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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]

#211

Post by calf »

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…

Aaronson is one of the world's top quantum computing scientists, he's a professor at I believe UT Austin.

He's also written papers that are basically philosophy of physics. It would be interesting to go over what he has actually said on this topic.

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

#212

Post by Scubabear68 »

As a lay person, this was beautifully written, and I feel like I understand the issues to a degree better than I have before from casual reading.

Very important to people like me, because I really struggle with advanced math. I dropped an EE degree because while I could do the math, it was incredibly hard and in no way intuitive to me.

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

#213

Post by azalemeth »

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."

Very much this. The (standard model's) "answer" is that the four vector potential probably is the "most real" and we're all just excitons along for the ride.

At some point the definitions become almost circular and opinions about what it fundamental have shifted a bit over the centuries. The cgs system of units -- which differs profoundly from SI in the treatment of electromagnetism -- was associated with those who viewed D and H rather than E and B the most fundamental. I'm quite happy with the level of theory used being appropriate to solve the problem at hand. There's always a bit of wiggle room around exactly what that problem is, however ;-)

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

#214

Post by pishpash »

eigenket wrote: post #180
mikhailfranco wrote: post #165

Earlier quoted context omitted.

I am very sympathetic to Gisin and his cause, but he does not propose any sensible resolution. By the way, not a fault, and no blame for him. Pointing out logical deficiencies always comes before a satisfying solution, and he is to be praised for his insight. There are many interesting ways to probe this problem.... here's one: Say I tell you to imagine a circle, an ideal Platonic circle in a Cartesian coordinate sys…

> But pi is has infinite information It does not, according to any sane way of defining its information content. For example the Kolomogrov complexity of pi is clearly finite - I can write down a program for a Turing machine which will run (forever) and keep writing down digits of pi as it does so.

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 physical process of photons arriving in some area, then that specification's information increases with more terms added. Pi, being almost random by every statistical measure, has as much information as a random string, in fact, in any normal conception of information. You cannot wave that away by machine manipulation tricks or by defining a new constant, and this is borne out also by the parent's physical argument that in reality there are no low-complexity universal constants, but that there may be limits to information density (in space and time).

Continuous physics can be a manipulation of limiting quantities without being literal.

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

#215

Post by neutronicus »

toth wrote: post #192
adrian_b wrote: post #151

Earlier quoted context omitted.

Even the vacuum version is incomplete without adding an equation for force or energy, because no meaning can be assigned to the electromagnetic field or potential otherwise than by its relationship with the force or energy. Even today, there exists no consensus about which is the correct expression for the electromagnetic force. Most people are happy to use approximate expressions that are known to be valid only in r…

I agree that to fully specify electromagnetism you also need to include how the fields affect charged matter. So EM = Maxwell's equations + Lorentz force equation (not sure why you say there is no consensus about what this is, that is new to me). This is just a matter of taste, but OTOH I would not include descriptions of how some materials respond to the fields in the continuous limit as part of a definition of EM.…

You also need to include how charged matter affects the forcing fields in Maxwell's equations (i.e. moving charges depositing a current field).

I actually basically agree with your viewpoint, I studied Plasma Physics in graduate school in a regime where we did _not_ use Navier-Stokes or constitutive relations and everything was in fact just little smeared-out packets of charge moving according to the Lorentz Force Law and radiating.

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

#216

Post by nyssos »

eigenket wrote: post #184
nyssos wrote: post #141

Earlier quoted context omitted.

There are operators with continuous spectra. The previous commenter was accidentally half-right, in that the usual intro QM picture where everything lives in L2 really isn't fully rigorous, but this is fairly easy to resolve. The correct setting is a rigged Hilbert space: given an algebra of operators A on a Hilbert space H, let S be the maximal subspace of H such that |sa| is finite for any s in S, a in A. These are…

I take minor issue with the phrase "correct" here. Thats one way you can do things but its also works completely fine to not do that. Another way of setting these things up has your states be honest elements of L2, and says observables are just POVMs (i.e. maps from a space of measurable sets to positive operators which obey some natural restrictions like additivity). Then given a measurable subset A of the spectrum…

Sure, I should have been clearer: a rigged Hilbert space is the right setting for bras and kets. You can also get rid of them entirely. In my experience QM classes unfortunately tend to split the difference by slinging around suggestive nonsense like \int_{x} |x><x|.

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

#217

Post by eigenket »

pishpash wrote: post #214
eigenket wrote: post #180

Earlier quoted context omitted.

> But pi is has infinite information It does not, according to any sane way of defining its information content. For example the Kolomogrov complexity of pi is clearly finite - I can write down a program for a Turing machine which will run (forever) and keep writing down digits of pi as it does so.

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 giant table that is part of your program.

I honestly can't parse this.

> Pi, being almost random by every statistical measure, has as much information as a random string

This is wrong. You can consider something like a simple communication task. Alice and Bob share a phone line and she is attempting to tell him a number. Every second the line allows her to send a bit to Bob. For a truly random number she has to use the line infinitely many times to tell him the number. To send pi she can send a finite number of bits which amount to a program to compute pi and he can do the computation on his end.

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

#218

Post by calf »

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…

Why is randomness non-computable? In computer science, the theorem is that the set of all Deterministic Finite Automata is equivalent to the set of all Nondeterministic Finite Automata. It is a non-obvious theorem that is a one page proof taught in every junior level theory of computation course. This theorem is what lets deterministic and nondeterministic Turing machines to be used interchangeably in many subsequent proof sketches in these classes.

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

#219

Post by codethief »

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

As the sibling hinted at, Gisin's statement is quite sloppy and – at the very least – confuses "definite" "information"¹ (a given real number) with "uncertain" "information" (entropy), at least if you follow the definition of entropy by the book: The probability distribution for an observable that takes on (exactly) the value of a given real number with probability 1 has entropy 0.

That being said, Gisin's approach is still interesting and his results can still be valid. But he starts with the assumption that real (irrational) numbers are unphysical, i.e. that – in a sense – our observable from above can actually only take on certain (rational) values, and then he derives certain predictions from that.

¹) Putting "information" in quotation marks here because no one really knows what it is.

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

#220

Post by [deleted] »

s1artibartfast wrote: post #191
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…

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.

[deleted]
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