How Fast Does Gravity Travel?

[Les Sleeth]

At another science forum site someone asked about the speed of gravity. I posted a link to a news article about Kopeikin's experiment and published results: http://www.nrao.edu/pr/2003/gravity/

Some excerpts are:

“’We have determined that gravity's propagation speed is equal to the speed of light within an accuracy of 20 percent,’ said Ed Fomalont, an astronomer at the National Radio Astronomy Observatory (NRAO) in Charlottesville, VA. The scientists used the National Science Foundation's Very Long Baseline Array (VLBA), a continent-wide radio-telescope system, along with the 100-meter radio telescope in Effelsberg, Germany, to make an extremely precise observation when the planet Jupiter passed nearly in front of a bright quasar on September 8, 2002.

“The observation recorded a very slight ‘bending’ of the radio waves coming from the background quasar by the gravitational effect of Jupiter. The bending resulted in a small change in the quasar's apparent position in the sky.

“‘Because Jupiter is moving around the Sun, the precise amount of the bending depends slightly on the speed at which gravity propagates from Jupiter,’ Kopeikin said.

“‘Our main goal was to rule out an infinite speed for gravity, and we did even better. We now know that the speed of gravity is probably equal to the speed of light, and we can confidently exclude any speed for gravity that is over twice that of light,’ Fomalont said.”

I’d thought this was all but accepted by scientists, until another member there posted this link to a paper rebutting Kopeikin's results: http://www.metaresearch.org/media%20and%20links/press/SOG-Kopeikin.asp

Here are some relevant quotes from that paper:

“Abstract. New findings were announced on 2003/01/08 by S. Kopeikin, claiming to have measured the ‘speed of gravity’ and finding it essentially equal to the speed of light. These findings are invalid by both experimental and theoretical standards because the quantity measured was already known to propagate at the speed of light. The hyped claims therefore do a disservice to science in general and the advancement of physics in particular because the announced findings do not represent the meaning of the actual experimental results and cannot possibly represent the physical quantity heretofore called ‘the speed of gravity,’ which has already been proved by six experiments to propagate much faster than light, perhaps billions of times faster. Several mainstream relativists have also stated their disagreement that the experiment really measured what it claimed to measure.

“Kopeikin's latest paper on the internet, giving the basis for his findings announced at the AAS meeting, contains some egregious errors. The following claims appear therein: ‘… a moving gravitating body deflects light not instantaneously but with retardation caused by the finite speed of gravity propagating from the body to the light ray. … We calculated this correction for Jupiter by making use of the post-Minkowskian approximation based on the retarded Lienard-Wiechert solutions of the Einstein equations. … Speed of gravity cg must enter the left side of the Einstein equations (2) … This will lead to the wave operator depending explicitly on the speed of gravity cg.’

“None of these statements is correct even in GR, provided only that ‘the speed of gravity’ retains its classical meaning for the past two centuries of force propagation speed. The Einstein equations require the potential field of all bodies to act from the body's instantaneous direction, not its retarded direction, because they set propagation delay for the gradient to zero. But Kopeikin adopts the Sun acting from its instantaneous position and Jupiter acting from its retarded position, which is inconsistent. In fact, although the Sun moves 1000 times more slowly than Jupiter, it is 1000 times more massive, making any hypothetical retardation effects comparably important. The Lienard-Wiechert equations consider retardation in mutual distance, but not in direction – the latter being a much larger effect of propagation delay. And the parameter on the left side of the Einstein equations is c2, and therefore has nothing to do with the speed of gravity, as we noted above. This does not prevent Kopeikin from calling it ‘cg’ and solving for this parameter as if it were the speed of gravity, which is what he has done.”

I have a few questions. Is there general agreement now that Kopeikin’s team failed to measure the speed of gravity? Is it generally agreed that the speed of gravitational force is virtually instantaneous? In the article above they cited the following thought experiment which seems to make sense:

“A common thought experiment asks: ‘What would happen to the Earth's orbit if the Sun suddenly ceased to exist?’ The answer is now clear. The usual relationship ‘force is the gradient of the potential’ would instantly end. The Sun's potential field would then begin to dissipate, taking 8.3 minutes to dissipate out to the distance of the Earth's orbit; so effects such as light-bending and clock-slowing would persist for that long. But the Newtonian component of gravitational force, the force that keeps Earth in its orbit, would cease almost instantly, and Earth would fly off along a straight line like a weight on a spinning merry-go-round that broke free from its moorings.”

Mainly I wanted to ask this. If the speed of gravity is virtually instantaneous, what are people’s thoughts about what gravity is doing to space that would cause that? For example, would it be improper to see mass as having a “constricting effect” on space?

