How important to geometric theories is the GPB confirmation of the geodetic effect?

There's no physical relationship between frame dragging and electromagnetism. Read the entire link. It's related by analogy. It's no 'wonder' that analogy is made between the two different natural phenomena.
From your link: http://en.wikipedia.org/wiki/Gravitoelectromagnetism

"Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations forelectromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equationsfor general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles.
The analogy and equations were first published in 1893, before general relativity, by Oliver Heaviside as a separate theory expanding Newton's law,[1] differing essentially only by some small factors."

This is how you derive frame dragging from the Kerr metric. GR.

Derived from the Kerr metric: in geometric units.

L/m = (R^2)dphi/dTau - (2M^2/r)dt/dTau

Where:

R^2 = r^2 + M^2 + 2M^3/r

And r = M for the maximum extreme Kerr.

Now set angular momentum, L/m, at zero and solve for dphi/dt

dphi/dt = 2M^2/rR^2 [1]

Making substitutions for maximal extreme Kerr for r and R^2 you get

dphi/dt = 1/2M [2]

Equations [1], [2] describe the angular motion of an object free falling towards an extreme Kerr, with zero angular momentum. This object in free fall [with no forces acting upon it] will be frame-dragged into a Kerr orbit at r = M for this extreme case. [1] is for all cases and reduces to [2] in the maximal extremal case.

You can review this is in project F The Spinning Black Hole I linked earlier in the thread.

 

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Thanks, Bruce. That’s what I thought, that the name is misleading because it comes from an analogy with electromagnetism, where the motion of an "electric" charge produces "magnetic" side effects.

http://einstein.stanford.edu/content/sci_papers/papers/nz-Thorne_101.pdf

Well, that certainly explains why there was no press release, eh, Farsight.

 

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Wow, I'm stoked. Kip Thorne is so much fun to read. That's two for me. Clifford Will and Kip Thorne. I almost got to meet him after the conference Edwin Taylor invited me to. I'd just started Exploring Black Holes and Edwin thought it was cool that a non university refinery worker was interested in using the just published EBH to learn some gravitational physics. He was giving two workshops, EBH and Feynman's QED sum of all paths and he knew I lived nearby so he invited me to his workshops. It was so cool. I ferried Edwin, and his wife Carla, around San Diego for the weekend conference. He was going to Caltech to visit Kip on the tuesday following the conference and I was hoping he might ask me to drive them but alas he knew I was working that day and I was to dumb to ask if he wanted me to. Thanks for both reads.

 

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As brucep has said, the link you provided doesn't say what you claim. This is not the first time this has happened, you could please try to make more of an effort to check the links you provide to see if they really say as you then claim they say.

In the case of electromagnetism and gravity the similarity of the equations will be known to anyone who has studied them. For example, in relativity you obtain the curvature tensor via the commucation relations of covariant derivatives, while in gauge theory you get the Maxwell tensor from from the gauge covariant derivatives. In GR you're talking about space-time curvature while in a gauge theory you're talking about curvature of a principle G-bundle. Some Bianchi identities for Riemannian curvature are dual to the Jacobi constraints, while a gauge field's generators must satisfy directly Jacobi's equation. One of the Bianchi identiies follows from the covariant derivative of the Riemann curvature tensor, while Maxwell's equations follow from gauge derivatives of the Maxwell gauge curvature tensor. These are mathematical structures which are extremely similar, someone with a working understanding of one side will be able to get a good grasp of the other without learning everything from scratch. This is one of the reasons physics uses mathematics so much, it highlights structures like this. This is an example of how powerful and useful having formal mathematical structure to models can be. Perhaps one day you'll realise this.

The fact \(\nabla \times\) appears in places doesn't necessarily mean something is rotating or two things are the same. I think this is a discussion we've had before in regards to the magnetic field, where you made assertions about how there's something fundamentally curl related about the magnetic field compared to the electric field. I think it was Guest and myself who explained to you how it can be the electric field which gets hit by the curl operator in Maxwell's equations, not the magnetic field. Is this a topic we need to revisit in order to try to help you grasp it?

 

Bruce, you asked the question, and you're finding ways to dismiss my response. Gravitomagnetism was developed by Heaviside.

