Gravimagnetism: The Curious Link Between Gravity and Magnetism

[meemoe_uk]

I was thinking about gravimagnetism, in particular the curious comparisons to electromagnetic results. In my physics studies on electromagnetism, I remember one exercise asking to describe the setup for generators and motors, i.e. conducting coil and magnet. One of the results to be obtained was : which way does the coil force the magnet as it enters the coil? The movement of the magnet through the coil is opposed by the induced magnetism of the coil. OK, but then the exercise asked to prove that if it were the other way, coil attracted the magnet through the coil, then it would be a violation of the 1st law of themodyanics. i.e. a magnet on a closed track passing through the coil would build up KE indefinately. OK, but this proof would also infer the equivalent gravimagnetism setup would break the FLoT. Since this isn't allowed, some other physics must happen to stop the violation. What is it I wonder?
http://en.wikipedia.org/wiki/Gravimagnetism" mentions that "if two wheels are spun on a common axis, the mutual gravitational attraction between the two wheels arguably ought to be greater if they spin in opposite directions than in the same direction."
Wiki doesn't say that due to that result of physics ( I can't remember what it's called, someone tell me, I'll call it the minimal potential law ) entities will naturally 'fall' towards their lowest potential energy states, therefore as the velocity of rotation of the wheels increases, the attraction between the wheels will become stronger and amplify the gravimagnetic effect, a postive feedback loop.
In protest someone might point out that the lowest energy state of the wheels is zero velocity, so the minimal potential law would suggest the wheels would come to stop ( by friction ) not speed up. However theorectic science has for a long while had gravity as a negative force, gravity force has a minus sign in equations, and the convention isn't just arbitary. If the wheels spun fast enough, gravimagetism would present a lower energy state than zero velocity, and the wheels would 'fall' towards this feedback loop.

In practice, the most likely candidates for gravimagnetism are spinning quasars and neutron stars.

Anyway, what are the 'official' theorectics on how the electric motor gravity equivalent set up doesn't break the FLoT?

I was thinking since relativity seems to slow things down in there internal workings, maybe this is where the energy is balanced out?

 

[Jonathan Scott]

I'm having some difficulty following what you're saying. We know by Lenz's Law that an induced current opposes the motion which induces it. I'm guessing you're suggesting that since like charges repel in electrostatics but all masses attract by gravity, there's some sort of sign change which might mean that a gravitomagnetic field would strengthen the motion which induces it. That seems unlikely to me; I'd guess that since the induced field and motion both change sign, we'd still be in the same position, although I don't have a clear enough picture of what you have in mind to make a definite statement.

Apart from that, the similarities between electromagnetism and gravity are rather limited; as soon as one gets into situations where the gravitomagnetic field is relevant, the flat space approximation means that the analogy does not hold accurately in conventional Euclidean background coordinate systems for example as used to describe orbits. The lack of an "opposite charge" in gravity also means that various things available in electromagnetism, such as a purely magnetic field over a finite volume of space, are not possible in gravity.

 

[meemoe_uk]

>I'm guessing...there's some sort of sign change which might mean that a gravitomagnetic field would strengthen the motion which induces it.
Good guess.

I'd like to test you, too much of the time on these forums the reason why people don't understand is because they aren't qualified to know, not because the question poster is being vague.

>I don't have a clear enough picture of what you have in mind to make a definite statement.
Looks like you haven't studied gravitomagnetism much. These are the base questions which should ignite interest, if not gravitomagnetism isn't for you. The picture is simple.

Give answers in terms of the relativistic effects which cause the phenomena.
1. A closed track on which a magnet travels freely around on. A conductor coil through which the magnet travels through on some part of the track. The coil opposes the motion of the magnet as it travels through the coil.
Why?

2. Two conductors wires side by side of indefinate length. When an electric current travels through each wire in the same direction the wires attract each other.
Why?