In that case, the constricting effect would simultaneously affect every place the force extends, and then disappear concurrently everywhere if, as in the example above, the Sun suddenly ceased to exists.

 

[Integral]

I do not think that there is a lot of controversy about the speed of gravity. It is pretty well accepted that it is c, we just need to find a way to measure it. There was some controversy around the paper you mention, due to the claims of finally having found a way to measure the speed of gravity. Critical analysis later found errors in the methods, which invalidated the results. We remain without experimental verification of the theory.

 

[jcsd]

Assuming GR is correct or at the very least it gives a near-perfect model for a very wide variety of situations then gravity propagates at c, few scientists would disgaree with these assumptions much less relativsts.

Howver this is specifically the propagtion speed of gravity thta is being talked about is the propagation speed and the article plays semantic games with this and it also seems to make claims that are at the very least contraversial, it doesn't seem to be a greta source of information. However it is right in one respect as from what I see most people agree that Kopeikin's results don't match his conclusion and thta he was not in actuality measuring the speed of gravity.

 

[Rob Woodside]

A plague on both their houses. Integal is right.

 

[pervect]

A common thought experiment asks: ‘What would happen to the Earth's orbit if the Sun suddenly ceased to exist?’ The answer is now clear.

The answer to this old chestnut is in the sci.physics.faq. Let me know if you need the link, I suspect you or anyone else who is interested can find it if they look around (but if you can't find it, I'll post the link). The very easy answer is that the sun cannot cease to exist, this violates some important conservation laws.

What one _can_ do, in principle at least, is to blow up the sun. To avoid getting the Earth caught in the explosion, it's convenient to imagine splitting the sun into two parts, one goes "up", the other goes "down". If one does this it will take 8 minues for the disturbance in gravity to propagate to the Earth.

This is quite comparable to electromagnetism. One might ask the question "What happens to the electric field at some distant point if one makes a charge disappear". The answer is the same, the conservation of charge means that one cannot make a charge disappear, or create charges - the best one can do is to create a dipole by separating a postive and negative charge. Gravity is very similar, though since the masses have the same sign, one actually creates a quadropole moment by separating them.

 

[Les Sleeth]

I do not think that there is a lot of controversy about the speed of gravity. It is pretty well accepted that it is c, we just need to find a way to measure it. There was some controversy around the paper you mention, due to the claims of finally having found a way to measure the speed of gravity. Critical analysis later found errors in the methods, which invalidated the results. We remain without experimental verification of the theory.

I am really curious about this, so I hope you'll indulge me a bit more. I don't know if you read the entire paper rebutting Kopeikin's results, but what did you think of these so-called experiements:

By contrast, gravitational forces are large, readily detected, and control the dynamics of most of the visible universe. Gravimeters easily detect the gravitational force from, and motion of, a person entering a room, for example. The propagation speed of gravitational force is bounded by six experiments to be much faster than the speed of light [[5]]. For example:

1**** In 1825, Laplace determined that the minimum speed of gravity consistent with observations was at least 10 million times the speed of light, c.

2**** Modern, high-precision solar system observations show that the direction from which the Sun's light comes, and the direction toward which the Sun's gravity pulls us, are not the same. The former is retarded by the time it takes light to travel from Sun to Earth, 8.3 minutes; and the latter is not retarded by any detectible amount.

3**** Eclipses of the Sun by the Moon occur about 40 seconds before the time of the Sun's maximum gravitational pull on the Moon. The delay indicates that light and gravity do not have the same propagation speed.

4**** A 1997 laboratory experiment by Walker & Dual showed that gravitational signals propagated much faster than light signals.

5**** Binary pulsars (with large masses and speeds) show that the speed of gravity must be at least 20 billion times the speed of light.*

*********** In classical Newtonian gravitation, that propagation speed is infinite [[6]]. But instead of getting closer to GR if propagation in Newtonian gravity is reduced to the speed of light, the gravitational model disintegrates and fails to represent reality in a gross way. Nature insists that gravitational forces must propagate without any delays nearly as large as light-speed delays.*

Are these "experiments considered relevant?

However this is specifically the propagtion speed of gravity that is being talked about is the propagation speed and the article plays semantic games with this and it also seems to make claims that are at the very least contraversial,

I am confused a bit (a lot probably). Can you explain why you see critique of Kopeikin's work as semantics? Does the speed of gravity refer to what happens in a gravitational field, or does it refer to the force of gravity? In that thought experiment where the Sun disappears suddenly, will it take 8.3 minutes for Earth to feel the loss of the Sun's gravitational attraction, or will that happen almost instantly?

