Apropos the Meissner Effect : how is a totally still magnetic field expelled from the interior of a superconducting body, when it is cooled below the transition temperature? From whence do the supercurrent elements obtain their impulse ; how can they suddenly become screening currents, without a cause?
Conversely, it is quite understandable that bringing a superconducting body into a magnetic field-- in this case the supercurrent elements obtain their impulse from a changing magnetic field, via the Lenz-Faraday Law. But in the above case, the magnetic field is absolutely still, and so cannot possibly provide the mechanism to set up surface screening currents.
An other explanation. Cooper pairs randomly drift through the crystal with a non-zero kinetic energy. When the motion of Cooper pairs is non-dissipative, then the disordered drifts can align via the Lorentz force to minimize the magnetic energy in the interior. So the magnetic energy is expelled from the bulk without changing the kinetic energy of electron pairs and the total free energy of the crystal decreases.
This is the difference between a perfect conductor and a superconductor. A change has to happen for something to become a superconductor and expel the magnetic field. For example, the temperature drops. In a simple type 1 superconductor this results in there being an energetic advantage in Cooper pairs forming, and all the pairs end up in one state which has currents in it that expel any magnetic fields present.
The energy needed to generate the currents comes from the energetic advantage of forming cooper pairs. There is a trade-off between temperature (and so the energy advantage of forming Cooper pairs) and the strength of magnetic field which can be expelled, so strong magnetic fields intrude into superconductors and suppress superconductivity, depending on the temperature, and very strong fields suppress it completely.
The most significant thing about the Meissner effect, to my mind, is that two different time orders of events produces the same result : cooling down then placing in a magnetic field, versus, placing in a magnetic field, then cooling down.
Perhaps these two different time orders are in some way mixed-- or connected. Perhaps this is the reason why in the latter case, the flux is expelled from the interior in a static magnetic field :---- so the end result matches up with the former case.
This possibility is sketched here:
Preprint Connexion between two events that are separated in time for ...
The two effects are the same thing. Like if an empty balloon was inflated under water in a bucket. It displaces the water upwards and so has to do work. The same work would be required if the balloon was inflated above the water and then pressed down into it, and also, if the energy required to fill the bucket with water is counted, the difference between the potential energy required to fill the bucket with water with and without the balloon in it.
It has to be realised that superconductivity is intimately connected with Relativity-- observers moving uniformly in different frames :
"The first two, the Meissner effect (B=0) and zero resistivity (E=0) can be thought of as one and the same thing, when viewed through the prism of Relativity, insofar as the electric field transforms partly into the magnetic field and vice versa, in different frames, moving uniformly with respect to each other."
Cf : http://dx.doi.org/10.13140/RG.2.2.17687.60326
Once this is understood, then the notion that the Meissner Effect should be looked at in terms of the different perspectives of observers becomes more transparent :
Preprint Connexion between two events that are separated in time for ...
The considerer above, Malcolm White , posted an interesting analogy with the inflation of a balloon both below and above the water.
In this analogy, the motoring up of the screening currents, by the changing magnetic field, as the superconductor is brought inside a magnetic field, would correspond to the inflation of the balloon.
The analogy departs from the comparison, however, in the case of a static magnetic field, simply because here there is no inflation of the balloon-- or rather no apparent mechanism for the inflation of the balloon.
Just like there is no apparent mechanism for the expulsion of the magnetic flux.
It is agreed that this flux -is- expelled, but there is a question mark as to the mechanism.
If it were -the same- mechanism, ie. the inflation of the balloon, then the question would be redundant. But the proof it cannot be the same mechanism is furnished by the divers speculations, above, on the possible mechanism.
From our perspective, (hopefully without confusing the matter) we think it -is- the same mechanism, but displaced in time.
The inflation of the balloon is equivalent to the creation of the Cooper pairs and the condensate. This releases energy that does the work to "inflate the balloon". In the same way that a plastic bottle of water will swell and lift even a heavy weight above it when it freezes.
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