speed of gravity

[hellokeith]

After doing a rather exhaustive online search on the topic of gravity, gravitational waves, and the speed of gravity, I've concluded that the "speed of gravity", i.e. the time it takes for a change in a large gravity mass to influence another mass, must be significantly faster than the speed of light.

1. Calculations of planetary orbits assume an instantaneous force of gravity. For example, Mars comes to its closest point with Jupiter, there is no delay in the gravitational effects. There is some anectdotal evidence that when assuming gravitation force is delayed due to it being purportedly the speed of light, that those orbital calculations break down quickly and are woefully inaccurate. Hence why all orbital calculations which take gravity into account assume it is instantaneous, and the most accurate planetary orbit calculations are based off gravity itself with no field delay.
2. While the earth does see via visible light a sun position that is ~8 minutes old, the earth does not orbit the position where the sun was ~8 minutes ago, it orbits the actual position of the sun.
3. "But the gravitation field moves along with the sun/jupiter/other massive object, thus it is always there and updated, that's why we don't see a delay." This is essentially the same false myth about swinging around a pole that is a lightyear long and expecting the end to be going faster than the speed of light. Think about it, if the gravitational field of the sun is updated at the speed of light, Pluto which is many billions of miles away won't see that graviational field update for quite some time, and its orbit will either decay or expand. Why? Because the sun moves, and a pretty good distance in fact. So if the speed of gravity is C, then the gravitational field emanating from the massive object cannot be updated faster than that.

Hence the speed of gravity is much faster than the speed of light. I won't theorize that it is infinite/instantaneous, though quantum entanglement is supposedly instantaneous, so there could be some precendence.

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Update March 1, 2008

Space.com - "Pioneer anomaly" reers its ugly head again, defies current gravity models

NASA Baffled by Unexplained Force Acting on Space Probes
By Charles Q. Choi
Special to SPACE.com
posted: 29 February 2008

Mysteriously, five spacecraft that flew past the Earth have each displayed unexpected anomalies in their motions.

These newfound enigmas join the so-called "Pioneer anomaly" as hints that unexplained forces may appear to act on spacecraft.

A decade ago, after rigorous analyses, anomalies were seen with the identical Pioneer 10 and 11 spacecraft as they hurtled out of the solar system. Both seemed to experience a tiny but unexplained constant acceleration toward the sun.

A host of explanations have been bandied about for the Pioneer anomaly. At times these are rooted in conventional science ? perhaps leaks from the spacecraft have affected their trajectories. At times these are rooted in more speculative physics ? maybe the law of gravity itself needs to be modified.

Now Jet Propulsion Laboratory astronomer John Anderson and his colleagues ? who originally helped uncover the Pioneer anomaly ? have discovered that five spacecraft each raced either a tiny bit faster or slower than expected when they flew past the Earth en route to other parts of the solar system.

 

[CycloWizard]

I think the key is that the time scale of orbits is so large relative to the time scale of gravity propagating at the speed of light from major influencing bodies. For example, it takes the Earth 525960 minutes to orbit the sun, while it takes the sun's gravity only about 8 minutes to get to the Earth. Further, the sun's gravity has been propagating for a long time such that transient effects are no longer important.

 

[hellokeith]

the sun's gravity has been propagating for a long time such that transient effects are no longer important

:Q

Transient effects? You do realize just how massive is the sun? And that the sun is moving. It's moving around a point in the solar system, and that point is not always within its diameter. It's moving around the outside of a galaxy. And it's moving along with that galaxy away from other galaxies. The sun is never in the same position, not ever. Same with all the planets in our solar system. So explain how this magical (but only traveling at the speed of light) gravitational field knows where to move through space such that it keeps up with the very complex and fast movement of the sun?

 

[CycloWizard]

Originally posted by: hellokeith

the sun's gravity has been propagating for a long time such that transient effects are no longer important

:Q

Transient effects? You do realize just how massive is the sun? And that the sun is moving. It's moving around a point in the solar system, and that point is not always within its diameter. It's moving around the outside of a galaxy. And it's moving along with that galaxy away from other galaxies. The sun is never in the same position, not ever. Same with all the planets in our solar system. So explain how this magical (but only traveling at the speed of light) gravitational field knows where to move through space such that it keeps up with the very complex and fast movement of the sun?

Yes, I understand that. "Transient," at least to engineers, means roughly "the time it takes to reach steady state." Since the universe is never truly in a steady state, this may have been a poor choice of words on my part.

