Merged Relativity+ / Farsight

[W.D.Clinger]

The magnetic field B surrounding the electron is zero within the rest frame of the electron, so it's even easier to depict: Show your readers a blank diagram. What you have done in item b, however, is to show something like the magnetic field within a coordinate system in which there is a current running through your central point and orthogonal to the page. Your items a and b therefore depict different physical systems, which is already misleading.

It isn't zero. The electron has a magnetic dipole moment. Of course as ben m has pointed out, a magnetic dipole doesn't look like item b, so there's still a valid criticism to be made.

I appreciate the correction. I had been assuming Farsight's first diagram was intended to show the electric field around a macroscopic central source, and made the mistake of substituting "electron" for that central source without revising the consequences of my earlier assumption.

 

[Farsight]

So if I set up a magnetic field that loops round in a clockwise direction, and set it down next to another source of a magnetic field looping round in a clockwise direction - lets say a pair of electric currents going in the same direction so their magnetic fields loop in the same direction - they'll repel?

Huh.

Please do not try to confuse other readers edd. Stick with charged particles which have an electromagnetic field. Wherein like particles repel and unlike particles attract like this:

Any other readers: see Hyperphysics re "two wires carrying current in the same direction attract each other, and they repel if the currents are opposite in direction". Like this:

 

[edd]

You know, I think other readers would find it a lot simpler to do the more conventional thing and consider just the electric field - preferably with arrows on the field in that case as well, so that they can work out the electrostatic force on the particle.

After all the dipole moments are not usually very big and don't matter at large distance, and then if needed one can separately calculate the effect of the magnetic dipoles. And you'd certainly want to neglect the effect for, say, those nuclei with zero magnetic dipole.

I think it's certainly easier than what look like surprisingly arbitrary rules above.

 

[edd]

Farsight, I'd also (without accepting that your diagrams are right or useful) suggest that you add directions to your diagrams since otherwise it looks like you could take a pair of repelling electrons, rotate one 180 degrees to change the direction of the twist, and suddenly watch it attract its neighbouring electron.
I'm sure you don't want someone to come away with that impression?

 

[Farsight]

That means the lines shown in your diagrams are directed—we should think of them as having arrowheads on them.

They are usually shown with arrowheads, but I removed them quite deliberately. You will be familiar with this image from Andrew Duffy's PY107. The picture is accompanied by this text: "Lines of force are also called field lines. Field lines start on positive charges and end on negative charges, and the direction of the field line at a point tells you what direction the force experienced by a charge will be if the charge is placed at that point". The issue with that is that the force experienced by a charged particle depends on the other charged particle. Two electrons repel, and there is no positive charge to start your field line. The article goes on to say "if the charge is positive, it will experience a force in the same direction as the field" which suggests that two positrons will be attracted to one another.

Your "current-in-the-wire" remark also implies symmetry within the plane but limited symmetry in 3-dimensional space. More on that in a moment...

See the opening posts for more on the current-in-the-wire where the field has a cylindrical disposition. The electron's field has a spherical disposition, but it is difficult to depict curled as opposed to curved lines.

The electromagnetic field does deserve depiction, but item c not only fails to do so accurately, it is downright misleading. That has been a common criticism of your diagrams since the day you started this thread. Please listen when the physicists explain to you why item c is misleading.

I'm always listening, but no way is that picture downright misleading. It delivers vital insight.

The electromagnetic tensor field is hard to depict within a 2-dimensional diagram because the electromagnetic field is 6-dimensional.

Here we go again. A tensor is a mathematical object. It is used to describe the electromagnetic field, but it is not what that field is. That field is "a state of space" according to Einstein. And that space is three-dimensional. You then add the time "dimension" as per Minkowski's time axis comment.

The electric field E surrounding an electron is symmetric under all rotations and reflections about the source. That's easy to depict: draw something like item a and tell your readers it would look the same under all rotations and reflections about the central point.

Sigh. There is no electric field surrounding an electron. The electron is field. Electromagnetic field. Or electron field if you prefer. But not electric field, and the electron itself is not some billiard-ball or pointlike speck in the middle.

What you have done in item b, however, is to show something like the magnetic field within a coordinate system in which there is a current running through your central point and orthogonal to the page. Your items a and b therefore depict different physical systems, which is already misleading.

