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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]

#221

Post by JohnFen »

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."

So, a bit like how the conventional depiction of electric flow is in the opposite direction of the actual electron travel?

It doesn't matter in terms of the math (in the vast majority of situations), so while the conventional idea of electric flow is incorrect, we keep it anyway.

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

#222

Post by s1artibartfast »

JohnFen wrote: post #221
psuedobrain wrote: post #200

Earlier quoted context omitted.

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."

So, a bit like how the conventional depiction of electric flow is in the opposite direction of the actual electron travel? It doesn't matter in terms of the math (in the vast majority of situations), so while the conventional idea of electric flow is incorrect, we keep it anyway.

I think it is closer to the conventional view of current as the travel of electrons down a wire.

Current moves far faster than electrons. it is more similar to a wave in the ocean with the electrons being the water molecule.

As a result, and counterintuitively for most, the speed of electrons will give you a completely wrong answer for when a light will turn on after you flip a switch.

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

#223

Post by pishpash »

eigenket wrote: post #217
pishpash wrote: post #214

Earlier quoted context omitted.

Not true either. The original Kolmogorov complexity is for finite strings. Plus, the program would need to store that for whichever special strings you choose you will use this function but for other ones not. That will be a giant table that is part of your program. That's also a different point than the parent's. Seems they're saying if you were to specify pi as the limit of some expansion that describes the physica…

> The original Kolmogorov complexity is for finite strings. I wrote "Kolmogorov complexity" not "original Kolmogorov complexity" so this isn't particularly relevant. The application of the concept to the infinite string which represents pi is essentially trivial. > Plus, the program would need to store that for whichever special strings you choose you will use this function but for other ones not. That will be a gian…

I urge you to go back and look at how Kolmogorov complexity is defined. It includes the notion that a program needs to decide whether to output the string directly or to generate it from some program.

You're assuming Alice and Bob have already pre-synchronized what kind of computing machine is going to be used, one in which pi is the output of a relatively short program, as opposed to another type of machine where some other random-looking number has that property (random to you, pseudo-randomly generated via some machinery for all you know). You are assuming many things away.

Also it is absolutely not trivial to extend Kolmogorov complexity to infinite strings. There are multiple formulations and they are a lot more difficult than for finite strings. Not the computation part but the complexity assignment part.

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

#224

Post by lr1970 »

The Maxwell equations are conventionally being taught and written as 4 equations for two 3 dimensional vectors instead of a single equation for a single anti-symmetric 4-dimensional tensor. Also, the tensor exaction is explicitly relativistic covariant while in the vector equations formulation this fact is well hidden and requires quite a long proof to see it.

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

#225

Post by jiggawatts »

nyssos wrote: post #145
guardingit wrote: post #123

Earlier quoted context omitted.

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.

> 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…

> baking in a lot of assumptions about the setting that fail to generalize

That’s the point! That’s the entire point!

Mathematicians want the most general, most abstract approach. They want to generalise to a wide range of problems and not be painted into any one specific example.

Physics theories have an opposite goal to this: the ideal theory ought to take no parameters, and produce “reality” as the one and only possible outcome. The ideal theory ought not generalise to un-physical models.

For example, the mathematics of general relativity have excess degrees of freedom that must be constrained through additional restrictions. Similar issues turn up almost anywhere matrices are used: they have too many degrees of freedom.

Geometric Algebra is typically a better fit for what actually goes on in physics.

For example, rotation matrices have precision issues, gimbal lock, and can’t be robustly interpolated. Rotations implemented using GA have none of these issues.

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

#226

Post by eigenket »

pishpash wrote: post #223
eigenket wrote: post #217

Earlier quoted context omitted.

