Is quantum collapse an interpretation?

[zonde]

Decoherence happens whenever quantum system and measurement device get entangled with environmental degrees of freedom.

So you don't know where to place decoherence. Because it works neither way.

 

[martinbn]

As I explained the non-unitary collapse cannot represent real dynamics b/c it mathematically contradicts dynamics represented by unitary time evolution.

This is something I don't understand. Why is it a contradiction? It seems that it is a contradiction only if you assume that there can be only one type of evolution. Why is it not possible for the system to evolve unitary for some time, then non-unitary and so on? I can see this would raise more questions about the specifics, but why is it a contradiction by itself?

 

[vanhees71]

So you think that you cannot have an interpretation without projection and at the same time you are convinced that you can have one without collapse. Aren't these two the same?

No, because it's just an effective description, neglecting the irrelevant microscopic details of absorption. The absorption is a local process, i.e., the photon hitting the polarizer and getting absorbed happens at the place where the polarizer is located, i.e., the largest relevant spatial extend is the size of the polarizer, but "collapse" (in this case the absorption of the photon filtering it out as an unwanted polarization state) means it's something happening instantaneously in the entire space, and that's violating causality and also the very construction of QED as a local relativistic field theory obeying the linked-cluster principle.

 

[martinbn]

No, because it's just an effective description, neglecting the irrelevant microscopic details of absorption. The absorption is a local process, i.e., the photon hitting the polarizer and getting absorbed happens at the place where the polarizer is located, i.e., the largest relevant spatial extend is the size of the polarizer, but "collapse" (in this case the absorption of the photon filtering it out as an unwanted polarization state) means it's something happening instantaneously in the entire space, and that's violating causality and also the very construction of QED as a local relativistic field theory obeying the linked-cluster principle.

Consider this, a photon is prepared in a state $\alpha|V\rangle+\beta|H\rangle$, later it is in the state $|H\rangle$. How did the state evolve unitarily? It is not possible. How do you explain that?

 

[vanhees71]

To get a unitary description, you'd have to consider an entire closed system, consisting of the photon and the polarizer. According to Q(F)T the time evolution of a closed system is unitary with the self-adjoing Hamiltonian of the entire system as the "generator". For the photon alone, it's of course not unitary since you "integrate out" a huge system, namely the macroscopic polarization filter!

 

[martinbn]

To get a unitary description, you'd have to consider an entire closed system, consisting of the photon and the polarizer. According to Q(F)T the time evolution of a closed system is unitary with the self-adjoing Hamiltonian of the entire system as the "generator". For the photon alone, it's of course not unitary since you "integrate out" a huge system, namely the macroscopic polarization filter!

Correct me if i am wrong but if you do that you end up with a mixed state either |V> or |H>, not just |H>. So you have a measurement problem, how do you get away with only unitary evolution?

 

[zonde]

To get a unitary description, you'd have to consider an entire closed system, consisting of the photon and the polarizer. According to Q(F)T the time evolution of a closed system is unitary with the self-adjoing Hamiltonian of the entire system as the "generator". For the photon alone, it's of course not unitary since you "integrate out" a huge system, namely the macroscopic polarization filter!

Well, but if you are not specifically after unitary description but rather after description of photon alone? Say you want to do some other things with photon and consider everything that happened with photon before, including polarizer, a state preparation.
You would consider that there is a photon with certain polarization, right?

 

[vanhees71]

Correct me if i am wrong but if you do that you end up with a mixed state either |V> or |H>, not just |H>. So you have a measurement problem, how do you get away with only unitary evolution?

But at the end you only consider the photons that are going through the polarizer, and these have a definite polarization!

 

[tom.stoer]

Why is it a contradiction? It seems that it is a contradiction only if you assume that there can be only one type of evolution. Why is it not possible for the system to evolve unitary for some time, then non-unitary and so on?

a) unitary time evolution:

$$|\psi(t\rangle) \to |\psi(t^\prime)\rangle = U(t^\prime,t) \, |\psi(t\rangle)$$

b) non-unitary collapse to some eigenstate:

$$|\psi(t\rangle) \to \hat{P}_\lambda |\psi(t)\rangle \sim |\lambda(t)\rangle$$

U is invertible, P is not. U is deterministic, P is not.