3. Now ask yourself, what is the gravity equivalent to these setups?


Next some minor details...

>the flat space approximation means that the analogy does not hold accurately in conventional Euclidean background coordinate systems for example as used to describe orbits.
What makes you think flat space is so crucial to orbits? Things orbit neutron stars you know. Gravity probe B has been orbiting Earth happily for years measuring the gravitomagnetic aspect of Earth.

>such as a purely magnetic field over a finite volume of space
I don't see this is true, nor ,if it is, why it's relavent. 1st of all, all fields are infinite according to standard model, including the strong nuclear force.

 

[Jonathan Scott]

>I'm guessing...there's some sort of sign change which might mean that a gravitomagnetic field would strengthen the motion which induces it.
Good guess.

I'd like to test you, too much of the time on these forums the reason why people don't understand is because they aren't qualified to know, not because the question poster is being vague.

>I don't have a clear enough picture of what you have in mind to make a definite statement.
Looks like you haven't studied gravitomagnetism much. These are the base questions which should ignite interest, if not gravitomagnetism isn't for you. The picture is simple.

Give answers in terms of the relativistic effects which cause the phenomena.
1. A closed track on which a magnet travels freely around on. A conductor coil through which the magnet travels through on some part of the track. The coil opposes the motion of the magnet as it travels through the coil.
Why?

2. Two conductors wires side by side of indefinate length. When an electric current travels through each wire in the same direction the wires attract each other.
Why?

3. Now ask yourself, what is the gravity equivalent to these setups? Next some minor details...

>the flat space approximation means that the analogy does not hold accurately in conventional Euclidean background coordinate systems for example as used to describe orbits.
What makes you think flat space is so crucial to orbits? Things orbit neutron stars you know. Gravity probe B has been orbiting Earth happily for years measuring the gravitomagnetic aspect of Earth.

>such as a purely magnetic field over a finite volume of space
I don't see this is true, nor ,if it is, why it's relavent. 1st of all, all fields are infinite according to standard model, including the strong nuclear force.

A more polite approach might encourage better answers.

The reason I don't have a clear picture of what you are suggesting is that there is simply no gravitational equivalent of a "magnet", with a gravimagnetic field but no static gravitational field. That is because there is only one sign of gravitational "charge" so it is not possible to construct the equivalent of electric currents in where one charge flows past the opposite charge in an overall uncharged medium.

Gravitomagnetism is normally an extremely tiny rotational effect superimposed on the normal static gravitational field. Within a gravitomagnetic field, an observer feels as if he is rotating even when he is not doing so relative to the distant stars, or feels as if he not rotating when he is actually rotating with the same angular velocity as that of the gravitomagnetic field (apart from any factors of 2 which depends on the conventions assumed for specifying the gravitomagnetic field strength).

You can in theory create a "purely gravitomagnetic" field by balancing the pull of gravitational sources in different directions, for example at the axis of a rotating ring and inside a rotating sphere, but such a field is of very limited extent.

The point about orbits is that if you want to calculate them accurately enough to need to take into account gravitomagnetic effects, you also need to take into account the curvature of space, as this has effects of similar magnitude. You can use a gravitomagnetic model on a small scale to describe approximately how gravitational effects vary locally under Special Relativity transformations, such as throwing an object a short distance on a very dense planet, but in that case your calculations are relative to the space of a local observer, which would appear to be slightly curved relative to background coordinates suitable for describing a complete orbit.

 

[meemoe_uk]

>A more polite approach might encourage better answers.
Likewise, directly answering the questions put to you might encourage a thankful reply. And don't use the 'no gravitomagnetism' excuse either ( see below ), given over 60 hours, you've failed to answer the elementary questions on electro-magnetism.

>there is simply no gravitational equivalent of a "magnet",
Oh dear. Sorry you think that. What where Hawking, Penrose, Clark, Tucker, Heaviside, Mashhoon and others thinking of when they used the term gravitomagnetism if not a gravitational analogy to magnetism? They'd be interested in your reply.
This explains the communication difficulty we are having.
Any mass that has angular momentum is a 'gravity magnet'.

