Why is there so much crackpot physics?

[Perpetual Student]

Yes.

There are at least two more reasons why quaternions have pretty much disappeared from physics and math curricula:

• Vectors generalize to higher dimensions. Quaternions don't. That generalization is needed for quantum mechanics and particle physics.
• Vectors generalize to differentiable manifolds, where the tangent bundle attaches a separate vector space to each point of the manifold. That generalization allows a simple formulation of covariant and contravariant transformations, which are needed for general relativity.

Since vectors are going to be needed for advanced physics anyway, it makes sense to introduce vector methods in freshman-level calculus and physics.

There is no such motivation for teaching quaternions at the freshman level. Quaternions are still taught in some undergraduate-level math courses, mainly because they're the most field-like extension of the complex numbers that can exist.^{[size=-1]1[/size]} Quaternions provide a simple and elegant representation for some practical problems, but their applicability is limited.

Quaternions were more important in the 19th century, when non-commutative multiplication was an interesting new idea and vector analysis had not yet been invented.

[size=-1]^{[size=-1]1[/size]}The word "field" has several meanings, even if we don't count the meaning Farsight's going to invent when he responds to ctamblyn.[/size]

Nice summary.

 

[tsig]

Agreed, but ignorance of mathematics does not fully explain crackpot thinking.

For most people, the mathematics used in modern physics puts physics out of their reach. Very few of them invent their own crackpot physics, or fall prey to crackpot physics invented by others. Even fewer write entire books full of crackpot physics, or post thousands of messages promoting crackpot physics.


Did your grandmother argue about those stories with those who were able to read English? Did she claim to read English better than those who really could?

Crackpot physics does not come from mathematical illiteracy alone, although that's part of it. Crackpots combine ignorance of math with irrational belief in their own superiority and stubborn refusal to learn from those who can actually read math or do physics.

It's the absolute certainty that they are right and everybody else is wrong that trips my trigger.

I have found that the less I know about a job the easier it looks.

 

[tsig]

I know what field means. I've been telling you guys about the electromagnetic field remember? You know, putting Clinger straight on his electric field and his magnetic field, that aren't fields, but instead just the linear and rotational forces that result from electromagnetic field interactions. You know I'm right about that. You cannot offer any criticism of Maxwell and Minkowski's screw nature of electromagnetism. So don't try to suggest I'm guessing. I'm not, and you know it.

Sure thing. And guess why? Because it's a quantum field structure with a definite three-part substructure. It's more complex than the electron.

Nor do quarks. Searching for structure is like probing a whirlpool with a barge pole and saying whatever's in the middle of this must be really small, because I can't feel anything. There isn't anything in the middle!

And the electron's field is not just part of what it is, it's what it is. It isn't a point particle.

I know how it works. Everything is field, or wavefunction if you prefer. The electron is not some point-particle billiard-ball thing with a mystical field tacked onto it, as if that field could somehow be taken away. It isn't just an "an excitation of the electron field". It's a particular field configuration with a topology and geometry. Go use TQFT to describe that. It definitely isn't some point-particle. When you see a dot on the screen you might think that it is, but it isn't. And again: the electron's field is what it is.

Now I really must go.

Is electricity right handed or left handed?


Got math?

 

[Farsight]

Electricity is typically the movement of electrons, so it's right handed. The usual math is Ampère's circuital law. See the right-hand-rule diagram, on the right. The article refers to electric fields and magnetic fields instead of the electromagnetic field. Like I was saying, better to think of them as the linear and rotational forces on a test particle resulting from electromagnetic field interactions.

 

[Farsight]

OK, shoot. Let's see if your definition is consistent with the one used in physics, or with your claims.

As I said a day or so ago potential is "more fundamental" than field, but I'll skip that. A field is typically a spatial disposition or structure. It isn't something separate from space. It's a "state of space". When that state is uniform and homogeneous, we usually say there's no field present. However a wave or field variation can propagate linearly through such space. A wave can also take the form of a standing wave whereupon the field-variation is now a standing field. These can combine in a variety of ways, altering the state of space away from the origin in a fashion that is different from a single linear or standing wave. Would you like me to draw you some pictures?

For the record: After my rebuttal of the last attempt to defend the claim that the AB effect is explained by classical electromagnetism, answer came there none, either in the form of counterargument or concession.

I gave quite enough "classical" references. And it's obvious that lpetrich has never heard of Ehrenberg and Siday, and you're working hard to spare him embarrassment. Move on.

 

[edd]

When that state is uniform and homogeneous, we usually say there's no field present.