When i.e. for which time shall the last evolution apply? which axioms or rules tell you when to use (a) and when to use (b)? what is the difference between an interaction with a measuremt device (b) and "something else" (a) ? what selects the target eigenstate to which the state shall collapse? ...?

 

[martinbn]

When i.e. for which time shall the last evolution apply? which axioms or rules tell you when to use (a) and when to use (b)? what is the difference between an interaction with a measuremt device (b) and "something else" (a) ? what selects the target eigenstate to which the state shall collapse? ...?

I agree, I even said that it poses many questions. But you say that it leads to a contradiction. My question is why? Is it obvious, not to me, or do you mean that it would be problematic as it poses more questions than it solves?

 

[martinbn]

But at the end you only consider the photons that are going through the polarizer, and these have a definite polarization!

We are going in circles. My questions is how do you explain that with only unitary evolution, given that the map from the fist state to the second is not unitary?

 

[vanhees71]

I can only repeat what I said before. Only the full time evolution of the entire closed system is unitary. If you project out parts of the system, their evolution is not unitary, because of that projection. I don't know, how I can reformulate this in other words. It's about evolution equations for open quantum systems. Maybe, it helps to read about the Lindblad equation:

https://ocw.mit.edu/courses/nuclear...s-fall-2012/lecture-notes/MIT22_51F12_Ch8.pdf

A more simple example, which entirely works with unitary time evolution is the Stern-Gerlach apparatus. After the particles are running through the inhomogeneous magnetic field you get a state, where the position of the particles is entangled with the spin state. Provided you have a well designed magnetic field you split thus a particle beam into sufficiently well separated partial beams, each of which contains particles with a certain value of the spin component in the direction of the magnetic field (usually this is taken as the $z$ direction, i.e., in each partial beam the spin state of the particles is a pure state $|\sigma_z \rangle$). If you just consider this partial beam (you can block all other partial beams by just putting an appropriate absorber in front), and what you have effectively is the projection of an arbitrary (spin state) $\hat{\rho}$ to the pure state $|\sigma_{z} \rangle \langle \sigma_{z}$. Of course you have a beam with less particles since you absorbed all the "unwanted" ones. At this point of course you have again an effective non-unitary description due to the absorption, where you don't consider the full dynamics of the particles + absorbing material.

The separation into partial beams with determined spin components, however was completely unitary, and you can as well do without any blocking of the unwanted particles, but only experimenting with particles out of one of the partial beams by just using only those at the corresponding location. Then you have a preparation with a unitary time evolution.

 

[tom.stoer]

The original question seems to be

Consider this, a photon is prepared in a state $\alpha|V\rangle+\beta|H\rangle$, later it is in the state $|H\rangle$. How did the state evolve unitarily? It is not possible. How do you explain that?

Sorry to say that, this is trivial.

If both $\alpha|V\rangle+\beta|H\rangle$ and $|H\rangle$ are normalized this is simply a unitary rotation. The unitary operator $U(t)$ which is nothing else but a $U(2) = U(1) \cdot SU(2)$ matrix can be constructed explicitly.

The easiest way to see this is setting

$$\beta(t) = \sqrt{1 - |\alpha(t)|^2} $$

and for some later time

$$\alpha(t_0) = 0 \;\Rightarrow\; \beta(t_0) = 1 $$But that is not really what decoherence and Everett is all about. In this formalism after a measurement of an observable the overall system is not in an eigenstate of this observable!

 

[Demystifier]

I can only repeat what I said before. Only the full time evolution of the entire closed system is unitary. If you project out parts of the system, their evolution is not unitary, because of that projection.

You are failing to distinguish projection from tracing out.

When the full system evolves unitarily, the subsystem evolves non-unitarily due to tracing out of the degrees of freedom that do not belong to the subsystem. This is related to decoherence, but a priori it has nothing to do with projection.

