Room-temperature superconductivity?

[nogo]

Googling Frank Znidarsic and following link chains I ended up at this video supposedly related to his work.

http://www.youtube.com/watch?v=Rr_s28wIOzQ

There are plenty of links about Znidarsic in there if you click on the video description button to expand it.

[choff]

Thanks nogo, I'm in a bit of a rush, but there's this link.

http://www.wbabin.net/science/znidarsic2.pdf

[johanfprins]

I am overloaded with work at present. When I have time, I will look at these references and I will then post a comment: However, do not expect this to happen very soon. Sorry.

[Teahive]

Not a foolish question at all, but THE QUESTION that the Copenhagen three should have asked before leading physics into never-never land. An electron IS a field, which, within our three-dimensional space manifests as a time-independent intensity distribution when the boundary conditions do not change with time. . This follows directly from Schroedinger's equation.

I am quite intrigued by the approach that everything can be explained as waves which must behave in accordance to the given boundary conditions. However all the (introductory) explanations I've seen so far represent the boundary conditions as "hard walls". Obviously this may be a useful simplification, but I wonder if it doesn't actually do more harm than good by hiding the interesting interactions. After all, if one follows the theory to its logical conclusion then the boundary conditions themselves must be expressed as waves.

It fits my model perfectly: The charge-carriers are stationary entities ("orbitals") which replace adjacent stationary entities by jumping from one occupied position to the next and replacing this entity which in turn jumps further. The energy for this comes from Heisenberg's relationship for energy and time: i.e. the energy to jump is loaned from the "vacuum" (However, this vacuum has VERY LITTLE in common with the one postulated for quantum field theory since it comes directly from the solution of Schroedinger's equation). Nonetheless, the kinetic energy used to move is returned to the "vacuum" and therefore the charge-carriers can move without generating entropy.

I must admit, I find the explanation involving loaning of energy hard to stomach. It may be one way to put it which yields the right result, but in terms of intuitive understanding of physics it seems roughly equivalent to saying that "magic happens".

I found it interesting that in your paper describing the superconducting phase in a vacuum you state that the initial speed of the electrons entering the gap may be taken as zero. But if their speed was actually zero, how would they be able to enter the gap? If, on the other hand, their speed was non-zero, would it not be possible to explain the current which flows as charge carriers maintaining their momentum in the absence of an electric field within the superconducting phase?

[johanfprins]

I am quite intrigued by the approach that everything can be explained as waves which must behave in accordance to the given boundary conditions. However all the (introductory) explanations I've seen so far represent the boundary conditions as "hard walls". Obviously this may be a useful simplification, but I wonder if it doesn't actually do more harm than good by hiding the interesting interactions.

What most people do not realize is that the "potential-energy term" of the Schroedinger equation is not really the potential energy of a particle with mass m, but a boundary condition which determines the shape, size and energy of the resultant wave.

After all, if one follows the theory to its logical conclusion then the boundary conditions themselves must be expressed as waves.

Correct and they are exactly that. For example if you have a square barrier, it is really nothing else but a region in space having energy at each point. A field which is the same as a stationary wave. Even the potential energy that an "electron" experiences around a nucleus is nothing else but a stationary electric field; i.e. a stationary wave. The intensity of the electron wave itself is such a field.

I must admit, I find the explanation involving loaning of energy hard to stomach. It may be one way to put it which yields the right result, but in terms of intuitive understanding of physics it seems roughly equivalent to saying that "magic happens".

The same concept is used in quantum electrodynamics (QED): And in the latter case it is even more like magic than in my case. According to QED the vacuum is a field with an "infinite energy"!

In my case the extra energy does belong to the wave that borrows it: To understand the latter, consider a wave on a violin string. This wave has no momentum but at every point along the string the string moves to continually transform kinetic energy into potential energy and back.

