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

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

#121

Post by wholinator2 »

mr_mitm wrote: post #112
metricspaces wrote: post #110

Earlier quoted context omitted.

> computer science leaking out Planck constant would like to have a word with you. But it is true that CS shines a light on the matter of mapping the infinite into bounded spaces. This matter of ‘cognition’ is the entire matter (npi) of contention. What is the actual relationship between number and perceived phenomena ? What is the deeper meaning of the concordance of mathematics and physics? Where do these magical c…

> Planck constant would like to have a word with you. Do you want to flesh this out? Are you suggesting that because phase space is quantized, position space must be quantized as well?

As someone who was once a, "I've watched a lot of YouTube videos about physics", person, i think it's very interesting how confident people are in their understanding of what is essentially the edge of physics, something only seen in a masters or doctorate degree. Specifically the whole spacetime and qm thing.

There's so many videos on it that you begin to feel like you really understand it after half a dozen or so repeat the same words at you. But the thing you don't realize is that those are literally the only words they could possibly communicate, and that's an infinitesimal fraction of the nuance of the real thing. Plus, there's a selection bias in that the videos that make you feel good get more views, so you're more likely to stumble upon videos that make you _think_ you understand it that videos that actually do, partly because the only videos that could make you understand are a graduate degrees worth of 80-100 hour lecture courses that you're gonna have to take notes on.

It makes me wonder if this is true for literally every subject. I fancy myself are least politically versed in modern events but is my entire understanding based on an entertainment-first version of an actual education? How much do i walk around using jargon that i don't really understand to make points whose true depth I'm completely unaware of?

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

#122

Post by nyssos »

kragen wrote: post #50
DiogenesKynikos wrote: post #28

Earlier quoted context omitted.

Maxwell's Equations have already been superseded by Quantum Electrodynamics, in the same way that Newtonian gravity has been superseded by General Relativity. Both Newtonian gravity and Maxwell's Equations are still very good approximations in their regimes of validity.

we are commenting on an article which describes in depth how quantum mechanics, including qed, falls squarely within the paradigm maxwell pioneered. that's why my comment specifically talks about the 'maxwellian paradigm' and not 'maxwell's equations', which is, by the way, not a brand name i thought it was too obvious to be worth saying that classical physics is still an excellent approximation to reality, but hopef…

> quantum mechanics, including qed, falls squarely within the paradigm maxwell pioneered

Does it, though? Sure, QED is a field theory, but it's perturbative where classical EM is exact, its fields are operator-valued distributions where classical fields are number-valued functions, its interactions are transition probabilities rather than forces - it's not clear to me that these are smaller jumps than introducing fields in the first place.

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

#123

Post by guardingit »

jiggawatts wrote: post #48
bsder wrote: post #3

Maxwell's theory is not hard to understand--once you have the proper tools. The problem is that because of trying to cram a degree into 4 years, you wind up having a class on electromagnetics without any understanding of vector fields . Electrical engineering is particularly bad about this. You never get exposed to the Hamiltonian formulations of classical mechanics, and you never get exposed to vector analysis. Cons…

Vector fields are just as incorrect, and ought to be relegated to history books as a mere stepping stone on the way to understanding. Geometric algebra can reduce Maxwell’s equations into a single, hilariously terse equation: ∇F = J Ref: https://en.wikipedia.org/wiki/Mathematical_descriptions_of_t...

Thanks for the pointer on Geometric Algebra. This looks to be a promising path to understanding relativity/QM/EM, and goes some way to explaining my unease with cross products and imaginary numbers.

Disclaimer: maths degree, so my unease was not a plain lack of understanding.

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

#124

Post by ThePhysicist »

toth wrote: post #104
ThePhysicist wrote: post #92

Earlier quoted context omitted.

You can make the electric field disappear by choosing the right gauge. Same goes for the magnetic field (can't make both disappear together though). The vector potential, in that sense, can be regarded as a more fundamental description of the electromagnetic field. It can't be observed directly though, but electric and magnetic field strengths are manifestations of the vector potential, they are not fundamental in th…

>You can make the electric field disappear by choosing the right gauge. Same goes for the magnetic field (can't make both disappear together though). What? No you can't. The fields are invariant under gauge transformations.

You're right, sorry I was thinking of a Lorentz transformation that would make either the magnetic or electric field disappear under certain conditions.

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

#125

Post by lupire »

metricspaces wrote: post #116
mr_mitm wrote: post #112

Earlier quoted context omitted.

> Planck constant would like to have a word with you. Do you want to flesh this out? Are you suggesting that because phase space is quantized, position space must be quantized as well?

