Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

damtp.cam.ac.uk

Post reply on HN
Print view View original

201–210 of 250 posts

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

#201

Post by s1artibartfast »

psuedobrain wrote: post #200
s1artibartfast wrote: post #191

Earlier quoted context omitted.

I wish most explanations wouldn't skip over the fact that field lines arent real, and just a tool to graphically depict what is going on. Statements like the following gets the causality entirely backwards. >the strength of an electric field depends on the number of electric field lines.

I think the question of whether field lines are real is more of a philosophical (of physics) question so it usually falls outside the scope of introductory material on E&M. However, some texts like Purcell and Morin do kinda take a stance on whether fields are real: "since it works, it doesn’t make any difference."

it works for a physics test, but is also part of the problem, as it misleads and prevents conceptualization, even for simple problems.

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

#202

Post by [deleted] »

timeagain wrote: post #193
s1artibartfast wrote: post #191

Earlier quoted context omitted.

I wish most explanations wouldn't skip over the fact that field lines arent real, and just a tool to graphically depict what is going on. Statements like the following gets the causality entirely backwards. >the strength of an electric field depends on the number of electric field lines.

It’s like saying that rain falls where there are blue regions on the weather map :)

[deleted]

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

#203

Post by Terr_ »

devmor wrote: post #172
steamer25 wrote: post #168

Prior to computer-generated 3D animation, I can imagine it was very difficult to float and spin vector-arrows in mid-air with enough accuracy to show what goes on without having to resort to reams of explanatory paragraphs. Eugene Khutoryansky is something of a lesser-known 3b1b that's more focused on physics than math. I found his animations very helpful for building intuition around Maxwell's equations: https://www…

Wow this video is actually great at imparting the concepts with animation. It's a little distracting how it looks like an ad for an adult themed video game, but it's very well thought out.

> It's a little distracting how it looks like an ad for an adult themed video game

Well-put: Does that demon-squid in the intro look like a Chihuly glass installation to anybody else?

Also I swear I've heard that song long ago on OCRemix.

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

#204

Post by [deleted] »

mr_mitm wrote: post #115
rini17 wrote: post #61

Earlier quoted context omitted.

If it really was continuous so that physical quantities were real numbers as defined in mathematics, then it is in contradiction to maximal information density. Because almost all real numbers contain infinite amount of information. Full argument is elaborated here "Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real? by Nicolas Gisin": https://arxiv.org/abs/1803.06824

All observable quantities are eigenvalues of some operator, which are real numbers but discrete. How can they contain infinite amount of information?

[deleted]

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

#205

Post by jereees »

steamer25 wrote: post #168

Prior to computer-generated 3D animation, I can imagine it was very difficult to float and spin vector-arrows in mid-air with enough accuracy to show what goes on without having to resort to reams of explanatory paragraphs. Eugene Khutoryansky is something of a lesser-known 3b1b that's more focused on physics than math. I found his animations very helpful for building intuition around Maxwell's equations: https://www…

This video is worth watching for the soundtrack alone. I came across Eugene’s channel before but somehow I missed this gem!

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

#206

Post by nyssos »

guardingit wrote: post #160
nyssos wrote: post #145

Earlier quoted context omitted.

> maths degree Then you want differential forms for EM, differential geometry more broadly for GR, and a bit of functional analysis for QM. The hype around geometric algebras (Clifford algebras over R) just comes from the fact that it's not the plug'n'chug explicit numbers and coordinates approach, which is all most people ever see. They do not do a good job of tracking the physical structure of electromagnetism, and…

Thanks for your comment. > They do not do a good job of tracking the physical structure of electromagnetism What do you mean by tracking the physical structure? By this, do you mean the typical EM formulation of Maxwell's laws produces Gauss's law and Faraday's law (which are instructive) where as the Geometric Algebra formula produces ∇F = J (less instructive?). > and in fact end up baking in a lot of assumptions ab…

> By this, do you mean the typical EM formulation of Maxwell's laws produces Gauss's law and Faraday's law (which are instructive) where as the Geometric Algebra formula produces ∇F = J (less instructive?).

