The h Bar

hola

18:02

Does you guys know where i can get the solutions manual to Concepts in Thermal Physics by the Blundells?

John Rennie

18:29

@blue: you around?

Anonymous

Yup

John Rennie

I couldn't resist doing that time app

Semiclassical

Here's a physics question. An example that Griffiths does in his E&M is a rotationally-symmetric current-carrying toroid e.g.

Anonymous

Lol, I see. Is it done? :D

Semiclassical

he uses a square cross-section in that case, but notes that the specific cross-section shouldn't matter so long as it's the same all the way around

John Rennie

18:32

@Blue Download here

Anonymous

Downloaded

John Rennie

It's a command line app so open a command prompt, cd to wherever the app is and just run it

Semiclassical

he then starts up a Biot-Savart law calculation, but only to the extent that he uses it to show that the contributions to the magnetic field cancel out in such a way that the result is everywhere circumferential i.e. $\vec{B}=B\hat{\phi}$ in cylindrical coordinates

What I'm wondering is if there's a simpler argument based on symmetry alone.

John Rennie

@Blue It will print the system time, which should be the UTC time, and also the local time i.e. the time as displayed to you.

If you're interested I put the source code there as well.

Anonymous

System time: 18:34:43
Local time: 00:04:43

Semiclassical

18:35

Presumably one also needs to invoke the fact that the magnetic field is divergence-free and transforms as a pseudovector

John Rennie

That all looks fine. The UTC time is indeed about half past six and your local time is 5.5 hours ahead.

Balarka Sen

@Semiclassical This should be no harder than proving the same thing for a planar current carrying circle.

Semiclassical

Do you mean one with a circular cross-section?

Note that the current in here is not circumferential.

John Rennie

@Blue if the time changes again immediately run the app and see what has changed i.e. is it the system time changing or the regional offset going wrong.

Anonymous

So I just run it again when the system shows wrong time?

Anonymous

18:36

Ah, okay

John Rennie

Yes

Anonymous

Gotcha

Balarka Sen

No, I mean, you just need to work with a single cross-section

Semiclassical

Ah.

Balarka Sen

I know the example you gave is not circumferential

Anonymous

18:36

Thanks, I'll let you know :)

Semiclassical

Just checking.

I'm also not convinced that one cross-section is enough, since the point is that you get cancellation of non-circumferential parts contributed from different cross sections

Balarka Sen

I know the "standard" proof, which uses the circuital law.

Semiclassical

hmmmm

tbh I'd be okay with a somewhat handwaving one, so long as it doesn't require invoking Biot-Savart

e.g. there's no way to have a magnetic field line which points radially away without violating X

@dmckee relevant XKCD: xkcd.com/451

Though my prejudice (when it comes to sci-fi, at least) is that I'm very skeptical about any sci-fi scenario being plausible in a meaningful way, at least when it comes to space travel etc

To the extent that I only find such sci-fi interesting insofar as I can suspend my disbelief. So for me an obsession with trying to create "realistic" scenarios is ill-founded from the start

if it's fiction, let it be fiction and let us appreciate it as such. trying to force it to be 'scientific' does an injustice both to the science and to the storytelling.

(ramble done)

@BalarkaSen also, I'm not sure what you mean by the 'circuital law'

What I know are Ampere's law and the Biot-Savart law, so that particular name isn't familiar to me

dmckee

@Semiclassical I certainly agree with the basic sense. But I like science fiction that assumes specific improvements over expected technology and tries to stick close to base reality otherwise, so I understand the motivation for such questions.

Semiclassical

I think the question is where you draw the line between "exploration of possible futures" and "scientific-sounding fantasy"

When it comes to space travel, my threshold for 'fantasy' is pretty low

By contrast, my threshold for stuff involving virtual reality is pretty high i.e. I'm willing to accept more of that as having some plausible basis

As an example: I think that stuff like space exploration and space combat in general are basically people transposing their experience with naval exploration and naval combat into a space setting

that makes for some interesting stories, but as science the analogy of "space is an ocean" is just nonsensical

but i'm rambling

@BalarkaSen oh, of course there's a question on this already lol: physics.stackexchange.com/q/168952/55641

John Duffield

18:55

@Semiclassical : it's a question of understanding electromagnetism, and paying attention to what Maxwell said: “electric currents are regarded as a species of translation, and magnetic force as depending on rotation”.

