User talk:Basti Schneider

Discussion continuation

Copied from Talk:Poynting vector [1], as this discussion belongs in user talk space, not article talk space:

In static fields

What would be the behaviour of the circular (?) energy flow if the cylindrical capacitor is replaced by a parallel-plate capacitor in this setting.

Isn't this whole explanation a bit inconsistent ? It even mixes up classical physics and quantum mechanics ! — Preceding unsigned comment added by Basti Schneider (talk • contribs) 13:05, 11 September 2012 (UTC)

You'd have to be more specific with the replacement example. This is a purely classical interpretation, nothing related to quantum mechanics. And no, I doubt you'll be able to find an inconsistency with this interpretation. — Quondum 18:06, 11 September 2012 (UTC)

Setting with parallel-plate capacitor: H-field has the the same direction, capacitor is placed within this H-field. Right plate of the capacitor is charged positive, left plate negative. So there still is $E\bot H$. With $S=E\times H$ Poynting vector points out of the capacitor, parallel to the plates. In this case there is no circular flow of energy. So there is no angular momentum either.

The charges of the discharge current are electrons. As electrons are particles the laws of quantum mechanics apply for them.

See: Angular_momentum#Angular_momentum_in_quantum_mechanics and Electron

Can you explain the physics of the setting described above ? Please explain exactly the path of the energy flow.

Basti Schneider (talk) 07:53, 12 September 2012 (UTC)

View the plates as finite, and the magnetic field as uniform throughout space (or at least in a large volume around it). The energy flow (and momentum) are vertically downwards between the plates, looping around the bottom edges, up on either side around the outside of the plates and back down between the plates due to the electric field around the outside of the plates. Due to the symmetry of the flow, there is no overall angular momentum. Energy–momentum is conserved exactly at every point in space; when the momentum due to S changes direction, the change of momentum is supplied by the stresses in the EM field. — Quondum 09:05, 12 September 2012 (UTC)

Ah okay, I expected this answer. Anticyclical 'vortexes' around the plates.

But you have to consider that this kind of energy flow isn't 'backed up' anymore by the classical E-field (and not by $\phi$ or $A$, either). On the upper and lower 'ending' of the parallel-plate capacitor the E-field becomes inhomogeneuous and on the outside of the capacitor the E-field is much weaker than between the plates.

But by definition the Poynting vector in any point of the setting is $S=E\times H$. But E is weaker outside of the capacitor than inside. Hence there is a difference between <mth>S</math> within the plates and on the outside of the plates, so there are problems in this approach to maintain the conservation of energy in the flow -> there is a change in the strength of the E-field if compared inside and outside of the capacitor ($H=const$).

Maybe you can argue, that the flow outside the capacitor is spatially more extended than in the inside, where it is more 'compressed'.

But in this case you should remember: In reality there are no spatially infinte H-fields.

Then the whole explanation fails once again as there exists the possibility that the E-field on the outside of the capacitor reaches in areas where $H=0$. But in theses areas with $H=0$ and $E\neq 0$, applies $S=0$ , too. $S=E\times H$ .

So in this case the conservation of energy in the S-flow is broken.

Basti Schneider (talk) 10:23, 12 September 2012 (UTC)

This is not the appropriate forum for personally disputing the standard interpretations, unless the article is incorrect. Any solution to Maxwell's equations automatically satisfy conservation of energy everywhere. The article references Poynting's theorem, which can also be used to understand the implication of a non-zero divergence of S such as you are postulating. — Quondum 10:53, 12 September 2012 (UTC)

Poynting's theorem doesn't solve this issue either:

$-{\frac {\partial u}{\partial t}}=\nabla \cdot \mathbf {S} +\mathbf {J} \cdot \mathbf {E}$

$\nabla \cdot \mathbf {S} +\epsilon _{0}\mathbf {E} \cdot {\frac {\partial \mathbf {E} }{\partial t}}+{\frac {\mathbf {B} }{\mu _{0}}}\cdot {\frac {\partial \mathbf {B} }{\partial t}}+\mathbf {J} \cdot \mathbf {E} =0$

$\mathbf {J} \cdot \mathbf {E} =0$ there is no free current J in this setting.

Hence, applying Poyntings theorem to the setting: parallel-plate capacitor, whose E-field extends the area with $H\neq 0$ leads to the conclusion that it is impossible to shield an H-field in presence of $\nabla \cdot {S}\neq 0$.

The equation says, that everytime the S-flow is blocked, it opens a new path by simple creating another E- or H-field.

The conclusion is: static E- or H-fields can't be shielded, if there is $\nabla \cdot {S}\neq 0$ in the area the shield is build around (for the surrounding environment the shield is the border surface of $\nabla \cdot {S}\neq 0$)

I don't know but I don't consider this as a fact.

Basti Schneider (talk) 16:02, 12 September 2012 (UTC)

Discussion moved to User talk:Basti Schneider — Quondum 16:25, 12 September 2012 (UTC)

The conclusion is that if S-flow cannot be "blocked" if you impose the condition that J = 0. The term J⋅E must be nonzero to absorb or produce the power. Static E and H-fields can be shielded, even in ways that reflect rather than absorb S. Consider, for example, a superconductive shielding sphere around your experiment. But this necessarily involves currents, as indicated by the formulae. You cannot impose the nonphysical condition that J = 0 everywhere outside your equipment and that H is confined in a way in which S is not conserved violates physical law. — Quondum 16:28, 12 September 2012 (UTC)

I realized this while I was thinking about it, too. With mu-metal it's similar.