> The original Kolmogorov complexity is for finite strings. I wrote "Kolmogorov complexity" not "original Kolmogorov complexity" so this isn't particularly relevant. The application of the concept to the infinite string which represents pi is essentially trivial. > Plus, the program would need to store that for whichever special strings you choose you will use this function but for other ones not. That will be a gian…

I urge you to go back and look at how Kolmogorov complexity is defined. It includes the notion that a program needs to decide whether to output the string directly or to generate it from some program. You're assuming Alice and Bob have already pre-synchronized what kind of computing machine is going to be used, one in which pi is the output of a relatively short program, as opposed to another type of machine where so…

I agree there is a bunch of complexity in generalising Kolmogorov complexity to general infinite strings. However I'm not really trying to do that here, all I want is enough to back-up the statement I made before, that the complexity of pi is finite. Doing that is much more trivial than what you're talking about.

Theres a bunch of fine detail in getting it down to defining an actual number measuring complexity which I don't care about at all, all I care about (in the context of this discussion) is that the number is finite.

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

#227

Post by chr1 »

mjburgess wrote: post #113
chr1 wrote: post #94

Earlier quoted context omitted.

You don't have to imagine an ordered grid. If grid unit is small enough (say plank length 1,6 10^-35) and the grid is chaotic, for the distances of ~ 10^-16 that we can measure, everything will look the same in all directions. This happens the same way in which steel demonstrates isotropic behavior although its microscopic structure is anisotropic. So there is no easy way to prove or disprove continuity of space.

The "underlying issue" often at stake in the debate is whether reality is a computer, since it would need to be discrete if so, and often whether a computer can be made to simulate it. However, what's missed here is that discrete is a necessary but not sufficient condition. Once you give any sort of plausible account of how reality could be discrete, as you've done here, you end up with non-computable aspects (eg., t…

I don't see how randomness can make anything non-computable. Sure you may not know the exact random numbers but you get a similar enough universe with any other sequence of random numbers.

Also continuous doesn't mean uncomputable either, because in many cases the infinite amount of computation for continuum does not add anything interesting and finite approximation works good enough.

> So the metagame is lost regardless: reality isnt a computer (/ no complete physical theories of reality are computable).

I don't see any evidence for this. For now we do not have a proof for one way or another. If for instance it turns out that quantum computers really can run Shor's algorithm factoring very large numbers, it would be a good evidence for continuum, but we are not there yet.

But even that would not be an evidence for reality not being a computer, since it will still allow the possibility of reality being a computer that can perform operations on real numbers.

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

#228

Post by Koshkin »

s1artibartfast wrote: post #222
JohnFen wrote: post #221

Earlier quoted context omitted.

So, a bit like how the conventional depiction of electric flow is in the opposite direction of the actual electron travel? It doesn't matter in terms of the math (in the vast majority of situations), so while the conventional idea of electric flow is incorrect, we keep it anyway.

I think it is closer to the conventional view of current as the travel of electrons down a wire. Current moves far faster than electrons. it is more similar to a wave in the ocean with the electrons being the water molecule. As a result, and counterintuitively for most, the speed of electrons will give you a completely wrong answer for when a light will turn on after you flip a switch.

> Current moves far faster than electrons.

Current is the movement of charges. It cannot “move” faster than said charges. (Or, perhaps, you meant the electomotive force that makes the electrons move along the wire, then sure, that thing spreads pretty quickly.)

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

#229

Post by Koshkin »

waveBidder wrote: post #171
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

But we never know any quantity to full precision, so it's not like we get infinite bits about any given quantity.

That depends on the unit of measure. We know that the charge of the electron is exactly 1, with the appropriately chosen unit.

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

#230

Post by s1artibartfast »

Koshkin wrote: post #228
s1artibartfast wrote: post #222

Earlier quoted context omitted.

I think it is closer to the conventional view of current as the travel of electrons down a wire. Current moves far faster than electrons. it is more similar to a wave in the ocean with the electrons being the water molecule. As a result, and counterintuitively for most, the speed of electrons will give you a completely wrong answer for when a light will turn on after you flip a switch.

> Current moves far faster than electrons. Current is the movement of charges. It cannot “move” faster than said charges. (Or, perhaps, you meant the electomotive force that makes the electrons move along the wire, then sure, that thing spreads pretty quickly.)

yes, the EM force, Field, or whatever it is called. I still struggle, mostly because I was taught a fundamentally flawed model for how electrical power is transmitted.
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