How to directly measure the speed of gravity

[Ivan]

Will this work? As we know, the speed of gravity is known to be equal to the speed of light. The following experiment could provide a reasonably accurate result.


Let’s say we place a satellite at the Lagrangian point L4 at t=0, see diagram. The satellite’s on-board clock is synchronised to the Earth’s clock. At t=0 the satellite would, in a gravitational sense, “see” the Earth at point P0, as gravity would take a finite time (approx 500 seconds) to reach the satellite. At t=0 the Earth would, in fact, be at point P1, or approximately 450.5 light seconds from the satellite, since the Earth would have moved to P1 500 seconds ago.
If we launched a time-stamped radio signal from the satellite at t=0 towards Earth, it would take approximately 401 seconds (99 second difference) for this signal to reach Earth, since the Earth has now moved from point P1 to point P2.

The above calculations assumes the speed of gravity is equal to the speed of light. If the speed of gravity was different, there would be a different delta in the time that the pulse reaches the Earth. In the scenario where the speed of gravity is infinite, we would only measure approximately a 45 second difference, as the satellite would experience an “instant” gravitational effect (t=0 is now at P0) from the Earth and we would be measuring just the finite speed of light.

Does relativity effect the calculations? I feel it would be insignificant. Have I made some gross assumptions? Are the calculations correct? Appreciate your comments.:)

[Jarvamundo]

did we? then why measure it?

[Ivan]

I was typing this up late last night. Perhaps I should have given short intro and brief explaination to why I think this setup/experiment is interesting and rephased some of my sentences.
I would much appreciate comments to my actual idea and calculations.:)

[Robh]

Ivan,

We know the gravitational interaction between two bodies is given by F=GMm/r^2. From this we can determine the orbital period of one body about another. Or for that matter, the orbits of two bodies about another. However, it tells us nothing about the speed of propagation of gravity.
As both the Earth and the satellite have an effective angular momentum about the Sun, you not are actually measuring the speed of gravity but their relative speeds of rotation as a result of the inverse square law used for gravity. With the satellite at the Lagrangian point, this speed is the same.
The evidence for gravity propagating at the speed of light is primarily theoretical and, as far as I know, not proven conclusively by any observational evidence.

Regards, Rob.

[GeoffW1]

Hi,

Certainly not proven conclusively, true.

Just to add a bit, I had read about the observations of a rare pair of binary pulsars, the orbits of which are decaying. By attributing this to gravitational radiation, or a drag on the orbits due to gravity, we get a speed for gravity the same as c to within 1%. But this is not conclusive yet.

For instance, critics claim that observations like this just confirm the speed of light to be the same as itself!! Rather self-evident.

Then, is the speed of gravity constant, in all circumstances?

After that, is gravity due to a particle which interacts with a field, or something more mysterious? So far we can't find the graviton, and more generally its speed depends on the particular theory you assume for it.

My feeble brain is overwhelmed at that point.

Cheers

[circumpolar]

Relativity effects would be significant.
In order to sync the two clocks in this situation you must account for both General & Special Relativity. Time correction calcs must be done for the clock (pulse) information.

Because the satelite at L4 needed to be accelerated to get there, Special Relativity states that IT'S clock must have slowed down (relative to control clock on Earth) during that acceleration.

Because the satelite at L4 is now spatially located in a different (lesser)gravitational-well from where is started from (Earth), General Relativity states that IT'S clock must speed up (relative to control clock on Earth).

I'm unsure if your experiment would work and will give it some thought.
But, Both Special & General Relativity corrections must be applied.

[circumpolar]

Also note that the corrections for the accleration (Special Relativity) would only be needed during it's acceleration (both +, -) with respect to the control clock on Earth.

The corrections for being in a different gravitational-well compared to Earth (General Relativity) would be ongoing.
Note:This value would also be changing during any change in distance with respect to the control clock on Earth.

