Merged Relativity+ / Farsight

[Reality Check]

Senex: the problem is that professional physicists or cosmologists think they know it all, when they don't. They are so convinced of this that they dismiss Einstein and the evidence, and Maxwell and Minkowski, and anything else that doesn't fit with what they know

Senex: The real problem is that statement is quite delusional .
Professional physicists or cosmologists (in fact scientists in general) are taught over and over again that they do not know it all.
Professional physicists or cosmologists do not dismiss
* Einstein and this mythical "evidence"
* Maxwell
* Minkowski

Professional physicists or cosmologists study what
* Einstein and this mythical "evidence"
* Maxwell
* Minkowski
actually say throughout their body of work.
They do not cherry pick or quote mine bite of quotations from them. They understand what an analogy is, e.g. Maxwell and Minkowski describing EM fields as like a screw does not mean that every EM field is a screw!

Professional physicists or cosmologists do not treat
* Einstein and this mythical "evidence"
* Maxwell
* Minkowski
as prophets .

What the professional physicists or cosmologists (and other knowledgeable people) in this thread are dismissing are Farsights invalid interpretations of physics and his obvious errors, e.g. that cartoon where he does not even know what the field lines are (they are not "lines of force"), what the magnetic field lines from a point source look like, that you cannot just add E and B fields and making up an image out of thin air is not science.

 

[Reality Check]

No, the kicker is that the electron's magnetic dipole means it can't be a point-particle.

Sorry, Farsight, but you do not need to confirm your ignorance of electromagnetism with that unsupported assertion !
A point particle has a dipole magnetic field as in the images you cited and as taught to students, e.g. Magnetic Field From a Moving Point Charge (pretty pictures so you will like it).
The electron having a magnetic dipole moment is support for it being at least a particle with a very small size. The accurate prediction of the measured magnetic dipole moment from QED which treats the electron as a point particle is support for the electron being a point particle.

 

[Reality Check]

I suppose somebody will now tell us that when a charged particle moves through an electric field, it creates a magnetic field.

You suppose wrong, Farsight:
When a charged particle moves it creates a magnetic field regardless of whether there is also an electric field or not.
Magnetic field due to moving charges and electric currents

 

[Reality Check]

I've shown the evidence for the wave nature of the electron. ...

Oh dear, Farsight. You are continuing to cherry pick the evidence that the electron has wave-like properties and ignoring the real world in which the electron also has point-like properties .
You need to learn what an electron is:

The electron (symbol: e−) is a subatomic particle with a negative elementary electric charge.[8] Electrons belong to the first generation of the lepton particle family,[9] and are generally thought to be elementary particles because they have no known components or substructure.[2] The electron has a mass that is approximately 1/1836 that of the proton.[10] Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value in units of ħ, which means that it is a fermion. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle.[9] Electrons also have properties of both particles and waves, and so can collide with other particles and can be diffracted like light.

P.S. Another fact debunking of the electron = photons model you are rather thoughtlessly supporting:

The experimental lower bound for the electron's mean lifetime is 4.6×10²⁶ years, at a 90% confidence level.[78][79]

So every time that magic happens and photons form electrons, these photons stay together basically forever. Thus the universe has gained negative charge over the last 13.7 billion years. But this violates the conservation of charge and we do not have any observations (that I know of) that show that the universe has an excess of electrons.

 

[Reality Check]

I'm not confused at all.

Yes you are, Farsight: E and B are defined as the electric and magnetic field. Thus you cannot call E and B the electric or magnetic force.

 

[Reality Check]

Sigh. Let's look that up shall we:

Yes, Farsight, let's look that up shall we:

Qualitative description
The electric field is a vector field. The field vector at a given point is defined as the force vector per unit charge that would be exerted on a stationary test charge at that point.
Definition
Consider a point charge q with position (x,y,z). Now suppose the charge is subject to a force Fon q due to other charges. Since this force varies with the position of the charge and by Coulomb's Law it is defined at all points in space, Fon q is a continuous function of the charge's position. This suggests that there is some property of the space that causes the force which is exerted on the charge q. This property is called the electric field and it is defined by...