Now consider a similar standing wave for an electron within a box. The amplitude of this wave is a complex function so when looking at its intensity there is now harmonic motion at any point within 3D space: Its intensity is purely potential energy. But it is a harmonic wave! Where is its concomitant kinetic energy? Owing to the complex amplitude this energy is situated outside 3D space and is not infinite: However, it is available for short time intervals owing to Heisenberg's relationship for energy and time. Thus when an orbital borrows energy it is energy it already has outside 3D space. So it is less magical than in the case of QED.

I found it interesting that in your paper describing the superconducting phase in a vacuum you state that the initial speed of the electrons entering the gap may be taken as zero. But if their speed was actually zero, how would they be able to enter the gap?

Compared to the speed with which they move through the superconductor the speed with which they enter is negligibly small. The latter speed is the drift speed they have within the injecting contact, which is not superconducting; and such a drift speed is tiny compared to the speed with which charge moves through a superconductor.

If, on the other hand, their speed was non-zero, would it not be possible to explain the current which flows as charge carriers maintaining their momentum in the absence of an electric field within the superconducting phase?

No. In such a case you have the situation that you have in an electron accelerator. The electrons are accelerated and then coasts toward their target, where they collide with the target. The latter does not happen for superconducting charge carriers since they cannot generate entropy in any manner, also not be colliding with the target contact. If they do this they are not part of a superconducting phase.

[Teahive]

Thanks for the explanation for borrowing energy. I guess at a certain point "magic" will always be necessary since we need a model of things we can't observe to explain what we observe.

Compared to the speed with which they move through the superconductor the speed with which they enter is negligibly small. The latter speed is the drift speed they have within the injecting contact, which is not superconducting; and such a drift speed is tiny compared to the speed with which charge moves through a superconductor.

How do you measure the speed at which charge carriers move through a superconductor? Why does this speed have to be particularly high?

No. In such a case you have the situation that you have in an electron accelerator. The electrons are accelerated and then coasts toward their target, where they collide with the target. The latter does not happen for superconducting charge carriers since they cannot generate entropy in any manner, also not be colliding with the target contact. If they do this they are not part of a superconducting phase.

If there is no electric field within the superconductor, as you point out, there is no acceleration of charge carriers. The charge carriers do not necessarily have to collide at the surface of the target contact. Once they enter the target contact they should behave like normal charge carriers in a conductor again, i.e. scatter after having travelled the mean free path through the conductor, on average. Those collisions do not generate extra entropy compared to a circuit without the superconductor.

[johanfprins]

How do you measure the speed at which charge carriers move through a superconductor? Why does this speed have to be particularly high?

A very good question. Since one cannot do a Hall measurent, I would think that the only way would be to do a time-of-flight (TOF) experiment. You apply an electric-field without injecting charge-carriers; then inject a pulse of charge-carriers and measure the time that it takes for the pulse to appear at the other contact. It should be noted that it is not "the same" charge-carriers that appear on the other side, since charge is transferred by the charge-carriers running a relay race. The injected charge effectively acts like a baton which is passed on from one charge-carrier to the next.

It will have to be a very fast TOF-measurement, since my models are consistent with speeds in the order of 10^5 meters/second.

If there is no electric field within the superconductor, as you point out, there is no acceleration of charge carriers.

Correct: You will be surprized how many "main stream experts" on superconduction refuse point blank to understand this obvious statement you have just made. See the discussion I am having on JREF.

The charge carriers do not necessarily have to collide at the surface of the target contact. Once they enter the target contact they should behave like normal charge carriers in a conductor again, i.e. scatter after having travelled the mean free path through the conductor, on average. Those collisions do not generate extra entropy compared to a circuit without the superconductor.

This is exactly what happens in a superconductor, except that the charge-carriers do have a mean free path which each completes before passing on the charge to the next charge-carrier. An injected charge-carrier does not "drift" all the way from one contact to the other during a single trip.

You are making very relevant staterments and asking very relevant questions: I appreciate it!

