If you do what CptBork is asking Farsight [the analogy troll] to do, derive Maxwell's equations, then you don't need to resort to nonsense discussions hinging on what analogy is correct. LOL. The amazing thing is Maxwell derived them for us. Now all we need to do is work through the derivation as the path to understanding.
The screw nature of electromagnetism
- Thread starter Farsight
- Start date
If you do what CptBork is asking Farsight [the analogy troll] to do, derive Maxwell's equations, then you don't need to resort to nonsense discussions hinging on what analogy is correct. LOL. The amazing thing is Maxwell derived them for us. Now all we need to do is work through the derivation as the path to understanding.
Alright, sorry for getting sidetracked by that. I was wrong in the way I said a particle moving through a magnetic field "produces" an electric field. I should have said an electric current. That current then produces a magnetic field on a plane perpendicular to the flow of the current. If I recall the physical experiments, a conductor moved through a magnetic field produces a current through the conductor. If I have that right, then what are you suggesting that is new, or different?
So, that's a lie.
As many, many people have pointed out to you, you have never shown that anything done in GR can be done with inhomogeneous space. You have admitted that you can't do the mathematics of GR, yet you continue to write claims about the nature of GR that are mathematical claims. In this case, you are lying that there is a demonstration that one can do all of GR with inhomogeneous space, a mathematical claim.
That's what happens in the current-in-the wire situation. But what you actually have there is electrons with their electromagnetic fields, and metal ions with their electromagnetic fields. If the electrons aren't moving the opposite fields mask one another, and you see no net field. But if the electrons are moving, the opposite electromagnetic field don't quite cancel, and the result is what we call a magnetic field. Moving the electrons don't so much create this as reveal it.
Your conductor is like the flip side of moving the electrons in the wire. There's no real issue there. But what's perhaps new to many people is the fact that quantum field theory is all about particles being "field excitations"? They aren't little billiard-ball things that "have" a field. They ARE field. Or waves if you prefer - there's not much different between a standing wave and a field, and a wave is a field-variation. So when you move that conductor and feel resistance, when you overcome that resistance and "produce" that current, the resistance you can feel is the electrons themselves.quantum_wave said:
So, you refuse to talk about even one of Maxwell's equations? And now you want me to derive the whole of electromagnetism before you'll talk about what Minkowski and Maxwell said about the screw nature of electromagnetism? Bah, you're just another ignorant naysayer whose physics knowledge is scant.
You are the one making grand claims here, Farsight. CptBork actually wants you to talk about Maxwell's equations and you are the one refusing.
Show us how your pictures lead to someone doing physics. Show us how to apply them to a simple physics problem.
As it stands, we have no reason to believe that your pictures have anything to do with electromagnetism. I can show a picture of a corgi and then write down Maxwell's equations; that doesn't mean that corgis cause electromagnetism.
Right, you're saying this to the same guy you were praising for showing a couple of years ago how the entirety of Special Relativity could be derived from Maxwell's equations and some basic postulates about relations between coordinate systems, without any knowledge of photons or fundamental particles or any of that. The only reason I stopped halfway was because the math guys felt I wasn't being rigorous and fundamental enough, that I should go all the way back to working in Lie symmetries and whatnot.
So I'd love to discuss Maxwell's equations, but I won't discuss them with you until you show me that it's actually worth my time. I don't need you to paint pretty word pictures analogizing Faraday's Law or any of the other equations, I want to see you derive them from the first principles you're pretending your model is built on. Then you can show us how you derive gravitomagnetism from those same postulates, and so on. It would benefit you too; you'd save loads of time by deriving everything there is to know about physics using your own ingenuity and unassailable ideas, and skip having to actually learn it for real the way real scientists do.
Alright, a conductor in an unexcited condition, will consist of metal atoms and the electrons in those atoms are staying home, not moving along the conductor. In that state the electrons are bound to the atoms by a natural opposite attraction or charge force. (is that the coulomb force?)
Am I right when I say that even when that conductor is stationary in a magnetic field, there is no current flow induced. The current is only induced when the conductor moves within the magnetic field.