I acknowledge that b does not adequately depict the electron's magnetic dipole. But if I pursued this you would doubtless criticise me for depicting a toroidal electron.

When you combine depictions of unrelated systems into item c, your depiction loses contact with physical reality: There is no longer any single physical system you are even trying to depict.

No, it makes contact with physical reality. At last. And it is a million times better than electrons and positrons slinging photons at one another.

You could fix that by revising your explanation of item a to say it shows the electric field E around a charged wire through which a current is also running...

Thank you for the suggestion, but that moves away from what Minkowski said about the field of the electron and the force-screw. It moves away from the fundamental physics which starts with the charged particle. Or should I say with four-potential and the photon, but let's come back to that.

As has been noted earlier within this thread, the electric field E and magnetic field B have different units. You can't just add them together, as the "+" sign in your diagram suggests.

Noted. Perhaps I could use something other than a + sign to get across the fact that they are different aspects of the greater whole.

For all of the above reasons (and for other reasons that will be explained to you momentarily by other people), the usual way to depict the 6-dimensional electromagnetic tensor field F_μν is to decompose it into fields of lower dimension. The usual way to do that is to decompose F_μν into two 3-dimensional vector fields E and B...

There's no other way for me to say this Clinger: this usual way is badly, badly, misleading. It has obstructed scientific progress for fifty years.

The reasons for that particular decomposition become evident when you look at the Lorentz force law...

Here's a snippet from the opening paragraph: If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B... It isn't a good start. You are into circular reasoning and something that fails to capture that "greater whole".

or at the components of F_μν. When written as a matrix, the components of F_μν have an obvious decomposition into a 3-vector that consists of the components of E together with a 3x3 matrix that contains all the components of B without any components of E. Although you have criticized that decomposition, it has a lot going for it. Your main criticism, consisting of incessant quotation of a single sentence from Jackson's Classical Electromagnetism, has taken that sentence out of context. Indeed, you often omit the first part of that sentence: "But the fields are completely interrelated". That interrelationship between E and B must be taken into account whenever we transform from one coordinate system to another, which is the topic of Jackson's 11.10. The very first equation of that section, equation (11.146), is the same as Einstein's equation (8) from Die Grundlage der allgemeinen Relativitätstheorie. When you interpret the rest of Jackson's sentence to mean we shouldn't talk about E and B at all, as you have often done within this thread, you are just reminding us of how you got lost at Einstein's equation (3).

I haven't got lost. I've found the way forward. Out of your cargo-cult darkness. Yes. And you heard about it here first.

ben m's question is relevant, and you shouldn't try to escape the question by proclaiming your idiosyncratic semantics. You could answer the question by specifying the symmetries of your diagrams in 3-dimensional space, as I did above by mentioning the relevant symmetries, but it's probably going to be easier for you to answer ben m's question using the orthogonal sections ben m suggested.

I don't try to escape questions. I responded to ben's question, he's free to clarify or demand a further response.

NB: please try to keep your posts succinct.

 

[Farsight]

Except that one can't very easily draw a picture of a spinor. A vector, maybe, but not a spinor.

Agreed. One really needs an animation of something like a 3-dimensional "hurricane" of wavefunction or action with frame-dragging in horizontal and vertical orientations combined.

Electric charge is NOT topological. It's an interaction strength. "Topological charge" or a topological invariant is something very different. Winding number, for instance. That link does not demonstrate that electric charge is a topological invariant.

Electric charge is a misnomer because "the field of the electron" is the electromagnetic field rather than the electric field. And that field is a state of space. A frame-dragged curved or should I say curled state, because the curvature is not just in one plane.

 

[edd]

Sigh. There is no electric field surrounding an electron. The electron is field. Electromagnetic field. Or electron field if you prefer. But not electric field, and the electron itself is not some billiard-ball or pointlike speck in the middle.

I think it's been pointed out to you before that the electron field is not the same as the electromagnetic field.

 

[ben m]

But the "the greater whole" that is the electromagnetic field surely deserves some kind of depiction, and I think item c achieves that quite well.

I don't see how you usefully "depict" the whole of something by taking two drawings representing different objects, then just smashing them together.

The archetypal point particle, which I do not agree with. The electron is more like the "spinor" depicted in c.

There is no "archetypal point particle", not even in the spherical-cow world of simple objects invented for pedadogy purposes, whose E field lines follow radii and whose B field lines follow circles. Maybe you haven't thought about this very carefully. Can you describe this particle using physics quantities?

