Why is Maxwell's theory so hard to understand? (2007) [pdf] • Hacker News Board

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#121

Post by NotAnEconomist » Wed, Jan 09, 2019, 2:51 PM UTC

axilmar wrote: post #100

NotAnEconomist wrote: post #29

Earlier quoted context omitted.

But the arms are predicted to vary in those cases by the same theory that LIGO is confirming: our rotation causes frame dragging, and there's some weird Sun-Earth orbital relativistic effects as well, right? I know the Sun-Jupiter orbit produces a large portion of the estimated 5,000 watts of gravitational emissions given off by our solar system. My mental model of this is that it perturbs the aether ("spacetime") th…

By aether, do you mean an underlying medium that allows forces to be propagated? I guess that using that definition, there is an 'aether'. The difference with the rejected concept of aether is that this "aether" is deformable by gravity, whereas the rejected one is not.

> By aether, do you mean an underlying medium that allows forces to be propagated? I guess that using that definition, there is an 'aether'.

That's what an 'aether' is -- that background medium which the interaction is happening within.

My conception of it is that Michelson-Morley disproved an infinitely rigid aether, which was the conception at the time and squared with Newtonian physics because it's equivalent to an infinite speed of information.

Einstein then corrected the aether models to account for the finite speed of information through the aether, and the impacts that aether waves have on causality.

My impression has always been that dropping 'aether' was merely a branding move, rather than anything technical about the term. (Not that I fault scientists for this, it's politically savvy -- but it's weird to see their marketing used as arguments decades later.)

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#122

Post by NotAnEconomist » Wed, Jan 09, 2019, 2:52 PM UTC

raattgift wrote: post #120

axilmar wrote: post #100

Earlier quoted context omitted.

By aether, do you mean an underlying medium that allows forces to be propagated? I guess that using that definition, there is an 'aether'. The difference with the rejected concept of aether is that this "aether" is deformable by gravity, whereas the rejected one is not.

> underlying medium that allows forces to be propagated General Relativity is a local theory concerned with the mechanisms that generate the metric, the geodesics implied by the metric, and the coupling of objects to those geodesics. The relevant forces are those which accelerate objects into non-geodesic motion (or boost them from one geodesic to another). Those are local[1] as well: electromagnetism and the nuclear…

Isn't every "field" in QFT basically an aether?

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#123

Post by NotAnEconomist » Wed, Jan 09, 2019, 2:56 PM UTC

raattgift wrote: post #119

NotAnEconomist wrote: post #29

Earlier quoted context omitted.

But the arms are predicted to vary in those cases by the same theory that LIGO is confirming: our rotation causes frame dragging, and there's some weird Sun-Earth orbital relativistic effects as well, right? I know the Sun-Jupiter orbit produces a large portion of the estimated 5,000 watts of gravitational emissions given off by our solar system. My mental model of this is that it perturbs the aether ("spacetime") th…

I just noticed this: > our rotation causes frame dragging Not exactly; it's the choice of accelerated coordinates and pretending that the coordinates are freely-falling that manifests seemingly odd coordinate-dependent physical effects. One can resolve these by switching to freely-falling coordinates, or by not pretending that the accelerated coordinates are freely-falling. In practice this means doing Special Relati…

Your answer is "not even wrong" -- it's overly pedantic terms which miss the point of my question.

Such as here:

> If you calculate out the geodesics, no; all the parts of Earth down to its individual molecules and below "want" to travel on geodesics sourced by the system and do so unless the stronger three forces interfere with that "want" (and in bulk Beiglböck and Dixon show that the Earth has a coordinate-independent centre-of-mass that does travel on a timelike geodesic, and you arrive at it by considering the vector position of each particle).

This is a very dressed up non-response, because my initial comment was about geodesics braiding around that central one, and the resulting complexity of the paths, emissions caused by that finer level of path resolution, etc.

Responding that you can calculate paths entirely misses the point.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#124

Post by raattgift » Wed, Jan 09, 2019, 6:56 PM UTC

NotAnEconomist wrote: post #122

raattgift wrote: post #120

Earlier quoted context omitted.

> underlying medium that allows forces to be propagated General Relativity is a local theory concerned with the mechanisms that generate the metric, the geodesics implied by the metric, and the coupling of objects to those geodesics. The relevant forces are those which accelerate objects into non-geodesic motion (or boost them from one geodesic to another). Those are local[1] as well: electromagnetism and the nuclear…

Isn't every "field" in QFT basically an aether?