>Gravitomagnetism is normally an extremely tiny rotational effect superimposed on the normal static gravitational field...
Guess what... I already know! I'm interested in gravitomangetism. I've covered the basics already.

>The point about orbits is that if you want to calculate them accurately...
10/10 on following up digressions. 0/10 for answering questions put to you.

Since you can't answer standard questions on relativity & electromagnetism, I doubt I need any more of your posts.
Thanks, I'll try reading Penrose, he talks about special ways of extracting energy from black holes.


P.S.
>...is simply no gravitational equivalent of a "magnet", with a gravimagnetic field but no static gravitational field.
Likewise, there is no magnetic field without a moving electric field. In a permanant magnet, the moving electric field is a net angular momentum of the elecrtrons in the constituent atoms. Usually the atoms are aligned. Magnetic atoms slightly resemble gyroscopes in the key aspect.

 

[Jonathan Scott]

Maxwell's equations and Lenz's law are available in any standard textbook (and online too) and if you don't know the answers you shouldn't be trying to understand gravitomagnetism.

Are you really unable to understand my main point? I didn't say there is no gravitomagnetism; I said that there is no gravitational equivalent of a conventional "magnet", that is something with a magnetic field but no electric field.

Also, contrary to what you said in your PS, there isn't necessarily any electric field associated with a magnet. Your concept of a "moving electric field" or even a "moving magnetic field" is not physical; overall the field has magnetic and electric components; the field of a moving charge includes a magnetic part as well as an electric part, and the field of a moving magnet includes an electric part as well as a magnetic part.

If you really want to understand gravitomagnetism, I found the book "Gravitation and Inertia" by Ciufolini and Wheeler very helpful, especially chapter 6 "The Gravitomagnetic Field".

 

[OB 50]

How is your scenario of two counter-rotating wheels any different than one stationary wheel and one rotating wheel? Where is the big mystery? Are you surprised that any time a single wheel is set in motion relative to a stationary object, it doesn't perpetually increase it's rotational velocity to infinity?

 

[meemoe_uk]

OBy...

>How is your scenario of two counter-rotating wheels any different than one stationary wheel and one rotating wheel?
It's not my scenario, that's the one from wiki. I'd say the difference is that while rotational energy can be relative(dependant on the view of the rest of the universe), it is in most respects absolute(independant of the rest of the universe). But that doesn't matter much to key behaviours I was looking at.

>Where is the big mystery?
For me it's why you're having to ask where the 'big mystery' is, as you call it, I think your referring to my initial question.
>what are the 'official' theorectics on how the electric motor gravity equivalent set up doesn't break the FLoT?

>Are you surprised that any time a single wheel is set in motion relative to a stationary object, it doesn't perpetually increase it's rotational velocity to infinity?
No. And if you'd read my previous posts you'd know I think in most cases gravi-magnetic forces aren't relavent.

Scotty...>there isn't necessarily any electric field associated with a magnet
I know the point your making and I think it's glossing over the important detail. There is an electric field associated with the magnetic field of a permanent magnet, but it is 'hidden'. *Do you know where it is? hint - I've already told you.
>Your concept of a "moving electric field" or even a "moving magnetic field" is not physical
?
What are you talking about now? Could you elaborate on this?

>overall the field has magnetic and electric components; the field of a moving charge includes a magnetic part as well as an electric part, and the field of a moving magnet includes an electric part as well as a magnetic part.

 

[Jonathan Scott]

I'll give you one more try to do the questions I've set you ( then I'll give the answers ). Read up on them, that way some good will have come from this thread. Otherwise I'm reporting you to the administrators for not being qualified to do your job!