[AlexN]

Upon initial reading and looking at the diagram I think in a non-relativistic universe, it would have merit.. relativity does make a bit of a mess of it..

Also - Making the assumption that the speed of gravity = C in an experiment designed to measure the speed of gravity seems a little odd. If you're going to assume the speed is C from the onset, why then carry out the experiment.. Also - You would need to factor in the radio time delay. Radio signals do not travel at C.

I think the equations need to be a lot more complex in order to accurately measure the speed of gravity. More to the point, You're accurately measuring the speed of gravity within the solar system, closer to earth. The numbers would change if you got closer to the sun. The numbers would be VERY VERY different if you were within a few light hours of a neutron star or a pulsar..

Lots more to do, but your equation, (if you take the assumptions as a given, and ignore relativity (Special and General) for a moment) works.. There are just a few finer points to be factored in.

[bojan]

Well, this is how science works..
First you make assumptions (that is hypothesis) , then you do some calculations based on those assumptions (that is theory) , then you measure the outcome (this is experiment).
If the outcome of experiment confirms calculation results, theory is correct.
If not, theory is not valid.

BTW, radio waves travel exactly at speed of light (in vacuum.. because they are also electromagnetic radiation, as well as visible light, x rays, gamma rays etc ).

[AlexN]

Fair enough.. Gotta start somewhere I suppose..


As far as radio waves are concerned, yes, within the vacuum of space they travel at the speed of light, then they enter Earths atmosphere and slow up... There would be a delay involved between sending a signal from the satellite and it reaching earth.

[Jarvamundo]

So the experiment would be "confirming the speed of gravity = c, according to SR assumptions" ?

Taking nothing away from the brilliance of SR and GR theory... but could these fundamental assumptions form part of the difficulties in experimentation, mentioned above; ie gravity probes failing to reduce their errors to something meaningful, lido finding nothing, although according to the "theory" and cheque book it should've...etc... ?

Caveat: Curious layman talking here...

.......also fyi from wiki The Speed of Gravity What the Experiments Say (http://www.metaresearch.org/cosmology/speed_of_gravity.asp)

[bojan]

Alex, thank you for the link.. very good reading !
I learned a lot from it.

[circumpolar]

Just to be clear, the speed of light (radio in this case) in a given medium, is proportional to the speed of light in a vacuum (299792458m/s), and inversly proportional to the Refractive Index of that medium.

When an electromagnetic wave transitions between different medium boudaries, it's velocity (speed & direction) must change. We still call this speed 'c' as it is the fastest speed posiable in that medium, even though it is now less then 299792458m/s.

Also, a simple way to determine the amount of directional change is to apply Snell's Law:
n SIN(i) = n' SIN(r)
Where n & n' are the respective Refractive Indices, and i & r are the deviation from perpendicular of the Incident ray & the Refracted ray.

I say simple because the more exact way to measure refraction is very complex and involves calculating the values of the wave phase and transition mediums at quantum levels and treating all points as harmonic oscillaters:P.

[sjastro]

Yet it is incorrect.

Steven

[bojan]

Hmmm
Could you be more specific?
Could you provide me (us) with more accurate information?

[sjastro]

The absence of gravitational aberration has nothing to do with the speed of gravity greatly exceeding the speed the light but rather the motion of the body in the field.

A common "pictorial" misinterpretation is to think of a planetary orbit like throwing a slingshot. The rope is represented as a single line of force which rotates around a centre. If gravity is represented this way then yes aberration is an issue.

The reality is we need to refer to a gravitational field instead of an individual line of force. A gravitational field can be represented as field lines radiating from a centre. An object in orbit around this centre moves from one field line to the next instead of being "confined" to a single (rotating) line of force. The movement of the object in the field cancels out the aberration effects due to gravity.