> Can you explain a bit more what you mean here please?

It's all downstream of geometric algebra leaving the metric implicit in its operations, basically

- The metric is an extremely important physical quantity: it doesn't necessarily look that way when everything is classical and flat, but you have to start caring about it in curved spacetimes.

- Even when the metric can be safely neglected, doing so makes it very easy to confuse degree (n-k) elements of your vector space V with degree k elements of its dual V. V and V are isomorphic but not canonically isomorphic - you have to choose a basis. And keeping track of where you introduce a choice of basis matters, because all physical quantities are basis-independent. Nature has no preferred coordinate system.

- Geometric algebra doesn't make sense on a general manifold: you have to embed it in a sufficiently large geometric algebra and inherit structure from the embedding. This is better than working in a particular coordinate chart but worse than doing differential geometry in a purely geometric way.

- Geometric algebra is not invariant under diffeomorphism, which means GR is dead in the water. You can build mostly equivalent theories by enforcing the equivalence principle in your dynamics instead, but it's more complicated and ironically far less geometric.

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

#207

Post by Ringz »

jereees wrote: post #205
steamer25 wrote: post #168

Prior to computer-generated 3D animation, I can imagine it was very difficult to float and spin vector-arrows in mid-air with enough accuracy to show what goes on without having to resort to reams of explanatory paragraphs. Eugene Khutoryansky is something of a lesser-known 3b1b that's more focused on physics than math. I found his animations very helpful for building intuition around Maxwell's equations: https://www…

This video is worth watching for the soundtrack alone. I came across Eugene’s channel before but somehow I missed this gem!

> … for the soundtrack alone

Did I sense mild sarcasm here?

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

#208

Post by pishpash »

mjburgess wrote: post #106
mikk14 wrote: post #100

Earlier quoted context omitted.

Some people would disagree with dismissing information as non physical. For instance: https://scottaaronson.blog/?p=3327 The argument there would be that stuffing an extra bit of information in an information saturated volume would make it collapse into a black hole.

It's not entirely clear "Energy" is a physical property either. By physical I mean a causal property of a system which is a basic constituent of reality. For example in E = 1/2mv^2, a particle has kinetic energy in virtue of being matter in motion -- it is motion and matter which are basic. Energy is just a system of accounting which tracks motion in the aggregate over time (with kinetic/potential just being the futu…

Nothing in physics is more basic than something else, as there are equivalent formulations in other quantities. Energy and momentum are as real as matter and motion. Matter is bundles of energy exhibiting inertia and motion is just some transformational relationship between phenomena in different areas of space-time. There is nothing "real" about any of this, only what animals like humans have evolved to model directly in their brains.

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

#209

Post by programjames »

jerf wrote: post #176
lll-o-lll wrote: post #56

Earlier quoted context omitted.

> the world is continuous Is it though? Does it matter one way or the other? Do we think reality is the math in some way, or is the math a really darn good model of the reality?

There are many times in physics where people have thought they've had to choose between either one thing or its opposite, where both choices had clear deficiencies. The ultimate solution ended up being a new hybrid that nobody thought of for a long time. I kind of suspect "is the universe continuous versus discrete" will come down to that. I don't know what a hybrid of such things looks like. With our current concept…

My guess is every physical value can be written as a sum of rational sines (i.e. sin(tau * a/b)).

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

#210

Post by DiogenesKynikos »

kragen wrote: post #128
denton-scratch wrote: post #119

Earlier quoted context omitted.

> 'maxwell's equations', which is, by the way, not a brand name Are you commenting on the capitalization of "Maxwell"? It is a proper name, and it should be capitalized.

admittedly so, but no, on the capitalization of 'equations' (and 'quantum' and 'electrodynamics'), which are not

It is common to capitalize the names of famous equations or theories.

Maxwell wrote tons of equations during his life, but there's only one set of "Maxwell's Equations." Maxwell himself never even wrote down Maxwell's Equations in the form we now know them.

Post reply on HN