In any case, flipping back through A Brief History of Time indicates that relativity does account for some non-Newtonian effects in planet orbits (e.g. small-scale oscillations) that result from the time required for gravity to propagate. The Newtonian model, in which gravity is treated as an instantaneous effect, is still generally used because it is much simpler and gives results with accuracy that is very good for the simplicity of the math involved. In other words, allowing gravity to propagate at a finite speed (i.e. the speed of light) perfectly models the behavior of the planets, while allowing it to propagate faster does not.

 

[Nathelion]

Ah yet another "I know how/why/when we can make X travel faster than light...". These are always fun

No, gravity is not an FTL effect. In fact, if it were, it'd be fairly simple to generate a time paradox.
If the sun were to mysteriously disappear (never mind how), it would, in fact, take 8 min or so for us to notice, no matter what. The gravity field of the sun would not magically disappear. It propagates at the speed of light and generally behaves like any old wave phenomenon.

The reason the time delay is usually ignored in orbital calculations is, like cyclowizard said, because it is a very minor source of error compared to other factors, so it's generally not worth it to expend the considerable extra computing power to include time delay effects.

As to the sun moving around the galaxy and all that jazz... who cares? Your inertial reference frame can be picked arbitrarily, so why not say that all those things are moving relative to the sun? The sun does orbit a point in space that is not always inside its physical boundaries, true, and that can be accounted for in Newtonian orbital modeling. But down to very high precision, the sun is essentially going to be in the same place it was in, say, 8 minutes ago relative to the rest of the solar system. The errors introduced by ignoring gravitational time lag is simply small enough that it can be neglected.

 

[Born2bwire]

Originally posted by: hellokeith
This is essentially the same false myth about swinging around a pole that is a lightyear long and expecting the end to be going faster than the speed of light.

Most of what I was going to say has already been stated, wanted to chime in about this. This can not be a myth associated with relativistic physics because the pole would have a finite mass, requiring you to add an infinite amount of energy should you want to rotate it at a linear velocity of c. I think what you are thinking about is the projector thought experiment. Where you have a projector shining a beam of light onto a screen an incredible distance away. If a bug walks across the lens of the projector, it's velocity on the screen will be increased by a factor approximately equal to the distance between the screen and projector. So theoretically, with a large enough distance, the shadow of the bug moving across the screen can be faster than the speed of light. This is not a myth though as there is nothing conflicting with relativity with regard to this phenomenon. This is due to the fact that the velocity of the bug's shadow on the screen is a phase velocity. The phase velocity of a signal can move faster than c, but it does not convey any information. It is the group velocity, which is always equal to or less than c, that propagates information. In real life, there are many examples where this can be true, like in waveguides. The way to think about it is, yes, we can get the bug's shadow to move from point a to b faster than light, but there is nothing that we can do with the shadow at point a that can allow us to encode and send information from a to b faster than light because the shadow is being produced and manipulated back at the projector.

 

[TecHNooB]

You should write a book.

 

[silverpig]

Originally posted by: Nathelion
Ah yet another "I know how/why/when we can make X travel faster than light...". These are always fun

No, gravity is not an FTL effect. In fact, if it were, it'd be fairly simple to generate a time paradox.
If the sun were to mysteriously disappear (never mind how), it would, in fact, take 8 min or so for us to notice, no matter what. The gravity field of the sun would not magically disappear. It propagates at the speed of light and generally behaves like any old wave phenomenon.

The reason the time delay is usually ignored in orbital calculations is, like cyclowizard said, because it is a very minor source of error compared to other factors, so it's generally not worth it to expend the considerable extra computing power to include time delay effects.

As to the sun moving around the galaxy and all that jazz... who cares? Your inertial reference frame can be picked arbitrarily, so why not say that all those things are moving relative to the sun? The sun does orbit a point in space that is not always inside its physical boundaries, true, and that can be accounted for in Newtonian orbital modeling. But down to very high precision, the sun is essentially going to be in the same place it was in, say, 8 minutes ago relative to the rest of the solar system. The errors introduced by ignoring gravitational time lag is simply small enough that it can be neglected.

If the sun is being accelerated by the galaxy, it's a non-inertial reference frame...

 

[Nathelion]

No, it's in freefall.

 

[hellokeith]

Originally posted by: Born2bwire

Originally posted by: hellokeith
This is essentially the same false myth about swinging around a pole that is a lightyear long and expecting the end to be going faster than the speed of light.

