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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]

#231

Post by nightlyherb »

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 is about the throughput of electrical charge at a specific point of an electrical circuit, while what you're describing seems to be about the latency or the speed of electricity.

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

#232

Post by mikeiavelli »

duped wrote: post #199
ThePhysicist wrote: post #93

Maxwell didn't have the nice differential geometric notations that we use today, which allow us to write his equations in a very concise and easy to understand form. His original paper is way more convoluted, so at the time it must have been really difficult to understand for everyone except the subject matter experts. And he was of course building on the work of Faraday, Ampere and others. But like with other theori…

Faraday didn't even know trigonometry, allegedly (he never studied mathematics). It's interesting that his student (Maxwell) who did have the mathematical background would extend his theories and figure out the math to explain it all

Maxwell was deeply influenced by Faraday's work but he was not his student: he first noticed Faraday’s work while he was at Cambridge in the 1850s. He found a way to translate Faraday’s experimental findings (expressed as the interaction of "lines of force") into a mathematical model (with fields), also taking into account Coulomb's and Ampère's laws. Maxwell then extended that model to take into account the conservation of charge / the continuity of currents.

While Maxwell’s work was inspired by Faraday's, it was also built upon the contributions of many other scientists (Coulomb, Ampère, Thomson, Neumann, Lenz, ...)

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

#233

Post by psychoslave »

lupire wrote: post #137
psychoslave wrote: post #73

Earlier quoted context omitted.

Given that no one, or at least no human, can experiment what reality in its whole, and as far as we want to honestly recognize the effective scope of our knowledge, probably we will never know in absolute terms. What matter is a subjective topic. What we all have in common is logistics constraints. So if some people set as a goal something that requires to settle if reality is more easily handled when modeled in cont…

Continuity just hides the ball. You say you can't comprehend how something can move from 1 to 2 discretely. But the paradoxical notion of infinite continuous change has been known since antiquity. It's faith either way. Discrete doesn't mean state changes are wholly globally arbitrary. Imagine a graph with nodes and edges, a state machine as computer sciences call it. I think it's easy to agree that the universe coul…

> You say you can't comprehend how something can move from 1 to 2 discretely.

I didn’t mean that, sorry if my words that induced you to believe so.

What I want to point out is that, to my mind, if I assume a discrete foundation of universe, on meta-cognitive level I must recognize it implies everything I experiment through my current attention might possibly be a just made up state without any compelling ontological relation to anything I can recall or think of. So, as far as I’m concerned, believing in continuity is just a lazy way to relax on a metaphysical Gordian knot.

> It's faith either way.

Yes and no. It’s probably easier to change scientific perspective to whatever model apply best for some purpose than to adhere to some philosophy about Nature.

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

#234

Post by mjburgess »

n4r9 wrote: post #179
mjburgess wrote: post #68

Earlier quoted context omitted.

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 re…

I suspect that Gisin has a very clear idea of what he means by "information" in this context, having worked for over 40 years at the forefront of theoretical physics with a specialisation in quantum information theory.

I don't have much issue with Gisin's solution, the idea that the reals are random is one solution to the problem of how to deal with them that I like (since, my meta-issue is whether reality is computable, I say it isnt, and randomness is not computable).

There's a problem for people who think reality can be modelled by computable functions of finite inputs: this makes classical physics non-deterministic, because chaos requires infinite precision for determinism.

So either you go for "reality is deterministic and continuous, and not computable" or "reality is non-deterministic, and discrete, and not computable"

either option in this fork includes properties that offend the minds of the people who want everything to be discrete.

I lean towards a preference for determinism & continuity (via, in QM, superdeterminism) since that's trivial to justify on our best physics

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

#235

Post by benterix »

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?

> Is it though? Does it matter one way or the other?

These are two very different questions. As for the former, I don't believe there is consensus at this point with good arguments for and against. As for the latter, if we can reliably prove that the reality is not analog but digital, it has consequences at various levels, and we might make better choices when using math to describe it/make approximations.

