The centenary of Super-Conductivity approaches

[happyjack27]

please don't insult me. i don't know all of the experiments. there are a lot. i do know that a photodetector behind a photomultiplier under very low light produces discrete "clicks" as it were.

So it means that different entities with energy an momentum are being recorded: Why are they undefined "particles" and not localized waves?

same difference. point is it's discrete rather than continuous. "particle-like" rather than "wave-like" if you prefer.

i also know they've experimentally measured the fine structure constant, i believe by the time it takes an electron to travel a certain distance across a voltage gradient? not sure of the setup there, but the implication is that perturbation theory is correct here, and perturbation theory implies particle-like interactions.

Perturbation theory assumes waves; so how can it imply undefined "particles"?

i don't know the details. but i know the taylor expansion (or some sort of expansion) has terms that are in units of probability per unit time of - let me put this as generally as possible - changing the quantumn numbers of an "entity" (as well as the numbers of) without changing the spatial locality. e.g. a photon decaying into an electron and positron w/time instantaneous probability c. with the position (absolute) momentum and energy all being conserved. these are "particle-like" behaviors in that it's like classical mechanics of billiard balls and it's localized in space and specifically among a small number of entities that meet in space, rather than all entities over a distributed field. this is what i mean by "particle-like interactions".

also they've verified the pauli exclusion principle and entanglement.

Two waves with opposite magnetic fields will obviously be able to share the same space, while two waves with parallel magnetic fields will repel: Where do undefined "particles" come into the picture?

i'm happy to drop this one.

many things predicted by QED. in fact, EVERYTHING predicted by QED from my understanding.

A theory which is built on subtracting infinity from infinity to get the electron's mass is obviously fudged to get the answer you want: This cannot be real physics.

are you familiar with l'hopital's rule? point being that infinities and infinitesimals come up all the time in calculus, and they're actually quite easy to deal with and it's all very reasonable and "real", as it were.

also, oh, and here's a big one: the tracks in a bubble-chamber! in modern day we use solid-state analogs.

This means that there is an entity with a center-of-mass; why call it "a particle" if you cannot define what a 'particle" is

by their curvature you can tell their charge-to-mass ratio * velocity, via the lorentz force. what happens is as they pass by other particles they impart energy to them, and then it is that energy that you see... well i suppose you can read more about how the original versions worked

. So why is it "a particle". A localized wave with a center-of-mass will do the same.

potato, potato. (uh, picture those with different "a" sounds.) though by "localized" you realize that's a major understatement. the localization is singular. i.e. it's a limit case. hence i say particle-like. wave-like would imply non-localized, and certainly not singularly-localized. but like i've said if you're representing the complete density function they're just different representations of the same thing. as far as interpretation is concerned it's just a matter of which one is simpler and more intuitive.

so there are a few examples.
now the question is how do you construct a mathematical apparatus that correctly predicts all these outcomes, using as few assumptions as possible? obviously it's going to involve spatial fields w/moving singularities, because that's, well, what we're seeing. e.g. a photograph ("spatial field") w/a black line on it ("singularity"). and this line is a "track" through time, i.e. the "singularity" moves through time. so you see this is a very direct consequence. we're adding nothing here.

None of your examples cannot be explained by a wave which moves slower than the speed of light and thus has mass energy and a center-of-mass.

i know. i've already said that. multiple times by now. the question is why choose one representation and not the other? well you choose whatever helps you the most for the particular problem you're working with.

I am afraid you just want to use the term "particle" for behavior which can just as well be modeled in terms of a wave. Why make this distinction if you cannot even define what a "particle" is?

you see i've already answered this to. because it happens to make the math simpler for the given problem. (i answered this first when i said "its a convenience") it's not always the case that the particle picture is more useful, of course. but in the case of just a gestalt visual intuition, it's certainly easier for me to see and reason with.

[happyjack27]

A wave is not a hypothetical entity like the concept of "a particle".

at risk of being hypocritical, yes it is. it is a mathematical abstraction.