This can not be a myth associated with relativistic physics because the pole would have a finite mass, requiring you to add an infinite amount of energy should you want to rotate it at a linear velocity of c. I think what you are thinking about is the projector thought experiment.. phase velocity.

I think you misunderstood me. Yes I am aware of group velocities and understand the limit of EM-based information transfer.

So I'll expound a bit..

1. Scientist says "gravity propogates at/near/less than the speed of light".
2. Sun is massive and emits a strong gravitational field.
3. Sun is moving, thus its gravitational field is also moving (changing), but those changes are propogating at/near/less than the speed of light.

What I am getting at here is that the changes in the gravitational field are not inconsequential, yet an orbital calculation of Neptune or Pluto for examle is not based on a light-time-delayed location of the sun.. it is based on the actual position of the sun. So you can't say that gravity propogates at/near/less than the speed of light and at the same time expect changes in the gravitational field to magically update faster than that.

We don't really know what gravity even is, so there is no reason to have a preconceived notion about its propogation speed. Again, quantum entanglement can be shown to operate faster than light speed and at great distances, yet it does not violate em-based information transfer limit. The same can be true of gravity. And the "famous" Jupiter/pulsar experiment a few years back did not prove anything in regards to gravity.. go read it for yourself and see if you come up with the same conclusions as the experimenters did.

 

[lousydood]

I'm not sure whether your confusion stems from a misunderstanding of inertial reference frames, or whether you simply think the (relatively) small motion of the Sun as it is tugged by planets is going to create gravitational waves with significant effect?

If you want to get into messy perturbation-of-orbits details, why not start by considering the 9-body problem? That's always fun.

 

[Born2bwire]

Originally posted by: hellokeith

Originally posted by: Born2bwire

Originally posted by: hellokeith
This is essentially the same false myth about swinging around a pole that is a lightyear long and expecting the end to be going faster than the speed of light.

This can not be a myth associated with relativistic physics because the pole would have a finite mass, requiring you to add an infinite amount of energy should you want to rotate it at a linear velocity of c. I think what you are thinking about is the projector thought experiment.. phase velocity.

I think you misunderstood me. Yes I am aware of group velocities and understand the limit of EM-based information transfer.

So I'll expound a bit..

1. Scientist says "gravity propogates at/near/less than the speed of light".
2. Sun is massive and emits a strong gravitational field.
3. Sun is moving, thus its gravitational field is also moving (changing), but those changes are propogating at/near/less than the speed of light.

What I am getting at here is that the changes in the gravitational field are not inconsequential, yet an orbital calculation of Neptune or Pluto for examle is not based on a light-time-delayed location of the sun.. it is based on the actual position of the sun. So you can't say that gravity propogates at/near/less than the speed of light and at the same time expect changes in the gravitational field to magically update faster than that.

We don't really know what gravity even is, so there is no reason to have a preconceived notion about its propogation speed. Again, quantum entanglement can be shown to operate faster than light speed and at great distances, yet it does not violate em-based information transfer limit. The same can be true of gravity. And the "famous" Jupiter/pulsar experiment a few years back did not prove anything in regards to gravity.. go read it for yourself and see if you come up with the same conclusions as the experimenters did.

The finite propagation of gravity in our solar system is largely inconsequential. Instantaneous propagation is an approximation that is made very often, like in electromagnetics. Very rarely do we bother to take into account the retardation of fields due to the finite speed of light. It can be done, like in a FDTD or Time Domain MOM simulation, but it is costly compared to steady-state time-harmonic solutions. Computational physics is not about modeling the exact phenomenon, it's about getting it close enough for government work at the fastest speed as possible. You'd be surprised at the amount of approximations and compromises that are taken in computational systems that still yield accurate results.

Quantum entanglement works at faster than light because, as you stated, it is not transfering any information. To say that gravity, a phenomenon that can certainly do so, can be instantaneous flies in the face of modern physics. We do have a good starting theory form general relativity on how gravity works and it has been shown that finite propagation general relativity does fix problems that the instantaneous Newtonian theory has.