The electric field is not the force. It is "some property of the space that causes the force".

The little fact that the electric and magnetic fields do not have the units of force should make that obvious to you. Sigh .

 

[W.D.Clinger]

per unit charge

We all know that, edd.

Yet only one of us continues to overlook that phrase, presumably because he has to overlook it to defend his crackpot claim that the E and B fields are forces, not vector fields related to forces via the Lorentz force law quoted by ctamblyn (and known to all of us except, apparently, you).

See above, the electric field vector field describes the force on a charged particle.

Describes possible forces, not is the force. There's a difference. That difference is important.

Only Minkowski said forces. Here we go:

"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..."

He said forces, so I'm not some crackpot, now am I?

Your argument reminds me of a fundamentalist preacher who believes the Authorized (King James) version was dictated word-for-word by some deity, not realizing the original words were written in languages other than English. If Minkowski's original German actually says the electromagnetic field can be divided into electric and magnetic forces, then he expressed himself poorly.

Reading his paper in translation, I see that his preceding paragraph is talking about the vector and electric potentials. His division of the electromagnetic field into vector and electric potentials is equivalent to decomposing the electromagnetic field into magnetic and electric fields.

When Minkowski says "If the field caused by the electron be described in the above-mentioned way", he's talking about the decomposition described in his previous paragraph. In other words, he is talking about the standard decomposition of electromagnetic fields into magnetic and electric fields (although he uses the vector potential and scalar potential instead of B and E).

What, then, might Minkowski have meant when he talked about taking his decomposition of the electromagnetic field into magnetic and electric components and dividing it into "electric and magnetic forces"?

One hermeneutic approach is to assume Minkowski believed the vector potential and scalar potential are forces. That is the interpretation being urged upon us by Farsight. If Farsight's interpretation of Minkowski's words is correct, then Minkowski was talking nonsense, because both the vector potential and the scalar potential are two mathematical operations removed from forces.

Another interpretation of Minkowski's words is that Minkowski assumed scientifically literate readers would understand that the "electric and magnetic forces" are the forces contributed by the electric field E and magnetic field B implied by the scalar and vector potentials Minkowski had discussed in his previous paragraph. That is my interpretation.

So there we have it. We can assume Minkowski was an idiot (which is a consequence of Farsight's interpretation) or we can assume Minkowski mentally collapsed a series of calculations that would be familiar to scientifically literate readers.

And it also says one should properly speak of the electromagnetic field Fuv rather than E or B separately. Doesn't it Clinger?

Pretty close. From his third edition, quoting two full sentences for context:

A purely electric or magnetic field in one coordinate system will appear as a mixture of electric and magnetic fields in another coordinate frame....But the fields are completely interrelated, and one should properly speak of the electromagnetic field F^αβ, rather than E or B separately.

That's on page 558, in the middle of section 10 of chapter 11. Jackson himself had been speaking of E and B for the 557 pages before that, and he continued to speak of E and B throughout the following 225 pages.

In that sentence, paragraph, section, chapter, and throughout the book, Jackson speaks of E and B as fields.

Using Jackson to argue we should never speak of the electric and magnetic fields is a hilariously crackpot argument.

The drawing isn't ideal.

No kidding.

Your cartoon depiction of the electromagnetic field is worse than useless. You've been promoting that cartoon in this thread for four years, and you still haven't come up with any scientific explanation of what that cartoon has to do with the electromagnetic field.

We realize your cartoon represents your own personal understanding of your own personal mental image of the electromagnetic field. The problem is that your own personal understanding of the electromagnetic field has no genuine relevance to the electromagnetic field tensor F_αβ as defined by Jackson or any other physicist.

That's why you have ignored all requests to explain the quantitative (or even the qualitative) basis of your cartoon.