[happyjack27]

ideally you want to choose a representation that maximizes the orthogonality of statistically independant "entities". that way you can deal with one "entity" at a time without having to concern yourself (or rather, having to do so minimally) with all sorts of contingent effect and affects. this is another way to say each "entity" in your representation really _is_ something else and you can clearly and easily distinguish one "entity" from another in the current basis. in many situations, the particle representation does a very good job at all this. that is, each "particle" is represented by a finite-dimensional vector, say 3d-position and 3-d momentum. so in an n-particle system you have a basis that consists of 6n scalars that are for the most part linearly independant.

in situations that involve many particles, however, the em interactions (and thus inter-dependance) make the complexity of the problem grow very quickly, so you'd want to find a different representation that expresses the system much more compactly, among other things. and that's where you'd go over to QFT which can handle an arbitrarily large number of particles with out much notational complexity by encoding information by way of "fields" rather than "particles". (the field is a particle density function. in the non-probabilistic limit the field is everywhere zero except for exactly where a particle is, where it is "1" (a delta function)) each field can represent an infinite number of particles of the same type and eigenstate, and you can express how the fields interact just by putting multiplicative terms inbetween them.

in any case to maximize the linear independance (work in a basis of maximal orthogonality / statistical independance) you'd do an eigendecomposition and that's where the theory of operators and the eigenvalues and states comes in... but now i'm going off topic and deep.

now really eigendecomp is one of many ways to do blind signal separation (which is on a deeper level what we're really trying to do here), and it is not with out its assumptions and consequent limitations. ideally you'd want a more robust method that has better statistical separation, and works just as well even when you drop certain simplifying assumptions such as linearity, a closed system, and a global spatial reference frame... the point of all this is well if you look at the end product, going back to why you're doing this in the first place, is that you want each element of the resulting basis to have maximal unique information and minimal overlap of information among the others, even -- especially -- in the circumstance of a whole slew of new information being added in randomly, e.g. white noise. and i think that would be the particle representation. or the particle field representation in the case of many particles; i.e. spatial basis.

EDIT: though you dond't actually do an explicit eigendecomp, you leave it implied and then ultimately solve it that way. and good thing, too, because well, you have infinite dimensional vectors and that would just take forever. literally.

DIT: though on the spatial thing you come into the problem of relativity. you're assuming that there is one proper inertial reference frame and this is it. where relativity says roughly that every mass has its own inertial reference frame in which all the laws of physics are the same as any other reference frame. so see there you'd have start with the set of all distinct reference frames and start simplifying from there. but that's to say you have to start by using all massive particles as the parts of your basis and then see what you can do to increase infomrational orthogonality from there. i suppose you don't actually _have_ to, but that would be a straightforward way to take relativity into account: from the fact that any inertial reference frame's description of the universe is no more or less valid than any other's. a fact which the end product would no doubt have to reflect. so you see because of relativity, inertial reference frames -- a.k.a. massive particles -- become a natural choice for one's basis.

[johanfprins]

of course there are other transforms. the term "wave" is generally associated with the fourier transform.

It should not be since the basis waves are not waves that can manifest independently in physics.

if you meant to refer to a different orthogonal system, i presumed you'd likewise use a different word.

There are orthogonal systems where each wave forming the system is a possible solution of the relevant wave equation. These are then used to model other waves which are not solutions of the same boundary conditions to model so called "time-evolution". This is not physics.

but it is no matter. the point is the function is a density function that describes what is and is not the thing, and one can choose any orthogonal basis to represent that. (though some might result in singularities and what not where others don't, depending on the nature of the function)

Correct, and you even get good results, but it is still not physics. You can "create" violin music from digital code but violin music does not consist of successive arrays of zeros and ones. That is why most modern physics has become a curve-fitting exercise; and is thus paranormal, or at best virtual.

to describe how it responds to changes you'd have to write down a time-evolution equation.