I don't know how you think these forums work, but I'm not any sort of "member of staff", nor even a mentor! Most of the replies you will get here are just from people like myself who are trying to help other people understand physics, and if you don't show some appreciation for that you're not likely to get much help at all. I certainly can't be bothered to waste time trying to explain how Lenz's law works, especially as there's a perfectly good Wikipedia entry on the subject.

The idea of "moving" electric or magnetic fields is a common misconception. Obviously fields can change, and the place at which a field has a particular value can move, but all the properties of the electromagnetic field at an arbitrary point in space and time are described by the electric and magnetic field, without any reference to velocities. The fields in any other frame of reference can be determined by the appropriate transformations, where a moving charge gives rise to a magnetic component and a moving magnet gives rise to an electric component.

Of course a real magnet can be considered to be built up at the microscopic level of atoms containing charge, including electrons moving around orbitals and even charge distributions moving around within nuclei. However, a magnet can easily be electrically neutral overall, so that it has no macroscopic electric field. As there is only one mass "charge", the gravitational equivalent is not possible.

 

[pallidin]

Ah, "frame-dragging"!

What an interesting effect. My understanding is that it is detectable only under the circumstances of very massive rotating objects, such as our own planet.

 

[meemoe_uk]

Here's the answers to the questions I set.

Give answers in terms of the relativistic effects which cause the phenomena.
1. A closed track on which a magnet travels freely around on. A conductor coil through which the magnet travels through on some part of the track. The coil opposes the motion of the magnet as it travels through the coil.
Why?

Answer: Unlike a non magnetic atom where the electron momentums roughly cancel out, the constituent atoms in a magnet have electron orbits that have a significant net angular momentum, and so a net angular coulomb charge momentum traveling at relativistic speed, at which space contraction is a significant effect. The stationary electrons in the conductor coil perceives the fast moving electrons in the magnet to be space contracted, while the protons in the magnet are not perceived to be space contracted. Thus the magnet appears to have a higher density of electrons than protons, thus a net negative coulomb charge, thus electrons in the coil with be repulsed by and oppose the magnet. This effect depends on the magnet's charateristic 'organised' polarity of constituent atoms. The resisting force of the coil to the magnet is the force necessary to knock electrons out of their loose bonding to the coil's conductor atoms.

2. Two conductors wires side by side of indefinate length. When an electric current travels through each wire in the same direction the wires attract each other.
Why?

Answer: The current in either one of the wires is composed of electrons traveling at a high speed where relativistic effects are considerable. Consider the point of view of one of these electrons. From it's point of view, the electrons in the other wire are traveling in the same direction and at roughly the same speed, so they are roughly at rest wrt each other. The protons in the other wire are stationary. Wrt to the electrons, they are moving at a high speed, and so relativistic effects are considerable. The important effect is relativistic space contraction. The protons are space contracted wrt to the electron, while the electrons in the other wire are not. Thus the electron perceives a higher density of protons to electrons in the other wire, therefore it perceives a net coulomb attraction. This effect applies to all the current-electrons, and also all the protons in the wires. Thus the wires attract.

3. Now ask yourself, what is the gravity equivalent to these setups?

Answer: For the parallel wires - Two streams of high energy matter pass each other on parralel paths. The high relative speeds of the streams causes space contraction perception for both streams when viewing each other. Thus the streams percieve each other to have higher density, and thus are attracted more.
For the coil and magnet, a gravity equivalent is highly impractical, but many hypothectical situations have been analysed ( see wiki and gravitomagnetism ). Some of the essential aspects, most notably the angular momentum, can be preserved in the following more likely situation. A fast spinning neutron star has a ring of material orbiting fast in the opposite direction to the neutron star's spin. The high relative speeds of the ring and star cause space contraction perception, thus higher density perception thus higher mass perception thus higher gravitational attraction. The higher gravity causes higher accelaration force on both the ring and star, therefore both the ring and star speed up, this constitutes a feedback loop in violation of the FLoT, which ought to be broken by some other physics.