What I missed in the beginning was the following: Whether a "normal" charge-carrier scatters many times within the material through which it is moving, or only scatters after it has left the material, it still scatters away the same amount of acceleration-energy, and therefore the entropy generated by scattering in both cases are essentially the same. A superconducting charge-carrier has this wonderful ability not to gain any energy which it has to dissipate at any point anywhere in the universe, ever. It is amazing that it can be so, but this is mandated by the second law of thermodynamics that it must be so for a perpetual cvurrent to manifest around a superconducting ring.

[Teahive]

It will have to be a very fast TOF-measurement, since my models are consistent with speeds in the order of 10^5 meters/second.

That would be a very high drift speed, but doesn't this basically amount to a test of signal propagation speed? As such, 1e5 m/s seems awfully low. Or am I confusing things?

This is exactly what happens in a superconductor, except that the charge-carriers do have a mean free path which each completes before passing on the charge to the next charge-carrier. An injected charge-carrier does not "drift" all the way from one contact to the other during a single trip.

This may well be the case. But which experimental observation actually contradicts a model where they do drift all the way through the superconductor?

You are making very relevant staterments and asking very relevant questions: I appreciate it!

Your replies are equally appreciated.

A superconducting charge-carrier has this wonderful ability not to gain any energy which it has to dissipate at any point anywhere in the universe, ever. It is amazing that it can be so, but this is mandated by the second law of thermodynamics that it must be so for a perpetual cvurrent to manifest around a superconducting ring.

Interesting that you write "superconducting charge-carrier". So do you think this is a property of the charge carrier itself?

Re the current in a superconducting ring, wouldn't this have to be induced from outside somehow, using external energy, since a perfect ring cannot show any directional preference for a current to flow?

[johanfprins]

That would be a very high drift speed, but doesn't this basically amount to a test of signal propagation speed? As such, 1e5 m/s seems awfully low. Or am I confusing things?

Again very perceptive: That is why I wrote that you must first apply the electric-field so that it stabilizes. Within the superconbductor it is exactly cancelled after stabilization. You then inject a pulse of charge using a very low external field so that the electric-field within the superconductor essentially stays exactly zero. You should then be able to measure charge-in and subsequent charge-out. Obviously I am speculating here since such an experiment has not yet been done: However, I am quite convinced that the outcome will be as I expect that it must be.

This may well be the case. But which experimental observation actually contradicts a model where they do drift all the way through the superconductor?

There is no experimental observation and it will probably be difficult to distinguish experimentally between the two. There is, however, a powerful quantum mechanical reason why this cannot be so for a long superconductor.

This is so since the time interval in which a charge-carrier can obtain enough energy to break free and move to an adjacent position is limited by Heisenbergh's "uncertainty" relationship for energy and time. There is a maximum distance R(C) possible within which it must come to rest to "return" the energy without having to increase the entropy. This is why the charge-carriers have to run a relay race through the superconductor. Obviously if the distance between the contacts is less than R(C) a single charge-carrier will be able to move the whole distance without adding to the entropy.

Interesting that you write "superconducting charge-carrier". So do you think this is a property of the charge carrier itself?

Yes! The charge-carriers must be anchored by opposite charges (they must form an insuating dielectric lattice-array) so that they can polarize in order to cancel an applied electric-field; and they must be near enough to each other so that adjacent distances are less than R(C) to be able to move from one anchor point to the nex in order not to increase the entropy. Any other type of movement will always generate entropy and the charge transfer will then not be possible without energy dissipation.

Re the current in a superconducting ring, wouldn't this have to be induced from outside somehow, using external energy, since a perfect ring cannot show any directional preference for a current to flow?

Again a very incisive question. The current around a superconducting ring cannot be induced from "outside" by a changing magnetic field generating a circular electric-field, since the charge-carriers cancel such a field by polarization.