A discreet unit of measure exists in dynamics & its relationship to position space is informed by Heisenberg’s theorem. (My actual point is that Reality is neither continuous nor discreet - it is an infinitesimal point and it is our mind — that likes to name and number things and relies on duality to make ‘distinctions’ — that creates the universe, the subjective reality that we perceive as inhabiting.)

What is an infinitesimal point?

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

#126

Post by lupire »

mjburgess wrote: post #52
hiAndrewQuinn wrote: post #43

My proudest moment in high school was getting a 5/5 on the calculus based AP Physics C exams at 15 with no calculus and only rudimentary algebra knowledge at the time. That experience permanently colored my thinking, and made me much more open to practicing thorough visual imagination as a way to solve problems. I found that practice useful all the way through my EE degree's vector fields courses a decade later. I th…

> continuity of spacetime is a convenient approximation I disagree, and there's no evidence for this. This is computer science leaking out; physics has no formulation of spacetime in discrete terms, and indeed, all of physics presumes continuity. In QM, the space of wavefns is infinite-dim continuous, and if wasnt, QM wouldnt be linear. Cognition is discrete, but the world is continuous.

Is wave function collapse continuous? Is photon absorption and emission continuous?

No one knows what the universe of truly made of.

Reality is measured up to certain error tolerances.

Don't confuse the map (math and physics) with the territory (reality).

Also, Stephen Wolfram would like a word with you.

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

#127

Post by TheOtherHobbes »

mjburgess wrote: post #52
hiAndrewQuinn wrote: post #43

My proudest moment in high school was getting a 5/5 on the calculus based AP Physics C exams at 15 with no calculus and only rudimentary algebra knowledge at the time. That experience permanently colored my thinking, and made me much more open to practicing thorough visual imagination as a way to solve problems. I found that practice useful all the way through my EE degree's vector fields courses a decade later. I th…

> continuity of spacetime is a convenient approximation I disagree, and there's no evidence for this. This is computer science leaking out; physics has no formulation of spacetime in discrete terms, and indeed, all of physics presumes continuity. In QM, the space of wavefns is infinite-dim continuous, and if wasnt, QM wouldnt be linear. Cognition is discrete, but the world is continuous.

This seems very unlikely.

If you're from Copenhagen every measurement is a lossy discontinuity that resets the wavefunction.

This is not an abstraction, it's directly observable.

As for discrete formulations:

https://en.wikipedia.org/wiki/Causal_dynamical_triangulation

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

#128

Post by kragen »

denton-scratch wrote: post #119
kragen wrote: post #50

Earlier quoted context omitted.

we are commenting on an article which describes in depth how quantum mechanics, including qed, falls squarely within the paradigm maxwell pioneered. that's why my comment specifically talks about the 'maxwellian paradigm' and not 'maxwell's equations', which is, by the way, not a brand name i thought it was too obvious to be worth saying that classical physics is still an excellent approximation to reality, but hopef…

> '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

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

#129

Post by kragen »

nyssos wrote: post #122
kragen wrote: post #50

Earlier quoted context omitted.

we are commenting on an article which describes in depth how quantum mechanics, including qed, falls squarely within the paradigm maxwell pioneered. that's why my comment specifically talks about the 'maxwellian paradigm' and not 'maxwell's equations', which is, by the way, not a brand name i thought it was too obvious to be worth saying that classical physics is still an excellent approximation to reality, but hopef…

> quantum mechanics, including qed, falls squarely within the paradigm maxwell pioneered Does it, though? Sure, QED is a field theory, but it's perturbative where classical EM is exact, its fields are operator-valued distributions where classical fields are number-valued functions, its interactions are transition probabilities rather than forces - it's not clear to me that these are smaller jumps than introducing fie…

many people have argued that qm is a larger jump than maxwell's approach, and i agree that that's a very reasonable position, which is why i found it interesting to read dyson arguing the opposite

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

#130

Post by lupire »

hiAndrewQuinn wrote: post #43

My proudest moment in high school was getting a 5/5 on the calculus based AP Physics C exams at 15 with no calculus and only rudimentary algebra knowledge at the time. That experience permanently colored my thinking, and made me much more open to practicing thorough visual imagination as a way to solve problems. I found that practice useful all the way through my EE degree's vector fields courses a decade later. I th…

You may have taken a slightly wrong lesson from that exam. AP exams are extremely curved (scoring about 70% or less is a 5), and are half multiple-choice, so a few clues can get the answer), and it's partly a conceptual test that doesn't rely on math.

But of course you're absolutely correct that continuous and discrete systems are approximately equal.

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