Note what Thorne said about space curvature as opposed to spacetime curvature. The distinction is crucial. You should pay attention to the general relativistic field equations for g and H become almost identical to Maxwell’s equations, and the geodesic equation of motion for an uncharged particle is identical to the Lorentz force law. I would urge you to investigate why this is so. Don't just dismiss it as mere analogy.

Yes it does support what I said. It isn't just an analogy.

It's gravitomagnetism that's relevant here, not gravity per se.

The space-time curvature of a gravitational field isn't like the Maxwell gauge curvature tensor.

I certainly didn't make assertions about how there's something fundamentally curl related about the magnetic field compared to the electric field. I've referred to curved space as distinct from curved spacetime, and to the electromagnetic field, emphasising that there's one field and two forces. In a nutshell: the electron has its electromagnetic field. If you're a charged particle with no initial motion relative to it you experience only linear force and say you're in an electric field. If you do have initial relative motion you also experience rotational force, and say you're in a magnetic field too. If the electron is going round a proton in a hydrogen atom you experience no linear force, only rotational force. Perhaps we need to revisit this to help you grasp it - but on another thread, let's not derail this one.

 

It doesn't. It even specifically says so on the page, where it points out common misinterpretations people have about the concept.

But it isn't a thing in and of itself, like some new force or combined force, but rather a comment about the similarity between the formulation of two distinct forces.

I didn't say they are physically the same but rather they are mathematically formulated in the same way, which is what gravitomagnetism is about.

The Riemannian curvature tensor relates to covariant derivatives via \([\nabla_{a},\nabla_{b}]V^{c} = R^{c}_{dab}V^{d}\). The generalised Maxwell tensor looks like \([D_{a},D_{b}]\phi = F_{ab}\phi\). The Bianchi identity for the Riemann curvature tensor \(R_{ab[cd;e]}\) can be written as \([[\nabla_{a},\nabla_{b}],\nabla_{c}] + [[\nabla_{c},\nabla_{a}],\nabla_{b}] + [[\nabla_{b},\nabla_{c}],\nabla_{a}] = 0\), which is the same Jacobi identity the gauge field generators \(T^{i}\), where \(F_{ab} = F_{ab}T^{i}\) satisfy, \([[T^{a},T^{b}],T^{c}] + [[T^{c},T^{a}],T^{b}] + [[T^{b},T^{c}],T^{a}] = 0\). The rank-4 curvature tensor \(R^{a}_{bcd}\) is mathematically similar in origin to the rank 4 coefficient array \(F^{i}_{jab} = (F_{ab})^{i}_{j} = \sum_{k}F_{ab}^{k}(T^{k})^{i}_{j}\). The generalised Maxwell equations follows from \(D_{[c}F_{ab}]=0\) also become \([[D_{a},D_{b}],D_{c}] + [[D_{c},D_{a}],D_{b}] + [[D_{b},D_{c}],D_{a}] = 0\). The covariant space-time derivative has a connection \(\nabla = \partial + \Gamma\) and we can express \(R^{a}_{bcd}\) in terms of \(\Gamma\) and it's derivatives. Similarly, the gauge covariant derivative looks like \(D = d + A\) and we can express \(F_{ab}\) in terms of \(A\) and it's derivatives.

They are both described in the mathematical language of fibre bundles, their connections and their curvatures. The mathematical similarities run much much deeper than the rather basic inverse square behaviour. Unfortunately I am certain you do not understand any of this, though you might profess otherwise, and so you just dismiss it or complain I'm getting lost in the mathematics. We can thank people like Einstein and Dirac for the sorts of things I've just said so clearly knowing and understanding this stuff doesn't hinder physical prowess. Not knowing it certainly can hinder you. As it hinders you.

Except that's a classical interpretation which isn't how the electron behaves. It doesn't 'go around' the atom like a planet goes around a star. This is pretty much the most basic concept in quantum mechanics. Obviously you do need to revisit it.... sorry, you cannot revisit something you haven't ever visited in the first place.

By the way, when you've managed to come up with one, just one, quantitative model from your claims which isn't blatant numerology please let us all know. It'll be the one time you're allowed to post your work in this forum and not be forced into the pseudo one.

 

Your response is unphysical [wrong] since you don't understand the physics. You, Farsight, not understanding the physics of frame dragging wasn't the topic of this thread. The topic is whether my interpretation of the GPB measurement of the geodetic effect could be considered scientifically valid or not.
You hijacked the thread when you intimated the GPB scientific team should have published some result which acknowledges a physical relationship between frame dragging and electromagnetism.