 

[meemoe_uk]

ok! This is a good page. Next time someone asks you to describe magnetism and it's relativistic cause, and you don't want to, post this link.
http://en.wikipedia.org/wiki/Lorentz_force

 

[Jonathan Scott]

Here's the answers to the questions I set. ...

You're apparently trying to "explain" the magnetic field in terms of electric fields seen from other points of view. This can work in some cases, but does not provide a useful general explanation.

It is not necessary to involve either microscopic internals or relativistic speeds to explain magnetism. Electrons in wires carrying current typically creep along at very slow average speeds. A single charged particle traveling at high speed gives rise to a magnetic field. Neither of these cases is handled by your description.

The Lorentz force law has nothing at all to do with your way of looking at magnetism, and I don't understand why you think that article is relevant in this case.

Note that if the appropriate notation is used, the electromagnetic field can be represented as a single complex object E+iB and the Lorentz force law (including a time-like part for the rate of change of energy) is trivial, as is transforming to any other frame of reference. An introduction to my own version of this notation, including the Lorentz force law, can be found in my little informal book "Complex Four-Vector Algebra" on the web, which you can easily find in Google. There's now a more widely publicised version of the same algebra known as the "Algebra of Physical Space" which uses slightly different notation; the textbook "Electrodynamics: A modern geometric approach" by W Baylis uses this notation throughout.

I've been putting up with your apparent total lack of common courtesy because your original question about gravitomagnetism seemed potentially quite interesting. Are you suggesting that if you have one rotating disk or ring and bring another one near it, you think that gravitomagnetism would mean that the change in field would cause the second one to start spinning in the same direction, which would then apparently induce an INCREASE in the spin of the first one, apparently getting energy from nowhere? If so, I'm sure that doesn't happen, and if the faster disk caused the other one to speed up, then it would obviously get slowed down by that, but I'd agree that there's a bit of a puzzle there in the analogy with electromagnetism.

 

[meemoe_uk]

It is not necessary to involve either microscopic internals or relativistic speeds to explain magnetism.
We'll have to differ.

Electrons in wires carrying current typically creep along at very slow average speeds.

Ohno, not that old trick. At least you got the word 'average' into make what you say techincally correct. See Archie Gore's well presented but flawed analysis of current flow to reach your conclusion.
http://www.geocities.com/archisgore/articles/speed_of_electricity.html
What he fails to note is, as a percentage, very few electrons in a conductor are knocked out of their atoms. When they do, they don't get far before they are captured by another atom, then they sit there for a long time.
He assumes that, whenever a voltage is applied, effectively every single atom in the conductor releases it's free electrons! In the calculations this brings the electron speed down by many orders of magnitude.

Any others in the slow electron camp here?

I'm giving up for now. You've got the whole forums staff backing you up, and I'm being stung at every post by them. If you want to see my unedited posts you'll have to PM me.

 

[Hootenanny]

You've got the whole forums staff backing you up, and I'm being stung at every post by them.

If you read the messages that have been sent to you, I think you'll find that it's your attitude that we object to and we aren't actually taking sides in the debate.

 

[Jonathan Scott]

Any others in the slow electron camp here?

I'm definitely in the non-relativistic electron camp.

You didn't answer my last question. Is the situation I described with the rotating rings the specific case in which you are interested?

If so, I don't have a calculated solution (and I expect it would be very tricky), and I'm sure that since curved space has a significant effect here, the similarities with electromagnetism are not sufficiently accurate to be a useful guide. However, some time ago I investigated what happens when you apply a Lorentz transformation to the classic system involving one body moving around another, and I found that for non-relativistic speeds the effective "magnetic" force between them is related to the relative velocity difference between the bodies. I think this suggests the plausible conclusion that the frame-dragging effect speeds up the slower ring but slows down the faster one, preserving energy and angular momentum overall.

 

[Jonathan Scott]

"Electrons in wires carrying current typically creep along at very slow average speeds."

