I Is quantum collapse an interpretation?

[zonde]

A have seen here on forum statements that quantum collapse is interpretation dependent, for example:

Collapse isn't a phenomenon, it's an interpretation. There are many interpretations of QM, and not all of them have collapse.

So I would like to ask for explanation that does not relay on quantum collapse for this phenomena:
We have unpolarized beam of light. It goes trough two orthogonally oriented polarizers. Assuming idealized polarizers we detect no light after second polarizer. Then we insert third polarizer oriented at 45 degrees between the first two. Now we observe 1/8 of the intensity of original beam of light.

How such experiment is treated in no collapse interpretations?

 

[Demystifier]

In the minimal interpretation, you just change the wording. Instead of saying "collapse" you say "update of information". Everything else remains the same as in collapse interpretation.

 

[zonde]

In the minimal interpretation, you just change the wording. Instead of saying "collapse" you say "update of information". Everything else remains the same as in collapse interpretation.

But certainly "update of [experimenter's] information" can not explain this experiment as something different has to happen with beam of light between two setups as we observe different results.

 

[tom.stoer]

In Everett's Interpretation we accept that the system including the measuring device, the laboratory, the observer and the environment really is in a state consisting of classically incompatible "branches" which are mutually "invisible". The mathematical description i.e. the state vector with superposition of components (called "branches", "worlds", ...) results from the unitary time evolution w/o collapse; the "invisibility" follows from decoherence. So we simply accept this prediction which fits to our observations - instead of introducing an ad-hoc collapse via an additional postulate. That means we believe that the state vector and its unitary time evolution describe the structure and th dynamics of the "real system out there" and does not only encode information we have access to and which we have to adjust based on measurement outcomes.

Without this realistic philosophical position there is no need to believe in Everett's Interpretation.

How such experiment is treated in no collapse interpretations?

Mathematically it's standard quantum mechanics w/o ever referring to collaps, projection etc. Born's rule must follow as a theorem from other axioms; we do have indications that this works, but afaik there is no consensus on this issue.

 

[Demystifier]

But certainly "update of [experimenter's] information" can not explain this experiment as something different has to happen with beam of light between two setups as we observe different results.

That's correct, the minimal interpretation does not answer such questions. That's why it is called minimal.

One of non-minimal interpretations without collapse is the Bohmian interpretation. To see how it explains phenomena like the one you described in the first post, see
https://arxiv.org/abs/1305.1280

 

[vanhees71]

But certainly "update of [experimenter's] information" can not explain this experiment as something different has to happen with beam of light between two setups as we observe different results.

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)!

 

[vanhees71]

That's correct, the minimal interpretation does not answer such questions. That's why it is called minimal.

One of non-minimal interpretations without collapse is the Bohmian interpretation. To see how it explains phenomena like the one you described in the first post, see
https://arxiv.org/abs/1305.1280

Well, as to be expected it's about non-relativistic particles. I'm not aware that there is a satisfactory BM treatment of photons. Note that photons don't even have a position observable to begin with. So how can BM with its preference for trajectories in position space ever describe photons?

 

[Demystifier]

Note that photons don't even have a position observable to begin with.

They do, it's just not Lorentz covariant. But that's not a problem for instrumental approaches to QM, because you can always define the position observable with respect to the Lorentz frame in which the detector is at rest. After all, the photon detector determines the photon position, doesn't it?

So how can BM with its preference for trajectories in position space ever describe photons?

There are many ways to do it, if you are ready to postulate a preferred Lorentz frame in a manner which does not contradict existing experiments.

 

[zonde]

In Everett's Interpretation we accept that the system including the measuring device, the laboratory, the observer and the environment really is in a state consisting of classically incompatible "branches" which are mutually "invisible". The mathematical description i.e. the state vector with superposition of components (called "branches", "worlds", ...) results from the unitary time evolution w/o collapse; the "invisibility" follows from decoherence. So we simply accept this prediction which fits to our observations - instead of introducing an ad-hoc collapse via an additional postulate. That means we believe that the state vector and its unitary time evolution describe the structure and th dynamics of the "real system out there" and does not only encode information we have access to and which we have to adjust based on measurement outcomes.

Thanks, for your explanation.
I would like to ask, at what point do you place "decoherence"? Does it happens in polarizers or in detector?

Mathematically it's standard quantum mechanics w/o ever referring to collaps, projection etc. Born's rule must follow as a theorem from other axioms; we do have indications that this works, but afaik there is no consensus on this issue.