Projection, on the other hand, is related to update of information, or in a slightly different interpretation, with collapse. But projection cannot be explained by decoherence or tracing out of unobserved degrees.

Of course, both operations introduce non-unitarity in a description of the system. Yet those operations are different mathematically, physically and philosophically.

 

[vanhees71]

Well what @martinbn had in mind is the projection rather than the unitary "rotation". I.e., according to the collapse postulate you have a transition
$$|\psi \rangle \mapsto |H \rangle \langle H| \psi \rangle, \qquad (1)$$
and if $|\psi \rangle$ and $|H \rangle$ are both normalized in general the projection is of course not normalized anymore.

But it's not said that this is really the result of the interaction of the photon with the measurement apparatus (that's the case for ideal filter measurements), but all that's really said by the formalism and what's accepted in the minimal interpretation exclusively is that in such a case the probability that one finds a photon to be H-polarized, given it's prepared in the polarization state $|\psi \rangle$ is given by $|\langle H|\psi \rangle|^2$. There is no evolution as in one, except in the sense of an effective description of the interaction between the photon and the polarizer, and since this is a description looking at the photon only in the sense of an open quantum system this "evolution" doesn't need to be unitary (as it must be for a closed quantum system, where the dynamics is due to a self-adjoint Hamiltonian).

 

[vanhees71]

You are failing to distinguish projection from tracing out.

When the full system evolves unitarily, the subsystem evolves non-unitarily due to tracing out of the degrees of freedom that do not belong to the subsystem. This is related to decoherence, but a priori it has nothing to do with projection.

Projection, on the other hand, is related to update of information, or in a slightly different interpretation, with collapse. But projection cannot be explained by decoherence or tracing out of unobserved degrees.

Of course, both operations introduce non-unitarity in a description of the system. Yet those operations are different mathematically, physically and philosophically.

Well, I think I was a bit sloppy here. In case of an ideal filter measurement (or better preparation) the tracing out, however, should indeed lead to a projection, or are you saying that any ideal filter measurement disproves quantum theory since it cannot be understood by unitary time evolution and tracing out the irrelevant degrees of freedom?

 

[Mentz114]

a) unitary time evolution:

$$|\psi(t\rangle) \to |\psi(t^\prime)\rangle = U(t^\prime,t) \, |\psi(t\rangle)$$

b) non-unitary collapse to some eigenstate:

$$|\psi(t\rangle) \to \hat{P}_\lambda |\psi(t)\rangle \sim |\lambda(t)\rangle$$

U is invertible, P is not. U is deterministic, P is not.

When i.e. for which time shall the last evolution apply? which axioms or rules tell you when to use (a) and when to use (b)? what is the difference between an interaction with a measuremt device (b) and "something else" (a) ? what selects the target eigenstate to which the state shall collapse? ...?

Have you seen this paper by L S Schulman ? I don't want to pay the price ...

Model apparatus for quantum measurements
Abstract

We present a model system that behaves as a measurement apparatus for quantum systems should. The device is macroscopic, it interacts with the microscopic system to be measured, and the results of that interaction affect the macroscopic device in a macroscopic, irreversible way. Everything is treated quantum mechanically: the apparatus is defined in terms of its (many) coordinates, the Hamiltonian is given, and time evolution follows Schrödinger's equation. It is proposed that this model be itself used as a laboratory for testing ideas on the measurement process.

https://link.springer.com/article/10.1007/BF01026572

 

[Demystifier]

Well, I think I was a bit sloppy here. In case of an ideal filter measurement (or better preparation) the tracing out, however, should indeed lead to a projection. I guess, there are simple models where such a thing is calculated in the literature.

If that was true, you would be right that there is no problem of measurement and there would be no need for various non-minimal interpretations of QM. But unfortunately it is not true, and this is exactly the origin of the problem of measurement. There is no model (simple or complicated), based merely on standard QM, in which tracing out leads to projection.

 

[vanhees71]

Hm, that's indeed an obstacle, because blocking out particles from a partial beam is almost trivial in the lab. You just put a beam dump.