 

*Ahem* So, what say you, AlphaNumeric, on BruceP’s interpretation?

*Cough* *Cough* Excuse me but I'm experiencing a little chest pain and shortness of breath at the moment. Jesus, it feels like pneumothorax.

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Brucep, just to be clear, I do believe that the GP-B experiment does represent a valid measurement of the geodetic effect.

If you define either the geodetic or frame-dragging effects, as the material changes, in this case to the gyroscopes, it should be considered a direct measurement. As a confirmation of the curvature of spacetime, both measurements are indirect the way I have been looking at it. We don't measure spacetime directly. We measure the changes observed in the gyroscopes over time. In my previous comments, I was confusing the effect with the curvature...

I may have had some part in the side track, when I mentioned that I found confirmation of the frame-dragging effect more important or perhaps interesting...

 

You didn't sidetrack the discussion. It's a great experiment. You're probably right. Thanks for all your comments. Frame Dragging has rock star status as a prediction of GR. Your comment is the reason I linked project F. It was Edwin Taylor's hope to write a text on gravitational physics that could be studied by undergraduates and interested amateurs [I surprised him with that]. It's a magical book. You can learn lots about how science is conducted from EBH by Taylor and Wheeler. The Christmas before the conference, Edwin invited me to attend in January, he sent me a copy of EBH inscribed by Edwin and autographed by John A. Wheeler.

 

Hi brucep, OnlyMe, everyone.

Thanks for your response, OnlyMe. Much appreciated.

Question to you and brucep: While the usual null geodesic is followed by something in inertial 'falling' in orbit around the earth, how does the 'gyroscopic' force (acceleration frame) of the gyroscopes used in the GP-B experiment satellite figure in the 'effects' and 'forces' at play and 'measured' etc etc., since the gyroscope frame is not 'inertial' per se, and hence there is some forces at play other than just following the null geodesic, and hence the measurements/effects are not so simply stated. Or are they as simple as have been stated already?

If you or anyone can clarify that aspect/question/observation for me, I would be very much in their debt!

Thanks.

.

 

The satellite and gyroscopes don't follow null geodesics. Null geodesics are only followed by those things moving at the speed of light, not by objects with mass. Something free falling will move along a geodesic but which geodesic depends on it's initial position and velocity.

 

No, "something in inertial falling in orbit around the Earth" doesn't follow a null geodesic. Something else follows null geodesics, so your question makes no sense.

 

I cannot say I really understand your question, the way it is presented. Perhaps you can find your own answer in the following...

A gyroscope once spinning always tries to maintain the same orientation in space over time or spacetime. By aligning the sattelite with a guide star, which for the purposes of the experiment is a distant fixed location in space, the sattelite itself should represent a "fixed" frame of reference for the experiment. Any variation in the orientation of the gyroscopes, relative to the sattelite's fixed orientation, must then be the result of the effect of changes in the local curvature of space, which can be associated with the earth's gravitational field — the geodetic effect, and/or the rotation of the Earth and its gravitational field — the frame-dragging effect.

The guide star's fixed location in space realtive to the earth is unaffected by the Earth, so it provides and extranal frame of reference to compare any changes in the gyroscope's orientation, which originates from any locally defined curvature of spacetime. It is a way to isolate the effects of any curvature.., cause by the earth and its rotation.

The actual experiment gets far more complicated than just that and had to account for a number of other variables, like any influences that the Earth's magnetic field had on the gyroscopes or any of the other components of the test.

 

That's a pretty darn good explanation.

 

Thankyou very much, AN, Tach, OnlyMe, brucep.

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Got it.

My bad. I meant to say 'natural path' unless a force acted upon it, rather than null geodesic'. Again, sorry for the wrong lead-in to the question, guys!

OnlyMe: I wanted particularly to get some perspective from you guys on the actual gyroscope motion themselves as 'accelerated motion' (ie spinning objects) following the natural path (given the original satellite motion etc) along the orbital path; and how that inherent accelerated frame (gyroscopic spin/axes) affects the path/masurements etc which are then interpreted as they are according to theory.

Cheers and thanks again.

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I like to say natural path and natural motion. For stuff with mass it's a geodesic and for light [em radiation] the natural path is a null geodesic.