If so, then relative motion between the conductor and the field accompanies the initiation of the current. Just trying to examine the pieces of the equation.
OK, if the electrons in the conductor aren't moving, the coulomb force is still there and working to keep the atom functioning, but without an external field in the picture yet. In order to get the electrons moving there has to be an external field introduced, so the atoms are subject to their natural charges and the natural forces between electrons and protons, plus the external effect of the new field. You are saying that there isn't any field produced, it is more that the electromagnetic force in the picture was there and it wasn't until they were brought to play together that the external field was revealed.Farsight said:
OK, I think I follow where you are. Particles can't be distinguished from their fields which in the case of a particle at rest would be their natural charges. Those particles with opposite charges can be joined into an atom or ion, in a bound state. The atom would have neutral charge and the ion would have a positive or negative charge. But in any case, the electrons, the protons, and the atoms that form from them are not solid in the sense of billiard balls (or some infinitely dense point even?), they are disturbed space, and the disturbance is caused by the charge as they stand alone, or by opposite charges when bound, but no infinitely dense point in space in terms of being matter as opposed to field.Farsight said:
This is the key point in what you said. In quantum mechanics the particle is a wave. Would we be going to far to say that there would be complex patterns of standing waves when particles are bound into atoms and molecules, and so objects then would be waves too; very complex patterns of waves sustained by the charges and fields involved?
Yes I am. You swan around here thinking you're God's gift to physics, and if anybody comes out with something you don't know about, you declare that it must be poppycock and put up some emotional smokescreen demanding a full derivation before you will even deign to consider it. That's called hubris.
No you wouldn't. I put one up, you're still playing the troll.CptBork said:
Bah, there will always be some excuse from you.CptBork said:
It isn't my model. I'm telling you about something both Minkowski and Maxwell referred to. Now go and read the OP, try to understand, and raise some worthy points of discussion. If you can't do that, go start your own thread, and leave this one to people who want to have a genuine sincere discussion about an interesting topic.CptBork said:
If the magnetic field is generated by the negative charge of an electron in motion, do other references alter the amount of perceived energy within the magnetic field? For example, say we have an electron with velocity V, so a magnetic field is generated for that velocity. If look at this same electron, but from a reference that makes the electon appear to be stationary (we both have the same V), does the magnetic field disappear in my reference since a stationary electron should not have a magnetic field? How does reference impact energy conservation relative to the magnetic field?
Relative to the cork screw model does observation reference determine the level of wind within the corkscrew? The above example would remove all the wind so only an electric field is seen?
Relative to the cork screw model does observation reference determine the level of wind within the corkscrew? The above example would remove all the wind so only an electric field is seen?
Yes, but electrons in metal kind of "slosh around". See wikipedia.
Yes. Think of a dynamo on a bike. If you stop pedalling the light stops shining.
Something like that. Think back to the column of electrons and the column of metal ions. There were always two sets of opposite fields there, but they were in balance, so it looked like there weren't any. Then you tip the balance by moving the electrons.
Yes, "disturbed space", or displacement current if you prefer. There isn't any hard little thing in the middle, just as there isn't some hard little thing in the middle of a hurricane.
Yes, but the charge is caused by something else. There is no hard little "charge" in the middle of an electron, just as there is no hard little thing at the centre of a cyclone or anticyclone.
I don't think so. See atomic orbitals on Wikipedia where it says electrons exist as standing waves. If you bump an electron totally out of an atom via the photoelectric effect, surely it still exists as a standing wave. You can diffract electrons. See On Vortex Particles by David St John. Also look at displacement current and note Maxwell's references to vortices.
It might be interesting, but is it physics?
Despite many, many people asking you, Farsight, you have never been able to show how anything you have ever posted relates to even a simple physics example. This is a serious problem and might be evidence of a serious mental problem.
But, please, try to show us how to use your picture in a physics problem of your choice.
Sorry, I'm not quite clear what you're asking. Perceived energy usually changes with motion, but actual energy typically doesn't. For example if you move towards an E=hf photon it doesn't change one jot, but you measure it to be blue-shifted. Conservation of energy applies. But on the other hand you typically have to add some energy to make something move. Like yourself. You changed, the photon didn't.