Ohno, not that old trick. At least you got the word 'average' into make what you say techincally correct. See Archie Gore's well presented but flawed analysis of current flow to reach your conclusion.
http://www.geocities.com/archisgore/articles/speed_of_electricity.html
What he fails to note is, as a percentage, very few electrons in a conductor are knocked out of their atoms. When they do, they don't get far before they are captured by another atom, then they sit there for a long time.
He assumes that, whenever a voltage is applied, effectively every single atom in the conductor releases it's free electrons! In the calculations this brings the electron speed down by many orders of magnitude.

From what I remember from my school days, the usual calculation of average drift velocity is based on an assumption that there is one free mobile electron per copper atom, and that mobile electrons are not associated with specific atoms but drift freely through the metal under the influence of electric fields. What makes you think that this isn't true? Can you quote any references? I've had a quick look around but can't find any source which contradicts what I previously learned.

 

[ZapperZ]

From what I remember from my school days, the usual calculation of average drift velocity is based on an assumption that there is one free mobile electron per copper atom, and that mobile electrons are not associated with specific atoms but drift freely through the metal under the influence of electric fields. What makes you think that this isn't true? Can you quote any references? I've had a quick look around but can't find any source which contradicts what I previously learned.

The fermi velocity is of the order of 10^6 m/s, while the drift velocity is significantly lower, of the order of 10^-3 m/s when the mean free path is taken into account. These calculations, especially for conductors like Cu, can be found in any solid state physics text such as Ashcroft and Mermin.

The fermi velocity of the electrons produces no net current and no net magnetic field, since these averages out to zero over all of the conduction electrons.

So you are definitely correct in your assessment.

Zz.

 

[Creator]

... The protons in the other wire are stationary. Wrt to the electrons, they are moving at a high speed, and so relativistic effects are considerable. The important effect is relativistic space contraction. The protons are space contracted wrt to the electron, while the electrons in the other wire are not. Thus the electron perceives a higher density of protons to electrons in the other wire, therefore it perceives a net coulomb attraction. ...

Meemoe;
Your 'microscopic' explanation here is sometimes used as a method for deriving the magnetic field using special relativity, but the method involves how the conduction electrons 'perceive' the proton lattice in ITS OWN wire. The method cannot be used as a way to explain why "electrons are attracted to the protons of the other wire", as you have tried to imagine.

You can easily see how your conclusion here is faulty simply by considering the case where there is no current in the other wire; In your scenario the conduction electrons in wire #1 still "perceive' a higher density of protons in the current-less wire , but now there is NO attractive force between the wires.

Or consider the case where the current is each wire is going in opposite directions. The electrons still 'perceive', in your explanation, the other wire's protons as higher density, but there is now experimentally repulsion between the wires. Obviously your explanation doesn't hold.

In reality, the motion of electrons (Current, I) in each wire sets up a magnetic field, B, around its OWN wire, and the current in each wire going through the other's field is what allows the two wires to experience force...in accordance with the standard formula...

F = I X B (times the length of the wire)

"X" is the cross product and the direction of the current (in the relative direction of the other wire's B field) determines if the force betwen two wires is attractive or repulsive.

Furthermore, as stated by others, the conduction electrons are not relativistic.
However, the standard derivation of magnetic field from special relativity can be done without consideration as to the magnitude of the velocity of the conduction electrons; whereas your scenario would be invalid in either case, no matter what the velocity.

I think Jonathan Scott did a good job trying to entertain your gravitomagnetic idea, but if you are unwilling to correct your initial electromagnetic assumptions, trying to draw the gravitational analog will be useless.

Creator

 

[Creator]

http://en.wikipedia.org/wiki/Gravimagnetism" mentions that "if two wheels are spun on a common axis, the mutual gravitational attraction between the two wheels arguably ought to be greater if they spin in opposite directions than in the same direction."
Wiki doesn't say that due to that result of physics ( I can't remember what it's called, someone tell me,...