Are you not mixing up collapse with Born's rule? Collapse "happens" at polarizers while Born's rule is applied at the end (at detector). Isn't this so?

 

[vanhees71]

They do, it's just not Lorentz covariant. But that's not a problem for instrumental approaches to QM, because you can always define the position observable with respect to the Lorentz frame in which the detector is at rest. After all, the photon detector determines the photon position, doesn't it?There are many ways to do it, if you are ready to postulate a preferred Lorentz frame in a manner which does not contradict existing experiments.

The photon detector defines the position of a local interaction between the photon and the detector material. Indeed you can live with a preferred frame as far as it is determined by the physical situation, and the detector-rest frame makes sense.

 

[zonde]

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)!

So your approach is to ditch particles (photons) up until detection. Well, I suppose it works for my example.
But if I replace photons with gold atoms and polarizers with SG apparatuses? What about this modified experiment?

 

[vanhees71]

I don't understand what you mean. Of course, I have an incoming photon, prepared in its state. Then it's interacting with the polarizer, either being absorbed or let through (with probabilities given by Born's rule for the prepared state). Those photons that come through are polarized accordingly to the polarizer's orientation. That's what a polarizer does after all!

There's no fundamental difference between this example and the SG aparatus. The only difference is that the SG apparatus doesn't filter (except you put some blocking material in some of the partial beams) but entangles position with the spin component in direction of the magnetic field. This is even described by unitary time evolution of QT since it's not an "open system" from the point of view of the gold atoms as in the case of the photons, where you have treated the polarizer effectively.

 

[zonde]

I don't understand what you mean. Of course, I have an incoming photon, prepared in its state. Then it's interacting with the polarizer, either being absorbed or let through (with probabilities given by Born's rule for the prepared state). Those photons that come through are polarized accordingly to the polarizer's orientation. That's what a polarizer does after all!

Hmm, probably I misunderstood you.
But then the idea of collapse is that polarization of photon "collapses" from it's initial polarization to the new polarization state according to polarizer's orientation if it goes through the polarizer. Isn't this the same what you are saying?

 

[vanhees71]

I don't know, what you understand by the term "collapse". Usually, it's understood that the quantum state after a measurement goes instantaneously into a corresponding eigenstate of the operator representing the measured observable. This process is clearly outside of the quantum dynamics based on local interactions (in relativistic QFT), and it violates Einstein causality. However, if you look more closely at it, this assumption is simply not needed and by nothing justified from the formalism and its application to the desription of real-world observations and experiments. That's why I am a proponent of the minimal statistical interpretation, which is practically just the flavor of the class of Copenhagen interpretations without a collapse assumption. I think, it's pretty close to what Bohr meant, although I cannot say with certainty what he really thought, because his papers are pretty enigmatic (too much philosophy for my taste). The same holds for Heisenberg's writing. I prefer Dirac and Pauli, which give a clear picture of quantum theory without philosophical additions that obscure the scientific content of the theory!

 

[martinbn]

@vanhees71 : But going from a superposition of vertical and horisontal polarization to let's say vertical, is not unitary. It is a projection. How do you explain things without it.

 

[vanhees71]

That's exactly what I said. The reason is that we treat the polarizer effectively, i.e., not as part of the quantum dynamics.

 

[martinbn]

That's exactly what I said. The reason is that we treat the polarizer effectively, i.e., not as part of the quantum dynamics.

That only pushes the projections further down the chain. The question, the way I understood it, was can you have an interpretation that never needs to use a projection (or something equivalent)?

 

[vanhees71]

I don't think so, because we "project" all the time by sorting out the states we want.

 

[zonde]

I don't know, what you understand by the term "collapse". Usually, it's understood that the quantum state after a measurement goes instantaneously into a corresponding eigenstate of the operator representing the measured observable.

Yes, this is my understanding. Did I said something different?

This process is clearly outside of the quantum dynamics based on local interactions (in relativistic QFT), and it violates Einstein causality.

It's local in my example. Well, if you consider EPR experiment then yes, it's non-local.

However, if you look more closely at it, this assumption is simply not needed and by nothing justified from the formalism and its application to the desription of real-world observations and experiments.

You have my simple example. So show how do you treat it without collapse.

The reason is that we treat the polarizer effectively, i.e., not as part of the quantum dynamics.