While this is a crude description (I can't make it any simpler) the full description is given here.

http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909087v2.pdf

Steven

[Jarvamundo]

FYI: Interesting recent views and lists of papers on the Quasar-Jupiter effects observations, also gravity measurement concepts in general from Washington Uni...
http://wugrav.wustl.edu/people/CMW/SpeedofGravity.html

Also this might be of interest http://lisa.nasa.gov/ a giant orbiting Michelson Interferometer experiment planned by NASA and ESA. Video here: http://www.lisa.aei-hannover.de/?page=lisavideo&sub=lisa&lang=en

[bojan]

Thanks guys, this is interesting reading for the coming weekend (being cloudy and rainy here in Melbourne) :thumbsup:

[bojan]

Would I be greatly mistaken if I state that gravity field moves along with the body which is cause of this geometry " defect" of the space-time? So, in effect, the gravity influence is (almost) instantaneous, and for an object causing it we have to wait until light reaches us to see it? (as described in document http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909087v2.pdf)

Could it be that the inflation that happened after BB has something to do with this?

[KenGee]

Arr we meet again Alex where do you get these links, one can only imagine you have somthing against mainstream science. Meta research is the clearing house for nutty ideas most famous for the founders belief in the "face of Mars".
Once we get instruments that are able to either detect gravity waves, or we find a GUT which might shed some light on other way to measure the messenger particles of q gravity.

[bojan]

Well.. SJastro suggested this link.

[sjastro]

The link I presented was the refutation of the claim that gravity travels faster than light using mainstream science.

With regards to the effects of gravity being instantaneous, a property of Minkowski space (as presented in the link), is that if information travels faster than light (such as instantaneous gravity), causality is violated.

Inflation is a product of Quantum Field Theory and was initiated by a false vacuum collapse shortly after the BB. The end result was the separation of the electomagnetic and strong forces and the rapid expansion of space-time. At this stage gravity was already a "free agent" and not directly affected by inflation.

Regards

Steven

[Jarvamundo]

OK here we go again...

The link (http://wugrav.wustl.edu/people/CMW/SpeedofGravity.html) i posted about "Has the Speed of Gravity Been Measured?" was from Clifford M. Will..... Can't get any more mainstream than this well published physicist (http://wugrav.wustl.edu/people/CMW/papers.html). Yes in sheer horror he did write a book call "Was Einstein Right". I know he said the E word... but hey hang on a minute... Deputy President of the International Society on General Relativity and Gravitation (2007-10; President from 2004-07)

Other links to the planned LISA experiment. ESA... if there is anymore mainstream than this, let me know

Other link from wikipedia (http://en.wikipedia.org/wiki/Speed_of_gravity) from the late Tom Van Flandern's theory of faster than light gravity. Tom published many papers and was well regarded as an expert in celestial mechanics... I've read his book and learnt alot about orbital dynamics. I dont subscribe to his face on Mars hypothesis.... but that doesn't mean i can't explore his other published works listed on wiki... Your angle is like saying "no one should subscribe to vegetarianism because hitler did"... http://en.wikipedia.org/wiki/Ad_hominem

ohh yes.. You'll also find some interviews of Clifford Will on youtube... these also are posted on several of NASA's new websites about blackholes...

From the Clifford Will's site.


Again KenGee, If there is somewhere else we should be looking please let us all know.

My deepest thanks and appreciation to the other folk who make up the knowledgeable wisdom contributing on this forum, and to the questions i'm interested in exploring.

Cheers,
Alex

[Nesti]

Geez, this conversation is so confusing.

From my understanding, there is no such thing as the speed of gravity. Einstein showed (and someone correct if I'm wrong here), that it is the field of acceleration (Gravitational Field) which propagates outward at c...it does this because it is the changes of the metric values which travel outward at c, nothing else, but these changes affect the expression of the field of acceleration left in its wake. The field is constantly maintained in the same manner, but remove the origin (energy/mass) and the metrics changes [to flat spacetime] and these changing values then propagates outward at c also. The expression of the field at any part is attributed to both the field origin - which dissipates at the rate of 'one over 'r' squared - as well as any local mass (energy/momentum) within the original field. The local energy and matter creates its own field of acceleration (local gravity) but merges in with the overall field too (it too dissipating and the rate of 'one over 'r' squared), so we can have local gravity fields within the larger field...ergo the concept of a 'Test Particle' is that it is infinitely small with infinitely small mass so it is able to 'survey' the metric at any given position but without affecting the field...of course it is hypothetical and just for the math.