Now that we are all on the same page (hopefully), let's look at meemoe's question as to why Wiki makes the above statement.

First realize that in rotating matter of mass m, the gravitomagnetic field arranges itself dipolar and axially along the axis of rotation just like a magnetic dipole arises from circularly rotating current in a wire loop.

In electromagnetism, LIKE poles of two magnetic dipoles REPEL, and UNLIKE poles ATTRACT.
However, for two gravitomagnetic dipoles, it is just the opposite...LIKE poles ATTRACT, and UNLIKE poles REPEL.

Thus for two axially symmetric rotating masses, (stacked on a common axis), and rotating in opposite directions, the LIKE gravitomagnetic poles are facing each other, and therefore ATTRACT, and thus (as wikipedia states) the gravitational attraction between them is GREATER than when they spin in same direction with unlike GM poles facing each other.

Did that make sense?
Anyway that is the (correct) explanation for the Wiki statement.

As for meemoe's next statement...

... therefore as the velocity of rotation of the wheels increases, the attraction between the wheels will become stronger and amplify the gravimagnetic effect, a postive feedback loop.

That statement is not correct...
For axially symmetric gravitomagnetic dipoles the increase in gravitational attraction acts parallel to the rotation axis and therefore we would NOT expect it to feed any increase in the rotation rate.

Thanks for paying attention.

Creator

 

[Jonathan Scott]

The interesting effect which meemoe_uk was apparently asking about is not the attraction or repulsion between the rings (which in the gravitational case is dominated anyway by the overall static gravitational attraction) but rather how the system reacts during a change.

In the electromagnetic case, a changing current in one ring will induce a current in the other, which of course (by Lenz's law) opposes the original change.

In the gravitomagnetic case, it would appear that the switched sign would mean that a changing current (angular momentum) in one ring would induce a change of the same sign in the other ring, which would in turn induce an increase in angular momentum in the first ring. This sounds as if it would violate some sort of conservation laws because each ring is apparently making the other one get faster.

However, after thinking about it some more, I think this might be a reasonably accurate description of what actually happens, yet no conservation laws are violated because external angular momentum and energy has to be provided to make the change. What happens is that the second ring effectively creates a slight drag against the external torque being applied to the first ring, but the drag is decreased if the second ring accelerates a bit as well. This is a bit like connecting them together with a spring (except that the angular velocities are not necessarily the same).

I'm not guaranteeing that this analysis is correct, but it seems plausible.

 

[Creator]

The interesting effect which meemoe_uk was apparently asking about is not the attraction or repulsion between the rings (which in the gravitational case is dominated anyway by the overall static gravitational attraction) but rather how the system reacts during a change.

Thanks for the post Jonathan. First, I think its worth looking at;(and I don't think this is about the magnitude of the gravitomagnetic effect since in certain astrophysical situations it could become significant), as Meemoe implied.

I see no indication that the OP was originally speaking of an angularly ACCELERATING ring; Meemoe clearly did not understand fully the simple case of uniform rotation and its dipolar effect...in either case, that would need to be clarified first...before going to the non-uniform velocity.
He has brought up so many different scenarios (including linear mass currents) that it was proper to address the basics first, especially for the benefit of other readers.

Apparently, he did bring Lentz's law into it but from the standpoint of a "moving magnet", which carries the implication of a magnetic FLUX change. You understood that same principle to mean a gravitomagnetic 'flux' change due to a change in rotation, but the physics of both are equivalent.

Application of the analog to Lenz's law is interesting for rotating mass currents...and you seem to want to address that so I will do so below.

In the gravitomagnetic case, it would appear that the switched sign would mean that a changing current (angular momentum) in one ring would induce a change of the same sign in the other ring, which would in turn induce an increase in angular momentum in the first ring. This sounds as if it would violate some sort of conservation laws because each ring is apparently making the other one get faster.