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

#236

Post by nyssos »

jiggawatts wrote: post #225
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…

> 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 po…

> The ideal theory ought not generalise to un-physical models.

Sure - but a theory that fails to generalize to physical models is a bad one. A good classical theory should be a straightforward deformation of the corresponding quantum and/or relativistic theory. In this respect the best versions of classical mechanics are the standard Lagrangian and Hamiltonian approaches.

> For example, rotation matrices have precision issues, gimbal lock, and can’t be robustly interpolated.

No physicist was ever under the impression that euler angles were any realer than any other way of parameterizing SO(3), that matrices were the linear transformations they represent, that manifolds are their charts, or any other trivial map-territory confusion. Paying careful attention to the distinction between real physical objects on the one hand and their representations on the other is the central theme of the last century of physics: that's basically all a gauge theory is!

This is exactly what I'm talking about with geometric algebra advocates only ever comparing it to the worst sort of high school coordinate-bashing imaginable. The argument always goes

- Look at this horrible vector algebra with explicit charts and numbers all over the place

- Now look at this nice coordinate-free geometric algebra construction

- Therefore geometric algebra is the right setting for physics

but it's a complete non sequitur, because the coordinate-freeness is doing all the heavy lifting. But everyone already works without coordinates wherever it's practical to do so! The question isn't whether you should work in terms of abstract objects or explicit coordinates, it's which abstract objects you should work with.

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

#237

Post by nyssos »

calf wrote: post #218
mjburgess wrote: post #113

Earlier quoted context omitted.

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…

> Nondeterministic Finite Automata.

The "Nondeterministic" in NFA means its transition function goes from states to sets of states, instead of from states to states. Informally, it can explore multiple paths in parallel for the cost of one. They're not probabilistic.

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

#238

Post by n4r9 »

mjburgess wrote: post #234
n4r9 wrote: post #179

Earlier quoted context omitted.

I suspect that Gisin has a very clear idea of what he means by "information" in this context, having worked for over 40 years at the forefront of theoretical physics with a specialisation in quantum information theory.

I don't have much issue with Gisin's solution, the idea that the reals are random is one solution to the problem of how to deal with them that I like (since, my meta-issue is whether reality is computable, I say it isnt, and randomness is not computable). There's a problem for people who think reality can be modelled by computable functions of finite inputs: this makes classical physics non-deterministic, because cha…

Well, I don't think Gisin's mind is offended by non-determinism:

> I argue that there is another theory, similar but different from classical mechanics, with precisely the same set of predictions, though this alternative theory is indeterministic

and in the footnote he describes indeterminism to mean:

> given the present and the laws of nature, there is more than one possible future

Out of curiosity, why do you lean towards superdeterminism and not other deterministic interpretations of QM such as Many-Worlds or Bohmian mechanics?

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

#239

Post by Tainnor »

Tainnor wrote: post #197
mrguyorama wrote: post #182

Earlier quoted context omitted.

Zeno's """Paradox""" was nonsense even in it's own time. Easier now that we understand Newton's laws of motion but his contemporaries were able to sufficiently dispute his idea even without them.

Not nonsense. The argument goes that if time and space are both discrete, then to move from A to B in finite time means that you have to perform infinitely many actions in finite time. Zeno didn't believe that the latter was possible. But he wasn't stupid, he obviously knew that motion was happening all the time in real life. His paradox really only makes sense in the context of Eleatic philosophy which assumes that…

> if time and space are both discrete

my mistake - that should have read "are both continuous".

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

#240

Post by intalentive »

It seems strange and unlikely that human beings should have access to an abstract language that “nature speaks”, as Dyson puts it.

“Here you are, a speck of thinking matter. Oh and by the way you just so happen to have a special capacity for mathematics, the secret language of the universe.”

Convenient, isn’t it?

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