The best way to think of this is to imagine that we have a single electron sitting there in space. It's motionless, and it has an electromagnetic field. You are also motionless, with a test particle, a positron, in your hand. This also has an electromagnetic field. You use it to feel the force that results from electromagnetic field interactions. This is linear, directly towards the electron, and you would claim that you are situated within an electric field. But then we rerun the scenario with you moving past the electron. Its electromagnetic field hasn't changed one jot, but you now feel a rotational force on your positron as well as a linear force. The positron's electromagnetic field hasn't changed either. You just now experience a "swirling around" motion like what you'd see if you threw a cyclone past an anticyclone.
I'd say no, the "winding of the corkscrew" doesn't change. The thing to bear in mind is that what you think of as an electric field isn't really a field. It's your name for what happens when you only experience the linear force because the "cyclone" and the "anticyclone" start off stationary with respect to one another. Counter-rotating vortices attract. They move directly towards one another. You only see the "swirling around" when you throw one past the other.
If I thought I was God's gift to physics, I'd be trying to overturn the conventional understanding, but instead I leave that to visionaries like yourself who haven't been biased by all the nonsense that actually works in real life. If demanding rigorous justification for an argument is hubris, then do you suppose that just openly accepting whatever crap someone decides to post is equivalent to honesty?
I didn't ask you to put one up and fingerpaint an analogy for it, I already know them all by heart. I asked you to derive it from first principles using your all-knowing model of how things really work, the same model that you claim explains gravitomagnetism too.
So you think it's worth my time to analyze your assertions if you don't put any work into showing the derivations and justifications for your conclusions?
Maxwell and Minkowski didn't refer to matter as being light twisting in on itself, and they most certainly never created a working model of such behaviour beyond basic analogies.
If you don't want to do physics and justify your claims, then don't post your junk in the physics section.
But they really did refer to the screw nature of electromagnetism. And Heaviside really did develop gravitomagnetism as an analogy of electromagnetism. And the NASA article on gravitomagnetism really does say if space is twisted and refers to vortices. Like Maxwell did. And they don't call 'em spinors for nothing. How on Earth do you think electromagnetic attraction and repulsion works? By electrons and positrons throwing photons at one another? As if hydrogen atoms twinkle? As if magnets shine? Or is it just magic? Pah, you might not understand it, but don't you start spitting feathers and getting all outraged just because somebody else does.
No outrage about it, only annoyance at your sheer lack of effort. If you can't give us a mathematical deduction of any of these things using your ideas, then there's no reason to believe you understand your own concepts, let alone science as it presently stands. Any semi-respectable scientist or philosopher who wants to overturn established concepts should at least be able to demonstrate their intimate familiarity with those concepts and why the proposed alternative is superior.
Contextomy strikes again. Minkowski began section 5 of "Raum und Zeit" with
So "force-screw in mechanics" corresponds to "Kraftschraube der Mechanik" and Kraftschraube corresponds to the application of an off-center force in rigid-body mechanics, a six-component combination of force and torque, just as electromagnetism is a described by a six-component combination of electric and magnetic field vectors. That Minkowski saw a mathematical analogy here in the way six-component objects transform under a change of coordinates is natural. That Farsight would attempt to highjack this reference to mathematical physics to support his peculiar notions is unnatural.