No. I'm not going to dismantle everything you say all the time, but uniformity and homogeneity do not preclude anisotropy, and therefore do not preclude non-zero fields.

 

[Farsight]

No, quite the opposite.

Yes. Maxwell didn't talk about vortices and screws for nothing. They aren't called spinors for nothing.

A whirlpool-like electron, with "nothing in the middle", would have elastic-scattering cross sections that vary like 1/q^2 F(q^2), where F(q^2) is a "form factor" describing the size and internal structure of the whirlpool.

Straw man.

In electron-proton scattering, F(q^2) is approximately 1/(1 + q^2/((1 fm)^2)), which is what QFT predicts for an extended object about 1 fm across.

The field is part of the object, it doesn't stop at 1fm.

A pointlike electron would have an elastic scattering cross section that varies like 1/q^2. I.e., it looks like F(q^2) = 1.

LEP has done this experiment. Electron-positron scattering has a cross section that varies like 1/q^2, with no additional F(q^2) cutoff down to 0.00001 fm. The electron is not a whirlpool.

Wrong conclusion. You're scattering one whirlpool off another.

Congratulations on having a mental picture of the electron as a whirlpool, but mental pictures aren't enough. Actual physicists have mental pictures, and mathematical predictions, and experimental tests. The cross section for scattering off of an extended object, like a whirlpool, does NOT have a simple 1/q^2 dependence. Scattering off a point particle DOES have a simple 1/q^2 dependence. This experiment has been done many times, most powerfully by LEP, and your mental picture fails the experimental test.

No, yours does, along with your conclusion, because we can diffract electrons. How can you diffract a point particle ben? How can a point particle spin? How in an atomic orbital can a point particle exist as a standing wave? Magic? Quantum mysticism that defies all human understanding?

 

[Kwalish Kid]

Wrong conclusion. You're scattering one whirlpool off another.

Please show us your calculations. Without this, you are simply presenting a religious position.

 

[ctamblyn]

As I said a day or so ago potential is "more fundamental" than field, but I'll skip that. A field is typically a spatial disposition or structure. It isn't something separate from space. It's a "state of space". When that state is uniform and homogeneous, we usually say there's no field present. However a wave or field variation can propagate linearly through such space. A wave can also take the form of a standing wave whereupon the field-variation is now a standing field. These can combine in a variety of ways, altering the state of space away from the origin in a fashion that is different from a single linear or standing wave. Would you like me to draw you some pictures?

I asked for a definition. What you have provided is not the definition of a field, but your personal mental image of certain types of field, which is of questionable applicability to nature.

Here's a good one: https://en.wikipedia.org/wiki/Field_(physics)

A field, in physics at least, is just a physical quantity defined over a region of spacetime, varying from place to place and/or time to time. It's nothing more than a function mapping spacetime events to values of a physical quantity.

The electric and magnetic 3-vector fields? As the names suggest, they're fields. The Faraday tensor you love? That's another field, related to those first two. The e/m 4-vector potential? That's a field too. How about the ordinary scalar potential? Yep, despite not being Lorentz-invariant. How about the local density of a fluid in the continuum approximation? Yes, that counts. As does its velocity. As does its temperature, and so on.

There are oodles of different types of field - we're not limited to simple scalars, vectors and antisymmetric tensors of rank 2. In canonically-quantised QFT you have operator-valued fields which annihilate and create field quanta (particles), while in the path-integral formulation you can have Grassmann-number-valued fields which anticommute (these are required to represent fermions properly). In relativity theory you can have tensor fields of arbitrary rank (e.g. the Ricci scalar, the metric, the Riemann tensor, the stress-energy tensor, ...). And so on.

(Mathematicians have yet another type of "field", an algebraic object unrelated to the above.)

I gave quite enough "classical" references. And it's obvious that lpetrich has never heard of Ehrenberg and Siday, and you're working hard to spare him embarrassment. Move on.

Merely finding the word "classical" in a paper is not a counterargument, Farsight - or are you suggesting that your position is supported by music history literature too?

I hilighted the part of each source you quoted which exposed the flaw in your argument, including (most importantly) in Ehrenberg and Siday's original paper:

• Ehrenberg and Siday state they are using a wave model: http://www.internationalskeptics.com/forums/showthread.php?p=9286439#post9286439
• Michael Berry state that E+S used a semi-classical approximation (i.e. quantum mechanics): http://www.internationalskeptics.com/forums/showthread.php?p=9286571#post9286571
• Peter W. Hawkes and E. Kasper note that E+S used a semi-classical approximation: http://www.internationalskeptics.com/forums/showthread.php?p=9287090#post9287090

Anyone who understands classical electrodynamics knows that electrons are modelled as charged, usually pointlike, classical particles which obey the Lorentz force law F = qE + qv×B, according to which there is no AB effect. That's exactly why the ES and AB papers are remarkable - they showed that in a quantum mechanical model there was this novel effect that classical mechanics said was theoretically impossible.