The reason why a current starts flowing is to keep the superconducting phase in its lowest energy-state possible under the boundary conditions it finds itself under. This is achieved under these conditions by generating an opposite magnetic field to cancel the applied magnetic field; even when the applied magnetic field is not changing with time. Therefore one can first apply a magnetic field before cooling susch a ring through its critical temperature; allow the induced current to dissipate owing to the scattering of the normal charge-carriers, and then cool through the critical temperature: A current will still immediately be there to cancel the applied constant magnetic-field.

If such a charge-carrier could have been accelerated by an induced electric field, a superconducting ring would not have been able to trap a magnetic field through it after switching off the applied magnetic-field. When switching off the magnetic field it induces a reverse circular electric field which, if it can decelertate the charge-carriers, must stop the current around a superconducting ring in its tracks; but since they cannot be accelerated by this electric-field, the current remains and it traps its own magnetic-field through the ring.

[Teahive]

Again very perceptive: That is why I wrote that you must first apply the electric-field so that it stabilizes. Within the superconbductor it is exactly cancelled after stabilization. You then inject a pulse of charge using a very low external field so that the electric-field within the superconductor essentially stays exactly zero. You should then be able to measure charge-in and subsequent charge-out. Obviously I am speculating here since such an experiment has not yet been done: However, I am quite convinced that the outcome will be as I expect that it must be.

Has this kind of experiment been done for normal conductors? I'm not sure the additional, very low field is really negligible as in a conductor it's the field that is responsible for transmitting a signal/pulse much faster than the average drift speed.

There is no experimental observation and it will probably be difficult to distinguish experimentally between the two. There is, however, a powerful quantum mechanical reason why this cannot be so for a long superconductor.

This is treading on dangerous territory. Can we trust a specific prediction of a theory before that prediction has been repeatedly validated in an experiment?

This is so since the time interval in which a charge-carrier can obtain enough energy to break free and move to an adjacent position is limited by Heisenbergh's "uncertainty" relationship for energy and time. There is a maximum distance R(C) possible within which it must come to rest to "return" the energy without having to increase the entropy. This is why the charge-carriers have to run a relay race through the superconductor. Obviously if the distance between the contacts is less than R(C) a single charge-carrier will be able to move the whole distance without adding to the entropy.
[...]
and they must be near enough to each other so that adjacent distances are less than R(C) to be able to move from one anchor point to the nex in order not to increase the entropy. Any other type of movement will always generate entropy and the charge transfer will then not be possible without energy dissipation.

But how does a "coasting" charge carrier increase the entropy if it does not interact with the superconductor? It would simply pass through without scattering.

Again a very incisive question. The current around a superconducting ring cannot be induced from "outside" by a changing magnetic field generating a circular electric-field, since the charge-carriers cancel such a field by polarization.

Sorry, I may have pushed this in the wrong direction by misusing the word induced. I meant it in the more general sense of "caused", not in the sense of elecromagnetic induction: The current that flows is caused by an external magnetic field. Without magnetic field there would be no current in a superconducting ring.

The reason why a current starts flowing is to keep the superconducting phase in its lowest energy-state possible under the boundary conditions it finds itself under. This is achieved under these conditions by generating an opposite magnetic field to cancel the applied magnetic field; even when the applied magnetic field is not changing with time. Therefore one can first apply a magnetic field before cooling susch a ring through its critical temperature; allow the induced current to dissipate owing to the scattering of the normal charge-carriers, and then cool through the critical temperature: A current will still immediately be there to cancel the applied constant magnetic-field.

If, in accordance with Meissner and Ochsenfeld, the superconductor expels the magnetic field during the transition through the critical temperature then the magnetic field inside the superconductor does indeed change at the point of transition, which should induce (this time in the electromagnetic meaning) a current. Your explanation appears to go the other way to arrive at the same result: the superconductor must cancel the applied magnetic field, and this can only happen through a current, therefore a current must flow.

The current then won't dissipate because it has no cause to do so in a superconductor. However in my understanding the current is equal to energy "trapped" within the superconducting ring. This energy would be released if you destroyed the ring or heated it through the critical temperature. And the energy would have come from outside the ring.