Here is "Kraftschraube" in modern context: http://vorhilfe.de/forum/Kraftschraube/t176804
And the coordinate transform of a six-component screw looks like this:
$$ \begin{pmatrix} S'_x \\ S'_y \\ S'_z \\ V'_x \\ V'_y \\ V'_z \end{pmatrix} = \begin{pmatrix} R(\vec{\theta}) & 0 \\ \begin{pmatrix} 0 & -T_z & T_y \\ T_z & 0 & -T_x \\ -T_y &T_x & 0 \end{pmatrix} R(\vec{\theta}) & R(\vec{\theta}) \end{pmatrix} \begin{pmatrix} S_x \\ S_y \\ S_z \\ V_x \\ V_y \\ V_z \end{pmatrix}$$
where
$$ R(\vec{\theta}) = \exp \begin{pmatrix} 0 & -\theta_z & \theta_y \\ \theta_z & 0 & -\theta_x \\ -\theta_y & \theta_x & 0 \end{pmatrix} = \begin{pmatrix} \cos \theta + \frac{\theta_x^2}{\theta^2} (1 - \cos \theta) & \frac{\theta_x \theta_y}{\theta^2} (1 - \cos \theta) \; - \theta_z \, \textrm{sinc} \theta & \frac{\theta_x \theta_z}{\theta^2} (1 - \cos \theta) \; +\theta_y \, \textrm{sinc} \theta \\ \frac{\theta_x \theta_y}{\theta^2} (1 - \cos \theta) \;+\theta_z \, \textrm{sinc} \theta & \cos \theta + \frac{\theta_y^2}{\theta^2} (1 - \cos \theta) & \frac{\theta_y \theta_z}{\theta^2} (1 - \cos \theta) \;-\theta_x \, \textrm{sinc} \theta \\ \frac{\theta_x \theta_z}{\theta^2} (1 - \cos \theta) \;-\theta_y \, \textrm{sinc} \theta & \frac{\theta_y \theta_z}{\theta^2} (1 - \cos \theta) \; +\theta_x \, \textrm{sinc} \theta & \cos \theta + \frac{\theta_z^2}{\theta^2} (1 - \cos \theta) \end{pmatrix}
$$
The coordinate transform of E and B fields looks like:
$$ \begin{pmatrix} B'_x \\ B'_y \\ B'_z \\ E'_x \\ E'_y \\ E'_z \end{pmatrix} = \begin{pmatrix} \begin{pmatrix} \gamma + \frac{\beta_x^2}{\beta^2} (1 - \gamma) & \frac{\beta_x \beta_y}{\beta^2} (1 - \gamma) & \frac{\beta_x \beta_z}{\beta^2} (1 - \gamma) \\ \frac{\beta_x \beta_y}{\beta^2} (1 - \gamma) & \gamma + \frac{\beta_y^2}{\beta^2} (1 - \gamma) & \frac{\beta_y \beta_z}{\beta^2} (1 - \gamma) \\ \frac{\beta_x \beta_z}{\beta^2} (1 - \gamma) & \frac{\beta_y \beta_z}{\beta^2} (1 - \gamma) & \gamma + \frac{\beta_z^2}{\beta^2} (1 - \gamma) \end{pmatrix} & - \frac{\gamma}{c} \begin{pmatrix} 0 & -\beta_z & \beta_y \\ \beta_z & 0 & -\beta_x \\ -\beta_y & \beta_x & 0 \end{pmatrix} \\ c \, \gamma \, \begin{pmatrix} 0 & -\beta_z & \beta_y \\ \beta_z & 0 & -\beta_x \\ -\beta_y & \beta_x & 0 \end{pmatrix} & \begin{pmatrix} \gamma + \frac{\beta_x^2}{\beta^2} (1 - \gamma) & \frac{\beta_x \beta_y}{\beta^2} (1 - \gamma) & \frac{\beta_x \beta_z}{\beta^2} (1 - \gamma) \\ \frac{\beta_x \beta_y}{\beta^2} (1 - \gamma) & \gamma + \frac{\beta_y^2}{\beta^2} (1 - \gamma) & \frac{\beta_y \beta_z}{\beta^2} (1 - \gamma) \\ \frac{\beta_x \beta_z}{\beta^2} (1 - \gamma) & \frac{\beta_y \beta_z}{\beta^2} (1 - \gamma) & \gamma + \frac{\beta_z^2}{\beta^2} (1 - \gamma) \end{pmatrix} \end{pmatrix} \begin{pmatrix} B_x \\ B_y \\ B_z \\ E_x \\ E_y \\ E_z \end{pmatrix}
\gamma = \frac{1}{\sqrt{1 - \beta^2}} = \cosh \tanh^{\tiny -1} \beta
$$
So some of the the topics that Minkowski assumed his audience understood are today on Wikipedia pages:
http://en.wikipedia.org/wiki/Liénard–Wiechert_potential
http://en.wikipedia.org/wiki/Screw_theory#Coordinate_transformation_of_screws
http://en.wikipedia.org/wiki/Lorentz_transformation#Matrix_forms
http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle
http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity#The_E_and_B_fields
So as to the final paragraph of the quote, I propose a more literal translation as:
or in English translation:Raum und Zeit said:
Alternately:Saha translation said:
Wikisource translation said:
So "force-screw in mechanics" corresponds to "Kraftschraube der Mechanik" and Kraftschraube corresponds to the application of an off-center force in rigid-body mechanics, a six-component combination of force and torque, just as electromagnetism is a described by a six-component combination of electric and magnetic field vectors. That Minkowski saw a mathematical analogy here in the way six-component objects transform under a change of coordinates is natural. That Farsight would attempt to highjack this reference to mathematical physics to support his peculiar notions is unnatural.