Except that the "time-evolution" operator is contrived. Why not solve the Schroedinger equation to get a closed solution as a function of a time-changing potential energy for every instant in time?

my subtle philosophical differences with some of that aside, you miss my point.

I do no think so since I know pretty well the standard dogma that you are advocating and with which I disagree. The "time-evolution" operator, if indeed such a monster must exist, must first describe the change in boundary conditions with time, and then the Schroedinger equation must be solved for each one of these intermediary boundary conditions. Perturbation theory is not a good way to do this.

and this is an altogether different thing than an atemporal expression of the state in a given basis.

Each intermediary state is an atemporal state in its own right which should be solved using the whole wave equation at that instant of time ; subject to the boundary conditions which prevail at that instant of time.

it is irrespective of the basis you choose to represent the state.

Mathematically maybe but not when you do real non-paranormal physics.

yes, of course i know that. "concern" more properly. that is besides the point. what "concerns" you; why does it "bother" you; how do you think it might be problematic; etc.

Because I am a physicist that tries to understand nature; not just calculating it in any function space just to get an accurate fit to the measurements. If an alien has never seen a violin and analyses a compact disc he might deduce that violin music consists of digital code: But this is not the case.

i don't. they are two different pictures of the same thing.

Why is there? Because "a particle" has never been defined

the question is what is the most useful picture for the particular problem.

Yes for persons like Heisenberg and Dirac who thought that mathematics is more important than understanding and visualizing the mechanics of physics. As a physicist I reject such an attitude as being paranormal.

which thinks ma as far as an intuitive visual understanding, the particle picture is the one that most clearly and simply describes the known properties, IMHO.

Fine but if he is a physicist he must know why this approximation works for a localized wave, and not call it "a particle" which he cannot define. Try Ehrenfest's theorem and interpret it correctly as a wave with mass intensity and a center-of-mass.

i'll give you that a point is a mathematical abstraction. but in the same sense so is a 3-dimensional space,

Not true, since I can move within three-dimensional space and experience it. I cannot pick up a singular point with tweezers.

.and so is a wave.

Not true, since I can create an energy field in space and detect it.

as regards whether there are such entities in nature, however, and esp. when it comes to "singularities", i beg to differ. the event horizon of a black hole?

It is a boundary at which time stops and on the way to this boundary time alows down gradually due the increase in gravity: Where is a singularity involved?

the fusion of two nuclei?

Why is the entanglement of two waves to form a single new wave a singularity? You can do it in your bathroom by allowing two drops of water to "fuse".

beta decay?

this is not a singularity; it is a wave disentangling like a drop of water breaking up into smaller drops.

phase transition from a solid to liquid or liquid to gas (nucleation)?

That is not a singularity but the normal morphing of matter

lasers?

It is the entangling of many smaller waves to form one wave, like many droplets forming a puddle of water: Where does "singularity" comes into it?

the extinction of a species?

so the dynosuars died out at a single point in time: Wow!

the first stage of morphogenesis of an embryo?

This is to a certain extent a miracle, but now fairly well understood in terms of DNA reactions: I do not see any "singularity" in the proces

the emission of a photon by an electron?

the disentanglement of an electron wave with mass into a wave moving away at light speed c and leaving behind an electron wave with a lower mass: Where is your singularity?

the resulting light spectrum produced in spectroscopy? the list is endless...

My friend, you are confusing boundaries with "singularities". Show me the "boundary" around a single point: This is what we are talking about, not real boundaries which you for some reason want to classify as "singularities".

please. again this "i know you are but what am i." stuff doesn't do anything for me.

Please just define what you are talking about.

i fail to see the point of any of this discussion!

Yes I agree with you since I like to talk about concepts that can be defined and visualized in terms of our previous experience (this is called physics) not about "what is easy to use mathematically", or defining boundaries as "singularities" when they are not.

[happyjack27]

of course there are other transforms. the term "wave" is generally associated with the fourier transform.