[johanfprins]

Has this kind of experiment been done for normal conductors?

Unfortunately I am not an expert on TOF, but I am sure that it has been done since I can remember having listened to lectures on such experiments.

I'm not sure the additional, very low field is really negligible as in a conductor

When switching on an electric-field in a material it must transmit through the material at the speed of light. That is why in metals it takes a charge-carrier ages to enter one contact and to reach the other contact, but why a current establishes itself right through the metal at the speed of light. So yes in this case you are correct.

According to my model for superconduction, when switching on an electric-field across a superconductor, the electric-field also establsihes itself over the whole material with the speed of light; but this applied electric field becomes cancelled by polarisation of the stationary, localised charge-carriers which constitute the SC-phase. The field does thus not establish a current which near-immediately (as allowed by light speed) starts flowing everywhere; so that a pulse of charge-carriers do not eject with light speed at the opposite contact.

In the case of a superconductor a current only initiates at the contact at which you inject charge, and this charge only reaches the ejecting contact after it has passed by means of a relay race to reach the other contact. Although still at a very high speed, the time for a charge-pulse to reach the other contact is far shorter than the speed of light. This just made me think that a TOF experimernt on a superconductor might be a cinch using the available TOF apparatuses.

A superconductor acts like a special type of bucket brigade consisting of a row of people. Each person along the row holds a bucket of water. When at the beginning of the row the first person is handed an extra bucket with water, he cannot hold both buckets, so that he passes on the bucket that he has had to the next person, who now has two buckets, so that he passes on the bucket that he has held; etc,. etc. Thus the last person in the row only receives a second bucket after a relatively long time-lapse, and then throws the water of the bucket he has had all along on the fire. So only now the injected charge appears on the other end.

This is treading on dangerous territory. Can we trust a specific prediction of a theory before that prediction has been repeatedly validated in an experiment?

I agree that it is dangerous, but sometimes it is just not physically possible to distinguish experimentally between two possibilities, and then one is forced to see which alternative gives more consistent results than the other alternative.

For example, it is impossible to measure experimentally whether there is an electric-field energy around a solitary charge, since any measurement will involve another charge. Thus the correct attitude must be that there can be such a field or there cannot be such a field. The physics community has decided, even though it cannot be proved experimentally, that there must be such a field. I think they made the wrong choice and this led us to fudging physics by means of renormalisation.

The reason why I am willing to trust my choice of two possibilities is that it has consistently led to consistent results and enabled me to model all superconductors ever discovered in terms of a single mechanism.

But how does a "coasting" charge carrier increase the entropy if it does not interact with the superconductor? It would simply pass through without scattering.

A material is not like a vacuum through which a particle-charge can coast when it enters a field-free region. The superconductor also has an electronic energy spectrum and thus a Fermi-level. An injected charge will enter the SC at its Fermi-level and can thus not avoid interaction with the existing valence-electron spectrum of the superconductor. It has to pass on its charge by means of the existing valence-electrons within the superconductor.

Furthermore, even if it could coast you must first find a mechanism that cancels an applied electric-field within the superconductor. My model gives the mechanism for cancelling the field, as well as the mechanism of how injected charge is transferred from one superconducting charge-carrier to the next without any scattering occurring and without generating kinetic energy which must be dissipated anywhere within the univrse.

Sorry, I may have pushed this in the wrong direction by misusing the word induced. I meant it in the more general sense of "caused", not in the sense of elecromagnetic induction: The current that flows is caused by an external magnetic field. Without magnetic field there would be no current in a superconducting ring.

Quite correct: The presence of the magnetic field increases the energy of the superconducting phase, and a current starts to flow when this energy becomes so high that it would destroy at least part of the superconducting phase. By then generating a current the superconducting phase succeeds to store magnetic energy externally from itself and thus to remain in a lower energy superconducting state.