As an aside, one of the posters at that other site asked "I would like to know how you account for the fact that the instantaneous position of target bodies are required for any successful orbital insertion?" Do you see how that relevant to this argument?

 

[jcsd]

I am confused a bit (a lot probably). Can you explain why you see critique of Kopeikin's work as semantics? Does the speed of gravity refer to what happens in a gravitational field, or does it refer to the force of gravity? In that thought experiment where the Sun disappears suddenly, will it take 8.3 minutes for Earth to feel the loss of the Sun's gravitational attraction, or will that happen almost instantly?

As an aside, one of the posters at that other site asked "I would like to know how you account for the fact that the instantaneous position of target bodies are required for any successful orbital insertion?" Do you see how that relevant to this argument?

What I mean by semantics is thatbin some infact most parts they are clearly not talking about the propagation speed of gravity, infact they seem to be talking about (quasi-)static gravitational fields (as there's no gravity waves propagting in these fields not very relevant) and certain irrelvant limitations placed on theories of gravity by observations.

 

[jcsd]

Sorry I missed this bit out.

As an aside, one of the posters at that other site asked "I would like to know how you account for the fact that the instantaneous position of target bodies are required for any successful orbital insertion?" Do you see how that relevant to this argument?

No it's not really relavnt as we're talking about th espeed of propagtion of gravity, i.e. the speed at which changes in the garvutional field propagate.

 

[Les Sleeth]

. . . we're talking about the speed of propagation of gravity, i.e. the speed at which changes in the gravitational field propagate.

Three more quick questions for you.

So, it is true then that Kopeikin's interpretation about the meaning of the speed of gravity is correct regardless of whether his experiment demonstrated it's nearness to c, is that correct?

If so, can you answer my question of how long it would take for Earth to feel the gravitational effects of the Sun suddenly disappearing. Is it the time it takes for light to travel from the Sun to Earth?

Finally, is the problem here the source of the critique of Kopeikin's study? It is Meta Research and Tom Van Flandern. Is this just another TD guy with another theory?

 

[ohwilleke]

If so, can you answer my question of how long it would take for Earth to feel the gravitational effects of the Sun suddenly disappearing. Is it the time it takes for light to travel from the Sun to Earth?

I have to agree that I have doubts that this is a meaningful question.

1. In GR gravity is a function of mass-energy density.
2. Mass-energy is conserved.
3. Therefore, the only way the a gravitation field from a particular localized clump of mass-energy, say, the sun, can change over time is for the displacement of the mass-energy to change.
4. The mass-energy itself is subject to limiting its changes in displacement to something less than c as a result of SR.

Thus, this places some hard limits on the extent to which gravitational energy can change.

I suppose that the ideal kind of thought experiment you'd like to have is similar to the experience of an observer seeing lightning before hearing thunder. If gravity propogates faster than light, than you would as an observe, feel a tug of gravity for the distant event before you had visual evidence of it. For example, suppose that a star ejected a highly massive clump of matter straight towards you (it may emit another in the opposite direction). You would suddenly feel a strong raviational pull towards the emitting star before seeing any evidence of its emission.

Alternately, you could have two space ships with precise measurments of their own locations. They go a long way from each other and agree in advance that one will move in a particular direction at a particular local time. Suppose that the ships are also emitting radio waves at each other. You should see a discrepency.

I'd imagine that the uncertainies involved in such precise detection of subtle events would make it very hard to estimate.

 

[pervect]

Does the speed of gravity refer to what happens in a gravitational field, or does it refer to the force of gravity? In that thought experiment where the Sun disappears suddenly, will it take 8.3 minutes for Earth to feel the loss of the Sun's gravitational attraction, or will that happen almost instantly?

As an aside, one of the posters at that other site asked "I would like to know how you account for the fact that the instantaneous position of target bodies are required for any successful orbital insertion?" Do you see how that relevant to this argument?

The speed of gravity is usually interpred exactly in the same way that the speed of light is - the electric field of a charge spreads out to infinity (well, that's an idealization, actually), but when you wiggle it, changes in the field propagate at a certain speed - that speed is 'c', the "speed of light". If you "wiggle" a mass, the gravitational field may propagate out to infinity, but changes in the field as a result of the wiggling are expected to propagate at 'c'. Because gravity is such a weak force, nobody has been able to experimentally measure gravity waves (the anology to electromagnetic radiation) yet, much less measure their speed.