With F_αβ, we can calculate. We can also calculate using the electric field E and the magnetic field B, and we get the same results using E and B that we get using F_αβ. (That's a mathematical theorem.)

You, however, can't calculate. You haven't been able to do anything at all with your cartoon depiction, aside from claiming your cartoon somehow illustrates some important insight. It's really too bad that, despite four years of trying, you've been unable to explain what that insight might be.

 

[lpetrich]

A big problem with Farsight physics, for lack of a better name, is its lack of awareness of space-time unification. That was Hermann Minkowski's great breakthrough in 1907. He showed that a consequence of special relativity was that time is like another space dimension, though with some special properties. Lorentz boosts he showed to be much like rotations. At first, Einstein himself thought of it as not much more than an ingenious mathematical trick, though he eventually came to recognize that it was more than that.

-

In the language of Lie algebras, space-time symmetry is O(3,1). Factoring out space and time reflection gives SO⁺(3,1), the part of O(3,1) continuous with the identity.

Turning (time) = i*(an additional space dimension) makes the symmetry group O(4). Taking the pure rotations, the part continuous with the identity, gives SO(4).

Since SO(3,1) is closely related to SO(4), we can use the representations of SO(4) as a guide to those of SO(3,1). It turns out the algebras SO(4) and SO(3) are related:
SO(4) ~ SO(3) * SO(3)

-

SO(3) is also the algebra of quantum-mechanical angular momentum, and if you've taken a mathematical sort of course on quantum mechanics, you have likely run into it.

SO(3) representations can be labeled with angular momentum j, and the dimensions with the projected angular momentum m. For integer j, SO(3) reps can be identified with order-j spherical harmonics, and also with symmetric traceless tensors with j indices. For general j, SO(3) reps can be identified with symmetric combinations of (2*j) spinors.

Thus, if one wants to see what one gets with two vectors, one does
(1) * (1) = (2) + (1) + (0)
A symmetric traceless 2-tensor, a vector multiplied by the antisymmetric symbol, and a scalar: something multiplied by the Kronecker delta. Symbolically:
x_i*y_j = t2_ij + ε_ijkt1_k + t0*δ_ij

-

Now to SO(4). One can denote reps by a pair of angular momenta.

A vector is (1/2,1/2) and a spinor is (1/2,0) + (0,1/2), having 2 irreducible parts.

Let's now make a 2-tensor. One gets (1,1) + (1,0) + (0,1) + (0,0):
(1,1) = symmetric traceless 2-tensor
(0,0) = scalar
(1,0) + (0,1) = antisymmetric 2-tensor
The latter one is split in two because of duality: T_ij = +- (1/2)*ε_ijkl*T_kl

-

To decompose 4D into 3+1, let's now split SO(4) into SO(3) * SO(1) = SO(3), since SO(1) is the empty algebra. There's a simple way to do that. Find all sums of projected angular-momentum values from the two parts of SO(4) and then strip out SO(3) states from them. I'll illustrate.

SO(4) vector (1/2,1/2) thus gives (1), (0), (0), (-1). The (1) must belong to a SO(3) (1), and that expands into (1), (0), (-1). That leaves a (0), which is, of course SO(3) (0). Thus,
(1/2,1/2) -> SO(3) (1) + (0)

Space-time (4D) -> space (3D) + time (1D)

Let's now try the antisymmetric 2-tensor, what the electromagnetic field is in full 4D.
(1,0) -> (1) + (0) + (-1) -> SO(3) (1)
(0,1) -> (1) + (0) + (-1) -> SO(3) (1)

One thus gets two SO(3) 3-vectors out of it, just as one sees for electromagnetism.

-

Of course, one can do a 3+1 decomposition directly, but the Lie-algebra approach is good for giving hints for what to look for.

 

[Farsight]

It's like: imagine you (mistakenly) believed all mammals are terrestrial.
Me: "But the whale, for example, is aquatic,"
You: "Get off it. I've shown TONs of evidence that the whale is a mammal---lungs, mammary glands for crying out loud."
Me: "That is evidence that the whale is a mammal. The whale is both a mammal and aquatic. Do you have any evidence that the whale is not aquatic?"
You: "Stop ignoring the evidence. You're denying that the whale has mammary glands?"