You also mention the Jupiter experiment, but the controversy in that is not whether or not gravity has a finite speed, but the interpretation of the results. However, we do not need the Jupiter results to calculate the speed of gravity. This has already been done by observing the decay rate in pulsars. The Jupiter paper was noteworthy because they claimed that it was a direct measurement as opposed to the indirect verification from these other pulsars. Indirect measurements to verify theories is a backbone of astronomy. We can only directly measure a minute amount of the phenomenon in our universe. Instead, we have to look at our theories to decide what we expect to happen in certain situations and see if they predict the correct results. For example, one that I've stated before on this forum, we know a good deal about the Crab Nebula because of the emitted radiation. We know that it is a plasma with a static magnetic field. We know the strength of this magnetic field and its orientation by observing the power spectrums and such that we measure from the emitted radiation, all of which are derived from the theory of synchrotron radiation. We'll never be able to go out the the nebula and directly measure the fields in the plasma, but we have a very good idea of what they are from passive observations.

Steve Carlip

 

[Biftheunderstudy]

Instantaneous gravity is a newtonian view. General Relativity is a field theory and does away with static cases much like Maxwell's equations allow dynamic interactions in EM theory. In fact, in much the same way that finite propagation speed is derived in EM, finite propagation of gravity is derived in GR. That being said there are still some schools of thought which have gravity propagating at slightly less or slightly larger than c and still work. Most of this leeway is from the errors in the pulsar experiments.

Strikingly the errors in these experiments are the smallest in astronomy, ie. we know their masses to something like 5 decimal places. These experiments have indirectly proven the existence of gravity waves and almost all the GR predictions you can make about a binary system. So given a finite propagation of gravity, it still has to be close to c, nowhere near instantaneous.

 

[Gannon]

"yet it does not violate em-based information transfer limit. "

What exactly is the "limit of information transfer" based on? where can I read up on this? anyone?

 

[Braznor]

Isn't the wave function collapse instantaneous?

 

[CycloWizard]

Originally posted by: hellokeith
I think you misunderstood me. Yes I am aware of group velocities and understand the limit of EM-based information transfer.

So I'll expound a bit..

1. Scientist says "gravity propogates at/near/less than the speed of light".
2. Sun is massive and emits a strong gravitational field.
3. Sun is moving, thus its gravitational field is also moving (changing), but those changes are propogating at/near/less than the speed of light.

What I am getting at here is that the changes in the gravitational field are not inconsequential, yet an orbital calculation of Neptune or Pluto for examle is not based on a light-time-delayed location of the sun.. it is based on the actual position of the sun. So you can't say that gravity propogates at/near/less than the speed of light and at the same time expect changes in the gravitational field to magically update faster than that.

We don't really know what gravity even is, so there is no reason to have a preconceived notion about its propogation speed. Again, quantum entanglement can be shown to operate faster than light speed and at great distances, yet it does not violate em-based information transfer limit. The same can be true of gravity. And the "famous" Jupiter/pulsar experiment a few years back did not prove anything in regards to gravity.. go read it for yourself and see if you come up with the same conclusions as the experimenters did.

As I tried to explain before, experiments have confirmed that gravity propagates at the speed of light. This is why relativity is a superior theory to Newton's theory of universal gravitation - by accounting for the finite propagation time of gravity, it perfectly models the motion of the planets, whereas the Newtonian formulation has some small errors.

edit: This is actually covered very clearly in chapter 1 or 2 of A Brief History of Time. It's a little long for me to quote here, but it's only a page or two if you have access to the book.

 

[Braznor]

Originally posted by: CycloWizard

Originally posted by: hellokeith
I think you misunderstood me. Yes I am aware of group velocities and understand the limit of EM-based information transfer.

So I'll expound a bit..

1. Scientist says "gravity propogates at/near/less than the speed of light".
2. Sun is massive and emits a strong gravitational field.
3. Sun is moving, thus its gravitational field is also moving (changing), but those changes are propogating at/near/less than the speed of light.

What I am getting at here is that the changes in the gravitational field are not inconsequential, yet an orbital calculation of Neptune or Pluto for examle is not based on a light-time-delayed location of the sun.. it is based on the actual position of the sun. So you can't say that gravity propogates at/near/less than the speed of light and at the same time expect changes in the gravitational field to magically update faster than that.

We don't really know what gravity even is, so there is no reason to have a preconceived notion about its propogation speed. Again, quantum entanglement can be shown to operate faster than light speed and at great distances, yet it does not violate em-based information transfer limit. The same can be true of gravity. And the "famous" Jupiter/pulsar experiment a few years back did not prove anything in regards to gravity.. go read it for yourself and see if you come up with the same conclusions as the experimenters did.