The fact that the field of a uniformly moving charge always points towards the current position of the charge, not the retarded position, doesn't have anything meaningful to say about the speed at which light travels - nor does it have anything meaningful to say about the speed at which gravity travels.

We don't go around saying that the speed of light is faster than the speed of light because the electric field points towards the current position of the charge - neither should we say that the speed of gravity is faste than the speed of light because the gravitational field points (approximately, at low velocities) towards the current position of the mass.

You really should read the sci.physics.faq, it explains this nicely.

It also mentions that because you can't destroy charge (nor mass), you can't answer the question "what would happen if mass/charge were suddenly to disappear". The best answer is that neither one can disappear, they are conserved quantities.

 

[Les Sleeth]

You really should read the sci.physics.faq, it explains this nicely.

It also mentions that because you can't destroy charge (nor mass), you can't answer the question "what would happen if mass/charge were suddenly to disappear". The best answer is that neither one can disappear, they are conserved quantities.

Thanks, I most definitely will read it.

I don't think I see too clearly why the hypothetical question can't be considered however. I suspect I listened too much to that second article I referenced, but I could see there might be a difference between effects within the field, and how quickly gravity would disappear if its source went absent. It seems like one concept says, "this is how fast gravity moves EM through it," and the other concept says "this is how fast gravity would disappear if its source were no longer there."

Is this a meaningless distinction?

 

[Chronos]

.. is the problem here the source of the critique of Kopeikin's study? It is Meta Research and Tom Van Flandern. Is this just another TD guy with another theory?

Tom Van Flandern is among the most famous pottery magicians on the net. He proposes instaneous propogation of gravity and claims the gps system uses no relativistic corrections [which is totally wrong]. Kopeikin's conclusions have, however, been challenged by a number of other credible sources. Here is a more recent paper by a fairly well respected authority
http://arxiv.org/abs/gr-qc/0403060

 

[Les Sleeth]

Tom Van Flandern is among the most famous pottery magicians on the net. He proposes instaneous propogation of gravity and claims the gps system uses no relativistic corrections [which is totally wrong]. Kopeikin's conclusions have, however, been challenged by a number of other credible sources. Here is a more recent paper by a fairly well respected authority
http://arxiv.org/abs/gr-qc/0403060

Thanks Chronos, and everyone else. I think I see it. Geez, it's just more evidence that something making sense doesn't make it true. No wonder everyone is so conservative about considering new theories.

 

[CeeAnne]

Birkhoff's Theory also says that gravity waves propagate at the speed of light. If the Sun suddenly disappeared, Earth would continue to orbit for another 8 minutes. That's a neat idea ... one by one, starting with Mercury, the planets would head off at a tangent ... and we couldn't know it was happening by observation of Mercury and Venus ... by the time the light from them reached Earth, so would the lack of gravity and sunlight. But the Moon would continue to orbit Earth ... that is truly weird.

 

[Andrew Mason]

I do not think that there is a lot of controversy about the speed of gravity. It is pretty well accepted that it is c, we just need to find a way to measure it. There was some controversy around the paper you mention, due to the claims of finally having found a way to measure the speed of gravity. Critical analysis later found errors in the methods, which invalidated the results. We remain without experimental verification of the theory.

I may be showing a lack of appreciation for some of the subtlties of General Relativity, but if gravity is the property of all matter and energy, how can gravity travel any faster than matter and energy travel?

Why does it have to really move at all? Matter changing into energy and vice versa should have absolutely no effect on the total gravitational field.

So why do we have to invent a theory of the graviton and the speed at which it is supposed to move? No one has ever detected a graviton despite serious attempts for over 30 years. Perhaps there is a reason for that.

AM

 

[Nereid]

There was PF another thread on a similar topic recently Les, here (it also contains a link to sci.physics.faq does gravity travel at the speed of light).

To take an 'experimental' look at this. First, LIGO, and other gravitational wave detectors, are starting to come online (there's a link on the LIGO page to Einstein@Home, where you can contribute spare CPU cycles on your PC to help make the detection!) and hopes are high that an 'inspiral event' (e.g. two neutron stars orbiting every closer until they merge/collide), or an asymmetric supernova will be 'seen' in the next few years. If either event also generates 'observable' EM (e.g. light, radio, gammas), or even neutrinos, we will also have some solid results on the 'speed' of gravity. AFAIK, Kopeikin's is the only half-way credible observation of the speed of gravity so far, and as Chronos pointed out, he got his sums wrong.

