Atom in a Decayed / Non-Decayed State

[StevieTNZ]

Zeilinger explains it thus(though I have no idea how a particle would know that information about it is being transmitted to an observer):"The superposition of amplitudes ... is only valid if there is no way to know, even in principle, which path the particle took. It is important to realize that this does not imply that an observer actually takes note of what happens. It is sufficient to destroy the interference pattern, if the path information is accessible in principle from the experiment or even if it is dispersed in the environment and beyond any technical possibility to be recovered, but in principle still ‘‘out there.’’ The absence of any such information is the essential criterion for quantum interference to appear."

https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.71.S288

I disagree, because the fundamental Schrödinger equation can't go from a pure state (that is, superposition) to a mixed state (no interference), without someone mucking around in the middle between the unitary evolution of the Schrödinger equation and destroying interference patterns and one state arising.

Unless you mean otherwise?

EDIT: even, if in principle the information is available, I would say, as Caslav Brunker has communicated to me, the interference pattern would be supressed but there in principle.

 

[vanhees71]

True, but Glashow's claim is not about what is objectively observable. In his scenario, nothing is objectively observed until the box is opened; that's part of the specification of the scenario. Yet he makes claims about what happens before the box is opened. Any such claim, given his specification of the scenario, is interpretation dependent.

True, and it's irrelevant as far as physics is concerned, because you cannot empirically check it, because when you empirically check it you have to open the box. So it's like discussing how many angels fit on the tip of a needle or whether the chicken or the egg was first... You can write tons of quantum-esoteric books about this subject and unfortunately they may sell better than good textbooks on the subject ;-)).

 

[WernerQH]

I disagree, because the fundamental Schrödinger equation can't go from a pure state (that is, superposition) to a mixed state (no interference), without someone mucking around in the middle between the unitary evolution of the Schrödinger equation and destroying interference patterns and one state arising.

Right, unitary evolution and the focus on the wave function appear to necessitate some "mucking around", because it can't be the whole story. But there is a decent way of combining unitary evolution and "measurements": the Schwinger/Keldysh closed time-path formalism.

"[K]nowledge of the transformation function referring to a closed time path determines the expectation value of any desired physical quantity for a specified initial state or state mixture."
(J. Schwinger, J.Math.Phys. 2, 407, 1961)

There is no talk of collapse, because in the Heisenberg picture the state vectors are constant. All that quantum theory is concerned with are operator products and traces over them.

 

[vanhees71]

The paper by Keldysh is much better readable to learn about the Schwinger-Keldysh real-time contour:

L. Keldysh, Diagram Technique for Nonequilibrium Processes,
Zh. Eksp. Teor. Fiz. 47, 1515 (1964), [Sov. Phys JETP 20 1965 1018],
https://www.jetp.ac.ru/cgi-bin/e/index/e/20/4/p1018?a=list

 

[WernerQH]

The paper by Keldysh is much better readable to learn about the Schwinger-Keldysh real-time contour:

L. Keldysh, Diagram Technique for Nonequilibrium Processes,
Zh. Eksp. Teor. Fiz. 47, 1515 (1964), [Sov. Phys JETP 20 1965 1018],
https://www.jetp.ac.ru/cgi-bin/e/index/e/20/4/p1018?a=list

True, Schwinger's paper is heavy going. I learned about the Keldysh formalism from the reviews by Chou et al (Physics Reports 118, 1-131) and Rammer and Smith (Rev.Mod.Phys. 58, 323-359), and I once even bought Rammer's book "Quantum Field Theory of Non-equilibrium States".
I think the method deserves to be much more widely known, but most presentations are extremely technical, and in standard cases the end result is just the Golden Rule.

 

[vanhees71]

Other very nice treatments are

P. Danielewicz, Quantum Theory of Nonequilibrium Processes I, Ann. Phys. 152, 239 (1984),
https://doi.org/10.1016/0003-4916(84)90092-7.

P. Danielewicz, Quantum Theory of Nonequilibrium Processes
II. Application to Nuclear Collisions, Ann. Phys. 152, 305
(1984), https://doi.org/10.1016/0003-4916(84)90093-9.

and for the relativistic case

N. P. Landsmann and C. G. van Weert, Real- and
Imaginary-time Field Theory at Finite Temperature and
Density, Physics Reports 145, 141 (1987),
https://doi.org/10.1016/0370-1573(87)90121-9.

Last but not least there's also a nice treatment in Landau&Lifshitz vol. X.

 

[WernerQH]

Last but not least there's also a nice treatment in Landau&Lifshitz vol. X.

Thanks! I was unaware of the sections in vol. X.

I was somewhat biased against Landau&Lifshitz, because I just hate their discussions of "measurement" in vol. III. :-)
One should really teach quantum theory starting with QFT.

 

[Demystifier]

One should really teach quantum theory starting with QFT.

Or why not teaching whole physics by starting with QFT? In fact, there is a textbook doing exactly that:
https://www.amazon.com/dp/9814579394/?tag=pfamazon01-20