Do Entangled Quantum Particles Remain Aligned After Initial Preparation?

[EPR]

No. Decoherence can explain why there is never any interference observed between different irreversible measurement results. But it cannot explain why we only observe one result when there are multiple possible ones.

Until we check to see if the atom has decayed(with whatever means are available), the atom has 2 distinct states - decayed and not decayed(just not at the same time).
This is solved somewhat inelegantly by the act of measurement.

 

[vanhees71]

I don't think that's a good way to describe it. What I would say is that we design a measurement process so that distinct values of the observable that we are trying to measure become correlated with macroscopically distinguishable properties of the measurement device. We don't do anything additional to handle the case that the microscopic system we are measuring is in a superposition of eigenvalues of the observable being measured.

Of course, but this implies what I said: We construct the apparatus such that a macroscopic pointer reading gives a sufficiently unique value for the measured observable. We'd not accept a device which gives such unsharp readings that you can't say what the value of the measured observable this reading refers to.

 

[stevendaryl]

That's a big "if". For an experimentalist, a radioactive atom that has not decayed (after, say, 1 hour) is absolutely indistinguishable from an atom that is newly "prepared". For him it is in the same "state". But for the theorist, if he believes in the reality of the wave function, the state has changed after 1 hour.

Just as a preliminary disclaimer: I don't believe in "observation collapses the wave function", but I do believe that as a rule of thumb, it (almost?) always gives the right answers. So let me use that interpretation.

Let's simplify to say that an atom can be in two states: undecayed or decayed. According to QM, if you start with an atom in the undecayed state, then its state will change over time. Even if it starts out in a pure undecayed state, it will with time develop a nonzero amplitude for being in the decayed state. (The fact that the atom is unstable means that the undecayed state is not an energy eigenstate).

But if you periodically check to see whether the atom has decayed or not, then your observation will reset it to the pure undecayed state. In other words, observing the atom to be undecayed resets it to be in its initial state.

So you are right, that if after one hour you observe that the atom is undecayed, it will be in the same state it was at the beginning of the hour.

 

[vanhees71]

That's also known as the quantum-Zeno paradox :-)).

 

[stevendaryl]

Of course, but this implies what I said: We construct the apparatus such that a macroscopic pointer reading gives a sufficiently unique value for the measured observable. We'd not accept a device which gives such unsharp readings that you can't say what the value of the measured observable this reading refers to.

The issue isn't whether the readings are "unsharp". It's whether there can be a superposition of different outcomes. If a device is in a superposition of "the pointer points to the left" and "the pointer points to the right", then it doesn't give a unique measurement result. This isn't an issue of "sharpness". It doesn't matter how distinct the two measurement results are, if the device can be in a superposition of the two. So your original claim, that we only see one result because we designed the device that way, is just not correct.

 

[stevendaryl]

The issue isn't whether the readings are "unsharp". It's whether there can be a superposition of different outcomes. If a device is in a superposition of "the pointer points to the left" and "the pointer points to the right", then it doesn't give a unique measurement result. This isn't an issue of "sharpness". It doesn't matter how distinct the two measurement results are, if the device can be in a superposition of the two. So your original claim, that we only see one result because we designed the device that way, is just not correct.

This issue is only partly resolved by decoherence, as @PeterDonis said. Decoherence tells us that there can't be (at least, not easily) a superposition of macroscopically distinguishable "pointer states". But it's not because one of the possibilities disappears. It's because the superposition spreads to the environment.

 

[WernerQH]

But if you periodically check to see whether the atom has decayed or not, then your observation will reset it to the pure undecayed state. In other words, observing the atom to be undecayed resets it to be in its initial state.

I'm aware that this sounds convincing for some theoreticians. Unfortunately it is not a practical way for dealing with radioactive waste. It's the typical discrepancy between quantum theory and the real world.

 

[stevendaryl]

I'm aware that this sounds convincing for some theoreticians. Unfortunately it is not a practical way for dealing with radioactive waste. It's the typical discrepancy between quantum theory and the real world.

I don't understand what you're saying is a discrepancy.

 

[WernerQH]

I don't understand what you're saying is a discrepancy.

Can you prevent radioactive decay through measuring?
The quantum Zeno effect is not practical.

 

[vanhees71]

The issue isn't whether the readings are "unsharp". It's whether there can be a superposition of different outcomes. If a device is in a superposition of "the pointer points to the left" and "the pointer points to the right", then it doesn't give a unique measurement result. This isn't an issue of "sharpness". It doesn't matter how distinct the two measurement results are, if the device can be in a superposition of the two. So your original claim, that we only see one result because we designed the device that way, is just not correct.

What I tried to say is that a measurement device for measuring an observable $A$ is constructed such that it always delivers a definite outcome for the valud of this observable, no matter in which state the system is prepared (and of course with final resolution/accuracy).

You cannot observe from a single measurement, whether your system is in a pure state and then in a superposition wrt. the eigenbasis of $\hat{A}$ or not. A single measurement by construction delivers one definite value for $A$, not more not less. It doesn't make sense to talk about "measuring a superposition or not". We don't measure "state kets" (providing the formal description of a preparation procedure) nor "self-adjoint operators" (providing a formal description of a measurement procedure)!

By preparing an ensemble of systems in a given state (for which you need an appropriate device too) and always measuring $A$ you get a probability distribution for the outcome of measurements of $A$. To experimentally determine the state given some preparation procedure (maybe leading to an unknown, usually mixed, state) you need to do more then just the measurement of one single observable.

For a thorough discussion about "state determination", see L. Ballentine, Quantum Mechanics.

 

[WernerQH]

I don't understand what you're saying is a discrepancy.

Sorry, to me the discrepancy is so obvious that I was baffled by your question. Experimenters have never observed a radioactive atom in a superposition of decayed and non-decayed states, with half an electron and half a neutrino escaping to infinity. A coherent superposition, if it exists, lasts for at most a fraction of a second. Yet theoreticians envision wave functions that evolve gradually over the course of hours, days, or even years. I find it baffling how people can think of such a wave function as a faithful description of a single radioactive atom.