It should not be since the basis waves are not waves that can manifest independently in physics.

i don't follow. the fourier domain is the domain of harmonic oscillation. and harmonic oscillation pervades physics. (as it represents conservation of energy)

if you meant to refer to a different orthogonal system, i presumed you'd likewise use a different word.

There are orthogonal systems where each wave forming the system is a possible solution of the relevant wave equation. These are then used to model other waves which are not solutions of the same boundary conditions to model so called "time-evolution". This is not physics.

i'm not sure i follow this either. you mean to say that if you get the boundary conditions wrong then your solution will be wrong? well of course, no argument there.

but it is no matter. the point is the function is a density function that describes what is and is not the thing, and one can choose any orthogonal basis to represent that. (though some might result in singularities and what not where others don't, depending on the nature of the function)

Correct, and you even get good results, but it is still not physics. You can "create" violin music from digital code but violin music does not consist of successive arrays of zeros and ones. That is why most modern physics has become a curve-fitting exercise; and is thus paranormal, or at best virtual.

and when was physics anything besides? my god, if you think our present explanations are ridiculous, you should see the ones they came up with before!

to describe how it responds to changes you'd have to write down a time-evolution equation.

Except that the "time-evolution" operator is contrived. Why not solve the Schroedinger equation to get a closed solution as a function of a time-changing potential energy for every instant in time?

i presume by "contrived" you mean it lacks generality. and you're suggesting time-slicing? not sure what you're suggesting, but if its mathematically valid you'll get no objection here.

my subtle philosophical differences with some of that aside, you miss my point.

I do no think so since I know pretty well the standard dogma that you are advocating ....

perhaps this profound short-stop is precisely what prevents you from hearing truly me.

and with which I disagree. The "time-evolution" operator, if indeed such a monster must exist, must first describe the change in boundary conditions with time, and then the Schroedinger equation must be solved for each one of these intermediary boundary conditions. Perturbation theory is not a good way to do this.

again i'm not exactly sure what you're suggesting. but i don't think you'd get a different result, presuming you're careful enough. (dot all your mathematical i's and cross the t's, so to speak.)

and this is an altogether different thing than an atemporal expression of the state in a given basis.

Each intermediary state is an atemporal state in its own right which should be solved using the whole wave equation at that instant of time ; subject to the boundary conditions which prevail at that instant of time.

btw, i wish you wouldn't respond to what i'm saying with a greater granularity than the ideas i'm trying to communicate actually are. it seems a good way to gaurantee missing the forest for the trees. regarding the time-independant vs. time dependant shordinger equation, i'm not sure you understand how it works out. they generally DO solve the time-independant one, first finding the eigenvalues and then the eigenstates, and then the time-dependant solution usually turns out to be the time-dependant solution times a phase-angle (e^something), which is exactly what you'd expect it to be, seeing that energy is conserved and all... if you're talking about open systems; more complex time behavior such as a dissipative system, well that's still an open problem as far as i know and on that i wish you luck.

it is irrespective of the basis you choose to represent the state.

Mathematically maybe but not when you do real non-paranormal physics.

again i don't know what you mean by non-paranormal. for it to be visually intuitive, yes, certainly not all basi are alike. but i'm speaking as you gathered mathematically, they are all logicaly the same - any statement you make in one representation is true of the system in any representation. or false in all, if that statement is false. logically consistent, by definition.

yes, of course i know that. "concern" more properly. that is besides the point. what "concerns" you; why does it "bother" you; how do you think it might be problematic; etc.

Because I am a physicist that tries to understand nature; not just calculating it in any function space just to get an accurate fit to the measurements. If an alien has never seen a violin and analyses a compact disc he might deduce that violin music consists of digital code: But this is not the case.

same here.

[happyjack27]

i don't. they are two different pictures of the same thing.

Why is there? Because "a particle" has never been defined

??? don't usderstand you response here except a seemingly random plug of your mantra.

the question is what is the most useful picture for the particular problem.