The constancy of light - in vacuum or otherwise - becomes unworkable since spacetime becomes sympathetic to light's constancy. We have NO background template or benchmark with which we may make comparison, and since the gravitation field itself is forever in dynamical change, how can we ever hope to make any successful measurement. If the photon carried information about the global system, then perhaps there would be a way forward.

One of Einstein's most important descriptions of spacetime went something like "dimensions are not a vessel in which space-time is contained, yet events are spatially [and temporally] separated"...if we have just one photon in an empty field, then there is no field! Any measurement conducted WILL also affect local spacetime, thus any data and conclusions as you yourself impart a field influence. Also, who's frame of reference will you be using, as ALL frames are valid?

Einstein deduced the speed at which the metric is influenced (and gravity wave propagation) is equal to the speed of light simple because the math showed that it does. I personally attribute this to the properties of spacetime itself and not the light (photon): The stress energy.

Anyway, for me the question of the speed of gravity makes no sense...whereas light constancy and simultaneity means everything!

If you want something that operates faster than light, a non-influence perhaps, I feel that the regulation of the force [mediating] particles and particle physical values (mass, charge, isospin etc) are instantaneous. Yes, I know this breaches a central condition of SR...but I also believe particle information doesn't necessarily have to 'move' in order to propagate throughout the universe (On this one Steven, I'm talking regulatory function of particle values only and regulation/fixing of the number of force particles, and not the passage of any information or influence, in this way causality might not be violated).

[sjastro]

The issue is not the speed of gravity itself but whether changes to the field strength itself result in information of the change being transmitted at the speed of light. This information is conveyed in the form of gravitational waves.

According to GR gravitational waves are transmitted at c, by allowing the components of the metric tensor to vary with time. The mechanism is similiar to altering the strength of a magnetic quadrupole which results in electromagnetic radiation travelling at c.

Regards

Steven

[Nesti]

Yes.

"by allowing the components of the metric tensor to vary with time"...ummm, who's time are we talking about here Steven? A moving frame of reference would not agree with the same account because the very same light source which was used to measure as a comparison is constant in both frames...in ALL frames...or was the field in motion because the origin is actually moving, and the mover is in fact stationary? Light has no reference frame, ergo it lies to us by offering only a constancy. There is no cosmic ether wind, therefore no fixed background structure with which to measure against.

It's fine to talk about gravity when it's this or that, but the moment you want to get specific, ie make a comparison between the speed at which the metric changes versus the speed at which light propagates, you cannot. A fast moving passer-by would see a slow changing metric, true?

[sjastro]

It doen't matter if each observer measures a different rate of change of the metric components, the resultant gravitational wave still travels at c. The difference measured by each observer is the frequency of the wave.

This is how light behaves as well. All observers will measure the speed of light as c, but the frequency of light due to Doppler shift will vary according to the motion of the source relative to each observer.

Regards

Steven

[Nesti]

I'm aware of the apparent doppler shift (light's signature change within a field of acceleration), but that's not my argument. What's the benchmark going to be, ie how do you know if your results are going to be true if you have no frame of reference with which to measure against? Any data will be related to the observer's (measurement device's) frame ONLY. This is not a true measure. Any result will merely be an apparent measure for a single frame of reference only. And since we're talking about observations at a distance, a second observer would (perpendicular to the experiment say) would not be able to verify any result as it's frame of reference is unique.