If, in accordance with Meissner and Ochsenfeld, the superconductor expels the magnetic field during the transition through the critical temperature then the magnetic field inside the superconductor does indeed change at the point of transition, which should induce (this time in the electromagnetic meaning) a current.

The latter sounds very logical, but cannot happen in this way since a superconducting charge-carrier cannot ever be accelerated by an electric field, whether it is applied over two contacts or by means of magnetic induction. This is so because the charge-carriers always polarise to cancel an electric-field. If they cannot do this anymore, they are not superconducting charge-carriers anymore.

Your explanation appears to go the other way to arrive at the same result: the superconductor must cancel the applied magnetic field, and this can only happen through a current, therefore a current must flow.

I have to do this since the charge-carriers can never be accelerated by any applied electric-field.

The current then won't dissipate because it has no cause to do so in a superconductor. However in my understanding the current is equal to energy "trapped" within the superconducting ring. This energy would be released if you destroyed the ring or heated it through the critical temperature. And the energy would have come from outside the ring.

The energy is not just stored "within" the ring but also within the magnetic-field. It is a balancing act so that the superconducting phase can stay a siuperconducting phase while there is a magnetic-field.

Yes the phase has a higher energy than it will have without the magnetic field, but it is still within a lowest energy ground-state as allowed by the change in boundary conditions which is caused by the presence of the magnetic field. This is why the current runs indefintely afterwards: There is no lower energy state into which it can relax. Obviously when you destoy the ring, you change the boundaery conditions and thus destroy the lowest energy ground-state that is manifesting.

All currents within a superconductors flow just for one reason: They flow because the superconductor macro-wave wants to stay within a lowest energy ground-state as allowed by the boundary conditions it finds itself under. If the superconducting charge-carriers do not react to maintain such a state, the superconducting phase will have extra energy that it can dissipate and it will then not be s uperconducting phase anymore.

[johanfprins]

Has this kind of experiment been done for normal conductors?

Unfortunately I am not an expert on TOF, but I am sure that it has been done since I can remember having listened to lectures on such experiments.

I'm not sure the additional, very low field is really negligible as in a conductor

When switching on an electric-field in a material it must transmit through the material at the speed of light. That is why in metals it takes a charge-carrier ages to enter one contact and to reach the other contact, but why a current establishes itself right through the metal at the speed of light. So yes in this case you are correct.

According to my model for superconduction, when switching on an electric-field across a superconductor, the electric-field also establsihes itself over the whole material with the speed of light; but this applied electric field becomes cancelled by polarisation of the stationary, localised charge-carriers which constitute the SC-phase. The field does thus not establish a current which near-immediately (as allowed by light speed) starts flowing everywhere; so that a pulse of charge-carriers do not eject with light speed at the opposite contact.

In the case of a superconductor a current only initiates at the contact at which you inject charge, and this charge only reaches the ejecting contact after it has passed by means of a relay race to reach the other contact. Although still at a very high speed, the time for a charge-pulse to reach the other contact is far shorter than the speed of light. This just made me think that a TOF experimernt on a superconductor might be a cinch using the available TOF apparatuses.

A superconductor acts like a special type of bucket brigade consisting of a row of people. Each person along the row holds a bucket of water. When at the beginning of the row the first person is handed an extra bucket with water, he cannot hold both buckets, so that he passes on the bucket that he has had to the next person, who now has two buckets, so that he passes on the bucket that he has held; etc,. etc. Thus the last person in the row only receives a second bucket after a relatively long time-lapse, and then throws the water of the bucket he has had all along on the fire. So only now the injected charge appears on the other end.

This is treading on dangerous territory. Can we trust a specific prediction of a theory before that prediction has been repeatedly validated in an experiment?

I agree that it is dangerous, but sometimes it is just not physically possible to distinguish experimentally between two possibilities, and then one is forced to see which alternative gives more consistent results than the other alternative.