Here is "Kraftschraube" in modern context: http://vorhilfe.de/forum/Kraftschraube/t176804
And the coordinate transform of a six-component screw looks like this:
$$ \begin{pmatrix} S'_x \\ S'_y \\ S'_z \\ V'_x \\ V'_y \\ V'_z \end{pmatrix} = \begin{pmatrix} R(\vec{\theta}) & 0 \\ \begin{pmatrix} 0 & -T_z & T_y \\ T_z & 0 & -T_x \\ -T_y &T_x & 0 \end{pmatrix} R(\vec{\theta}) & R(\vec{\theta}) \end{pmatrix} \begin{pmatrix} S_x \\ S_y \\ S_z \\ V_x \\ V_y \\ V_z \end{pmatrix}$$
where
$$ R(\vec{\theta}) = \exp \begin{pmatrix} 0 & -\theta_z & \theta_y \\ \theta_z & 0 & -\theta_x \\ -\theta_y & \theta_x & 0 \end{pmatrix} = \begin{pmatrix} \cos \theta + \frac{\theta_x^2}{\theta^2} (1 - \cos \theta) & \frac{\theta_x \theta_y}{\theta^2} (1 - \cos \theta) \; - \theta_z \, \textrm{sinc} \theta & \frac{\theta_x \theta_z}{\theta^2} (1 - \cos \theta) \; +\theta_y \, \textrm{sinc} \theta \\ \frac{\theta_x \theta_y}{\theta^2} (1 - \cos \theta) \;+\theta_z \, \textrm{sinc} \theta & \cos \theta + \frac{\theta_y^2}{\theta^2} (1 - \cos \theta) & \frac{\theta_y \theta_z}{\theta^2} (1 - \cos \theta) \;-\theta_x \, \textrm{sinc} \theta \\ \frac{\theta_x \theta_z}{\theta^2} (1 - \cos \theta) \;-\theta_y \, \textrm{sinc} \theta & \frac{\theta_y \theta_z}{\theta^2} (1 - \cos \theta) \; +\theta_x \, \textrm{sinc} \theta & \cos \theta + \frac{\theta_z^2}{\theta^2} (1 - \cos \theta) \end{pmatrix}
$$
The coordinate transform of E and B fields looks like:
$$ \begin{pmatrix} B'_x \\ B'_y \\ B'_z \\ E'_x \\ E'_y \\ E'_z \end{pmatrix} = \begin{pmatrix} \begin{pmatrix} \gamma + \frac{\beta_x^2}{\beta^2} (1 - \gamma) & \frac{\beta_x \beta_y}{\beta^2} (1 - \gamma) & \frac{\beta_x \beta_z}{\beta^2} (1 - \gamma) \\ \frac{\beta_x \beta_y}{\beta^2} (1 - \gamma) & \gamma + \frac{\beta_y^2}{\beta^2} (1 - \gamma) & \frac{\beta_y \beta_z}{\beta^2} (1 - \gamma) \\ \frac{\beta_x \beta_z}{\beta^2} (1 - \gamma) & \frac{\beta_y \beta_z}{\beta^2} (1 - \gamma) & \gamma + \frac{\beta_z^2}{\beta^2} (1 - \gamma) \end{pmatrix} & - \frac{\gamma}{c} \begin{pmatrix} 0 & -\beta_z & \beta_y \\ \beta_z & 0 & -\beta_x \\ -\beta_y & \beta_x & 0 \end{pmatrix} \\ c \, \gamma \, \begin{pmatrix} 0 & -\beta_z & \beta_y \\ \beta_z & 0 & -\beta_x \\ -\beta_y & \beta_x & 0 \end{pmatrix} & \begin{pmatrix} \gamma + \frac{\beta_x^2}{\beta^2} (1 - \gamma) & \frac{\beta_x \beta_y}{\beta^2} (1 - \gamma) & \frac{\beta_x \beta_z}{\beta^2} (1 - \gamma) \\ \frac{\beta_x \beta_y}{\beta^2} (1 - \gamma) & \gamma + \frac{\beta_y^2}{\beta^2} (1 - \gamma) & \frac{\beta_y \beta_z}{\beta^2} (1 - \gamma) \\ \frac{\beta_x \beta_z}{\beta^2} (1 - \gamma) & \frac{\beta_y \beta_z}{\beta^2} (1 - \gamma) & \gamma + \frac{\beta_z^2}{\beta^2} (1 - \gamma) \end{pmatrix} \end{pmatrix} \begin{pmatrix} B_x \\ B_y \\ B_z \\ E_x \\ E_y \\ E_z \end{pmatrix}
\gamma = \frac{1}{\sqrt{1 - \beta^2}} = \cosh \tanh^{\tiny -1} \beta
