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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]

#61

Post by rini17 »

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.

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

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

#62

Post by dwenzek »

I'm just a bit surprised that this post says nothing about Heaviside who rewrote Maxwell's equations in the form commonly used today.

According to wikipedia [1], Heaviside significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death.

[1] https://en.wikipedia.org/wiki/Oliver_Heaviside

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

#63

Post by Helmut10001 »

> It is better for the progress of science if people who make great discoveries are not too modest to blow their own trumpets.

This is a nice remark, but very difficult to implement in practice. In reality, many non-modest people will overrate their contributions, while the few modest people will have a hard time to act non-modest in certain situations. We are in a world where modesty is even rarer than 100 years ago. I am sure many important discoveries are hidden in the myriad peer reviewed publications published just for quantitative reasons.

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

#64

Post by r0uv3n »

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.

> physics has no formulation of spacetime in discrete terms

There are some attempts of working with discrete spacetime (e.g. causal set theory), but yeah, all our best descriptions so far very much assume smooth spacetime.

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

#65

Post by omnicognate »

rsecora wrote: post #60
mjburgess wrote: post #52

Earlier quoted context omitted.

> 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.

Its 99 years since Einstein published the paper on the photoelectric effect whith had far-reaching consequences. [1] And 93 years since the first Solvay Conference. [2] [1] https://en.wikipedia.org/wiki/History_of_quantum_mechanics [2] https://en.wikipedia.org/wiki/Solvay_Conference

What's your point? Everything they did, including Einstein's (and everyone else's at the time) quantum mechanics work, was based on continuous space and time variables.

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

#66

Post by omnicognate »

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.

> Cognition is discrete

There's little evidence even of this, except in the trivial sense that language (minus prosody) is composed of discrete units.

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

#67

Post by greysphere »

lll-o-lll wrote: post #56
mjburgess wrote: post #52

Earlier quoted context omitted.

> 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.

> 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?

Imagine there was a grid for space. For simplicity consider a regular grid of size 1unit in one direction and 1unit in a perpendicular direction. If such a grid existed, using one unit of ?something? would move you 1 unit along the axes of the grid, but you'd need 2 units of ?something? to move root2 units 45deg to the grid. Any discrete grid of any shape or size or pattern would have something like this, some sort of preferred alignment, but as far as we can tell there no such preference. Physics in free space is rotationally invariant and thus not on a grid thus continuous.

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

#68

Post by mjburgess »

rini17 wrote: post #61
mjburgess wrote: post #52

Earlier quoted context omitted.

> 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.

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 the people who use thinks like the word "information" in this context are confusing thermodynamic, logical, probabilistic, (+ many others) and equivocating.

"Information" is not a physical quantity, and there cant be a "volume" of it. Nor does this have anything to do with real numbers.

It is impossible for there to be any system extended in space and time to "zoom infinitely" into a continuous range and hence record an infinite amount of information. No one claims this, and the formulation of physics (entirely on real numbers) does not require it.

Rather to say, eg., space is continuous, is to say its unbroken. There is no physical quantity which is becoming infinite.

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

#69

Post by mjburgess »

omnicognate wrote: post #66
mjburgess wrote: post #52

Earlier quoted context omitted.

> 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.

> Cognition is discrete There's little evidence even of this, except in the trivial sense that language (minus prosody) is composed of discrete units.

It is discrete insofar as we're talking about sequences of thoughts, ie., reasoning.

What offends the minds of some people is the world might not be like their mind at all. They want always to analogise everything to Reason.

Everything should be countable, everything should be knowable, etc.

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

#70

Post by frozenport »

I taught this subject at the graduate level.

With an emphasis on basis functions and computing we could do it in a single semester.

The more interesting thing was that most students had practically no useful previous knowledge despite formally having some years of eduction on the subject

My insight was the biggest issue was the eduction system failing the students and not anything specific to Maxwell’s equations.

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