 

[Farsight]

You know, I think other readers would find it a lot simpler to do the more conventional thing and consider just the electric field - preferably with arrows on the field in that case as well, so that they can work out the electrostatic force on the particle.

See what I said to Clinger about the typical image and two electrons repel, and there is no positive charge to start your field line. Two positrons repel too, so drawing outward radial arrowheads for positrons and inward radial arrowheads for electrons doesn't quite work.

After all the dipole moments are not usually very big and don't matter at large distance, and then if needed one can separately calculate the effect of the magnetic dipoles.

Sounds like a good reason to keep item b the way it is.

And you'd certainly want to neglect the effect for, say, those nuclei with zero magnetic dipole.

One thing at once, edd. You start with the electron. Then you move on to the proton, then the hydrogen atom, et cetera.

I think it's certainly easier than what look like surprisingly arbitrary rules above.

They aren't arbitrary. Counter-rotating vortices attract, co-rotating vortices repel.

Farsight, I'd also (without accepting that your diagrams are right or useful) suggest that you add directions to your diagrams since otherwise it looks like you could take a pair of repelling electrons, rotate one 180 degrees to change the direction of the twist, and suddenly watch it attract its neighbouring electron. I'm sure you don't want someone to come away with that impression?

True. It's difficult to depict three-dimensional chirality.

I think it's been pointed out to you before that the electron field is not the same as the electromagnetic field.

Yes, I know all about this edd. In classical electromagnetism we talk of the electric field and the magnetic field and the electromagnetic field, wherein the electron has an electromagnetic field. But in QFT we talk of the photon field and the electron field, and the photon field is said to be the electromagnetic field.

 

[Farsight]

I don't see how you usefully "depict" the whole of something by taking two drawings representing different objects, then just smashing them together.

Read the screw nature of electromagnetism and then you will. Come on now, you don't seriously think the electron and the proton are playing catch with photons do you?

There is no "archetypal point particle", not even in the spherical-cow world of simple objects invented for pedadogy purposes, whose E field lines follow radii and whose B field lines follow circles.

There are no point particles. Like I've said item b keeps it simple and steers clear of toroidal photons.

Maybe you haven't thought about this very carefully. Can you describe this particle using physics quantities?

I've obviously thought it through. What particle? The electron? No I can't describe the electron with physics quantities. I have to describe it with something that delivers insight and understanding.

 

[ben m]

Please do not try to confuse other readers edd. Stick with charged particles which have an electromagnetic field. Wherein like particles repel and unlike particles attract like this:

Except that this is wrong. You justified the "spiral" by using a nonsensical particle with circular B-fields like those of a wire. Now you're using the spiral to "illustrate" that like charges repel and opposites attract? Nonsense. Charged particles don't have circular B fields, and they attract and repel one another based entirely on the E fields.

(In particular, let's ignore problems with your spirals for a moment. Consider a spin-up electron and a neighboring spin-down electron. Do they attract or repel? Repel, obviously. Consider a spin-up electron and a neighboring spin-up electron. Do they attract or repel? Repel, obviously. But flipping the electron over changes the sign of all the magnetic fields---in your spiral diagram that corresponds to changing from left-hand to right-hand twist. So your illustration is nonsense. )

 

[ben m]

Read the screw nature of electromagnetism and then you will. Come on now, you don't seriously think the electron and the proton are playing catch with photons do you?

Wow, changing the subject already?

You drew a spiral. You claimed that the spiral represents something to do with electromagnetic fields. I asked you to justify that step-by-step.

 

[Farsight]

Except that this is wrong. You justified the "spiral" by using a nonsensical particle with circular B-fields like those of a wire. Now you're using the spiral to "illustrate" that like charges repel and opposites attract? Nonsense. Charged particles don't have circular B fields, and they attract and repel one another based entirely on the E fields.

Groan. You can lead a theoretical physicist to knowledge, but you can't make him think

Once more time: charged particles have electromagnetic fields. And yet again I refer you to the Minkowski quote from Space and Time:

"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".