The speed of light through space depends upon the properties of the light and the properties of the space, therefore two separate observations cannot ever verify the same event. This also includes the doppler frequency shift of light will be entirely depandant on the properties of two separate spaces and two separate photons...thus, two equally valid and separate realities...ergo the name Relativity.

[sjastro]

Mark,

The absolute frame of reference you are alluding to doesn't exist.
There is no benchmark, no absolute measurement that can be used as a basis for comparison.
Each observer is making a valid measurement in their own frame of reference. No observer is more right or wrong than any other observer.

Consider a wire suspended in the field of a magnet. If you move the wire in the field, a current is induced in the wire. Nothing more than classical electrodynamics at work.
If you move the magnet instead of the wire, a current is also induced, if you move the wire and magnet together there is no current. The point is that in different frames of reference, observers will measure a current or they don't. There is no preferred or standard reference.

The speed of gravitational waves is an invariant quality like the speed of light or the electron charge, it has the same value for all observers.

Regards

Steven

[Nesti]

That's exactly my point Steven and I do see what you are saying. But you're still making an observation of one frame of reference from yet another frame of reference and then labeling the entire universe to this or that. Furthermore, to achieve such evidence you will need some distant event that has both a light source to measure against and a substantial mass/energy event. Both metric value change and light wave MUST propagate through the same spacetime region to the measurement equipment to ENSURE that the spacetime topology is consistent for both. But, you will never know the topology of the spacetime if the light is riding the bow of the metric wave (so to speak). You will never have a valid argument as we still only ever observe an 'apparent' constancy of light, an 'apparent' change in metric values and an 'apparent' doppler shift in a gravity wave and in light. Any two apparents don't make a whole.

Also, don't be surprised if something funny happens, that light outruns the metric at c also...as that would kill any an all arguments about spacetime and confirm Einsteins two constants of the universe in SR.

For me there are two absolutes, the constancy of light speed and laws, everything else is malleable, and that must also include not only spacetime, but also the metrics ability to vary. So if light were impeded through space the rate at which the metric could propagate would vary also. Any change in the metric could never get ahead of light itself (as shown in Minkowski space and the null cone) This universe is built upon the properties of light and properties of energy, not space and/or time. Saying that changes in the metric can propagate faster than light would be like saying the metric ignores its own topology, ergo operates outside spacetime itself.

If someone asked me how fast does the metric values change in a gravitation field, I would have to say that the metric gets its instructions from light. If light took 50 years to move from the central core of our sun to its surface, then so would any changes in the metric.

At the end of the day, we're talking about a phantom...gravity waves, ie detectable changes in the metric have never been observed, they only ever leave their footprints (tidal effects), and many have given up on ever finding them. The notion that you can detect them using light is great if you're looking for a permanent research grant, so those people tend to look toward more promising horizons; dark matter (LOL). This is yet another classic example as to why String Theory offers so much promise, in that higher dimensional metrics can orchestrate all of these spacetime disjointed pieces in to an orderly pattern, an orderly reality.

[sjastro]

Actually I'm not implying that at all.

A frame of reference is intimately tied to the measurement or observation being made. Implying that it can be applied to the Universe is suggesting the existence of an absolute frame of reference.

This is not SR or GR.

By the nature of your post you seem to support the existence of an absolute frames of reference.

Am I right in this assumption?

Regards

Steven

[Nesti]

I'm assuming by "an absolute frame of reference" you're talking about a global frame of reference ...the one Einstein used to establish SR and then abolished stating that there is not background frame of reference at all.

If that's what you mean, then no, that's not what I'm saying at all.

I'm talking about applying what you observe in any one particular reference frame and then assuming it goes for any other reference frames. You cannot assume that. You would need to test that assumption in all other frames before you could call it a global feature of the universe. You can never say that the propagation of a metric in flat space would be the same as it would be within a Black Hole [say]...nor do we know that the character of light would be preserved either. Likewise, we cannot make the same assumption when close to a massive gravitational body or region of space that the metric is as we know it to be.
Example: Unaccountable structures in the rings of Saturn cannot be attributed to what we currently know about classical mechanics, SR & GR; why is that?...so we cannot assume that we know elsewhere either.