$$
So some of the the topics that Minkowski assumed his audience understood are today on Wikipedia pages:
http://en.wikipedia.org/wiki/Liénard–Wiechert_potential
http://en.wikipedia.org/wiki/Screw_theory#Coordinate_transformation_of_screws
http://en.wikipedia.org/wiki/Lorentz_transformation#Matrix_forms
http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle
http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity#The_E_and_B_fields
So as to the final paragraph of the quote, I propose a more literal translation as:
rpenner+Google Translate said:
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The only reason anybody 'needs to rely' on analogy 'to make a scientific argument' is because that's 'all they got'. Unfortunately this type of argument never seems to amount to much more than unscientific bullshit. That's all you got Farsight. Unscientific bullshit. This would be an example of a simple derivation for 'frame dragging' in the Kerr geometry.
Derived from the Kerr metric and the principle of extremal aging [Noether theorem]: in geometric units. The angular momentum per unit mass. A fundamental constant of the motion over the natural path [geodesic inertial path] in the Kerr spacetime.
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 extremal Kerr rotating black hole.
Set the angular momentum per unit mass, L/m, at 0 and solve for dphi/dt
0 = (R^2)dphi/dTau - (2M^2/r)dt/dTau
dphi/dt = 2M^2/rR^2 The frame dragging relativistic effect. The angular velocity of an object falling along a radial path with no angular momentum. So now we know what the prediction is and we can check it when we get the opportunity [50 year wait for the Gravity Probe B].
CptBork wants to see the Farsight model prediction? This is supposed to be a scientific discussion. Something that isn't couched in analogy. Really not to much to ask from somebody who claims to understand so well.
Here's the prediction for the extremal Kerr black hole. The extremal Kerr rotation parameter approaches the limit c.
Making the substitutions for r and R^2 you get
dphi/dt = 2M^2/M(M^2 + M^2 + 2M^3/M) = 1/2M
For a 10 solar mass Kerr black hole
M_solar mass = 1477m
dphi/dt = 1/10(2*1477m) = 1/29,540m/s = .0000338524m/s. So this derivation predicts several things about the relativistic effect we call frame dragging. It predicts 'frame dragging' is natural phenomena. It predicts what it will be 'measured at' if the derivation is shown to be 'scientifically true'. It predicts the relativistic effect increases as M_meter decreases for this extremal case.
This wasn't an analogy. If it was an analogy I wouldn't be able to write down a prediction that could be falsified during evaluation by the scientific method. So Farsight your methods eliminate the need for experimental science. You probably think that's cool.