Cool page here for those actually interested: http://rugth30.phys.rug.nl/quantummechanics/ab.htm

ETA: I dug out The Feynman Lectures (II, 15-11), as he provides a very clear description of this effect:

...
You remember that for a long solenoid carrying an electric current there is a B-field [i.e. a magnetic field] inside but none outside, while there is lots of A [the 3-vector potential] circulating around outside, as shown in Fig. 15-6. If we arrange a situation in which electrons are to be found only outside of the solenoid - only where there is A - there will still be an influence on the motion, according to Eq. (15.33). Classically, that is impossible. Classically, the force depends only on B; in order to know that the solenoid is carrying current, the particle must go through it. But quantum-mechanically you can find out that there is a magnetic field inside the solenoid by going around it - without ever going close to it!
...

And how is that effect detected? By shifts in the position of interference fringes. It's about as non-classical as you can get.

 

[Farsight]

It's still a quantum-mechanical effect...

Shame the articles say "classical". But now you know about Ehrenberg and Siday.

In other words, Heaviside's version is a perversion of Maxwell's revealed truth, because it is misleading about the nature of the electromagnetic field.

No, what Clinger says is a perversion of the truth because he doesn't understand electromagnetism at all. Like I said, provided you pay attention to the distinction between field and force as per that Minkowski quote, everything is fine. The problem comes when you start thinking of the force as a field in its own right.

(Maxwell and Minkowski book-thumping snipped...)

Don't conveniently drop the Minkowski quote, lpetrich. Here it is again. Pay attention, I've bolded a few words to reinforce my point:

"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".

Hermann Minkowski^WP was the one who showed how special relativity leads to the notion of a space-time continuum.
So if you deny space-time, you deny Hermann Minkowski.

I don't. I just point out that it's a mathematical artefact.

More seriously, the idea of space-time makes absolute hash out of the notion that motion is somehow more fundamental than time.

Don't talk wet, lpetrich. Hold you hands up. See that gap, that space between them? You can't see the space itself, but you can see that there is a space between them. So space is empirical. Now waggle your hands. That's motion. It's empirical too. Now you show me some time flowing.

He was trying to think of some non-mathematical analogy for something that's easy to describe mathematically.

And it's an apt one too. Electromagnetism really does have a screw nature. That's why Maxwell said A motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw. He didn't say it for fun, Loren.

Don't make me laugh. Do you understand the mathematics of it? Like the mathematics of electromagnetism as a gauge theory.

Well enough. And I'm the only one here who actually understands electromagnetism, remember? So I don't just understand the mathematics, I understand the meaning of it. You don't. Remember this post? Your understanding goes as far as the photon is a blob of light. You might want to check out where it all began, with Hermann Weyl. William Straub's website is pretty good. See this.

From Jackson's great tome:

one should properly speak of the electromagnetic field Fuv rather than E or B separately

It's like talking about E instead of Ex, Ey, Ez, or like B instead of Bx, By, Bz.

No it isn't. E isn't a field. It's a force resulting from the interaction of one electromagnetic field with another. The electromagnetic field has a screw nature. Two dynamical vortices move linearly apart. They do this because of Fuv interaction, not because there's some E fields with radial lines sticking out of them.

Except that semiclassical refers to quantum-mechanical calculations that make some use of the classical limit.

Stop kidding yourself, lpetrich. Look at this:

"It is interesting to note that the reasoning of Ehrenberg and Siday was based almost wholly on classical mechanics, the only wave-optical notion being the elementary interference relation that phase difference = k x (path difference)".

Here's a fair-use excerpt of the paper.

"In the optics of light the value of p as a measured quantity is finite and single valued and is continuous except at a finite number of surfaces separating different media. As will become apparent later, however, more general mathematical expressions can be used in place of the simple values usually given, and in electron optics they arise in fact automatically. Particular expressions are admissible only if they do not violate the conditions implied for the validity of Fermat’s result. Firstly, the difference of Fermat’s integrals along any two paths must be defined .anywhere in space where the optical properties are to be investigated. This requires that the refractive index should be fixed everywhere in space once it is fixed in the neighbourhood of one point, so that p must be single valued. Secondly, it should have no singularities through which Fermat’s integral would become infinite. And thirdly, any discontinuities should be of such a nature that they appear as limiting cases of a continuous p. This is true for the boundary between two optical media but would not be true if, for example, p were proportional to a cyclic coordinate which is limited to the values 0 to 2~ in order to make it singlevalued, for the numerical values of the integrals along either side of an irremovable discontinuity will not be equal even when the lines are infinitely close together. That would make the weak variation required by Fermat’s principle impossible..."