And no, I don't support the existence of an "absolute frames of reference". That's the whole point I've been trying to make all along. As well as an extension to that I've just talked about.

[Nesti]

Let me clean up this sentence so that it's clearer.

I wrote earlier:
"But you're still making an observation of one frame of reference from yet another frame of reference and then labeling the entire universe to this or that."


Let me reword that to this:
"But you're still making an observation of one frame of reference and then assuming that ALL other frames of reference within the entire universe hold that same property/feature...and we don't really know if that argument holds true for light in the first place, we assume it does because of SR (popular support is not absolute). So an observation of the speed of a metric against the speed of light in one frame may be completely different within some other frame because of the properties within that region...light may well be unimpeded, but the metric may be. This is why I wrote earlier, {the speed of light through space depends entirely upon the properties of the light and the properties of the space}...so that must go for the Metric also, actually it applies to everything, because if the Metric is unaffected by properties of spacetime, then it is separate from spacetime, and that does nothing but introduce the ether argument."

[sjastro]

There is no such thing as the speed of a metric. The components of the metric tensor are the 10 gravitational potentials that define GR as a theory of gravity (Newtonian gravity has only one potential). If the metric tensor components are time dependent, the field strength changes and gravitational radiation is emitted. What is observed are gravitational waves as a perturbation of Minkowski (flat) space-time. The gravitational potentials of the perturbed metric are propogated as waves at the speed of light.
A gravitational wave is the rippling of flat space-time, the metric simply describes the geometry of the rippled space-time.
Since the speed of the gravitational wave equals the speed of light both are invariant in all frames of references.

Regards

Steven

[Nesti]

The speed of a gravitational wave is the physical activity, the speed at which the metric MAY change is the result of the waves activity...we're talking about two aspects of the same subject matter...what's your point?

[Nesti]

Aren't there 16 components of a [symmetric] Metric Tensor which define the potential of the field? (Figure attached).

such as in Metric Gij = g(1,1), g(1,2)...g(4,4). (16 in total)

An accelerated field being;
TIME g(1,1) = 1 this is non-attractive
SPATIAL g(2,2)/(3,3)/(4,4) = -1 these are attractive

Classifying a 'Symmetric Metric', or , 'Flat Metric':
1. All components other than (1,1 / 2,2 / 3,3 / 4,4) must equal 0 if the field is to be classed as symmetric.
2. If the field is 'flat', then all 16 components must equal 0.
3. For a 'Non-Symmetric Metric' version (a co-variant or absolute differential version) (Ricci, Levi-Civita) partial differentials (alteration to the chain rule in coordinate form) separate-out specific components so that the overall Metric may change, while preserving other components (Christoffel's connections, later) which represent the forces.

(NOTE: these are reversed (inverse the signs) in modern notation which was created for ease of use, so, -1, 1, 1, 1)

So now I come back to my earlier comments, in that the speed at which the metric may change (Yes, defined by the speed at which the gravitational wave may propagate) must also be defined by the spacetime topology in which the wave must travel. That goes with light too. So if light normally travels at c, but is hindered by the topology of a particular region, how can the Metric (the wave) possibly be measured against light if both are affected by the same topology. Both light and wave are joined at the hips (so to speak). And since the variations you are looking for are so minute and the ability to survey the Metrics at all points within the travelled path are so limited, there's no hope of getting any meaningful verification of the speed of the gravitational wave.

This argument goes for the search for gravitational waves in the first place. If light is defined by its own properties AND that of the space it travels (The Metric), how can you separate gravitational wave from light wave???

BTW. From my understanding, a gravitational wave isn't a wave IN spacetime, but a wave OF spacetime. light is composed of properties of itself and that of the space it is traveling through (again, "Joined at the hip").

