B Does the EPR experiment imply QM is incomplete?

[vanhees71]

QT seems not to be very inconsistent but very successful in describing the observed and quantitatively measured world. It's obvious that our contemporary theoretical understanding of nature is incomplete. It's quite arrogant to expect something else!

 

[zonde]

My point is that the assumption that there is a well-defined (single) outcome is contradicted by unitary evolution, if you consider the measurement device itself to be a quantum system.

But I'm talking about an idealized situation in which you have an isolated composite system that consists of a measurement device plus the system that it's measuring. You can describe the composite system quantum mechanically.

My objection is that quantum system can't be considered isolated at the moment of collapse. Consider one subsystem of entangled state. When it undergoes pre-measurement the state of other subsystem becomes determined (assuming detection as rather passive process in respect to measured property).
So unitary evolution after collapse can be there, but only if you consider larger system.

 

[stevendaryl]

My objection is that quantum system can't be considered isolated at the moment of collapse.

In an hypothetical world in which there is nothing but a measuring device and a particle that it measures, then what happens? Does the measuring device get a result that is an eigenvalue, or does it become a superposition?

 

[zonde]

In an hypothetical world in which there is nothing but a measuring device and a particle that it measures, then what happens? Does the measuring device get a result that is an eigenvalue, or does it become a superposition?

Hypothetically in such a hypothetical world particle does not interact with measurement device at all.

 

[stevendaryl]

Hypothetically in such a hypothetical world particle does not interact with measurement device at all.

Why would you say that? Two subsystems can't interact if they are the only things in the universe?

 

[zonde]

Why would you say that? Two subsystems can't interact if they are the only things in the universe?

For a particle to end up in new quantum state this state has to be available. If there are no quantum states to which particle can change it stays in the quantum state in which it is already.

 

[stevendaryl]

For a particle to end up in new quantum state this state has to be available. If there are no quantum states to which particle can change it stays in the quantum state in which it is already.

Who said that there were no other quantum states available?

 

[zonde]

Who said that there were no other quantum states available?

You proposed two options and none is valid. Particle can't change to other state (eigenvalue of measurement operator) if the system together can't satisfy Schrodinger equation. And particle can't become delocalized superposition because particles are localized.

 

[Lord Jestocost]

@vanhees71
In comment #143 you describe what Schlosshauer terms “measurement-as-axiom”. But this is not of help if one starts to think about “measurement-as-interaction”: How does individual measurement outcomes come about dynamically?

 

[stevendaryl]

You proposed two options and none is valid. Particle can't change to other state (eigenvalue of measurement operator) if the system together can't satisfy Schrodinger equation. And particle can't become delocalized superposition because particles are localized.

Sorry, I have no idea what you are talking about.

 

[Mentz114]

In an hypothetical world in which there is nothing but a measuring device and a particle that it measures, then what happens? Does the measuring device get a result that is an eigenvalue, or does it become a superposition?

It depends on the Hamiltonian and the initial states of the system and apparatus.

My point being that it is possible for unitary evolution to result in an eigenstate.

 

[stevendaryl]

It depends on the Hamiltonian and the initial states of the system and apparatus.

My point being that it is possible for unitary evolution to result in an eigenstate.

But there are certainly cases where you can prove that that can't happen.

For example, if the initial state has reflection symmetry about some point, but each of the "pointer states" lacks this symmetry, then you can show that unitary evolution cannot result in a definite pointer state.

 

[Mentz114]

But there are certainly cases where you can prove that that can't happen.

For example, if the initial state has reflection symmetry about some point, but each of the "pointer states" lacks this symmetry, then you can show that unitary evolution cannot result in a definite pointer state.

True. But that would be a poorly designed instrument. From what I've read it is important that the apparatus has an observable that has the same eigenstates (or close to) as the system being tested.

 

[stevendaryl]

True. But that would be a poorly designed instrument. From what I've read it is important that the apparatus has an observable that has the same eigenstates (or close to) as the system being tested.

That's what I'm talking about. Take the example of a spin measurement: If the particle is spin-up, then some pointer points to the left. If the particle is spin-down, then the pointer points to the right. The initial state of the pointer is a neutral position that is left-right symmetric.

So you prepare an initial state for the particle that is an equal superposition of spin-up and spin-down. The initial state is left-right symmetric. The final state (if it gives a definite result) is not.