Please tell me what you mean by aether, as rigorously as you can, and then I can give you an answer to the question which seems to be bedevilling you.

Meanwhile I can guess at what you're asking:

The Standard Model (a QFT) has interacting quantum fields obeying purely local dynamics. The behaviour "here-and-now" depends on the field-values "here". It does not depend on field-values "now" but far from "here". Moreover, the Standard Model is Lorentz-invariant, meaning its laws hold in any inertial frame of reference, thus the scare quotes in the previous sentence.

The luminiferous aether that Michelson & Morley were looking to measure was motivated by finding a single special (and universal, or at least covering the whole solar system) inertial frame of reference in which Maxwell's equations hold exactly. No such frame exists; there is a huge democracy of inertial frames in which relativistic electrodynamics is exact in the classical limit. ( https://en.wikipedia.org/wiki/Preferred_frame )

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#125

Post by raattgift » Wed, Jan 09, 2019, 7:19 PM UTC

NotAnEconomist wrote: post #123

raattgift wrote: post #119

Earlier quoted context omitted.

I just noticed this: > our rotation causes frame dragging Not exactly; it's the choice of accelerated coordinates and pretending that the coordinates are freely-falling that manifests seemingly odd coordinate-dependent physical effects. One can resolve these by switching to freely-falling coordinates, or by not pretending that the accelerated coordinates are freely-falling. In practice this means doing Special Relati…

Your answer is "not even wrong" -- it's overly pedantic terms which miss the point of my question. Such as here: > If you calculate out the geodesics, no; all the parts of Earth down to its individual molecules and below "want" to travel on geodesics sourced by the system and do so unless the stronger three forces interfere with that "want" (and in bulk Beiglböck and Dixon show that the Earth has a coordinate-indepen…

Sorry. Nowhere in any of your previous HN comments is either the word geodesic or anything that makes it obviously clear that you know how the geodesic equation works.

I'm confused though: if you know enough about general relativity to understand vorticity, why are you going on about a gravitational aether (especially without specifying exactly what you mean)?

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#126

Post by jules » Fri, Jan 11, 2019, 1:02 PM UTC

Certhas wrote: post #110

jules wrote: post #102

Earlier quoted context omitted.

I'm not trying to play with words...by EM I mean Maxwell's equations and the Lorentz force law. I think that's the conventional meaning. The point is that these two are taught in an EM class as if it's a single coherent theory that tells you what point charges do. Mass distributions don't solve the issue in a satisfactory way, in my opinion. If you replace a particle with a finite size sphere you've solved the infini…

If you take a non-relativistic model of your matter content, then the theory becomes non-relativistic. That's trivial. So take a relativistic model for your matter and you have no problem [1]. EM gives you a theory of EM Fields and their interaction with matter. It shouldn't be surprising that EM doesn't give you a theory of matter. I maintain there is no conceptual problem with EM, the problem is with your electron…

I don't think making a relativistic theory of charged matter that approximates anything in the real world is as easy as you think. Charged dust will behave in very complicated ways, so I'd have to see a differential equation that models it.

I'm not saying that the point particle model is reasonable. I'm saying that it seems reasonable given what is said in a standard EM course.

Let me phrase it in a different way. In classical mechanics you have lots of problems of the form "the state of the system at time 0 is X, what is the state at time t?".

The problem with EM is that it doesn't have a relativistically invariant answer to such questions when point charges are involved. And, as far as I am aware, there also isn't a standard relativistically invariant answer involving a charge distribution, or at the very least it's not commonly taught.

Maybe you think that I shouldn't find this surprising, but given how EM is taught, I'd say that my surprise is fully justified.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#127

Post by jules » Fri, Jan 11, 2019, 1:16 PM UTC

DoctorOetker wrote: post #109

jules wrote: post #102

Earlier quoted context omitted.

I'm not trying to play with words...by EM I mean Maxwell's equations and the Lorentz force law. I think that's the conventional meaning. The point is that these two are taught in an EM class as if it's a single coherent theory that tells you what point charges do. Mass distributions don't solve the issue in a satisfactory way, in my opinion. If you replace a particle with a finite size sphere you've solved the infini…

I would like to respond to your reply at https://news.ycombinator.com/item?id=18846249 and I was going to use among other things the example of an electron in a uniform magnetic field. So I was totally surprised when I read this comment already mentioning > ... "What happens if I put an electron in a uniform magnetic field?" ... Either 1) this is pure coincidence (and you are contrasting the difficulty of the 2 elect…

It's fundamentally the same issue, and the same difficulty.