It's more like I provide the evidence that the whale is a mammal, and you insist it's a fish.

You have shown evidence for the wave nature of the electron.

Well I'm glad you accept that it is evidence. We've made some progress.

You have not shown evidence against the particle nature of the electron.

No I haven't. I haven't felt any need because we say the electron is particle knowing it has a wave nature. See QFT on wiki where you can read this:

"In quantum mechanics, a particle (such as an electron or proton) is described by a complex wavefunction, ψ(x, t), whose time-evolution is governed by the Schrödinger equation:

It's the Schrödinger wave equation for a particle.

The electron is both a wave and a particle. Diffraction (and coherent interactions generally) often involve the wave nature. Scattering (and incoherent interactions generally) often involve the particle nature.

I can only reiterate that the particle is a wave, and the wrong inference is drawn from scattering experiments. Again it's like hanging from a helicopter probing a whirlpool with a bargepole, and declaring that the billiard-ball in the middle must be really really small.

You didn't have a problem with this for atoms, remember? You admitted easily that (a) a hydrogen atom can diffract, with a wave nature extending as far as you like, and also (b) a hydrogen atom has an particle-like radius which experiments find to be 0.5 angstroms.

I didn't say the Bohr radius was a particle-like radius. Think of a cyclone and an anticyclone where you can see the eye of the latter circling the eye of the former at a distance of 5 miles. You don't have a storm 5 miles across.

Same thing for an electron. (a) an electron can diffract, with a wave nature extending as far as you like, and also (b) an electron has an particle-like radius which experiments find to be much, much smaller than 0.5 angstroms, smaller than 1pm, smaller than 1fm, in fact it looks pointlike.

Again this is the wrong inference. I really don't know why it persists.

 

[Farsight]

I am sure you have shown the evidence for the wave nature of the electron, but I do not see you show that electrons are not also point-like.

I've given the ample evidence for the wave nature of the electron, and I've challenged the alleged evidence for the pointlike nature of the electron, saying it's a wrong inference. I can't do much more than that.

The relevant Wikipedia article is this one: Wave-particle duality. What is wrong with that?

It's a lot to comment upon. And as I said you can diffract an electron so it has a wave nature. And see above, it's the Schrödinger wave equation.

Evasion noted. You reacted but you did actually not respond to what I said.

You said what would you yourself think if your opponents used these kinds of evasion all the time? when I'm not evasive. I respond faithfully to physics posts. But I don't respond too well to when did you stop beating your wife? You are attempting an ad-hominem by claiming I'm evasive. It doesn't work. Stick to the physics.

 

[Farsight]

That's an awfully small nit to pick, especially since you couldn't actually tie that nit to any logical mistakes that followed from it. And you're wrong anyways. The matrix representation of a tensor is the map, the tensor itself is the territory.

It's a big nit. The tensor is not the territory. See for example the Cauchy stress tensor which "is a second order tensor of type (2,0) (that is, a linear map), with nine components σij that completely define the state of stress at a point inside a material in the deformed placement or configuration". It's a map. It isn't the territory.

It's more than "not ideal". It's flat-out wrong.

I'm afraid it isn't, Zig. It's just something new to you.

Hey, you're the one who insisted that we deal with electromagnetic fields as single, unified thing, and not simply as separate electric and magnetic fields. It's a bit rich to now appeal to textbooks when those textbooks treat them separately.

The underlying issue is that textbooks don't teach electromagnetism too well.

Yes, actually, you do.

No, you do not create a magnetic field by moving a charged particle, just as you do not create a magnetic field by moving past the charged particle. The electromagnetic field is the "state of space" where the charged particle is. Moving through this space shows you another aspect of its state.