No kidding, it's all about electron optics. For good reason, might I add.

 

[Farsight]

...Well, it is your dog. So clean up after it yourself, train it better or just keep it in your own yard. The choice remains yours.

It's not my dog. I haven't got a dog.

Seems to be another aspect of crackpot physics. A particular distain for some analogies while a 'rule of law' type of adherence to others. In fact in most cases I've seen it seems to be a perception of physics predominantly by just analogy.

Says The Man who isn't talking physics, and tries it on with a bit of sly "crackpot" abuse. Pah. Talk physics. If you don't, you might just as well stick a label on your forehead that says Troll.

 

[ctamblyn]

Stop kidding yourself, lpetrich. Look at this:

"It is interesting to note that the reasoning of Ehrenberg and Siday was based almost wholly on classical mechanics, the only wave-optical notion being the elementary interference relation that phase difference = k x (path difference)".

My highlights.

ETA: Do you actually know what the AB effect is, and how it is detected?

ETAA: Here are some hints (read the abstracts):

http://pra.aps.org/abstract/PRA/v34/i2/p815_1

...The relative phase shift was measured between two electron waves passing through spaces inside and outside a tiny toroidal ferromagnet, ...

http://adsabs.harvard.edu/abs/1999Natur.397..673B

...This phenomenon reflects the dependence of the phase of the electron wave on the magnetic field, known as the Aharonov-Bohm effect, which causes a phase difference, and hence interference, between partial waves encircling the conductor in opposite directions. ...

 

[Farsight]

I asked for a definition. What you have provided is not the definition of a field, but your personal mental image of certain types of field, which is of questionable applicability to nature. Here's a good one: https://en.wikipedia.org/wiki/Field_(physics)
A field, in physics at least, is just a physical quantity defined over a region on spacetime, varying from place to place and/or time to time. It's nothing more than a function mapping spacetime events to values of a physical quantity.

What physical quantity? A quantity of oranges? There's no other way to say this: my definition is better than the one you got off wiki. You know why? Because it isn't my definition. It's Einstein's. In fact it even predates him. See Einstein's 1929 presentation on the history of field theory and pay attention to this:

"The two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric".

So it isn't my personal mental image now is it?

The electric and magnetic 3-vector fields? As the names suggest, they're fields...

Aaargh! No they're not! Haven't you paid even the slightest attention to what I've been saying? To what Minkowski said? To the fact that Maxwell unified electricity and magnetism and voila, gave us the electromagnetic field? E and B aren't fields! They're forces!

The Faraday tensor you love? That's another field, related to those first two. The e/m 4-vector potential? That's a field too. How about the ordinary scalar potential? Yep, despite not being Lorentz-invariant. How about the local density of a fluid in the continuum approximation? Yes, that counts. As does its velocity. As does its temperature, and so on...

Oh for Chrissakes, ct. There is not a "water temperature field" in my bath.

Merely finding the word "classical" in a paper is not a counterargument, Farsight - or are you suggesting that your position is supported by music history literature too?

Now you're just getting ridiculous. See the excerpt in my post to lpetrich above.

Anyone who understands classical electrodynamics knows that electrons are modelled as charged, usually pointlike, classical particles...

Waves are classical. The electron was discovered in 1897 by JJ Thomson, its charge was established by Millikan in 1911, and the wave nature of electrons was confirmed in 1927 by JJ's son and by Davisson and Germer. Now go tell ben that the electron isn't a point particle.

And how is that effect detected? By shifts in the position of interference fringes. It's about as non-classical as you can get.

Oh come on, ct. That's what Michelson and Morley were doing.

Right, physics lesson over, boys. Gotta go.

 

[Perpetual Student]

Good grief:

Aaargh! No they're not! Haven't you paid even the slightest attention to what I've been saying? To what Minkowski said? To the fact that Maxwell unified electricity and magnetism and voila, gave us the electromagnetic field? E and B aren't fields! They're forces!

How sad but revealing! The concept of field seems to be beyond Farsight's comprehension:
FIELD
Perhaps a review of the wiki article might be of some help.

