wake always be increasing?

[D H]

Newton's law of gravitation does indeed require instantaneous action at a distance. So, what happens if we modify Newtonian gravity to take into account the finite transmission time? Chaos is what happens. For example, orbits are no longer stable, and a solar system simulation based on this correction would yield much less accurate results than would a solar system simulation based on Newton's law. Numerous crackpots, including some PhD physicists, have used this as an argument against general relativity.

 

These arguments against general relativity are straw man arguments. While general relativity does say that gravity propagates at the speed of light, it says a lot more than that. There are other affects such as frame dragging in addition to this propagation delay. The net result is that these effects nearly cancel for objects with lowish densities (much less than the Schwarzschild density), lowish relative velocities (much less than light speed), and separated by largish distances (much greater than the Schwarzschild radii). The limiting result is Newtonian gravity.

 

What about those cases where distances are small, velocities are large? That describes Mercury. At the end of the 19th century Mercury's orbit was known to deviate from calculations based on Newtonian mechanics. General relativity perfectly explains those deviations. This was one of the reasons for the relativity quick acceptance of general relativity by physicists.

 

 

 

[JohnB]

DH, I wasn't arguing against relativity, I don't know much relativity.

 

I was asking what happens, how is it dealt with?

[D H]

I didn't think you were arguing against relativity, John. I did tell you in words that the combined effects of frame dragging, gravitomagnetism, and finite transmission speed nearly cancel in our solar system. If you want the math behind those words, it gets real hairy real fast. If you want to read more, here are some relevant keywords to help you along the way:

- Parameterized post-Newtonian formalism

- Post-Newtonian expansion

- Linearized gravity.

Edited December 12, 2010 by D H

[swansont]

The short answer, as I understand it, is that the warping of spacetime happens at the speed of light, and without accelerations, it is static. So, from an inertial frame's view, the attraction of the earth to the sun doesn't rely on where the sun was eight minutes ago, because the sun had already warped the spacetime at all points along the earth's orbit. So the direction of the force is to where the sun is now, absent any accelerations. (This is the result that leads some to think that the speed of gravity is infinite).

 

When you have accelerations, the warping changes, and those are the interactions that propagate at c. This is more easily seen with two large-mass objects, because both of them will experience a noticeable acceleration, and thus feel a force toward the position of there the partner would have been, absent the acceleration; the energy loss from this is predicted to be the source of gravity waves, and the decay of a binary pulsar orbit (PSR B1913+16) has been observed to fit this prediction.

http://en.wikipedia.org/wiki/PSR_B1913%2B16

[md65536]

Whether gravitons or spacetime deformation, presumably you could eventually have the "orbiter" actually catching up to it's own "wake" at some point. My brain hurts just trying to picture that situation.

As gravity waves and light both propagate at a speed of c, you pretty much have that a mass is attracted to where another gravitational body appears to be at that moment.

 

I've tried imagining a mass catching up to it's own "wake" and I'm pretty sure that it must involve it traveling at superluminal speeds, which is impossible for good reason.

 

I think this idea is similar to something like "Imagine the orbiter catching up to its own delayed image, and seeing multiple copies of itself... can it crash into itself?" The answer is no; all three of the ideas in that sentence are impossible.

[D H]

As gravity waves and light both propagate at a speed of c, you pretty much have that a mass is attracted to where another gravitational body appears to be at that moment.

Not really. There are other effects such as frame dragging and gravomagnetism. Ignore those and you do indeed get that "mass is attracted to where another gravitational body appears to be at that moment", and you also get a system that is far worse than Newtonian mechanics. Take all of general relativity into account and you get something that is much closer to Newtonian mechanics than that simplest "lag only" gravitational model.

 

 

 

[JohnB]

md65536, yes you would need superluminal speeds for an object to catch up to its own wake. (About 6.28 times c I would think. ) My thought was more the idea of the central object reacting to when the orbiter was at the north position, while in reality the orbiter was already at the east position. Thinking of gravity as lines of force, the line would curve. So that if we considered multiple positions the lines wouldn't look like the spokes of a wheel but would look like a spiral. This would mean that the "force" in the lines travels further than the actual distance between the two objects and that the orbiter would appear further away (gravitationally speaking) than it actually is. (At this point, grey stuff is starting to dribble out my ears. )

 

DH. Sorry, it was the strawman comment that made me think that you thought I was arguing against relativity. I'm trying to get a mental picture of how it all works and having some difficulty as the above shows. I know that some physics can be counter intuitive, but I'm struggling with the overall concepts in this case.

 

From the comments of swansont and yourself it seems to me that if you view gravity as a piece of string joining the objects then the idea only holds for non relative motion, after that it breaks down. However if you view gravity as a property of spacetime, the steel ball on the rubber mat, then the deformation is always there and the "lag" ceases to apply. The gravity "funnel" always exists and is indepenent of the position of the orbiting object. Is that about it? I'll do some further reading also as this has piqued my interest.

 

So does this mean that gravitons can't exist, since they would act like "lines"? (Unless they propagate at FTL speeds?)

 

Edit to add: Gravomagnetism? I heard about this long ago as a spectrum of energy joining gravity and magnetism analagous to electromagnetism. There was supposed to be another one between electricity and gravity and a fourth using all three. I thought this idea had been dropped, or am I misunderstanding? (Again)

Edited December 13, 2010 by JohnB

[md65536]

Not really. There are other effects such as frame dragging and gravomagnetism. Ignore those and you do indeed get that "mass is attracted to where another gravitational body appears to be at that moment", and you also get a system that is far worse than Newtonian mechanics. Take all of general relativity into account and you get something that is much closer to Newtonian mechanics than that simplest "lag only" gravitational model.

Are you saying that frame-dragging etc warps space-time differently for gravity vs light? Or that light and gravity waves propagate along different geodesics or at different speeds? If so, that's something I don't understand. If you are not saying that, then I stand by what I said.

 

To use a particle metaphor, one might say that photons and gravitons from a point on the gravitational mass arrive at the same time from the same direction (their path is the same geodesic across space-time warped by any number of phenomena). The result is that the gravitational mass "feels" (according to the pull of gravity) at any moment to be exactly where it appears to be at that moment.