Within a given reference frame, either there is a magnetic field, or there is not. When you specify motion, you are specifying the reference frame. The fact that there's a magnetic field in reference frame A does not mean that there is a magnetic field in reference frame B. Yes, these are all part of the electromagnetic field tensor, but the components of the tensor are not arbitrary, and they DO change when you change reference frames.

A reference frame is merely a state of motion. It isn't a region of space. Changing your reference frame is merely changing your motion through a region of space which has a given state, which is what the electromagnetic field is. You don't change that space by moving through it.

The math is a description of the field. But the field itself, the actual physical field, is a tensor, because it has all the properties of a tensor.

See above. The tensor is the map. The field is the territory.

What you have done by adding the magnetic and electric fields together is analogous to adding the sides of a rectangle together and declaring that you've calculated the length of the diagonal. Well, you haven't.

It's more like combining what you think of as a square, with what you think of as another square, in an attempt to show you that what you've really got is a cube.

 

[Farsight]

This sounds like the sort of sentence that ought to precede a description of how to define the "direction" and "degree of twist" of a state of space.

Uh huh.

... and indeed it sounds like Farsight is about to tell us which vector field is twisted... .. but actually he only knows what vector fields are NOT twisted. (And possibly only because we told him so.)

Huh? Space is twisted. The field is the state of space.

If you don't know what vector you are talking about, how are you so certain it's twisted?

If you mean how do I know that space is twisted one answer is because electromagnetism and gravitomagnetism are related, see GP-B and note the twist.

How can you pretend make clear statements about the curl of a vector field you can't name, can't plot, and can't describe, and therefore whose curl you've obviously never evaluated? If an actual scientist did this in a paper, it'd be called "scientific fraud". I don't say that idly: Jan Henrik Schön's fraud investigation criticized him for publishing plots that he originally presented as data but later admitted were illustrative cartoons.

It's a discussion forum! I've quoted Maxwell and Minkowski and I've given evidence and references about the screw nature of electromagnetism. And you're carping about scientific fraud? Strewth!

I repeat my diagnosis. Farsight has a vague mental picture of some twisted lines around a point. Now, of course, he's struggling to find something about electromagnetism he can cite that justifies his spirally drawing. It's like if a kid draws a picture of an animal---six legs, wings, tentacles, breathes fire---and tells you it's his favorite animal, he knows all the facts about it, and if you haven't heard of it it's because you're dumb. But also that he doesn't know what it's called, it's unfair to ask, he's still trying to find it in the encyclopedia, which is also dumb.

Ad-hominems are no substitute for addressing the physics.

I take it you concede on the electron being a point particle, and you agree that it's a wave. OK: what sort of a wave?

 

[Farsight]

Nobody's dismissing the claimed evidence, and your invoking of Einstein and Maxwell and Minkowski seems so much like a theologian -- invoking some sacred book that one believes to contain revealed truth.

Science doesn't work that way. About Maxwell and Einstein and Minkowski and the like, we have no trouble pointing out that they had made mistakes when we conclude that they have. We don't consider their writings revealed truth.

Sigh. I refer to Einstein and Maxwell and Minkowski and all the evidence in papers and articles, and lpetrich tries to dismiss it all by saying I'm like a theologian with a sacred book. Incredible.

 

[Roboramma]

Did you read this part of the post that you quoted, Farsight?

How can you pretend make clear statements about the curl of a vector field you can't name, can't plot, and can't describe, and therefore whose curl you've obviously never evaluated?

 

[Farsight]

Yet only one of us continues to overlook that phrase, presumably because he has to overlook it to defend his crackpot claim that the E and B fields are forces, not vector fields related to forces via the Lorentz force law quoted by ctamblyn (and known to all of us except, apparently, you)...

You were hoist by your own petard, Clinger, in this post. It's too late to change your tune now. Here's the winning point:

"The electric field is a vector field. The field vector at a given point is defined as the force vector per unit charge that would be exerted on a stationary test charge at that point."