Yes for persons like Heisenberg and Dirac who thought that mathematics is more important than understanding and visualizing the mechanics of physics. As a physicist I reject such an attitude as being paranormal.

again with the paranormal thing. you understand that nature does not care what you call it, it will go on doing what it does whether you (or I) like it or not. the best we can do is try to understand what that is that it does the best we can. and IMO you are right for seeking an understanding that's visual intuitive. though i'm quite sure there are and have been many physicists who would disagree with the both of us on this point.

which thinks ma as far as an intuitive visual understanding, the particle picture is the one that most clearly and simply describes the known properties, IMHO.

Fine but if he is a physicist he must know why this approximation works for a localized wave, and not call it "a particle" which he cannot define. Try Ehrenfest's theorem and interpret it correctly as a wave with mass intensity and a center-of-mass.

i'm not familiar with ehrenfest's theorem. i'll have to look it up.

[happyjack27]

so many threads! we sure do talk a lot.

i think i'm going to take a break.

but on the singularities-boundary thing. maybe its just a difference in terminology. by singularity i mean a discontinuity in an otherwise continuous space. such as a bifurcation (hence the morphogensis thing) (and on evolution i was talking about species, btw. when the last tyrannosouras died, for instance, tryannosouras suddenly went from not extinct to extinct. also if you look at per bak's criticality you see like many physical phenomena they follow a log-log plot, which suggest statistical multifractal ... spaces of spaces of discontinuity. and yes, it does probably damp out at the large and small ends of the scale).

a trivial example is the attraction of an electron and positron grows like 1/r^2, and at the origin that function is discontinuous. and there's no experimental evidence to suggest that the physical reality is any different. in fact, when they meet, they anihilate, leaving only a photon. (EDIT:which one might say is a charge and its opposite orbiting at infinite speed - exactly what you'd expect if the physical reality really was discontinuous at the origin) and yet another example is that seemingly instant moment of going from one set of particles to another represents a discontinuity in the particle type.

and you know if you dont' like me using the word "particle" so often then you can just leave it at "tracks on a a bubble/cloud/solid-state chamber". however you want to describe it, the spatial discontinuity is, to the finest resolution that we can measure, just that: discontinuous. some day in the future we might find finer structure in it. personally i think there is finer structure. but for now we've got to work with what we got, and the simplest and most general description we can think of that fits the all evidence. however crazy that description may turn out to be, it's ultimately saner than one that does not fit the evidence or is more complex without being in any measurable way distinct, or is more specific than experiments can justify - well, those are candidate theories awaiting verification. in any case that's what we got.

and most systems of differential equations are non-linear and thus rife with discontinuities. so it would be pretty remarkable if nature some how found laws of physics that weren't. (while also making it look in so many ways like it didn't!) in any case, so far the universe seems to fit the assumption of being r^2 integrable, at least, among other things.

so maybe with that word -- discontinuity -- we have more of a shared concept. in any case what you call "boundaries" in this context seems to me a lot like what i call "singularities". a sudden change in the midst of gradual changes.

[happyjack27]

i don't want to entangle two separate threaded discussions so let me just note here in case its missed: i made two non-minor edits to a tangential post of mine above, marked with "EDIT" and "DIT" (sic) respectively.

[happyjack27]

also on the point of mathematics and visual intuitiveness. math is by definition - in fact arguably this is THE definition of math - logically consistent. nothing that is not logically consistent can be visualized, as it would represent two contradictory states occupiying the same space. likewise everything that is logically consistent can in some form or another by visualized. some MUCH more easily than others, of course. and that is where i take issue both with you on your contention (or my interpretation of it, rather, and i apoligize in advance if i have inadvertenly made a straw man argument here) that it is paranormal because it doesn't agree with visual intuition - it does, it CAN be visualized. it just sometimes takes more work to see if certain relations are possible or not under a given set of assumptions (i.e. are not "paranormal" to use your words) sometimes it even takes decades. anwyays this is where i take issue also with the "pure mathematics" physicists who ask you not to visualize it. if you aren't visualing it, then you can't truly understand the mathematics you are doing! and when they tell me, "but what if the mathematics can't be visualized?" i'll respond: "such a thing does not exist. all mathematics can be visualized, or it is not logically sound, and thus not mathematics." and furhtermore the taks of mathematics is to understand spatial relations, in it's purest form it is not these numbers and formulas but the visualization itself that these numbers, formulas, and rules merely serve to represent.