Second, observations of some neutron star binaries (with at least one member a pulsar) show decaying orbits. The rates of decay very nicely match the hypothesis that energy is being lost from the systems in the form of gravitational radiation, as predicted by GR (some hard working scientists got Nobels for this). Since gravity travels at c in GR, these results provide indirect support for GR and the speed of gravity being c (this is explained in more detail in the Baez page).

Third, and most generally, GR has passed all its obsevational and experimental tests to date - including one which would have shown a deviation if GR were out by as little as 1 part in 20,000. While these tests have only probed GR in a limited range of domains (astonishing as that might seem - the tests go right up to the whole universe, size-wise), one can say that there is no experimental or observational evidence, direct or indirect, that even hints at the speed of gravity being anything other than c.

 

[Nereid]

So why do we have to invent a theory of the graviton and the speed at which it is supposed to move? No one has ever detected a graviton despite serious attempts for over 30 years. Perhaps there is a reason for that.

Andrew, that same thread I mentioned in my previous post also discussed the graviton, cf gravitational radiation. As mentioned in that thread, the graviton is not a key part of GR (indeed, you could argue it isn't in GR at all); what GR does predict is gravitational radiation (aka 'waves'), and there's very good observational results - albeit indirect - for that!

 

[Andrew Mason]

Andrew, that same thread I mentioned in my previous post also discussed the graviton, cf gravitational radiation. As mentioned in that thread, the graviton is not a key part of GR (indeed, you could argue it isn't in GR at all); what GR does predict is gravitational radiation (aka 'waves'), and there's very good observational results - albeit indirect - for that!

What I don't get, and I don't pretend to grasp the mathematics of GR, is how mass can be created or destroyed. It can be converted into energy but the energy has the same relativistic mass. Is total gravity not the same? I can see that the gravitational field at a distance to change with time. But that change should not occur any more rapidly than the change of position of the mass which produced the gravitational field.

AM

 

[jcsd]

What I don't get, and I don't pretend to grasp the mathematics of GR, is how mass can be created or destroyed. It can be converted into energy but the energy has the same relativistic mass. Is total gravity not the same? I can see that the gravitational field at a distance to change with time. But that change should not occur any more rapidly than the change of position of the mass which produced the gravitational field.

AM

The speed at which the arrangement of matter changes will affect the properties of the wave e.g. it's wavelength, but they don't affect the speed at which the wave will propagate. Think of an osciallting charge, the speed at which it oscillates affects the frequency of the em wave produced, but it doesn't affect the speed at which that wave propagates.

 

[Les Sleeth]

Second, observations of some neutron star binaries (with at least one member a pulsar) show decaying orbits. The rates of decay very nicely match the hypothesis that energy is being lost from the systems in the form of gravitational radiation, as predicted by GR (some hard working scientists got Nobels for this). Since gravity travels at c in GR, these results provide indirect support for GR and the speed of gravity being c (this is explained in more detail in the Baez page).

Thanks Nereid for your great explanation. I think my next questions are naive, but I didn't find the answers from your links or Googling.

Besides acceleration, is any of reason those orbits are decaying, and theoretically emitting gravitational radiation, because the loss of mass from EM radiation? Also, is gravitational radiation predicted to just keep zipping along to the ends of the universe?

Finally, does gravitational radiation have any effects on things? If I were floating out in space and were sensitive enough to feel gravitational radiation, would I feel force? Is gravitational radiation believed to be contributing to the expansion of the universe in anyway?

 

[Andrew Mason]

The speed at which the arrangement of matter changes will affect the properties of the wave e.g. it's wavelength, but they don't affect the speed at which the wave will propagate. Think of an osciallting charge, the speed at which it oscillates affects the frequency of the em wave produced, but it doesn't affect the speed at which that wave propagates.

I don't see why changes in the arrangement of matter have to result in gravity radiating anything, and in particular radiating energy. If all motion is relative, one cannot distinguish between a moving mass (which according to your suggestion radiates gravitational waves) and a stationary mass. So how do you tell when a 'moving' mass should radiate gravitational waves and a 'stationary' one not?

If gravitation creates gravitational waves, there would almost have to be a kind of 'magnetic' form of it for moving masses to provide the necessary symmetry between moving and non-moving masses, much like for the electric field for charges.

AM

 

[jcsd]

I don't see why changes in the arrangement of matter have to result in gravity radiating anything, and in particular radiating energy. If all motion is relative, one cannot distinguish between a moving mass (which according to your suggestion radiates gravitational waves) and a stationary mass. So how do you tell when a 'moving' mass should radiate gravitational waves and a 'stationary' one not?

Changes in arrnagemnts of matter needn't result in graviational waves, but they can do. One can distinguish between the situations which produce gravity waves and those that don't, solution where no gravitational wvaes appear are called static solutions.