The reason I mentioned 2 charges orbiting around each other is to avoid getting into a discussion about the uniform magnetic field, and that maybe the extra radiation energy is just coming from the uniform magnetic field, and that energy is still conserved because the total energy was infinite to begin with.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#128

Post by Certhas » Mon, Jan 14, 2019, 7:36 PM UTC

jules wrote: post #126

Certhas wrote: post #110

Earlier quoted context omitted.

If you take a non-relativistic model of your matter content, then the theory becomes non-relativistic. That's trivial. So take a relativistic model for your matter and you have no problem [1]. EM gives you a theory of EM Fields and their interaction with matter. It shouldn't be surprising that EM doesn't give you a theory of matter. I maintain there is no conceptual problem with EM, the problem is with your electron…

I don't think making a relativistic theory of charged matter that approximates anything in the real world is as easy as you think. Charged dust will behave in very complicated ways, so I'd have to see a differential equation that models it. I'm not saying that the point particle model is reasonable. I'm saying that it seems reasonable given what is said in a standard EM course. Let me phrase it in a different way. In…

The teaching will vary greatly depending on teacher. But I remember that I was told that rigid bodies, and hence centre of mass thinking did not work in relativistic mechanics. It's very possible that as a student I never put that together with the inadmissibility of point charges in EM.

I must insist though that EM has no problem with initial value formulations. It simply doesn't provide you with a theory of matter. It turns out that that theory of matter really requires QM, hence in EM we never bother with non-QM models of relativistic matter. That's why you have to look in the GR literature.

As a pedagogical point I can agree that the limits of the conceptual foundations of our theories are never really explored enough. EM turns out to be fine, the field tensors are completely measurable, but that's a really cool paper that isn't taught either:

https://link.springer.com/chapter/10.1007/978-94-009-9349-5_...

As for charged dust, it works even if you switch on GR as well:

http://www.numdam.org/article/AIHPA_1973__18_2_137_0.pdf

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#129

Post by aj7 » Sat, Jan 19, 2019, 12:53 AM UTC

twtw wrote: post #49

aj7 wrote: post #45

Say what? Start with the integral representations of the equations a la Halliday and Resnick. You can do tons of useful problems. Once you understand vector calculus, you will understand the equations as written in differential form. Then, pick up a copy of Purcell to see how magnetism comes out of the Lorentz transformation of electrostatics. If you are mainly interested in applied problems, go through Corson and Lo…

You seem to be responding to the title, not the essay. Dyson describes the theory as "simple and intelligible" once you accept the concept of fields, which was very much foreign in Maxwell's time.

You’re right. I’m fairly embarrassed.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#130

Post by whatshisface » Sun, Jan 20, 2019, 9:27 PM UTC

jacobolus wrote: post #75

iorrus wrote: post #36

Earlier quoted context omitted.

Exactly, one of the main reasons why maxwell is so hard to understand is that everything is expressed using quarternions unlike Heaviside who expressed the equations using the vector notation we see them expressed in today. In reality ‘Maxwell’s’ equations are in fact Heaviside’s.

Arguably the reason that generations of STEM students have been horribly confused about 3-dimensional vectors and rotations (including electric/magnetic fields), etc. is that they were reframed in the confused and non-generalizable Gibbs/Heaviside language, instead of in Grassmann/Clifford’s formalism in which vectors and bivectors can be properly described as separate types of objects. It can be so much nicer. http:…

Geometric algebra obscures the point that what really matters is the algebraic structure. There are many ways to construct things that behave the same way (subgroups of matrices, vectors and the cross product, and so on), and while it is nice to invent one construction that gives you everything, you risk loosing sight of the fact that each construction is arbitrary and what really matters is its algebraic structure. That's why it's good to expose students to many partial, fragmented devices, so that they will realize the deeper point that underlies them all. With spin matrices, it is obvious that they are arbitrary manifestations of a group, but if a student were to spend their entire education manipulating blades they might start getting the idea that in some sense the universe was "made out of them."