 

[ben m]

Farsight might also wish to note that Ehrenberg and Siday begin their paper, i.e. establishing that they will use a wave equation for the electron, by citing Louis de Broglie. Does that name ring a bell, Farsight? Pioneer of quantum mechanics, perhaps?

 

[edd]

What physical quantity? A quantity of oranges? There's no other way to say this: my definition is better than the one you got off wiki. You know why? Because it isn't my definition. It's Einstein's.

So now you think it suits you Einstein is suddenly unquestionably right again? This is a joke.

 

[ctamblyn]

What physical quantity? A quantity of oranges? There's no other way to say this: my definition is better than the one you got off wiki. You know why? Because it isn't my definition. It's Einstein's. In fact it even predates him. See Einstein's 1929 presentation on the history of field theory and pay attention to this:

(...Einstein very much not providing support for this argument snipped...)

Einstein is talking about two specific fields -- both of which, incidentally, I mentioned in my previous post as examples of fields. You presumably imagine that this in some way addresses my objections or answers my request for a general definition of "field". Well, no, it doesn't. Not in the slightest. You have, however, confirmed my belief that you don't use the same definition of "field" as the physics community, so at least we've cleared something up.

On the subject of you posting papers with the word "classical" in them even though they contradict your position when you actually read them:

Now you're just getting ridiculous.

Every link - without exception, absolutely every one you posted - contradicted your argument in unambiguous terms. I even quoted some of the relevant parts of the articles for you, but you seem to imagine that just because you were able to quote-mine some other part of the article that contained the word "classical" that you have proven you point. Well, no, you haven't, but you have confirmed my belief that you don't understand Ehrenberg and Siday's discovery. I guess this is progress, of sorts.

On my pointing out that the AB effect can be detected by observing shifting of interference fringes:

Oh come on, ct. That's what Michelson and Morley were doing.

Er... no... they were looking at inteference fringes in light, in a totally different context which is completely irrelevant to the present discussion.

When you begin to study quantum mechanics, you learn very quickly indeed that you can detect interference in, e.g., two-slit experiments with electrons. You even get to do it yourself in a lab. This is really basic stuff, the denial of which is damaging in the extreme to the credibility of your claims about understanding quantum mechanics in general (and the AB effect in particular).

You have the opportunity to prove me wrong. Answer these questions, if you can:

(1) What is the Aharonov-Bohm effect?
(2) How is it detected experimentally?

 

[ctamblyn]

Farsight might also wish to note that Ehrenberg and Siday begin their paper, i.e. establishing that they will use a wave equation for the electron, by citing Louis de Broglie. Does that name ring a bell, Farsight? Pioneer of quantum mechanics, perhaps?

I'll just note, for kicks, that they end their paper by predicting a certain well known and unambiguously quantum-mechanical phenomenon:

One might therefore expect wave-optical phenomena to arise which are due to the presence of a magnetic field but not due to the magnetic field itself, i.e. which arise whilst the rays are in field-free regions only. Consider now an arrangement as in Figure 3. O denotes a point source of electrons which is focused by the lens M at the point P. Through the pair of slits separated by l a set of interference fringes will arise so that the distance of the nth maximum from P is given by d = bλ₀n/l. If, now, a magnetic flux is established normal to the plane of the paper through the area a, then, according to (43), the order of interference at any point of the focal plane is changed by
...
[equation 50 snipped due to my laziness]
...
Thus, a flux of 3.9 ✕ 10^-7 gauss cm² is required to change the order of interference by 1, and half of this flux will change the maximum at P to a minimum.

It is very curious that equation (50) associates a phenomenon observable at least in principle with a flux; one expects a change of flux, but not steady flux, to have observable effects. The effect has, however, a certain analogy in the existence of a permanent current in a superconducting ring due to a magnetic flux through it.

Highlighted for Farsight's benefit.

 

[Reality Check]

Yes. Maxwell didn't talk about vortices and screws for nothing. They aren't called spinors for nothing.

Maxwell may have talked about vortices and screws.
These are also the "lies to children" that high school teachers teach their students.
So what, Farsight?

Electrons are never called spinors because they are two different things. Electrons have spin bout the words screw and vortex are rarely used in the scientific literature about electrons and never about the spin. Unless someone is idiotic enough to think that electron spin is classical spin, electrons have an extent and thus the charge on their surface follows a cylindrical screw path !
Spinors are mathematical objects that appeared in Dirac's equation.

 

[godless dave]

Shame the articles say "classical". But now you know about Ehrenberg and Siday.

Do they say "classical", or do they say "semi-classical" or "classical analogue"?