 

[PeterDonis]

The initial state is left-right symmetric. The final state (if it gives a definite result) is not.

More to the point of your previous comment, unitary evolution results in a superposition of "spin-up and pointer pointing to the left" and "spin-down and pointer pointing to the right", i.e., an entangled state which is left-right symmetric, but which does not have a definite state for the pointer. To get a definite state for the pointer from a starting state that is left-right symmetric, you would need some non-unitary process somewhere.

 

[zonde]

That's what I'm talking about. Take the example of a spin measurement: If the particle is spin-up, then some pointer points to the left. If the particle is spin-down, then the pointer points to the right. The initial state of the pointer is a neutral position that is left-right symmetric.

So you prepare an initial state for the particle that is an equal superposition of spin-up and spin-down. The initial state is left-right symmetric. The final state (if it gives a definite result) is not.

Your reasoning is valid (as far as I can tell), but it does not mean that contradiction with unitary evolution is unavoidable.
We can say that yes there is sudden change in the state of the system, if there is another sudden change in another system somewhere (nearby). And both systems taken together satisfy Schrodinger equation. It's like entangled pair of particles, taken separately there is sudden change in particle state. Taken together both particles add to the same combined state even after this sudden change.

 

[PeterDonis]

We can say that yes there is sudden change in the state of the system, if there is another sudden change in another system somewhere (nearby). And both systems taken together satisfy Schrodinger equation.

Where are you getting this from? Do you have a peer-reviewed reference that proposes a model like this?

 

[zonde]

Where are you getting this from? Do you have a peer-reviewed reference that proposes a model like this?

No, I have references for experiments that observe phenomena like this:
http://arxiv.org/abs/1508.05949
http://arxiv.org/abs/1511.03189
http://arxiv.org/abs/1511.03190

 

[PeterDonis]

I have references for experiments that observe phenomena like this

These are all recent experiments testing for violations of the Bell inequalities with more loopholes closed. That has nothing to do with what we're discussing. Measuring the spins of a pair of entangled particles that start out in a left-right symmetric state still cannot produce a state that is not left-right symmetric by unitary evolution. Read my post #165; the extension of what I said there to the case of a pair of spin measurements on entangled particles is straightforward and doesn't change my conclusion.

 

[stevendaryl]

Your reasoning is valid (as far as I can tell), but it does not mean that contradiction with unitary evolution is unavoidable.
We can say that yes there is sudden change in the state of the system, if there is another sudden change in another system somewhere (nearby). And both systems taken together satisfy Schrodinger equation. It's like entangled pair of particles, taken separately there is sudden change in particle state. Taken together both particles add to the same combined state even after this sudden change.

I'm not sure if I understand what you're suggesting, but something similar happens in Many-Worlds. If one pointer points to the left in one world, it points to the right in another, so the Many-Worlds model remains left-right symmetric.

 

[zonde]

Read my post #165; the extension of what I said there to the case of a pair of spin measurements on entangled particles is straightforward and doesn't change my conclusion.

I am not questioning your conclusion. I completely agree with it. And if am not mistaken @stevendaryl agrees with it as well.

 

[zonde]

I'm not sure if I understand what you're suggesting, but something similar happens in Many-Worlds. If one pointer points to the left in one world, it points to the right in another, so the Many-Worlds model remains left-right symmetric.

Yes, that's very similar to MWI, only it is restricted to single world.

 

[Mentz114]

[]
So you prepare an initial state for the particle that is an equal superposition of spin-up and spin-down. The initial state is left-right symmetric. The final state (if it gives a definite result) is not.

I don't understand why left/right and up/down are significant. Is the initial state not also 'up/down' symmetric. The final state of what ?
I don't know what point you are making.

The superposition of states in the X basis after the spin has been prepared as Z+ (say) cannot be a physical state, because at that moment the is no angular momentum in any direction but Z. So the superposition refers to non-existent values or at best two zeros.

The only physically consistent interpretation is that a mixture is prepared.

 

[PeterDonis]

I am not questioning your conclusion. I completely agree with it.

No, you don't. You said:

it does not mean that contradiction with unitary evolution is unavoidable.

This is incorrect; the contradiction between unitary evolution and definite pointer states is unavoidable. That is true even if you measure a pair of entangled systems instead of a single system; under unitary evolution, each individual pointer device still ends up entangled, not in a definite state.