Cheers
Mark

[sjastro]

Although a tensor of rank 2 in 4 dimensional space has 4^2=16 components there are only 10 independent components since the metric tensor is symmetric.
For example if you express the tensor as a 4 X 4 matrix you will find the components above the leading diagonal are the same as below the diagonal. Hence the total number of independent or unique components is 16-6=10.



No as explained above the non diagonal components don't have to equal zero.

If the field is flat (and orthogonal) the leading diagonal are non zero constants (usually 1,-1,-1,-1 Lorentzian or -1,-1,-1,-1, Minkowski) . All other components are zero.


The worldline of a photon is a null geodesic irrespective of the topology.
The metric of the perturbed space doesn't change. That's because even though the wave is moving the "shape" of the wave remains the same.
Unless of course if you consider space-time in front of the wave being flat and the metric assuming the perturbed space as the wave passes through.

In the real world however it is impossible to measure a metric as it is a mathematical equation not a value.
Gravitational waves will hopefully be detected by the forces they exert.

Regards

Steven

[Nesti]

Thanks for clarifying my Metric; much appreciated.



Surely that can only be so from the reference frame of the photon?! Because from any other frame it must traverse all topology along its geodesic pathway, ie light getting bent as it moves along its geodesic within a gravitational field, true? (I'm assuming we don't have two convenient sets of rules out there for how a photon behaves...like in QM)

So, if the photon must traverse its geodesic path, then surely gravity waves must get affected also (assuming that there are many local gravitational fields), otherwise we could easily get a situation where a gravity wave arrives ahead of the photon...which just isn't possible.




Again, are you talking purely from the photon's frame of reference?




I agree with that.




The universe itself might as well be a mathematical equation. I do realise that the entire Metric is purely for our understanding, and that the universe itself just 'does it'.



Dare I say the word 'Apparent'...again. :P


Cheers
Mark

[sjastro]

Whether a photon has a "frame of reference" has always been a debateable point. Since the world line is a null geodesic (ds^2=0), in the photon's frame it can simultaneously occupy every point along the worldline in the space-time of the wave, or it can be interpreted as a Lorentz contraction to zero length of the photon path.

From an observer's frame of reference the null geodesic is straightforward, it means the photon travels at c irrespective of the topology of space-time or the photon's trajectory.



No. The field equations for gravitational waves reduce to Helmholtz equations. The solutions are sinusoidal functions of constant amplitude and frequency and travelling at c. The shape of the wave doesn't change, hence the metric for the space-time of the wave doesn't alter.

Regards

Steven

[Nesti]

Assuming there are many EQUALLY massed objects in a localised region of space:

Q1. Does the speed of any gravity wave vary with the topology, given that there are now many variations in metric values within the [composite] field?

Q2. Is there a distortion in the propagation because of the composite field?

Yes, I realise the discussion has come full-circle, but if a photon must follow a geodesic derived from a composition of many fields, then any single gravity wave must also be distorted otherwise its propagation would be more direct than the light's geodesic (which is actually the straightest path anyway).

If gravity waves always propagate at c, and if the masses within our composite field are all equal to each-other, then all waves properties must be equal also (shape etc). So we should have interference patterns appearing (exaggerated metric values) in the composite field...these regions of interference should hold either a reduction in the expression of curvature, or a hightened expression of curvature...the same as we see in all other types of fields. If we do not see this, then metric values hold no relation to the physical reality we observe only a mathematical 'similarity'. We could just as easily say the light mediates the gravitational field for itself, creating its own geodesic path based upon other sources of light.

[sjastro]

Good grief these questions are becoming harder.:)



Not likely. The gravitational wave may lose energy but not speed, when it interacts with matter that has caused the variation in topology.
This is analogous to the interaction of electromagnetic waves with matter. The waves may be scattered or absorbed but the resultant wave is still travelling at c with reduced energy and longer wavelength.



I assume you mean if there there is a change to the wave's metric.