...So there we have it. We can assume Minkowski was an idiot (which is a consequence of Farsight's interpretation) or we can assume Minkowski mentally collapsed a series of calculations that would be familiar to scientifically literate readers.

No, you can assume that the field vector at a given point is defined as the force vector per unit charge that would be exerted. So when Minkowski said force, he meant force. Simple.

...Jackson himself had been speaking of E and B for the 557 pages before that, and he continued to speak of E and B throughout the following 225 pages.

Quite. And one should properly speak of the electromagnetic field F^αβ, rather than E or B separately.

...Your cartoon depiction of the electromagnetic field[/url] is worse than useless. You've been promoting that cartoon in this thread for four years, and you still haven't come up with any scientific explanation of what that cartoon has to do with the electromagnetic field...

LOL.

 

[Farsight]

Did you read this part of the post that you quoted, Farsight?

Yes. I didn't go into it because it might have caused confusion. The thing is Robo, is that the vector fields you're used to aren't actually fields. They don't describe the electromagnetic field. They describe the linear and/or rotational forces that result from electromagnetic field interactions. Hence:

"The electric field is a vector field. The field vector at a given point is defined as the force vector per unit charge that would be exerted on a stationary test charge at that point."

So what does describe the electromagnetic field? The Fμv field tensor. But Einstein referred to a field as a state of space, and you have no concept of the state of space it's describing. For that you have to do your own research and read what Minkowski etc said and think gravitomagnetism and frame-dragging and vorticial attraction and repulsion. Maxwell didn't refer to vortices for nothing. A cyclone and an anticyclone will move linearly together and/or circle round one another, which is how the electron and positron move in positronium. You can represent a cyclone with a spiral, see this image, but in no respect is there anything actually there with straight inward or outward radials or with concentric circles.

All: OK, I'm afraid I have to go. I hope you've all learned something. If you're not sure about something I've said, ask around elsewhere, and if there's anything following on from all this you want to talk about, please start a new thread.

 

[W.D.Clinger]

I can only reiterate that the particle is a wave, and the wrong inference is drawn from scattering experiments.

The first half of that sentence is true. You can only reiterate. You cannot provide scientific evidence that "the wrong inference is drawn from scattering experiments."

Again this is the wrong inference. I really don't know why it persists.

The second of those sentences is also true. You really don't know why physicists persist in drawing inferences your gut tells you are wrong.

I've given the ample evidence for the wave nature of the electron, and I've challenged the alleged evidence for the pointlike nature of the electron, saying it's a wrong inference. I can't do much more than that.

Entirely true. You've given ample evidence for the wave nature of the electron, which no one ever disputes. You have also challenged the pointlike nature of the electron, without being able to support that challenge with any kind of scientific argument. You are apparently incapable of doing much more than that.

The underlying issue is that textbooks don't teach electromagnetism too well.

Yet those textbooks have taught electromagnetism well enough for engineers and scientists to create the modern technological world.

Although you reject almost everything written in those textbooks, you still rely on them for the cherry-picked quotations that, in your mind, outweigh all of the equations and scientific evidence contained within those textbooks.

A reference frame is merely a state of motion. It isn't a region of space. Changing your reference frame is merely changing your motion through a region of space which has a given state, which is what the electromagnetic field is.

False. You are conflating the map with the territory. Your reference frame is the map. (In fact, the technical terms are "chart" and "atlas".) Changing your reference frame (map, chart, atlas) is just a coordinate transformation. Coordinate transformations don't change your motion through space; they change only your description of your motion through space.

You have consistently failed to understand the nature and importance of coordinate transformations in relativity and physics at large. You have failed to distinguish the map from the territory.

It's a discussion forum! I've quoted Maxwell and Minkowski and I've given evidence and references about the screw nature of electromagnetism.

Yes, you have cherry-picked Maxwell and Minkowski and Einstein, consistently quoting the vague analogies they themselves describe as imperfect, while ignoring the technical basis for what they say (such as Einstein's ten functions g_μν).