If gravitation creates gravitational waves, there would almost have to be a kind of 'magnetic' form of it for moving masses to provide the necessary symmetry between moving and non-moving masses, much like for the electric field for charges.

There is quite a good analogy between gravtiational waves and electromagnetic waves, but it is not an exact analogy so don't expect it to be exactly the same in all ways. Though gravity does conincendentially have soemthing comparable to magnetism in electromagnetism.

 

[yogi]

Andrew Mason - Wheeler gives a simple explanation why Einstein deduced that gravitational waves are required - it has to do with the time difference between the forces that would result when masses are moving away from each other and when they were moving toward each other - there would be an energy difference because of the finite propagation time of the forces - and consequently this must be accounted for by some form of radiation. (Wheeler - A Journey Into Gravity and Spacetime, at page 187) Two masses in motion have to do more work on their outbound journey than they recover on their inbound journey). Einstein vacillated for a while as to whether gravity waves actually existed - and finally concluded that they are required to account for the energy differences.

Of course, if the field acts instantly, there will be no gravitational waves.

As an aside - If the electric potential of a moving charge is centered on the present position of the charge rather than the retarded position, what experiments verify that electric and magnetic fields as force producing effects (as opposed to electromagnetic radiation - which is governed by wave dynamics) propagate at c?

 

[tribdog]

Maybe a year ago there was an article in Discover about some new theory that gravity might get weaker and weaker between objects as they move away from each other, but could get stronger after a certain distance. It sounds like someone who just doesn't like the accelerating expansion of the Universe and is trying to find a cure, but it made it into Discover. Have you heard anything about this?

 

[ohwilleke]

Maybe a year ago there was an article in Discover about some new theory that gravity might get weaker and weaker between objects as they move away from each other, but could get stronger after a certain distance. It sounds like someone who just doesn't like the accelerating expansion of the Universe and is trying to find a cure, but it made it into Discover. Have you heard anything about this?

Nope. That is not what he is trying to do. That guy is M. Milgrom, and his theory, MOND, is viewed, even by those who disagree that it has the correct mechanism for its result, as phenomenologially sound (i.e. it correctly predicts the way nature really acts under a wide, although not necessarily infinite, range of circumstances). (The article is "Nailing Down Gravity", Discover Vol. 24 No. 10 pp. 34-41 (October 2003) by Tim Folger).
More accurately, it predicts that after the accelleration due to gravity reaches a critical point (called a0), that gravity thenceforth declines as 1/R rather than 1/R^2 which Newtonian theory predictions.

The mainstream interpretation of the phenomena is that dark matter provides increased gravitational effects at the fringes of large, spread out galaxies. But, across a wide range of galaxies (e.g. spiral, elliptical, high surface brightness, low surface brightness, dwarf), a MOND theory produces results that match observation closely to predict galactic dyanmics from luminous objects with essentially no room to fudge with fine tuning factors. MOND also reproduces from first principals the Tully-Fisher relation, another well established phenomenological law.

His theory, since that article, has been expanded into a relativistic version of Bekenstein this summer (in this article: http://arxiv.org/abs/astro-ph/0403694), which accurately reproduces galactic scale lensing and eliminates many of the theoretical issues (conservation law violations, etc. in the less sophisticated versions of the theory) from this approach. Bekenstein's formula incorporates a cosmological constant, just as GR theorists like to under consensus dark energy models. J. Mannheim and Moffat have proposed different gravity modifications with similar phenomenological results.

MOND predictions for cosmic background radiation are substantially similar to those of cold dark matter.

MOND applications to cosmology are limited, because it is a theory designed to deal with data which some used to imply dark matter, where the observations are largely at the galactic level, rather than dark energy which is behind cosmic accelleration and which operates at a much larger scale. Generally speaking, however, the cosmological implications of MOND are not terribly different at a superficial glance from mainstream views. Still, this is a matter that has not been well digested so to speak. Not a lot of people have taken a close look at the issue and most have done so sufficiently recently that no one else has had much of a change to analyze it. The most recent article I've seen on various forms of modified gravity and cosmology is this one from December 2004: http://arxiv.org/PS_cache/hep-th/pdf/0412/0412030.pdf

Click on prior posts by me and in them you'll find links to some of the journal articles on point.

 

[Nereid]

For those unfamiliar with MOND, http://www.astro.umd.edu/~ssm/mond/ provides a whole lot of material. Like all sites which promote a particular viewpoint, you need to take what's presented there with a grain of salt (e.g. the entries in the 'league table' have been selected to highlight MOND's strengths vs the mainstream, and downplay its weaknesses) - not that there's anything deliberately false, but that the emphasis is quite intentional.