The magnetic field a “rotor” field, with a North pole and a South pole, because the North pole is just looking at the rotation from one direction, and the South pole is just looking at it from the other. There are no one-sided coins, and there are no magnetic monopoles either.

Semiclassical

insofar as the Biot-Savart law captures that, I'm fine with it

I mean, one answer to my question would just be to note that I can break up the coil into a bunch of pairs of loops

and that their fields combine so as to give only a circumferential field

That's probably the right way to look at it. I'm just trying to see if that's really the simplest argument.

with that in mind, I very much like the answer given in the linked question

it's exactly the kind of result I wanted

John Duffield

It is. The crucial point is that the people who say magnetic monopoles must exist on grounds of symmetry are totally misunderstanding Maxwell's unification. You cannot remove the magnetic aspect from the electron's electromagnetic field. In this respect the electron doesn't have an electric field, so electric charge is a misnomer, so magnetic charge is misguided.

That's from Ampère and the history of electricity

Semiclassical

ehh. I'll assent that it's misguided to hope for magnetic monopoles on the grounds of classical electrodynamics.

That doesn't mean they can't be motivated by other considerations. (I don't know enough about monopoles in QFT language to say what those are, though.)

John Duffield

19:11

@Semiclassical : it isn't some issue of classical electrodynamics, it's a matter of understanding what real actual electromagnetism. IMHO the linked answer doesn't make much sense. The field magnetic field inside a solenoid isn't radial.

Semiclassical

Makes perfect sense to me. The analogue for the solenoid would be: Suppose the field at the center of a solenoid had a component in the $\hat{x}$ direction. If I were to make a reflection across the xz-plane, then this reflection preserves this component. But such a reflection is equivalent to reversing the currents, which should reverse the direction of the magnetic field. So any such component would break the symmetry and it can't be there.

Main thing I don't like about it is that it doesn't tell you much about what happens when you're off-axis in the infinite solenoid.

John Duffield

The main thing I don't like about it is that it shows no understanding of electromagnetism. IMHO it's the same with the Wu experiment and parity violation:

Semiclassical

19:29

Ehh. The point to me is that an appropriate spatial reflection is equivalent to reversing the currents

And reversing the current should reverse the generated magnetic field

The only way for that to be internally consistent is if the field on the axis is parallel to the axis.

John Duffield

IMHO it's better to consider the current in the wire. Two wires with currents flowing the same way will attract one another. When they do, you might be tempted to say one’s a North pole and one’s a South pole. But the two wires are the same, and two North poles repel, they don’t attract. Ditto for two South poles. You only get repulsion when the two wires have currents flowing in the opposite directions.

Expecting to find a monopole is like expecting to find one opposite.

bolbteppa

the way we find anti-particles...

Semiclassical

Okay? As I said, I’m fine with saying that classical electrodynamics has no need for magnetic monopoles

So if there’s any reason to wonder about monopoles beyond mathematical curiousity, it’ll have to come from outside that tradition

As I understand it, there are such motivations within quantum electrodynamics. But that’s clearly a different story than the classical theory

John Duffield

@Semiclassical : if it does come from outside that tradition, it's wrong. The electromagnetic field is something real. It doesn't matter what theory you use to describe it, the electron still has an electromagnetic field rather than an electric field. So electric charge is still a misnomer, so magnetic charge is a wild goose chase. The crucial point it misses is that Maxwell unified electricity and magnetism a hundred and fifty years ago.

See articles like this. Sometimes it feels like Maxwell had never been born.

bolbteppa

19:45

'Joseph Polchinski, a string-theorist, described the existence of monopoles as "one of the safest bets that one can make about physics not yet seen"'

Semiclassical

Ehhh. Just because they’re definitely unified in the classical domain (aka in any setting I’d ever be able to test myself) doesn’t mean that this unity must hold universally

bolbteppa

Since we're arguing by author reference

'I'll counter that with a reference from someone before the 1900's thank you very much'

Semiclassical

I don’t have enough expertise to say one way or another whether particles carrying magnetic charge are possible, to be clear

bolbteppa

Maxwell's equations look unified when you allow for magnetic monopoles:

Magnetic monopole

A magnetic monopole is a hypothetical elementary particle in particle physics that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net "magnetic charge". Classical theories of electromagnetism, represented by Maxwell's equations, disallow magnetic monopoles. Modern interest in the concept stems from particle theories, notably the grand unified and superstring theories, which predict their existence. Magnetism in bar magnets and electromagnets does not arise from magnetic monopoles, but from electric charges (i...