$W=\int \limits _{-0}^{t}P\partial t$ or ${\frac {W}{A}}=\int \limits _{-0}^{t}S\partial t$.

Applying this simple formulae to the circular S-flow it should generate Joules over Joules just by letting time pass !

Or the energy in the S-flow is considered as reactive power, but Poynting's theorem states something different.

There are much more flaws in classical electrodynamics as proved in e.g. Abraham-Lorentz, Aharonov-Bohm, Aharonov-Casher effect etc. , so I'm careful !

I don't know how the angular momentum of an energy-flux, that is not even physical (as seen above), can be transferred to electrons.

Basti Schneider (talk) 17:50, 12 September 2012 (UTC)

Any path along which the discharge current flows must cross the B-field. The reduction in angular momentum of S due to the E field reduction is exactly the right amount to balance the angular momentum imparted via the Lorentz force to the current-carrying path.

I'm not too sure why you're relating this to quantum mechanics. Maxwell's equations are not considered to hold in the quantum extreme. The Abraham–Lorentz force is classical, but not exacty relevant here (there might be misconceptions relating to it in the past, but it has to be an emergent result of Maxwell's equations). — Quondum 18:15, 12 September 2012 (UTC)

Does the capacitor discharge quicker then, when placed in the H-field ? F=ma so the electrons should be faster ?

There must be a way to come from quantum mechanics to classical physics. So Aharonov-Bohm should be explainable classically, too, but it is not. But quantum mechanics explains it correctly.

The conclusion is: The flaw is in this case in the classical theory.

Did you know that the original Maxwell equations where formulated in quaternions, or in other words Lie-group SU(2) or O(3), not U(1) ?

Basti Schneider (talk) 18:41, 12 September 2012 (UTC)

If the path of the current is constrained to be the same with and without the field, there is no difference in discharge rate, because the force is perpendicular to the path and is transferred to the conductor. If it is free to follow variable paths, the discharge rate is affected.

Yes – classical mechanics is simply the limit of the quantum mechanical description as Planck's constant goes to zero (as far as I know). Why should the Aharonov–Bohm effect be explainable classically? It deals with the complex phase of an electron's wavefunction, which has no classical analogue. The interference that is the only way of observing it does not occur classically, with the electron considered as a particle.

Yes, I had heard about the quaternions being used. The current formulation in vector analysis exhibits the same symmetries as the quaternions; the formulations are fully equivalent. I prefer the formulation in geometric algebra, which pulls it all together rather neatly. U(1) probably only applies to the quantum description (I imagine it applies to the phase of the electron wavefunction), not to Maxwell's equations.

Of course classical theory is not accurate, and quantum mechanics largely is. But when the impact of quantum effects is inobservable, they agree. — Quondum 20:56, 12 September 2012 (UTC)

Why should the Aharonov–Bohm effect be explainable classically? It deals with the complex phase of an electron's wavefunction, which has no classical analogue. The interference that is the only way of observing it does not occur classically, with the electron considered as a particle.

This is exactly what I intended to say: There should be an classical analogue to quantum mechanics phase-shift, some authors consider a scalar potential.

The interference-phenomenas occuring in the Double-slit experiment do not have to be explained by quantum mechanics. They can be explained classically if one considers that particles have wave characterstics. The 'probabilistic' nature of the particle distribution on the screen is described statistically but there are approaches that keep the determinism -> Bohm interpretation.

See: Double-slit_experiment#Classical_wave-optics_formulation

Interference_(wave_propagation)

Photons are considered in classical physics as 'wavefunctions' as well, see electromagnetic radiation. This could also be applied to electrons. In history, interference was first observed classically e.g. in water-waves.

EM radiation is considered as a large packs of photons, in Aharonov-Bohm there is a (very) large number of electrons, that builds up the particle distribution on the screen.

So, if this aspect of the Aharonov-Bohm experiment could be explained classically (interference of the electron-waves), why isn't it possible ?

For large numbers of quants, quantum mechanics merges into classical physics.

The current formulation in vector analysis exhibits the same symmetries as the quaternions; the formulations are fully equivalent. I prefer the formulation in geometric algebra, which pulls it all together rather neatly. U(1) probably only applies to the quantum description (I imagine it applies to the phase of the electron wavefunction), not to Maxwell's equations.

Quaternions at least have the potential for SU(2) but todays maxwell equations are U(1). see Gauge fixing This is why QED has to be made invariant under U(1) 'by force'.

Maxwell used the quaternions like we use $\phi$ and $A$. A scalar-field and a 3-dimensional vector-field.

In this article is described how higher topology theories can be incompletely gauged. Landau_gauge#Maximum_Abelian_gauge

This is what maybe was done by Einstein's theory of relativity. Two degrees of freedom were occupied by the speed of light (one spatial and the temporal). <- But this is a lot of very much too speculative and I know this !!

But there are always hints in this direction, like non-locality etc.

Because of experiments like AB and others, and all these logical inconsistencies one has to accept, I suspect the classical electrodynamics a little bit.

The static case of the Poynting vector caught my interest because of a joke:

Take a permanent magnet and a charged capacitor and arrange them in a way, the fields cross orthogonally. Then you have energy without limits. And the key-point is: If one asks the equation $S=E\times H$, this statement is correct.

For Aharonov-Bohm also see Canonical_commutation_relation#Gauge_invariance. $\nabla \Lambda$ -> scalar potential !

Basti Schneider (talk) 07:51, 13 September 2012 (UTC)

You concept of classical mechanics seems somewhat unorthodox. You are throwing a lot of inaccurate statements about; A bit more reading may allow you to work out where you differ from established science. — Quondum 13:47, 13 September 2012 (UTC)