 

[PeterDonis]

I don't understand why left/right and up/down are significant.

Because that's how the spin measurement device was oriented for that particular measurement. You could indeed orient the device in any direction and still apply the same reasoning. But any particular spin measurement has to be done along a particular direction.

I don't know what point you are making.

The point he is making is that, if having a pointer that is not in a definite state after measurement means the measurement is poorly designed, then unitary evolution predicts that all measurements are poorly designed, since unitary evolution will never give you a pointer that ends up in a definite state after measurement.

 

[stevendaryl]

I don't understand why left/right and up/down are significant. Is the initial state not also 'up/down' symmetric. The final state of what ?
I don't know what point you are making.

That the assumption that a measurement always gives an eigenvalue is contradictory with the assumption that evolution is unitary.

The initial state of the lab plus particle is left-right symmetric. The final state of the lab is not.

I don't understand your difficulty. I'm imagining a measuring device with a literal pointer. It measures the z-component of the spin of an electron, and the pointer swings right if the result is spin-up, and swings left if the result is spin-down.

 

[zonde]

This is incorrect; the contradiction between unitary evolution and definite pointer states is unavoidable. That is true even if you measure a pair of entangled systems instead of a single system; under unitary evolution, each individual pointer device still ends up entangled, not in a definite state.

Ok, you are identifying definite state with definite (pure) quantum state. I don't.
Hmm, may this is exactly the same problem in my discussion with @stevendaryl.

 

[stevendaryl]

Ok, you are identifying definite state with definite (pure) quantum state. I don't.
Hmm, may this is exactly the same problem in my discussion with @stevendaryl.

Well, the difference between a macroscopic object, such as a measuring device, and a microscopic object, such as an electron, is that for any given macroscopic state (what we would intuitively, pre-quantum mechanics, think of a state, such as "the readout shows the number 32" or "the pointer points to the left" or "the left light is on") there are many, many microscopic states that correspond to it.

I don't have the mathematical sophistication to accurately describe the situation using quantum mechanics, but perhaps it's something like the following:

The complete system perhapse can be described by three variables: $|s, S, j\rangle$, where $s$ is the observable corresponding to the system being measured (an electron's spin, maybe), $S$ is the corresponding value of the "pointer variable", and $j$ represents all the other degrees of freedom.

To make it both simple and definite, we will assume that there are two possible values for $s$:$u$ and $d$, and three possible values for $S$: $0, U, D$. There are many (possibly infinitely many) values for the other degrees of freedom, $j$.

To say that the pointer accurately measures the z-component of spin is to say something like the following:

• If you start in the state $|u, 0, j\rangle$, and you allow the system to evolve, then you will end up most likely in a superposition of the form
  • $\sum_k c_{ujk} |u, U, k\rangle$
• If you start in the state $|d, 0, j\rangle$, and you allow the system to evolve, then you will end up most likely in a superposition of the form
  • $\sum_k c_{djk} |d, D, k\rangle$
• It follows from the linearity of the evolution operator that if you start in a superposition of the form $\alpha |u, 0, j\rangle + \beta |d, 0, j\rangle$, then you will end up in a superposition of the form $\alpha \sum_k c_{ujk} |u, U, k\rangle + \beta \sum_k c_{djk} |d, D, k\rangle$

By "end up", I mean applying the evolution operator $e^{-iHt}$.

Now, what I'm a little hazy about is how to deal with irreversibility in quantum mechanics. A measurement is irreversible. I don't know whether the irreversibility is completely explained by the fact that the final state is massively degenerate, compared to the initial state. That's the classical explanation. I don't know whether anything we have to say hinges on the interpretation of irreversibility.

Anyway, given the above assumptions about the evolution, we can always add classical uncertainty, by letting the initial state be an incoherent mixture of

$\alpha |u, 0, j\rangle + \beta |d, 0, j\rangle$

for different values of $j$.

 

[PeterDonis]

you are identifying definite state with definite (pure) quantum state. I don't.

Then what definition are you using? And why do you think it's relevant?

 

[PeterDonis]

what I'm a little hazy about is how to deal with irreversibility in quantum mechanics. A measurement is irreversible.

And unitary evolution is reversible, so right there you have stated the key inconsistency between unitary evolution and measurements.