Semiclassical

But as such I find myself inclined to be agnostic about them. Within the classical domain they’re clearly irrelevant, and this is good enough for me

bolbteppa

19:49

If we're going to pretend word salads are arguments, then anybody claiming Maxwell unified the electric and magnetic field saying they are no different, just different manifestations of the same electromagnetic field, should say that their equations should look the exact same, which they do with monopoles, however because frogs and rabbits it means they are not

3

Semiclassical

Ehh. One thing I’ll say in favor of not having magnetic monopoles is that it permits you to get the fields from the four-potential alone

Having magnetic charge, as they note on that page, forces you to include that extra term involving P

bolbteppa

That $P$ thing makes things really complicated

Semiclassical

yeah

bolbteppa

Now, imagine doing all this in $n$ dimensions for strings, and you have fun

Semiclassical

Yuck. So I don’t find that approach to be necessarily within my taste

bolbteppa

19:55

branessssss...

Semiclassical

Doesn’t mean it’s right or wrong, but it does make me not want to touch it if possible

Slereah

@Semiclassical topological defects~

Although monopole defects aren't easy to understand

Domain walls are simple enough

Semiclassical

Yeah, Dirac strings etc

I’ll reiterate once again that I don’t understand enough about how monopoles work in QFT etc to judge whether looking for them makes sense

Slereah

domain walls are pretty simple, it's just that you have different values of the vacuum in different region

and the boundary of these regions have a brutal change in the field value

Semiclassical

But I’m also not prepared to reject them as impossible or even as implausible just because they’re not part of classical electrodynamics

Slereah

20:00

But then it's less easy as dimension decreases because topological defects in $n$ dimensions correspond to the homotopy group $\pi_{2 - n}$

So domain walls just depend on the connected components

Cosmic strings depend on the fundamental group of the vacuum

and monopoles the sphere homotopies

Semiclassical

Nice thing about condensed matter theory is that you can actually find topological defects in nature

Slereah

that too

It's fairly easy with the Ising model

Semiclassical

Right

Slereah

Plus you can build the Ising model physically!

With little magnet arrows

We had one in class

Semiclassical

The boundary of a magnetic domain is literally a domain wall

Slereah

20:02

yes

since the two ground states are all spin down and all spin up

Semiclassical

Right

Slereah

So $\pi_0 = \mathbb Z_2$

Semiclassical

If you’ve got low temp anyways

Or maybe I’m thinking of a different model. I can’t always keep the names straight

What I always find disappointing is that liquid crystals are uniaxial nematics not biaxial nematicse

In the latter case you have a nonabelian pi_1

John Duffield

@bolbteppa : he was wrong. See symmetry magazine, that claim dates from 2002. Maxwell's equations might look symmetrical when you allow for magnetic monopoles, but again, the electron has an electromagnetic field. There are no particles that have an electric field only, so it's a wild goose chase to think there are particles with a magnetic field only.

Slereah

are there "cosmic strings" in liquid crystals?

Semiclassical

20:08

Wouldn’t a magnetic monopole in motion have an electric field?

Slereah

I do not know

You can violate the NEC with domain walls, which is nice

Semiclassical

Seems like it should just on symmetry grounds

Yeah, the Maxwell equations with magnetic charge include a magnetic current term that would drive the electric field

So a magnetic monopole isn’t a particle with magnetic field alone, not anymore than a single electric charge is a particle with only an electric field

Slereah

I do remember that the Maxwell equations are "symmetric" when monopoles are included, but that may have been for a specific theory

So I can't confirm if that's the case for topological defects

John Duffield

@Semiclassical : Dirac was the guy who proposed magnetic monopoles, on grounds of symmetry, or "mathematical beauty" if you prefer. Graham Farmelo talks it in Did Dirac predict the positron? He says Dirac’s "close friend Patrick Blackett, one of the leading players in the story’s denouement, denied it".

He also says "very few physicists took Dirac’s hole theory seriously. The theoretician Victor Weisskopf later recalled the idea ‘seemed incredible and unnatural to everybody’”. This concerned the Dirac's paper monopole paper which (page 62) according to Dirac showed "a symmetry between electricity and magnetism quite foreign to current views".