AFAIK, MOND's main weakness is with the multi-spectral observations of rich clusters - virial theorem applied to galaxy motions (from optical results) combined with X-ray data on gas temperatures and pressures combined with lensing data and now (still limited) microwave data on the SZ effect.

 

[Andrew Mason]

As an aside - If the electric potential of a moving charge is centered on the present position of the charge rather than the retarded position, what experiments verify that electric and magnetic fields as force producing effects (as opposed to electromagnetic radiation - which is governed by wave dynamics) propagate at c?

Perhaps I am misunderstanding your question, but if a "force producing effect" were to propagate, energy would be transferred. Since that does not happen for a charge in uniform relative motion, I don't see how an experiment could verify this for a uniformly moving electric charge.

AM

 

[pervect]

Perhaps I am misunderstanding your question, but if a "force producing effect" were to propagate, energy would be transferred. Since that does not happen for a charge in uniform relative motion, I don't see how an experiment could verify this for a uniformly moving electric charge.

AM

The logical experiment is to accelerate the charge and look at what happens to the force on the distant charge. Does it change right away, or does it take awhile?

The force on the distant charge is, of course, just the value of the electric field if the second charge is stationary.

Thus one need only ask - what happens to the electric field when one accelerates a charge?

The calculations can be carried out from Maxwell's equations. The result of these calculations show that wiggling (acacelerating) the charge produces changes in the field that propagate at 'c'. The emission of electromagnetic radiation is part of the process that keeps Maxwell's equations satisfied.

Working out the details is tricky, but the results can be seen from applets like the one below

http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

Thus light really does move at the speed of light, and changes in the electromagnetic field also have the same "speed limit".

 

[Andrew Mason]

The logical experiment is to accelerate the charge and look at what happens to the force on the distant charge. Does it change right away, or does it take awhile?

The force on the distant charge is, of course, just the value of the electric field if the second charge is stationary.

Thus one need only ask - what happens to the electric field when one accelerates a charge?

I don't think it is just a matter of accelerating the charge. It has to be an acceleration that results from an electromagnetic interaction with the charge.

A good example is the EM interaction between an electron and a bending or jiggling magnet in a synchrotron. The electro-magnetic force on the moving electron that is provided by the bending or jiggling magnets in the rest frame of the laboratory would appear to the electron (ie in the moving electron's frame of reference) as a moving field with electric and magnetic components. It would interact with the electric component only. (This has to be the case because in the electron's 'stationary' reference frame, the electron has no magnetic field for the magnet to interact with).

As soon as the electron motion changes due to the electrical interaction, the observer in the original electron frame perceives a magnetic field around the electron. It also perceives a change in the direction of the electric field of the electron, which has moved away from the observer. As the electron continues changing direction, the direction of the magnetic field that such an observer perceives continually changes, as does its electric field. These changes occur in all directions. The process continues as the electron deflects. The 'effect' of all this is that an electromagnetic wave propagates from the charge in all directions.

Maxwell's equations predict that the speed of such wave is $1/\sqrt{\epsilon_0 \mu_0}$. (Due to time dilation and length contraction, however, the direction of that radiation is almost entirely in the original direction of the electron's motion in the laboratory frame, where the electron's speed is very close to c).

Working out the details is tricky, but the results can be seen from applets like the one below http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

Thus light really does move at the speed of light, and changes in the electromagnetic field also have the same "speed limit".

What this applet does not show, is the electrical interaction that must be present in order to cause the electron's change in motion. It cannot simply change its motion like this without another electric field interacting with it.

AM

 

[ZapperZ]

A good example is the EM interaction between an electron and a bending or jiggling magnet in a synchrotron. The electro-magnetic force on the moving electron that is provided by the bending or jiggling magnets in the rest frame of the laboratory would appear to the electron (ie in the moving electron's frame of reference) as a moving field with electric and magnetic components. It would interact with the electric component only. (This has to be the case because in the electron's 'stationary' reference frame, the electron has no magnetic field for the magnet to interact with).

As soon as the electron motion changes due to the electrical interaction, the observer in the original electron frame perceives a magnetic field around the electron. It also perceives a change in the direction of the electric field of the electron, which has moved away from the observer. As the electron continues changing direction, the direction of the magnetic field that such an observer perceives continually changes, as does its electric field. These changes occur in all directions. The process continues as the electron deflects. The 'effect' of all this is that an electromagnetic wave propagates from the charge in all directions.

There's something not quite right here...