The first thing to recognize is that in Gravitomagnetism (using the linearized weak field approximations) a CHANGE in mass current results in a gravitoELECTRIC field, call it E_g.

This induced gravitoelectric field is a ('non-conservative') acceleration (gravity) field which is the analog to Faraday's law in EM in which an electric field is INDUCED by a CHANGING magnetic flux. (Sometimes E_g is referrred to as 'non-Newtonian' gravity, since it has no divergence).

Thus in a massive rotating disk (or ring) which CHANGES angular velocity, a new gravity field develops ...which is a result of a changing gravitoMAGNETIC field, according to the linearized GM field equation (in differential form)...

Curl E_g = - d(B_g)/dt...(ignoring mass source terms and constants) (B_g is the gravitomagnetic field)

Notice I put a neg. sign in front (which is typically used), which is the same as in the analogous EM case...
Curl E = -dB/dt

Now, Lenz's Law is necessary for conservation of energy. It is simply a way of stating a phenomenological result, but ignoring the implicit Maxwell's equation.
What really happens (in the EM case) is that a changing B flux INDUCES a circuitous Electric field which accelerates the charges in the neighboring coil IN A DIRECTION that conserves energy and produces a B field that opposes the original changing B field, (as per the above eqn.)

Likewise for GEM..(Forget two rotating disks...Use the simple case first, one rotating and the other stationary on a common axis) ... A CHANGE in angular velocity of the rotating disk INDUCES a gravitoelectric field which will accelerate the 'mass charge' (matter) in the 2nd disk. Whether this E_g field accelerates matter in the stationary disk in the SAME direction or OPPOSITE direction depends on the veracity of the 'sign" in the GM equation above.

[BTW, that is what Tajmar attempted to measure in his original experiment with accelerating SC rings, but instead of using a second ring, he used accelerometers to try to measure the induced gravity field].

So, IMHO, a correct understanding of the gravitomagnetic analog to Lenz's law requires understanding the INDUCED gravitoELECTRIC field, more specifically, IN WHICH DIRECTION that field is induced by a changing mass current...since that will determine IF there is conservation of energy, (IOW, if Lenz's law is fulfilled).

Did that make sense? or is it clear as mud?

Creator

 

[meemoe_uk]

Hi Creator, thanks for the nice replys.
> In your scenario the conduction electrons in wire #1 still "perceive' a higher density of protons in the current-less wire , but now there is NO attractive force between the wires.

That's because in the currentless wire the electrons are now, on average, the same velocity as the protons. The perceived coulomb attraction the current-electrons have towards the protons in the currentless wire is matched and neutralised by that of the electrons in the currentless wire.

>Or consider the case where the current is each wire is going in opposite directions. The electrons still 'perceive', in your explanation, the other wire's protons as higher density, but there is now experimentally repulsion between the wires. Obviously your explanation doesn't hold.

For this case, the electrons in each wire are attracted to the protons in the other wire. But this attraction is only half that of the repulsion the electrons have for the electrons in the other wire, which have twice the relative velocity energy of the protons, thus twice the perceived space contraction, thus twice the perceived coulomb repulsion, thus the wires repel.

>Furthermore, as stated by others, the conduction electrons are not relativistic.
They are when you consider their wave propagation velocity instead of their drift velocity. I expected zapperZ to lead onto this when he mentioned the fermi velocity. As the voltage-shockwaves (composed of photons or fast electrons) pass through the conductor, the fermi velocity of subject electrons ( ones that are hit by the previous fast electron\photon in the wave) is, for very brief time for each electron, perhaps only for one half vibration, at the quantity of the voltage, i.e. for a voltage of 240V a conductor constituent electron has 240 electron volts energy, which is about 3% light speed. Also, importantly, it's direction is in that of the electron flow. This is enough for small relativistic effects to be considerable. This is the origin of magnetic fields in active conductors.