John Duffield

20:31

To really know why there are no magnetic monopoles, you have to appreciate that the electromagnetic field is a combination of an electric field and a magnetic field, something like the "curl and convergence" image on the right:

Semiclassical

To be clear, my last point is just that a magnetic charge in motion would also have both an electric and a magnetic field. It just wouldn’t have them related in the same way as for an electric charge in motion.

And it turns out that you don’t need them such magnetic charges to describe classical electromagnetism as observed in experiments

So, again, I don’t object to saying that there’s no need for magnetic charges in classical electrodynamic

But I don’t think that people who think magnetic monopoles exist do so because they imagine that every magnetic field line secretly terminates on a magnetic charge

That would seem rather extravagant and implausible.

bolbteppa

20:47

Why bash the Dirac sea, hole theory, in the middle of this?

If monopoles turn out to be observed I can only imagine the word salad argument one would make up to justify it, despite previously denying it

Semiclassical

That is, I don’t think people want magnetic monopoles because they expect it to explain magnetic fields. We’ve got a perfectly sound theory for how the usual magnetic fields we observe exist in nature

John Duffield

IMHO you're missing the point, Semiclassical. There is no such thing as electric charge, or magnetic charge. The electron has an electromagnetic field. So it has electromagnetic charge.

Semiclassical

If it shows up in div E, then it’s an electric charge in my book

Slereah

Well people expect magnetic monopoles because they should be a generic feature in QED

Depending on the initial conditions of the universe, of course

Semiclassical

Which is again something coming from outside the tradition of classical electrodynamics

...which, again, seems hardly strange to me. Why should Maxwell’s theory be the end of the story?

John Duffield

20:52

@Semiclassical : IMHO too many books pay insufficient regard to Maxwell's unification. Including books on quantum field theory.

Semiclassical

Maxwell is authoritative on Maxwell’s theory. But to expect him to be authoritative on how electrodynamics should work in the quantum context seems not merely unrealistic but altogether unfair to him.

John Duffield

@Semiclassical : it isn't the end of the story, but his unification was a step in the right direction. People who talk about electric fields and magnetic fields as if they're two different things are taking a backward step. Electromagnetic field interactions result in linear and rotational forces.

When we contrive matters such that the magnetic forces cancel but the linear forces don't, we talk of an electric field. When we contrive matters such that the linear forces cancel but the rotational forces don't, we talk of a magnetic field. But again, the fields that are interacting that result in these forces aren't electric fields or magnetic fields, they're electromagnetic fields.

bolbteppa

I would imagine this:

qr.ae/TU1YPs

invalidates everything JD is saying

Literally every qft book unifies electricity and magnetism, beginning from the electromagnetic field tensor $F_{\mu \nu}$ btw

John Duffield

@Semiclassical : QED is a whole different kettle of fish. One that has its own problems. I was saying yesterday that I know how a magnet works. It doesn't work because it's spitting out photons. Magnets don't shine.

@bolbteppa : then show me a depiction of an electromagnetic field.

bolbteppa

Once you include magnetic charge in Maxwell's equations, as you see in that link, everything becomes a duality symmetry, and so it's just a choice when you call things X or Y

@JohnDuffield an electric field is a depiction of an electromagnetic field in a certain frame

John Duffield

21:00

@bolbteppa : no it isn't.

Semiclassical

$F^{i0}$

@bolbteppa I suppose in that story that the explanation for “why aren’t there classical magnetic monopoles” is that there’s no reason to pick an angle in that EB plane

Though

John Duffield

@bolbteppa : the electric field lines in this depiction aren't field lines. They're lines of force. They are trying to show you the forces that result when you set down an electron near a positron such that they have no initial motion. They move straight towards one another. But the arrowheads don't work, because two electrons repel, and so do two positrons.

bolbteppa

Maybe, I'm not sure tbh

Semiclassical

That only works if you can do the whole electric-magnetic duality as a continuous transformation

bolbteppa

If that whole angle thing is legit, one would ask why it chose that angle and not others?

Semiclassical

21:06

Well, I think the argument would be that said angle would have no experimental meaning

bolbteppa

@JohnDuffield what does that even mean, are you saying fields are not forces?