First of all, the magnets used as insertion devices in a synchrotron are called undulators and wigglers. I suppose "jigglers" would be a good description of what they do.

Secondly, the EM fields generated by electrons passing through such devices does NOT "propagates in all directions". In fact, it is highly directional, which is why we have these things, and why beamlines making use of them are usually tangential to the wiggler/undulators. See, for example,

http://www.synchrotron-soleil.fr/anglais/machine/magnetiques.html

It is why wigglers and undulators are used to generate free-electron lasers (FEL), or more accurately, the self-amplified spontaneous emission (SASE) FEL. The highly directional (and coherent) radiation generated by the oscillating electron bunches are then used to further amplify the generated beam.

Zz.

 

[Andrew Mason]

Secondly, the EM fields generated by electrons passing through such devices does NOT "propagates in all directions". In fact, it is highly directional, which is why we have these things, and why beamlines making use of them are usually tangential to the wiggler/undulators.

In the reference frame of the electron, the radiation must be a non-directional ripple centered on the electron's position. Why would there be any preferred direction in the electron's frame?

The highly directional nature of synchrotron radiation in the laboratory frame can be entirely explained by relativity, can it not?

AM

 

[yogi]

Assume two electromagnets separated by a distance "d" both attached to a common frame. If (1) is energized with a current step function, then turned off quickly - the magnetic field is hypothesized to condition space at the velocity of light - just as this magnetic field reaches electromagnet (2) we energize (2) with a polarity such that it will be repelled by the traveling field of (1) - the field of (2) would repel (1) when it arrives at (1) - but at that time (1) is not energized. So (2) is repelled away from (1) but (1) is not repelled away from (2) and since (2) and (1) are attached to a common frame - we have created a unidirectional force. Now we repeat the process and generate a second impulse and so on.

All aboard for the stars.

 

[pervect]

Assume two electromagnets separated by a distance "d" both attached to a common frame. If (1) is energized with a current step function, then turned off quickly - the magnetic field is hypothesized to condition space at the velocity of light - just as this magnetic field reaches electromagnet (2) we energize (2) with a polarity such that it will be repelled by the traveling field of (1) - the field of (2) would repel (1) when it arrives at (1) - but at that time (1) is not energized. So (2) is repelled away from (1) but (1) is not repelled away from (2) and since (2) and (1) are attached to a common frame - we have created a unidirectional force. Now we repeat the process and generate a second impulse and so on.

All aboard for the stars.

Here is a simpler method for "travelling to the stars" based on the same principle.

Construct a radio antenna, and beam radio waves out the rear of your rocket. It's called a photon drive. It's probably simpler to use a flashlight than a radio transmitter, but the radio transmitter anaology is closer to your magnet example.

In your case, you are generating radio frequencies when you switch the magnets off and on rapidly. (Note that to do this for a real magnet requires very high voltages because L = di/dt. So if you have an electromagnet with a lot of windings, it has a lot of inductance, and it takes a very high voltage to change the current through the magnet rapidly). This means in practice that you won't be able to generate a very high thrust with your drive, because in the nanoseconds that you have (assuming a separation between the magnets measured in feet) you just can't change the magnetic field very much with the sort of voltages and currents you can acutally generate.

This is equivalent to saying that a radio transmitter doesn't provide a lot of thrust.

Momentum is conserved - because electromagnetic fields carry both energy and momentum.

Photon drives are actually one reasonable approach to interstellar travel - one of the best implementations is to keep the power source (which is enormous, because photon drives are extreme energy hogs) off the spaceship. In other words, use a light sail, with a laser to drive it.

 

[Andrew Mason]

Assume two electromagnets separated by a distance "d" both attached to a common frame. If (1) is energized with a current step function, then turned off quickly - the magnetic field is hypothesized to condition space at the velocity of light - just as this magnetic field reaches electromagnet (2) we energize (2) with a polarity such that it will be repelled by the traveling field of (1) - the field of (2) would repel (1) when it arrives at (1) - but at that time (1) is not energized. So (2) is repelled away from (1) but (1) is not repelled away from (2) and since (2) and (1) are attached to a common frame - we have created a unidirectional force. Now we repeat the process and generate a second impulse and so on.

When you turn off (2) the magnetic field collapses on (2) and creates an emf in the coil which tends to sustain the magnetic field. So the field of (2) simply doesn't disappear that quickly.

Ultimately you are trying to create momentum without pushing back on anything. The only momentum would be from emission of em radiation: p= E/c And you are going to generate an enormous amount of heat in those coils to generate even that tiny amount of momentum.

AM