For example, it is impossible to measure experimentally whether there is an electric-field energy around a solitary charge, since any measurement will involve another charge. Thus the correct attitude must be that there can be such a field or there cannot be such a field. The physics community has decided, even though it cannot be proved experimentally, that there must be such a field. I think they made the wrong choice and this led us to fudging physics by means of renormalisation.

The reason why I am willing to trust my choice of two possibilities is that it has consistently led to consistent results and enabled me to model all superconductors ever discovered in terms of a single mechanism.

But how does a "coasting" charge carrier increase the entropy if it does not interact with the superconductor? It would simply pass through without scattering.

A material is not like a vacuum through which a particle-charge can coast when it enters a field-free region. The superconductor also has an electronic energy spectrum and thus a Fermi-level. An injected charge will enter the SC at its Fermi-level and can thus not avoid interaction with the existing valence-electron spectrum of the superconductor. It has to pass on its charge by means of the existing valence-electrons within the superconductor.

Furthermore, even if it could coast you must first find a mechanism that cancels an applied electric-field within the superconductor. My model gives the mechanism for cancelling the field, as well as the mechanism of how injected charge is transferred from one superconducting charge-carrier to the next without any scattering occurring and without generating kinetic energy which must be dissipated anywhere within the univrse.

Sorry, I may have pushed this in the wrong direction by misusing the word induced. I meant it in the more general sense of "caused", not in the sense of elecromagnetic induction: The current that flows is caused by an external magnetic field. Without magnetic field there would be no current in a superconducting ring.

Quite correct: The presence of the magnetic field increases the energy of the superconducting phase, and a current starts to flow when this energy becomes so high that it would destroy at least part of the superconducting phase. By then generating a current the superconducting phase succeeds to store magnetic energy externally from itself and thus to remain in a lower energy superconducting state.

If, in accordance with Meissner and Ochsenfeld, the superconductor expels the magnetic field during the transition through the critical temperature then the magnetic field inside the superconductor does indeed change at the point of transition, which should induce (this time in the electromagnetic meaning) a current.

The latter sounds very logical, but cannot happen in this way since a superconducting charge-carrier cannot ever be accelerated by an electric field, whether it is applied over two contacts or by means of magnetic induction. This is so because the charge-carriers always polarise to cancel an electric-field. If they cannot do this anymore, they are not superconducting charge-carriers anymore.

Your explanation appears to go the other way to arrive at the same result: the superconductor must cancel the applied magnetic field, and this can only happen through a current, therefore a current must flow.

I have to do this since the charge-carriers can never be accelerated by any applied electric-field.

The current then won't dissipate because it has no cause to do so in a superconductor. However in my understanding the current is equal to energy "trapped" within the superconducting ring. This energy would be released if you destroyed the ring or heated it through the critical temperature. And the energy would have come from outside the ring.

The energy is not just stored "within" the ring but also within the magnetic-field. It is a balancing act so that the superconducting phase can stay a siuperconducting phase while there is a magnetic-field.

Yes the phase has a higher energy than it will have without the magnetic field, but it is still within a lowest energy ground-state as allowed by the change in boundary conditions which is caused by the presence of the magnetic field. This is why the current runs indefintely afterwards: There is no lower energy state into which it can relax. Obviously when you destoy the ring, you change the boundaery conditions and thus destroy the lowest energy ground-state that is manifesting.

All currents within a superconductors flow just for one reason: They flow because the superconductor macro-wave wants to stay within a lowest energy ground-state as allowed by the boundary conditions it finds itself under. If the superconducting charge-carriers do not react to maintain such a state, the superconducting phase will have extra energy that it can dissipate and it will then not be s uperconducting phase anymore.

[icarus]

Prins:

For example, it is impossible to measure experimentally whether there is an electric-field energy around a solitary charge, since any measurement will involve another charge. Thus the correct attitude must be that there can be such a field or there cannot be such a field. The physics community has decided, even though it cannot be proved experimentally, that there must be such a field. I think they made the wrong choice and this led us to fudging physics by means of renormalisation.