[Grurgle-the-Grey]

This is a super-conduction thread! I've started another if you wish to discuss wave/particle duality.
So JFP thinks that all super-conduction effects can be explained by electrons in orbitals that are higher than the fermi level due to a local interstitial atom as I understand it.

Wiki on Josephson


This may be paraSchroedinger maths but it also has tested out in lab, and thus any candidate Model of SC must be able to explain it.
It seems to me that nothing that obeys Schroe's equation could be causing these lab results.

[johanfprins]

the fourier domain is the domain of harmonic oscillation. and harmonic oscillation pervades physics. (as it represents conservation of energy)

I do apologize since you are correct that I did not state that well. What I meant to say is that when using the Fourier domain, one should not forget that the basis functions are used as if there are not any boundary conditions stipulated in the beginning, and the boundary conditions can then be added afterwards. For example, on a violin string, a standing wave is given by the sum of two Fourier waves moving in opposite directions, even though such waves cannot exist on their own on the string, unless the string has an infinite length. In all the other domains, like for example Legendre polynomials, the basis waves are determined by the boundary conditions and thus gives the only solutions possible under those boundary conditions. A superposition of these basis waves does not give a solution that can manifest under the same boundary conditions. Thus it is my opinion that to superpose them and then relate the coefficients with probabilities is not physics since the basis wave that will manifest is determined by energy considerations which have nothing to do with probability amplitudes. I hope I have expressed myself more clearly. This is the reason why I posted that: There are orthogonal systems where each wave forming the system is a possible solution of the relevant wave equation. These are then used to model other waves which are not solutions of the same boundary conditions to model so called "time-evolution". This is not physics.

i'm not sure i follow this either. you mean to say that if you get the boundary conditions wrong then your solution will be wrong? well of course, no argument there.

I am glad we agree. But do you agree that a linear combination of these solutions cannot be a physically possible solution for the same boundary conditions even though mathematically it is the case.

and when was physics anything besides?

Here we disagree: A physics model must be predictive and not just fit the curves; or else you have a model which Pauli called: "It is not even wrong!" The BCS theory gives such a non-predictive model: Just as Bernd Matthias consistently pointed out while he was alive.

my god, if you think our present explanations are ridiculous, you should see the ones they came up with before!

That is why we should never accept in physics that any model is the final word and should always approach new inputs with an open mind to see whther we can make our models "less ridiculous".

i presume by "contrived" you mean it lacks generality. and you're suggesting time-slicing? not sure what you're suggesting, but if its mathematically valid you'll get no objection here.

Thanks we are getting somewhere on this topic. "Time slicing" means that in the case where the boundary conditions change with time, the only valid solution will be to solve the wave equation for each instant in time, since the boundary conditions change from instant to instant. Obviously, this is not required when the boundary conditions do not change.

In the case of an electron-wave, the wave does not change with time when the boundary conditions do not change with time: Thus you do not need a time-evolution generator. A free electron is a localized standing wave within an inertial reference frame since it has mass and must then have inertia: And when the observer is within the same reference frame, this wave will not evolve with time unless its boundary conditions are changed by an interaction with other entities.

Now comes the interesting part: if the observer is stationary within another inertial reference frame moving relative to the inertial reference frame of the electron, the boundary conditions, of the electron, do change according to the observer. This change is modeled by the Lorentz transformation, and it is then found that every point within the electron's wave intensity now has a different time coordinate, as it must have to be a moving wave. Only now does the wave has a de Broglie wavelength. A standing electron wave, like an electron orbital around a nucleus has nothing to do with a de Broglie wavelength since it has no momentum.

perhaps this profound short-stop is precisely what prevents you from hearing truly me.