 

[Demystifier]

are you saying that any ideal filter measurement disproves quantum theory since it cannot be understood by unitary time evolution and tracing out the irrelevant degrees of freedom?

I am saying that any ideal filter measurement disproves some of your claims on quantum theory.

 

[vanhees71]

Do you have a reference, where such a no-go theorem is proven?

 

[Demystifier]

Hm, that's indeed an obstacle, because blocking out particles from a partial beam is almost trivial in the lab. You just put a beam dump.

Now you are failing to distinguish blocking from projection.To paraphrase A. Peres, blocking happens in the laboratory, while projection happens in the Hilbert space.

 

[Demystifier]

Do you have a reference, where such a no-go theorem is proven?

See e.g. the Schlosshauer's book on decoherence, especially the section on the problem of outcomes.

 

[vanhees71]

Well, if I filter out all partial beams from a SG apparatus and keep only the one I want, it's pretty much what I'd (perhaps too naively) describe by a projection operator in the formalism. It gives me the correspondingly less intense beam (with the intensity drop given by the probabilities according to Born's rule). So you say that there is a difference between the description of blocking in the formalism and projection?

 

[Demystifier]

Well, if I filter out all partial beams from a SG apparatus and keep only the one I want, it's pretty much what I'd (perhaps too naively) describe by a projection operator in the formalism. It gives me the correspondingly less intense beam (with the intensity drop given by the probabilities according to Born's rule). So you say that there is a difference between the description of blocking in the formalism and projection?

Ah, we were talking about two different types of projection.

The projection above which you are talking about is deterministic. The non-unitary evolution due to tracing out is also deterministic.

I was talking about non-deterministic projection, when you don't know in advance in which state the system will end up. It is only this latter non-deterministic projection that lies at the origin of the problem of measurement in QM.

 

[vanhees71]

But again this latter kind of projection is, as you said above too, just "update of knowledge". Within the minimal interpretation nothing collapses here at all. Nobody would say that something collapses, only because I watch the outcome of the German Lotto game on Saturday and update my knowledge about this outcome of 6 randomly chosen numbers.

However, I'd wish I could gain this knowledge before the drawing, but that's not even possible within quantum theory, which still is a causal theory, and I can't "update my knowledge" before the fact is established, at least non within no-nonsense intepretations of QT, and the nonsense interpretations don't work, which is why we don't take them seriously as phenomenology "grounded" physicists.

 

[Fra]

We might discuss words at this point but...

Within the minimal interpretation nothing collapses here at all. Nobody would say that something collapses, only because I watch the outcome of the German Lotto game on Saturday and update my knowledge about this outcome of 6 randomly chosen

I would say that your _expectation_ about numbers collapsed.

To me the collapse is by definition an _unexpected_ update associated with the systems perturbation of the observers state ;)

I can't "update my knowledge" before the fact is established

As i see it there can also be an _expected_ update of your knowledge. But this is just the unitary "selfevolution" of the informationstate in time between observations.

In normal high energy experiments the observer is really all the apparatous and staff in the laboratory frame, and and interactions in the lab more or less follow classical physics and thus the issue of different parys of the lab have differeny information does not exist.this is how normal scientifc consensus is achieved.

So it becomes silly and unnecessary to speak of observer states. As that's simply all scientific knowledge in the lab frame.

Its when you imagine subatomic observers and trying to correlate their internal structure from their way of interaction and if you insist that "observation" must follow the same "rules" as does a physicsl interaction - that the choice of interpretation matters.

Its quite clear why that from a pure phenomological perspective this is not relevant. But from an explanatory theoretical
Unification attempt it must matter.

/Fredrik

 

[stevendaryl]

It's indeed very simple. An ideal polarizer is realizing an ideal von Neumann filter measurement, i.e., you prepare photons (or if you experiment with usual light, coherent states of the em. field) with a determined polarization. You just through away the unwanted stuff, not polarized in the direction given by the polarizer. You don't need to assume an instantaneous collapse, it's just a local (!) interaction between the em. radiation and the polarizer. The minimal interpretation just doesn't make the unnecessary assumption of an esoteric mechanism that "collapses" something instantaneous in entire space(time)!