Consider two massive bodies revolving around a center of mass. The strength of the field will change (as will the metric) as the orbit of each body decays and there is a non zero quadrupole moment.

Now consider the same two bodies but one body is simply moving past the other. Even though the fields may overlap there is no change to the field strength or the metric as there is now a dipole moment and zero quadrupole moment.

A gravitational wave moving through may overlap with the neighbouring field but there will be no change to the metric as the field strength of the wave or the neighbourhood has not changed.



Even if the masses are rotating around each other in decaying orbits to form a varying metric, a passing gravitational wave does not contribute to the quadrupole symmetry. It will not be influenced by the space time geometry and will still travel at c.

Regards

Steven

[that_guy]

isn't gravity the same speed as the speed of light?

[Nesti]

Full Circle #2 :D

[g__day]

I try and think of Gravity as the curvature of spce time - a field effect, versus particles transfering energy (Gravitons or Higgs Boson in a Higgs field) moving through the field.

In this regard it means not forces moving within the field, but the topology of the field can proprogate at some rate as being defined by say the "tension" of the field. This means I think of the limit of light's speed in our field as intellectually the equivalent to say plucking on a guitar string lightly or hard and wondering why the string moves at a certain frequency. Light propogates at the "tension" of the field.

So without defining what sets the "tension" of the field that is our reality - our Universe (and the speed of light being a constant I seem to remember from 2nd year Uni phyics can be derived from Maxwell's equations alone; with some tricky maths) one can intuit why gravity's rate of propogation could be the same as lights.

Now from (unreliable) memory about 7 years ago physicists (99.999%) of them believed the results of a deep space observation (Jupiter vs quasars http://www.jupiterscientific.org/sciinfo/sog.html) to confirm gravity changes in a field at the speed of light (those same 2 folk that say its not gravity - its electromagnetic force - disagreed with the finding).

By the way the first link on WIKI did some complex maths, but right at the start they said the Sun is 8.3 light minutes away (it changes Jan its less, July its at maximum distance) but it said the Sun's true position is 20 arc seconds East of where it appears. The Sun moves 15 arc seconds a second through our sky (or 15 arc minutes a minute) - why eclipses only last 3-4 minutes - the moon is 30 arc minutes in apparent diameter - so the Sun by my figures is 2 degrees East - not 20 arc seconds - of where it appears.

Cheers,

Matt

[Jarvamundo]

The first link published wiki is actually from a letter in a published journal, link here: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-3VX92WP-1&_user=10&_coverDate=12%2F21%2F1998&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1270808524&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a589c2677f7c6caef8bf80549eebb8b 4

Tom was also a research associate in the physics department at the University of Maryland, In the 1990's, he worked as a special consultant to the Global Positioning System (GPS).

An interesting read on relativity and the GPS issues can be found here: http://www.ldolphin.org/vanFlandern/

Still investigating myself.... just saying... the guys got street cred....and lots of it, lets go easy on the Adhoms

"He graduated from Xavier University in 1962 and then attended Yale University on a scholarship sponsored by the U.S. Naval Observatory (USNO). In 1969, he received a PhD in Astronomy from Yale. Van Flandern worked at the USNO until 1982, having become the Chief of the Celestial Mechanics Branch of the Nautical Almanac Office. Tom Van Flandern (1940-2009) predicted and comprehensively analyzed lunar occultations at the U.S. Naval Observatory in the 1970s. In 1979 he published pioneering papers on the dynamics of binary minor planets. He helped improve GPS accuracies and established Meta Research to support alternative cosmological ideas"


Matt you may be confusing the rotation of the earth (on it's axis) with the vector of gravity force form the sun (ie the orbit around the sun). eg the earth, whether it's rotating or not, is being pulled to 20 arc seconds in front of the sun's visual light position, the rotation calculations you have provided would not matter here?

[alpal]

Ivan,[B]




Hi Ivan,
can you explain your theory more clearly please?
I can't follow it.

cheers
Allan