Any possibility that you could demonstrate how assuming a solitary charge electric field necessitates renormalisation and assuming no field leads to results without renormalisation?

[johanfprins]

Prins: Any possibility that you could demonstrate how assuming a solitary charge electric field necessitates renormalisation and assuming no field leads to results without renormalisation?

That is a TALL order on a discussion thread, but of course a very relevant demand. You, of course, realise that to prove my point I have to challenge most of the main stream of physics which has been believed for nearly 100 years. This means that I, the "crackpot", suddemly finds myself confronted by hundreds of thousands of professors and their graduate students who have lived during the past 100 years,

I do not yet have the full solution, but I do have compelling evidence that there is not an electric field-energy around a solitary electron. I have outlined an approach in my book under section 34 called "The curious case of the solitary electron". One of my supervisors when I did my doctorate at the University of Virginia during the mid 1960's, Prof. Doris Kuhlmann-Wilsdorf, read a draft copy of the section, and e-mailed me that the ideas I have expressed might be Nobel Prize material. This response took my breath away since at that time she was writing a book on physics and religion which she based solidly on the main stream interpretation of quantum physics. Unfortunately she passed away soon afterwards. What remarkable person!

To give a short summary of what I consider to be the correct approach for the solitary electron: Firstly it is my contention that Schroedinger's wave equation is an approximation which is only valid for "bound" electrons. The reason for this is that this equation uses the electron's rest mass as an input, while the mass of an electron wave must be its energy. The equation can thus not be valid for a solitary electron or an electron moving past an observer with a speed v.

By manipulating Schroedinger's time-independent equation to get rid of the rest mass as an input, I ended up with an equation which relates to Maxwell's equation for a standing light-wave described in terms of a complex electric-field potential. Since mass-energy is inertia, and inertia relates to a resroring force trying to keep the electron in equilibrium, I solved this equation by using a harmonic potential, and ended up with a solution of the mass energy in terms of a radius of curvature which manifests along a fourth space dimension.

I also found that the mass-energy is totally determined by the electric field-energy so that there cannot be any electric-field energy in space "around" the electron.

It thus seems that a solitary electron, which is stationary within its inertial reference frame, might be nothing else but a light wave which stopped in its tracks. Since a light wave also has a magnetic component, this also explains why an electron-wave must have a magnetic field associated with it; which we obseve as a magnetic moment. The latter has nothing to do with the spin of a charge.

In fact, when solving the wave-equation with an applied magnetic field, one finds that the energy of the wave becomes a functiion of the angle between this magnetic moment and the applied magnetic field; and that there is no increase in energy when the magnetic moment is either parallel or antiparallel to the applied magnetic field. Thus there is a real physical cause why an electon's "spin" aligns either parallel or antiparallel to the applied magnetic field. It has nothing to do with an inbuilt probability into the laws of nature at all. The cat cannot be alive and dead at the same time!

And the evidence is compelling that the so-called "tunnelling-tail" has nothing to do with tunnelling at all, but is the curvature of space around mass.

When you transform the solution for a solitary, stationary electron wave by using the Lorentz transformation (i.e. how an observer will see this wave when it moves past him/her at a speed v) the De Broglie wavelength appears since the wave now has momentum. Since a standing matter wave, like an orbital atround a nucleus. has no mementum (like all standing harmonic waves known to date) these waves have nothing to do with a De Broglie wavelength.

The only reason why Schroedinger's wave seems to be determined by the Hamilton operator for a "particle" with mass m, is that the mass has been used as an input parameter, whereas it must be the solution of the differential equation for a matter wave. Thus to make this equation compatible with special relativity by devising a relativistic Hamilton operator might be nothing else than poppycock. In fact, Ibelieve that by doing this, Dirac has led physics completely astray: Even more than Bohr, Heisenberg and an Born did at the Solvay conference of 1927.

[icarus]

.... and so what does all this mean for the renormalisaton? It goes away because we don't use Dirac equation ... ? Is that the bottom line here?