A charged particle doesn't have an electric E field or a magnetic B field, it has an electromagnetic Fμν field. This doesn't have radial field lines or concentric field lines. So we depict is with the spinor spiral lines which offer an immediate instant intuitive understanding of charged-particle attraction and repulsion. As I said to Clinger, it is a million times better than electrons and positrons slinging photons at one another. Are you being evasive about that? Let me reiterate what I said in my previous response to you. Come on now, you don't seriously think the electron and the proton are playing catch with photons do you?

(In particular, let's ignore problems with your spirals for a moment. Consider a spin-up electron and a neighboring spin-down electron. Do they attract or repel? Repel, obviously. Consider a spin-up electron and a neighboring spin-up electron. Do they attract or repel? Repel, obviously. But flipping the electron over changes the sign of all the magnetic fields---in your spiral diagram that corresponds to changing from left-hand to right-hand twist. So your illustration is nonsense.)

That's a straw man argument that ignores the chirality I've already referred to. I've already said my depiction is flat and doesn't show the chirality. The spiral has helicity, but not chirality. Knots have chirality. You can't turn a left-handed knot into a right-handed knot by flipping it over. Flipping the electron over doesn't change it into a positron. Google on positron chirality. The Williamson / van der Mark electron has a chirality. Reverse the direction of the arrowheads for the opposite chirality, a positron, and you may appreciate why Wheeler thought of it as a time-reversed electron. It isn't an electron going back in time, the wavefunction motion is backwards with respect to the electron.

Wow, changing the subject already?

Not me mate. But you are dodging that playing catch with photons, aren't you?

You drew a spiral. You claimed that the spiral represents something to do with electromagnetic fields. I asked you to justify that step-by-step.

Yep. The spiral represents what you might call frame-dragging. Distorted space. But the depiction is flat, and lacks chirality.

 

[Reality Check]

Groan. You can lead a theoretical physicist to knowledge, but you can't make him think

Groan, Farsight has the delusion that he can read minds to find somones occupation and gets it wrong !
ben m is not a theoretical physicist.

We are not discussing anything very complex. It is simply the fact that the electromagnetic field is made up of separate E and M fields which can be treated together or separately as Maxwell knew, Einstein knew, millions of scientists know and everyone with a high school science education (except Farsight ) knows.

The rest of the post is
* Farsights usual obsession with electromagnetic fields and the delusion that they cannot be treated as separate E and M fields.
* Farsights usual obsession with quoting Minkowski and other analogies of the "screw" nature of electromagnetic waves.

 

[Reality Check]

Please can somebody do the decent thing and put Reality Check straight? As usual.

As usual you ignore the actual facts that I stated, Farsight:

Farsight:
You need to not lie about the contents of the news release NASA Announces Results of Epic Space-Time Experiment

No mention of gravitomagnetism appears there.
The simple fact is that frame dragging "twists" spacetime in GR.

Gravitomagnetism is merely the observation that in limited cases the equations of GR have an analogy with the equations of EM. Gravity Probe B happens to be such a situation so the general case of frame dragging reduces to the special case of gravitomagnetism. This is easily found in the literature or even NASA press releases !

Is the electron a photon with toroidal topology? (PDF) has been discussed here before. so there is no need to go over your obsession with this debunked model yet again .

Oddly enough no one (not even you Farsight) has "put me right". Maybe everyone else in this thread can actually read that NASA press release !

I will also point out (in case you did not know it) that the "twist" in spacetime that frame dragging produces is not anything to do with any "screw" in electromagnetic waves. It is more like the "twist" in a whirlpool.

 

[Reality Check]

And in a flat universe, there is no overall gravity.

And we now know that you do not know what a flat universe is Farsight or maybe even what gravity is !
The topology of the universe refers to its topology in space, not spacetime.
A flat universe is flat in space (its intrinsic curvature is zero so triangle angles add up to 180 degrees). What this basically means is that gravity is balanced by the momentum of expansion, i.e. the "overall" gravity is non-zero. Currently we know that the universe is flat to within about 0.4% from WMAP.

The only way that you can have no overall gravity in a universe is to have no mass or energy in the universe. Any mass or energy means that there is some overall gravity.

 

[Vorpal]

Just another way Maxwell's equations become prettier with magnetic monopoles than without...

As to combining the electric and magnetic fields, there's an interesting way to do it.

Maxwell's equations:
D.E = ρ
D.B = ρ_m
(D)x(B) - dE/dt = j
(D)x(E) + dB/dt = - j_m
dρ/dt + D.j = 0
dρ_m/dt + D.j_m = 0

where the subscripted m is for the magnetic-monopole charge and current density.

