The electron is in a superposition of spin states and quantum mechanical transition amplitudes can be computed, as usual.  There isn't any problem of principle involved. 

Dear Stam Nicolis,

My understanding of superposition is quite different from undefined spin state.

Nevertheless what is your opinion: Does the entanglement brake down or not? If yes is the reason that a potential measurement process is involved?

That's the result of a calculation, not of opinion. It's possible to do the calculation, compute the probability distribution of the two-electron state  and check when the probability distribution of the two-electron state factorizes into a product of probability distributions of one-electron states, which means that the two electrons aren't entangled.

As far as I know the entanglement brake only when there is a measurement. But the mere presence of magnetic field is not a measurement just interaction.

No, that's not true: entanglement simply means that the multi particle probability distribution isn't factorizable into a product of single-particle distributions, that's all.  (It's possible to say this in many ways, that sound different, but are equivalent to this statement.)

What you say is true and I never argued again such formulation. (absolutely out of question). I don't understand to what you say no? Do you say no to 'interaction itself without measurement does not lead to disentanglement?

It may or it may not- the result depends on the details. However it's possible to do this calculation, in any given case, using the known rules of quantum mechanics.

Remembering the double slit (where the observation of the electron in one slit destroys the superposition |left slit>+ |right slit>) I am almost convinced that the interaction between  the spin superposition |up>+|down> and the magnetic field if not observed would not lead to destruction in it.

Like in double slit where the superposition is not destroyed even when there is an interaction between the electron and the material where the slits are cut trough. Likewise ...the interaction of the electron in superposition and the magnetic field will not destroy the superposition if not observed.

This a general principle of QM! though  I have not seen it explicitly stated in textbooks among the general axioms (which is  a bad omission).

So I think I answered my own question: the EPR pair will stay connected when one of the partners goes through a magnetic field but one takes all measures to prevent observation of that interaction.

The only answer can come from doing the calculation. Any claim by words, that can't be illustrated by an explicit calculation doesn't make sense. In particular the term ``observation of the interaction'' needs to be specified.

Most eminent in physics is experiment! The mathematics has to be build in such a way to stick to it!!! Example - QM.

Einstein has said something in the sense that whatever you do you can not prove something that is not observable in experiment already.

By the way if you know how do they attach math to this principle? This is in fact the famous wave function collapse where the Schr. equation stops acting and one gets state |+>  or |-> from a superposition of both. Math doesn't give to much just a mere description in symbolic terms.

There's no problem of principle  in constructing the superposition of states and acting on it with the appropriate evolution operator and then studying how the two-particle probability distribution does-or doesn't-factorize in a product of the corresponding one-particle probability disributions. That's all that's needed and these days it's possible to perform the appropriate experiments. 

I'm not sure if the electron pair is the correct object to be discussed wihin Einstein-Podolsky-Rosen paradox (this is what you mean by EPR, not Electron Paramagnetic Resonance, right?).  Contrary to photons, electrons do have a mass (so they cannot travel with light velocity) and they also carry an electric charge repelling electrostatically one from the other --> their relative movement cannot be at constant speed, it is necessarily accelerated.  Then there is a Pauli exclusion principle, which suggests that their spins should be oriented in opposite dierctions but both laying on the line connecting them (this is the distinguished direction at t=0, when they are at the same place).  What will happen next?  Photons are insensitive to (localized) magnetic field, but electrons are.  Thus I don't think that measuring magnetic polarization, at later time, of one electron, says anything of the fate of the other one.  Interactions with other objects (here: magnetic field) destroys entaglement, if there was any.

Yes, by EPR of mean of course Einstein etc.

Electron EPR pairs can be created. I didn't ever heard that there is any influence on the spin entanglement as a consequence of their initial acceleration. It is not possible because these two distinct conservation laws (energy - acceleration and spin - entanglement). Today experiments are made mostly with photons. 

Yes, the entanglement will brake surely after interaction but not if the information of this interaction is kept inaccessible.

That's my understanding of QM, which I have illustrated with the double slit experiment. Namely if you don't observe the which way information the photon is in superposition of going through both slits.    

I think the same is true with a magnetic field and electron in superposition. I suppose that if all happens in a closed box the electron would still be in superposition of spin up and down (before it has left the box).

So, you think that before a measurement the electrons are still entangled? If one keeps this result inaccessible (doesn't make a measurement), no matter that the second electron has passed trough a magnetic field,  they are still entangled, because the magnetic field doesn't force this electron in |up2> or  |down2> state?

I suppose that if one mixes the both paths of up2 and down2, he can not understand if there was a magnetic field inside the area of interaction or not (switched on/off magnetic field).