So when we write F = qE for electrostatic fields, we are doing jujitsu going from force to fields

Semiclassical

But again it doesn’t rely work if you only have the duality transformation

bolbteppa

This is why learning physics without math instead using authors names as a substitute for equations is so fatally flawed

7

John Duffield

@bolbteppa : yes. The interaction between the electron's electromagnetic field and the positron's electromagnetic field result in linear forces if they have no initial relative motion. But if they do, if you throw the positron past the electron, the interaction between the electromagnetic fields results in linear and rotational forces.

bolbteppa

The electromagnetic field is classically described by an electromagnetic field tensor, $F^{\mu \nu}$, which, in a frame for which the magnetic field $B$ is zero, becomes an electric field, if you want to talk about Maxwell's unification you use $F^{\mu \nu}$

Slereah

21:09

QFT doesn't even use $F$ that much

It's all about the EM potential!

Semiclassical

Yeah.

Which is one reason magnetic monopoles do weird me out a bit, since you can’t do them using A alone

John Duffield

@bolbteppa : don't kid yourself. I know the maths. And what I also know is that in this expression: $\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$, the equals sign isn't "creates" or "generates". It's "is".

Slereah

I think it depends which theory you use to make magnetic monopoles

Semiclassical

I know too little to say either way, it just seems strange

John Duffield

@bolbteppa : hence the curl and convergence picture on the right:

Slereah

21:12

well fortunately for you, none have been detected so far!

Semiclassical

lol

Slereah

So probably nothing to worry about too much

bolbteppa

So those pictures are not pictures of an electromagnetic field, therefore you deny Maxwell's unification, cogito ergo sum?

Slereah

either there are none or inflation just blew them all over the place

Semiclassical

At the end of the day, we’re arguing about something that no one has observed yet or may ever observe

Slereah

21:13

Things that have been observed is only good for experimentalists!

John Duffield

@bolbteppa : no I don't deny Maxwell's unification. Maxwell drew those pictures in his 1871 paper Remarks on the Mathematical Classification of Physical Quantities.

bolbteppa

So are those pictures of an electric field, or an electromagnetic field, and why are you saying there is a difference when a minute ago you said there was none?

John Duffield

@Slereah : there are none, and there can be none, because space is a continuum.

Semiclassical

I just find it silly to suppose that magnetic charges being unnecessary in everyday E&M makes it foolish to reconsider them in the QED context

John Duffield

@bolbteppa : the electric field is on the left, the magnetic field is in the middle, the electromagnetic field is on the right.

bolbteppa

21:16

So you deny Maxwell's unification, by saying an electric field is different from (the electric part of) an electromagnetic field, even you, let alone those qft books, do it

Slereah

I don't even remember what vacuum has the appropriate $\pi_2$ structure to form monopoles

Semiclassical

Just because it was appropriate for what Maxwell was doing doesn’t mean it’s the end of the story in the QED context

Slereah

@bolbteppa don't be a sap

Stop talking to him

3

John Duffield

@bolbteppa : here's another drawing, by me:

Semiclassical

Yeah, this conversation has a definite “div E < 0” feel to it

Slereah

21:18

badum tish

bolbteppa

Sheer madness, fair enough, stopped

Semiclassical

@JohnDuffield what equation is that field on the right supposed to obey?

bolbteppa

I don't think hole theory is necessarily wrong though, just a bit crazy

Semiclassical

I wonder about it sometimes. When you do semiconductors etc, you do speak a lot about hole states as though they’re actual particles

One doesn’t mean that literally, but they are accepted as being appropriate descriptions of the relevant physics

John Duffield

@bolbteppa : no I don't deny Maxwell's unification. In On Physical Lines of Force 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". The curl + convergence is showing it.

bolbteppa

21:24

phonons is another thing I need to get to properly

Semiclassical

So it seems to point more broadly to the question of how different vacuums work in field theory, in particular how they’re supposed to be interpreted

Evidently that kind of thinking is very effective and useful. But I don’t know quite what it’s supposed to mean

bolbteppa

Do differential equations spit out irreducible representations of a group automatically, if so Dirac's motivation for the Dirac equation of just wanting a linear differential equation for covariance is kind of perfectly correct right?

John Duffield

@Semiclassical : when you have two of them together, they obey Coulomb's law ${\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}},$ and the Biot-Savart law $\buildrel F\over F\rightarrow=k_m\frac{q_1q_2}{r^2}{\buildrel v\over v\rightarrow}_1\times({\buildrel v\over v\rightarrow}_2\times\buildrel r\over r^)$.

Uh, sorry about that bad latex copy and paste.

Semiclassical

Happens.