This is of course always possible and if one is not willing that it can be so, you should not be doing physics. But perhaps, in this case, it might be you that is so caught up in main stream dogma that it prevents you from truly hearing me?

but i don't think you'd get a different result, presuming you're careful enough. (dot all your mathematical i's and cross the t's, so to speak.)

I think that when you do get the correct physics you will not have to use dubious mathematical procedures like "renormalization" and being forced to assume that a circular integral over a conservative vector field can be no-zero, in order to claim a paranormal physical result like Aharanov and Bohm have done.

one, first finding the eigenvalues and then the eigenstates, and then the time-dependant solution usually turns out to be the time-dependant solution times a phase-angle (e^something), which is exactly what you'd expect it to be, seeing that energy is conserved and all... if you're talking about open systems; more complex time behavior such as a dissipative system, well that's still an open problem as far as i know and on that i wish you luck.

This is what I find exasperating with you. You keep on telling me physics which I know as if I have never heard of it. I find it insulting. The fact is that by following that routine, they use the phase angle as if it is a boundary condition. It is not! It is the boundery conditions that determine the phase angle of a wave, not the other way around.

again i don't know what you mean by non-paranormal. for it to be visually intuitive, yes, certainly not all basi are alike. but i'm speaking as you gathered mathematically, they are all logicaly the same - any statement you make in one representation is true of the system in any representation. or false in all, if that statement is false. logically consistent, by definition.

I do not want to go into a long discussion here, that will be better done face to face in future. When it comes to deriving paranormal physics the most convincing example is the derivation by Aharanov and Bohm that an electron can respond to a magnetic field without its charge center moving through the field. And this is derived in terms of a "phase-angle" instead taking cognizance of the actual boundary conditions which apply; and by also violating the mathematics on which vector calculus is based.

[johanfprins]

So JFP thinks that all super-conduction effects can be explained by electrons in orbitals that are higher than the fermi level due to a local interstitial atom as I understand it.

You are not understanding it! There are no interstitial atoms involved, and the energy of the superconducting charge carriers are always below the Fermi-level. If they are above, there will not be enough of them to cause superconduction.

This may be paraSchroedinger maths but it also has tested out in lab, and thus any candidate Model of SC must be able to explain it.
It seems to me that nothing that obeys Schroe's equation could be causing these lab results.

You are wrong. Superconduction is completely modeled by the Schroedinger equation; provided the paranormal Copenhagen interpretation is dropped into a trashcan where it always should have been.

[Grurgle-the-Grey]

You are wrong. Superconduction is completely modeled by the Schroedinger equation

That is the hypothesis we are discussing, we are trying to decide whether it is right or wrong.
The Josephson AC and DC effects are established lab results, I'd be intrigued to see how you feel electrons from below the fermi level (ie. bigger work function??) can achieve these effects within Schroe's equation..

[johanfprins]

You are wrong. Superconduction is completely modeled by the Schroedinger equation

That is the hypothesis we are discussing, we are trying to decide whether it is right or wrong.
The Josephson AC and DC effects are established lab results, I'd be intrigued to see how you feel electrons from below the fermi level (ie. bigger work function??) can achieve these effects within Schroe's equation..

You have to see the whole model. I am going to do you a favor and send you an electronic copy of section 23 in my latest book in which I describe how superconduction actually occurs. Section 28, on Josephson tunneling, based on this mechanism, is on my website.

[Grurgle-the-Grey]

Thank you, but what I'm really interested in is how Schroe. compliant tunnelling can cause a DC voltage to give rise to an AC current so accurately that it was used as the international standard definition of a volt.
There are many theories that explain bits and pieces of SC but all are contradicted by other known SC phenomena.
Actually it seems to me that your theory is very similar to current thinking on ballistic electrons, what would you say are the main differences?