In the case of multiple filters, I don't see how von Neumann filters help explain intuitively what's going on.

You have a sequence of filters, the first oriented at angle 0^o, the next at 45^o, the next at 90^o. Some fraction of the photons, 12.5%, will make it through all 3 filters. You can't understand that in terms of removing photons. Because after the first filter, you've removed all the photons that were polarized at 90^o, but at the end, you still have some photons that were polarized at 90^o.

I know that you know how to calculate this case, but the words don't actually match up with the facts. At least, not in my mind. The way that you describe von Neumann filters, in terms of throwing out unwanted stuff, sounds like you're selecting based on pre-existing properties, but that's not the case.

 

[stevendaryl]

But again this latter kind of projection is, as you said above too, just "update of knowledge". Within the minimal interpretation nothing collapses here at all.

To me, Bell's inequality proves that measurement is not simply a matter of update of knowledge.

 

[stevendaryl]

Ah, we were talking about two different types of projection.

The projection above which you are talking about is deterministic. The non-unitary evolution due to tracing out is also deterministic.

I was talking about non-deterministic projection, when you don't know in advance in which state the system will end up. It is only this latter non-deterministic projection that lies at the origin of the problem of measurement in QM.

It seems to me that the two different types of projection are related. If you use a Stern-Gerlach device to steer a spin-up electron in one direction and a spin-down electron in another, then there doesn't seem to be anything non-unitary going on. But if that electron was from an entangled electron/positron pair, then the selection of spin-up for the electron implies that afterward, the positron is in a spin-down state. So entanglement mixes up the mysterious and non-mysterious type of projection.

 

[zonde]

I would say that at the level of minimal mathematical model filtering can be represented as projection of state vector and it is uncontroversial and interpretation independent.
But as it seems to me "collapse" is often understood as change of single particle. And models that have something to say about single particles are QM interpretations.

 

[zonde]

Well, if I filter out all partial beams from a SG apparatus and keep only the one I want, it's pretty much what I'd (perhaps too naively) describe by a projection operator in the formalism. It gives me the correspondingly less intense beam (with the intensity drop given by the probabilities according to Born's rule). So you say that there is a difference between the description of blocking in the formalism and projection?

Projection does not only change the length of the vector but it's direction as well. Blocking of unwanted beam gives you only intensity drop but it does not give you the change of spin states for particles in remaining beam. You can not split the beam in two beams where in one beam you have half-particles with spin up state and in the other beam half-particles with spin down state.

 

[atyy]

I don't agree.

For an instrumentalist (or positivist) neither time evolution nor collapse describe something that is "happening out there in the real world as described". But for a realist something in our mathematical model does indeed describe what is "really happening...". Because unitary time evolution and collapse are contradictory they cannot be real "in th for same sense". So you have to make a choice!

The choice of Everett's supporters is to interpret the unitary time evolution as a realistic description of a process happening out there in the real world (read Deutsch, as an example) and to reject the collapse.

I haven't seen any interpretation doing it the other way round, i.e. to reject unitary time evolution as being "real" but chose the collapse:-)

I agree - earlier you didn't state MWI. Of course, whether MWI makes sense is unknown.

 

[atyy]

Would you agree if I change the wording a bit? Say, collapse is needed when we make a sequence of projections i.e. more than one projection per setup?

I would prefer if you changed the scenario to include explicitly a sequence of measurements. Without the sequence of measurements, there is no collapse or projection. The filters themselves are not projection operators - I'm not sure how to do it with simple polarizers, but if one used polarizing beam splitters, one could use the unitary description in eg. http://www.phys.lsu.edu/~jdowling/publications/Kok07.pdf (Eq 7,8).

 

[tom.stoer]

I agree - earlier you didn't state MWI. Of course, whether MWI makes sense is unknown.

I mentioned Everett in my first post :-)

For a realist it's not the question whether it makes sense but whether it describes reality. Of course this is problematic b/c you can never (experimentally) falsify a theory which is talking about "what is really happening between observations". Nevertheless there are realists believing in our theories to describe essential aspects of reality.