But, uh

Within Maxwell’s equations, I don’t know how you’d get a field which satisfies those simultaneously

John Duffield

It's two electromagnetic fields interacting. The result is linear "electric" force and/or rotational "magnetic" force.

Maxwell's equations aren't Maxwell's equations. They're Heaviside's equations.

Semiclassical

21:32

So basically you propose that to properly understand E&M, one can’t accept the defining equations of that subject. (whether you call them Maxwell ‘s equations or Heaviside’s equations)

Slereah

@bolbteppa it's pretty hard to make an equation by hand that isn't an irrep :p

I mean you can, but it would be a bit weird looking

Anonymous

Maxwell's equations aren't Maxwell's equations

Slereah

Although of course, there's the whole vector equation that isn't a vector equation

Anonymous

That's nice to hear

Semiclassical

@Blue eh, as a historical claim I’m not totally skeptical of that

Soviets would have considered themselves as Marxists; doesn’t mean he’d have agreed with them

Anonymous

21:35

@Semiclassical I don't even understand the statement

Anonymous

It's basically saying $A\neq A$

Anonymous

Or are you saying those weren't given by Maxwell?

bolbteppa

I vaguely remember seeing differential equations produce irreducible representations, or maybe only some do

Slereah

Obviously only some

John Duffield

@Semiclassical : I'm saying you have to go back and read what Maxwell said.

Slereah

21:38

String action is a sum of every integer rep :p

Semiclassical

“What we refer to as ‘Maxwell’s equations’ refer to equations put forth by Heaviside, and therefore stuff Maxwell wrote does not have to conform with said equations.”

Slereah

Heaviside did the vector calculus aspect

But Maxwell did have the equations originally

They were just horribly written

Anonymous

@Semiclassical Alright, got your point

John Duffield

@Blue : yes, Maxwell's equations aren't Maxwell's. Read the history.

Semiclassical

Or perhaps “Maxwell’s work need not reduce down identically to what we call ‘Maxwell’s equations’l

Slereah

21:40

Also originally Maxwell's equations included charge conservation

Semiclassical

Oops

Slereah

Original equations were like this :

John Duffield

"The four modern Maxwell's equations can be found individually throughout his 1861 paper, derived theoretically using a molecular vortex model of Michael Faraday's "lines of force" and in conjunction with the experimental result of Weber and Kohlrausch". Baby, bathwater.

Slereah

a bit wordier

John Duffield

OK guys, I have to go. Bye.

Semiclassical

21:52

The point I’d take is that we tend to treat “Maxwell’s unification “ as synonymous with “Maxwell’s equations”, and that this is potentially quite reductionist

bolbteppa

Geometric algebra turns them into 1 equation apparently

Semiclassical

Weird

I should sit down when I get home and see if I can extend the duality transformation in a continuous way

vzn

yes, maybe 1000s of refs on maxwell, and how many mention "vortex model" + fluid dynamics? swept under the rug o_O

Semiclassical

Ie start with a theory containing both electric and magnetic charges and find a mapping to one with just electric charge

If one can do that, it makes the notion that the lack of electric charge is just a judicious choice of fields as rather plausible

Slereah

@bolbteppa Well two

$d*F = j$ and $dF = 0$

bolbteppa

22:00

page 4 says GA reduces it all to only 1 equation

mrao.cam.ac.uk/~anthony/…

Slereah

Well it's kind of an unstated thing

bolbteppa

Part of the propaganda/selling-points for doing GA :p

Slereah

$dF = 0$ is generally not written explicitely

It is equivalent to $F = dA$

bolbteppa

pages 22-23 also

They basically use $F = E + i B$ I think

Slereah

Oh man

That's the...

bolbteppa

22:03

Geometric algebra

Slereah

Dual field formalism?

I forget the name

bolbteppa

No, this is geometric algebra, different from that too

I think it ultimately boils down to the isomorphism between $SL(2,C)$ and the Lorentz group, i.e. representing vectors with matrices $x^{\mu} \to X = x^{\mu} \sigma_{\mu}$, but they pitch it like it's magic

Semiclassical

Double field maybe?

bolbteppa

David Hestenes

David Orlin Hestenes, Ph.D. (born May 21, 1933) is a theoretical physicist and science educator. He is best known as chief architect of geometric algebra as a unified language for mathematics and physics, and as founder of Modelling Instruction, a research-based program to reform K–12 Science, Technology, Engineering, and Mathematics (STEM) education. For more than 30 years, he was employed in the Department of Physics and Astronomy of Arizona State University (ASU), where he retired with the rank of Research Professor and is now emeritus. == Life and career == === Education and doctora...