Sigh. I refer to Einstein and Maxwell and Minkowski and all the evidence in papers and articles, and lpetrich tries to dismiss it all by saying I'm like a theologian with a sacred book. Incredible.

No, that's entirely credible. You may never have heard what fundamentalist theologians do with their sacred proof-texts, but I have. Your arguments are remarkably similar to theirs.

...Jackson himself had been speaking of E and B for the 557 pages before that, and he continued to speak of E and B throughout the following 225 pages.

Quite. And one should properly speak of the electromagnetic field F^αβ, rather than E or B separately.

If we take John David Jackson as an authority on this, which he is, then his example shows it is perfectly okay to speak of E and B together, as he did, understanding that E and B together are equivalent to the electromagnetic field F^αβ.

All: OK, I'm afraid I have to go.

True. I see you've been suspended.

 

[Senex]

Senex: The real problem is that statement is quite delusional .
Professional physicists or cosmologists (in fact scientists in general) are taught over and over again that they do not know it all.
Professional physicists or cosmologists do not dismiss
* Einstein and this mythical "evidence"
* Maxwell
* Minkowski...........

I'm not as naive as you may think (well, maybe but for different reasons). I joined this thread because I believed Farsight was being disingenuous and somehow able to carry off this epic thread for years that is active every day. As a student of influence I was interested in this and read many pages of the thread. After still not understanding fully I decided to join the thread.

Now I believe the word "disingenuous" needs gradients and most of the posts are good exercises in remembering how to do practical (hehe) problems from a text you may have been away from for a while. No one is being exploited.

Anyway, my work has been done on this thread

 

[Ziggurat]

It's a big nit. The tensor is not the territory. See for example the Cauchy stress tensor which "is a second order tensor of type (2,0) (that is, a linear map), with nine components σij that completely define the state of stress at a point inside a material in the deformed placement or configuration". It's a map. It isn't the territory.

You clearly don't understand what they mean by "map". When a mathematician says "map", they usually (and in this case) mean something which can take one set (of, say, numbers) and transform it into another set (of, say, numbers). That's called mapping. They do not mean that it's merely a representation. It is a thing in and of itself.

You're great at finding quotes with given terms in them, but you never actually seem to know what any of it actually means.

I'm afraid it isn't, Zig. It's just something new to you.

Yes, it's new to me. Lots of wrong things are new to me. But it's still wrong.

The underlying issue is that textbooks don't teach electromagnetism too well.

There's absolutely no problem with working with E and B fields as separate entities. In most cases, you simply do not need to perform any change in reference frame, so the connection between E and B becomes irrelevant to your calculations. And even in cases where you do need to change reference frames for your calculations, you can always take E and B, form the tensor, do the Lorenz transform on the tensor, pull E and B back out, and work with them independently again.

So no, there's nothing wrong with the textbooks, Farsight.

No, you do not create a magnetic field by moving a charged particle

Yes, actually, you do.

I understand what you're trying to argue: the electromagnetic tensor field itself exists independent of our choice of reference frame. But the individual components do depend on our choice of reference frame, so your deduction from that regarding magnetic fields is wrong. It's like claiming that if you rotate an object, its x dimension will not change, because you didn't squish the object. Well, no: rotation WILL change its x dimension, because its x dimension now measures a different aspect of the object. So too with the magnetic field: if you move a charge, it will have a magnetic field. If you do not move that charge, it will not. You have rotated the electromagnetic field tensor of that object in spacetime, and have thus changed its magnetic field.

See above. The tensor is the map. The field is the territory.

Nope, still wrong.

It's more like combining what you think of as a square, with what you think of as another square, in an attempt to show you that what you've really got is a cube.

Sure, OK, I'll concede that this analogy better describes your error.

 

[Ziggurat]

Quite. And one should properly speak of the electromagnetic field F^αβ, rather than E or B separately.

No. Either is proper. The tensor form is easier to work with if one must change reference frames, but other than that, there's no fundamental difference. They are mathematically equivalent.