You've totally missed the point, rpenner. Take a look at your proposed translation:
"The description of the field induced by the electron itself then trivially show that the separation of the field into electrical and magnetic force is a relative consideration with respect to the underlying time axis; most certainly both forces are to be described together in a certain, though not complete analogy to the force+torque object described by the screw theory topic of mechanics".
It still says the field. That's the electromagnetic field. Then it talks about electrical and magnetic force. But you said the coordinate transform of E and B fields. They aren't fields, they're forces. Which are "to be described together in a certain, though not complete analogy to the force+torque object described by the screw theory topic of mechanics". You apply a rotational magnetic force and you get a linear electric force. You apply a linear electric force and you get a rotational magnetic force. Because the Fμv electromagnetic field is what it is. And it is not the E "field" that we depict with radial lines of force. Nor is it B that we depict with concentric lines. Instead it is "the greater whole". I've depicted it in a simple fashion that doesn't cater for the electron being a magnetic dipole, why don't you try depicting it? And by the way, you might want to look at some pictures.
I've put up the OP with ample references. Robust references. And plenty of effort. I even put up one of Maxwell's equations for you and offered to talk about it. What have you done? Zip. All you've done is complained. At least rpenner has put some work in, even if he has as ever dug himself into a hole.CptBork said:
A couple of paragraphs is not plenty of effort, and the references don't say what you're trying to say.
Wow, you wrote down Faraday's law, you deserve a free cookie for that. You want to talk about it? Great. Show us how you derive it mathematically from your base postulates.
You're making a completely pointless distinction. In common parlance in physics, a "field" is just the attribution of any value or quantity to every point in space or space and time. The electric and magnetic fields attribute vector (and pseudovector) values to every point in space and time and are thus fields. Likewise, the local temperature and density of a block of matter, the local velocity of a fluid, and the population density and internal migration of residents of Great Britain are all (or could be described as) fields.
The magnitude of an electromagnetic field at a given location is fully specified or 'measured' by six real numbers, which can be collected together into a single asymmetric tensor-valued field ($$F_{\mu\nu}$$), two vector-valued fields ($$\bar{E}$$ and $$\bar{B}$$), or just six real-valued fields ($$E_{x}$$, $$E_{y}$$, $$E_{z}$$, $$B_{x}$$, $$B_{y}$$, and $$B_{z}$$). These are different notations with different uses and advantages, but the information content in each case is exactly the same. They're different notations for exactly the same physics.
The electric and magnetic fields also aren't forces in the Newtonian sense of the word. They aren't the mass x acceleration of anything and they don't have the SI units of force. You can talk about the electric and magnetic forces on a charge (given by the respective terms in the Lorentz force law), but it's strictly a misnomer to call the electric and magnetic fields themselves "forces".
No you don't. In a vacuum (i.e. in the absence of electric charges and currents), the two relevant Maxwell equations are
$$\begin{eqnarray}
\bar{\nabla} \,\times\, \bar{E} &=& -\, \frac{\partial \bar{B}}{\partial t} \,, \\
\bar{\nabla} \,\times\, \bar{B} &=& \frac{1}{c^{2}} \, \frac{\partial \bar{E}}{\partial t} \,.
\end{eqnarray}$$
\bar{\nabla} \,\times\, \bar{E} &=& -\, \frac{\partial \bar{B}}{\partial t} \,, \\
\bar{\nabla} \,\times\, \bar{B} &=& \frac{1}{c^{2}} \, \frac{\partial \bar{E}}{\partial t} \,.
\end{eqnarray}$$
These relate the curl of the electric and magnetic fields, respectively, to the time-variance of the magnetic and electric fields. The first equation implies that if the magnetic field is changing in magnitude over time, then the electric field must have nonzero curl, and vice-versa. The second equation similarly implies that if the electric field is changing in magnitude over time (in the absence of electric currents) then the magnetic field must have nonzero curl, and vice-versa.
Be aware this means it is perfectly possible for the electric field to be completely concentric, i.e. you can't simply recover the electric and magnetic fields as the "radial" and "concentric" parts of a combined field, as you seem to suggest in a diagram in your opening post, because an electric field need not always be radial.
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