As I tried to explain before, experiments have confirmed that gravity propagates at the speed of light. This is why relativity is a superior theory to Newton's theory of universal gravitation - by accounting for the finite propagation time of gravity, it perfectly models the motion of the planets, whereas the Newtonian formulation has some small errors.

edit: This is actually covered very clearly in chapter 1 or 2 of A Brief History of Time. It's a little long for me to quote here, but it's only a page or two if you have access to the book.

Wouldn't infinite gravity speed cause the universe to collapse? Wouldn't it be a detriment to the expansion of the universe?

 

[firewolfsm]

DON'T FORGET

If the sun was merely a spinning, symmetrical entity not moving in space, it wouldn't even gravitate (conservation of momentum.) And that it's because of it's movement that the planets follow it.

 

[silverpig]

Originally posted by: firewolfsm
DON'T FORGET

If the sun was merely a spinning, symmetrical entity not moving in space, it wouldn't even gravitate (conservation of momentum.) And that it's because of it's movement that the planets follow it.

huh?

It has mass, it gravitates.

 

[firewolfsm]

Something has to have velocity for it to gravitate.

 

[CycloWizard]

Originally posted by: Braznor
Wouldn't infinite gravity speed cause the universe to collapse? Wouldn't it be a detriment to the expansion of the universe?

Probably, but before Einstein, no one had even considered that possibility. The universe was seen as unchanging and essentially static. Einstein, besides being brilliant, also had the fortune of living at the time when very specific astronomical observations were being made that were the first "proofs" of his theories.

 

[CycloWizard]

Originally posted by: firewolfsm
Something has to have velocity for it to gravitate.

No, it doesn't. In fact, gravity has nothing to do with velocity at all. Even if you were right, every object has a velocity relative to another object.

 

[Born2bwire]

Originally posted by: firewolfsm
Something has to have velocity for it to gravitate.

What? No.

 

[firewolfsm]

In general terms, gravitational waves are radiated by objects whose motion involves acceleration, provided that the motion is not perfectly spherically symmetric (like a spinning, expanding or contracting sphere) or cylindrically symmetric (like a spinning disk).

A simple example is the spinning dumbbell. Set upon one end, so that one side of the dumbell is on the ground and the other end is pointing up, the dumbbell will not radiate when it spins around its vertical axis but will radiate if it tumbles end-over-end. The heavier the dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. If we imagine an extreme case in which the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off.

Some more detailed examples:

* Two objects orbiting each other in a quasi-Keplerian planar orbit (basically, as a planet would orbit the Sun) will radiate.
* A spinning non-axisymmetric planetoid ? say with a large bump or dimple on the equator ? will radiate.
* A supernova will radiate except in the unlikely event that it is perfectly symmetric.
* An isolated non-spinning solid object moving at a constant speed will not radiate. This can be regarded as a consequence of the principle of conservation of linear momentum.
* A spinning disk will not radiate. This can be regarded as a consequence of the principle of conservation of angular momentum. On the other hand, this system will show gravitomagnetic effects.
* A spherically pulsating spherical star (non-zero monopole moment or mass, but zero quadrupole moment) will not radiate, in agreement with Birkhoff's theorem.

More technically, the second time derivative of the quadrupole moment (or the l-th time derivative of the l-th multipole moment) of an isolated system's stress-energy tensor must be nonzero in order for it to emit gravitational radiation. This is analogous to the changing dipole moment of charge or current necessary for electromagnetic radiation.

 

[Biftheunderstudy]

Gravitational waves are different than plain ol' gravitation. Gravity waves are to gravity what EM radiation is to Electric and Magnetic fields. Its the oscillation thats different, but you did say something that is at least partially correct, a spherically symmetric object will not produce gravitational waves. However its not the velocity component that really produces them, a rotating sphere has velocity but no gravitational radiation.

The property that defines gravitational radiation is what is called a mass quadrupole moment which is like the 3rd time derivative of the moment of inertia with some other factors. In EM theory the first thing which can produce an EM wave is a dipole moment, in GR its a quadrupole moment.

That all being said, gravitational radiation can play a role in deriving the finite propagation speed of gravity in much the same way as deriving the wave equation in EM theory sets the propagation speed of light (its just the 1/sqrt(epsilon*mu in free space). If you work it out in GR(its a bit more tricky and I've selectively forgotten how to do it) you get c for the speed of gravity. Instead of the wave equation you have to use tensors and the d'Alembertian or Box as its called.