"Innovations in the book include the concepts of vector manifold, differential outermorphism, vector derivative that enables coordinate-free calculus on manifolds, and an extension of the Cauchy integral theorem to higher dimensions"

'Hestenes is adamant about calling this mathematical approach “geometric algebra” and its extension “geometric calculus,” rather than referring to it as “Clifford algebra”. '

Slereah

@bolbteppa Geometric algebra is related to the whole Clifford algebra thing

So probably

Semiclassical

22:09

Lol

Apropos of nothing cough I was looking at this Wiki article yesterday

bolbteppa

This is unfortunately not a medium where you can run rings around such cough's

Semiclassical

And what struck me as funny was comparing their description of the “# of chromosomes” history as compared with the historical note on the linked Chromosomes page

Notice a difference in subtext?

bolbteppa

The thing about science is, you sometimes need these authority arguments on some level, e.g. climate change, where all people really to go on is the authority of the people who studied this stuff, or when people want Popperian proof, that gets thrown out the window when you look at reality, nothing is certain, everything fluid

qft being a mess especially

e.g. from a legit review of Bjorken and Drell:
"Who is kidding whom? Do physicists expect mathematicians to take them seriously after reading books like these, which-through no fault of their own-make a mockery of rigorous mathematics and even, at times, of serious reasoning ? We would not be surprised if particle physics were to be one day renamed Zen-ical physics, or something like that."

Semiclassical

Well, what I find notable in the example is the slant each puts on Painter

So in the first one you have references to Painter’s “poor data and conflicting observations “, along with further anecdotes about photos in bio books which “clearly” showed 23 not 24

bolbteppa

Feynman makes a similar point

About people doubting their own measurements for years on something, I think Thompson's electric charge measurements

Millikan

calteches.library.caltech.edu/51/2/CargoCult.htm

Cargo cult science

Cargo cult science is a phrase describing practices that have the semblance of being scientific, but do not in fact follow the scientific method. The term was first used by physicist Richard Feynman during his 1974 commencement address at the California Institute of Technology. Cargo cults are religious practices that have appeared in many traditional tribal societies in the wake of interaction with technologically advanced cultures. They focus on obtaining the material wealth (the "cargo") of the advanced culture by imitating the actions they believe cause the appearance of cargo: by building...

Semiclassical

22:26

The overall slant being rather conspiratorial

Whereas the second one is rather sympathetic to Painter, noting that he wavered between 23 and 24, and that it took the development of better techniques to be sure

bolbteppa

That's a great example of ideology, the perspective of the first is pretty common

Semiclassical

And the thing is: I don’t know where the truth lies. I find the first one less credible due to how slanted it feels (which is rather hilarious given that it’s an article about rhetorical fallacies)

bolbteppa

There's a real absolutism to the first perspective, like they were all idiots who went against the tide of history or something, now of course we're immune to such thinking hum hum, or rather, those of us in the group who know better

Semiclassical

Right.

But I’m in no position to actually judge the history

Though I do find the following revealing: the bit about the textbooks isn’t from an academic source, but rather a book written for a popular audience

By contrast, the other sources in the first page seem to give far more credibility to Painter

bolbteppa

The first one says 46 (23 pairs unless I'm forgetting something) and links to his paper, the second implies he said 48 (24 pairs) in that paper, so I'm not sure if I'm following

Semiclassical

22:35

Getting a bit mixed up here

bolbteppa

second one*... first one*... :p

Semiclassical

Right now I’m only looking at the sources for the “appeal” article

And I have in mind sources [23], [24]

The middle of page 11 in the first one is pertinent

And in the second one the upshot is not “it’s really 23, silly” but “2n=46 is typical but not an absolute fact”

Which is a bit more of a meta-argument from authority point: Not only shouldn’t you treat an authority with undue deference, you shouldn’t treat narratives about authority with undue deference either

Slereah

23:24

Well you shouldn't trust anyone, really

but then again

You probably don't have the time to perform every experiment ever yourself

Plus you can't build a LHC yourself

2

0celo7

@ACuriousMind yoooo

@Semiclassical you too

what is the best way to number conclusions in a theorem environment

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