Take
F = E + i*B
ρ' = ρ + i*ρ_m
j' = j + i*j_m

Then
D.F = ρ'
- dF/dt - i*(D)x(F) = j'

Maxwell's four equations become two equations.

Why does this happen? Going from 3+1 to dimensions coequal, F is the independent components of
(EM tensor) + i*(dual of EM tensor)

with an appropriate sign convention.

I must say that I find this mathematical structure most interesting.

One can do a bit better if one treats the relationship between the EM tensor and its dual as a constituent relation appropriate to free space in standard electrodynamics but actually independent of Maxwell's equations themselves. Let's say the standard electromagnetic 2-form F, corresponding to (E,B) fields, and an extra 2-form H corresponding to (D,H) fields. Copying MTW's naming convention, we can call them the Faraday 2-form and the Maxwell 2-form, respectively. In vacuum,

H = λ₀⋆F,​

where λ₀ = √(ε₀/μ₀) is the admittance of free space, but in general (e.g., other medium or Born-Infeld EM theory or whatever) may be different.

Then writing U = H+iλF, J = J_e + iλJ_m, where the latter consists of the electric and magnetic current 3-forms and λ is a 0-form with units of admittance, then:

dU = J​

All of Maxwell's equations, including both electric and magnetic charge, become just that, and more curiously, they're completely independent of the metric, since it appears only in the constituent relation, in the Hodge dual. Sure, we had to split off a second equation to tell us how H and F are related, but arguably that's a property of the medium (or vacuum) we're dealing with, and so doesn't belong in Maxwell's equations.

This removal of metric dependence from Maxwell's equations, though not in the language of forms, was first done by Einstein in 1916: here, esp. equations (2) and (5), with (4) playing the role of the constituent relation. I could swear that one of MTW's exercises did that as well, deriving Einstein's results exactly, but I can't find it there now. Perhaps it was different book. Finally, Hehl and Obukhov have an interesting book on premetric electrodynamics, Foundations of Classical Electrodynamics.

 

[Reality Check]

Let's have a dedicated thread on this.

There is no need to have a dedicated thread on some uncaptioned cartoon that you made up, Farsight.
The facts have been stated already here in this thread:
* it is totally ignorant to add up E and B field lines.
* it is totally ignorant to think that the second image is the B field lines from a point source.
* it is a bit deluded to state that E and B fields do not exist and then draw cartoons of E and B fields . The proper cartoon according to you would be the EM field lines from an electron as derived from the actual EM field of an electron.

But feel free to start such a dedicated thread, Farsight - that will be a thread dedicated to the idiocy contained in that cartoon to be recorded for prosperity. The OP will be that cartoon and your caption stating exactly what it contains. Followed by references to the posts here stating the simple facts that the cartoon is wrong.

 

[Reality Check]

...usual "screw" obsession and rant snipped...
E is usually drawn with radial lines of force, and B is usually drawn with concentric lines.

Farsight: Google searches as citations is as idiotic as your cartoon .
Lying about the results of the Google search is even worse - there are few "concentric lines" in the B field lines search - they are radial arcs from one pole to the other. There is no similarity to that second image in your cartoon.
The E field lines from a point source are always drawn as radial lines as any high school science student knows.
The B field lines from a point source are always drawn as radial arcs from one pole to the other as any high school science student knows.

 

[Reality Check]

Item a depicts radial "electric lines of force" around a charged particle. Item b depicts "magnetic field lines" as per the current-in-the wire.

Oh dear, Farsight, it looks like I have to add
* ignorantly adds the E field lines of a single charged particle to the B field lines of a current (many moving charged particles)
* cherry-picks the second image to fit Farsight's wanted outcome (item c). Guess what the B field lines of a current look like from the side!
* makes up the fantasy that item c depicts a spinor. A spinor has no "depiction" - it has a mathematical symbol and analogies.
* still has no idea what topological charge is (nothing to do with electrical charge)!
to

The facts have been stated already here in this thread:
* it is totally ignorant to add up E and B field lines.
* it is totally ignorant to think that the second image is the B field lines from a point source.
* it is a bit deluded to state that E and B fields do not exist and then draw cartoons of E and B fields . The proper cartoon according to you would be the EM field lines from an electron as derived from the actual EM field of an electron.