Basically you are saying that "collapse" is emergent from more complete unitary dynamics. But that does not change the fact that it represents real physical phenomena.

 

[vanhees71]

If you have a collapse, it's never local, because it claims that the quantum state changes instantaneously, in the extreme case from a mixed to a pure state. That's outside the quantum dynamics based on local interactions.

Which real physical phenomena does the collapse represent? I don't know a single example!

 

[zonde]

Which real physical phenomena does the collapse represent? I don't know a single example!

Surely you know that photon beam interacts with polarizer. And I suppose that you consider it real physical phenomena.
So you don't think that collapse prepresents this phenomena, right?

 

[Mentz114]

Surely you know that photon beam interacts with polarizer. And I suppose that you consider it real physical phenomena.
So you don't think that collapse prepresents this phenomena, right?

Surely you can call it what you like ? We know it is a projective measurement between light and polarizer and the physics is well understod. As with SG apparatus.
You think it should be part of the unitary evolution but there is no reason to expect that.

 

[vanhees71]

Surely you know that photon beam interacts with polarizer. And I suppose that you consider it real physical phenomena.
So you don't think that collapse prepresents this phenomena, right?

No, the local interaction between between the em. field and the matter in the polarizer represent this phenomenon, according to QED. I don't need a collapse to describe it.

 

[vanhees71]

Surely you can call it what you like ? We know it is a projective measurement between light and polarizer and the physics is well understod. As with SG apparatus.
You think it should be part of the unitary evolution but there is no reason to expect that.

On a microscopic level, it is part of the unitary evolution, but it is completely sufficient to describe the interaction of the photon with the polarizer effectively with the polarizer being described classically. Then the polarizer is reduced to a projection operator to the polarization state given by its orientation.

This effective description is of course not given by unitary S-matrix since we don't resolve the microscopic interaction between the photon and the polarizer.

 

[Mentz114]

On a microscopic level, it is part of the unitary evolution, but it is completely sufficient to describe the interaction of the photon with the polarizer effectively with the polarizer being described classically. Then the polarizer is reduced to a projection operator to the polarization state given by its orientation.

This effective description is of course not given by unitary S-matrix since we don't resolve the microscopic interaction between the photon and the polarizer.

The part I've emphasized is a source of controversy, is it not ?

If a measurement has to extract /add information from/to a system then it cannot avoid changing the state of some part in a non-unitary (dissipative) way. This is implied by thermodynamics which seems to apply at macroscopic and microscopic scales.

 

[martinbn]

I don't think so, because we "project" all the time by sorting out the states we want.

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?

 

[mikeyork]

But certainly "update of [experimenter's] information" can not explain this experiment as something different has to happen with beam of light between two setups as we observe different results.

"Update of information" does not require an experimenter. It requires only interaction for information to be updated in the knowable (not necessarily known) universe. Once information exists in the knowable universe it cannot be contradicted by experiment. This is a basic assumption of science.

 

[tom.stoer]

Are you not mixing up collapse with Born's rule? Collapse "happens" at polarizers while Born's rule is applied at the end (at detector). Isn't this so?

The collapse happens at no specific point in space. The quantum state does neither depend on space, nor does it live in space; it lives in an abstract Hilbert space.

The collapse simply happens whenever and wherever it seems appropriate to project the full quantum state - after unitary time evolution - to some subspace selected via observation. If you measure an eigenvalue then you project the full state to the corresponding subspace. So the collapse happens in your mind when you readjust the information you have.

The collapse is nothing real; it cannot be real in the same sense as the unitary time evolution b/c it contradicts this unitary time evolution.

So the consequence is either to use the collapse as a tool for calculations giving up a realistic interpretation of the quantum state, or to insist on a realistic interpretation of the quantum state and giving up the idea of a collapse.

 

[atyy]

The collapse happens at no specific point in space. The quantum state does neither depend on space, nor does it live in space; it lives in an abstract Hilbert space.

The collapse simply happens whenever and wherever it seems appropriate to project the full quantum state - after unitary time evolution - to some subspace selected via observation. If you measure an eigenvalue then you project the full state to the corresponding subspace. So the collapse happens in your mind when you readjust the information you have.

The collapse is nothing real; it cannot be real in the same sense as the unitary time evolution b/c it contradicts this unitary time evolution.

So the consequence is either to use the collapse as a tool for calculations giving up a realistic interpretation of the quantum state, or to insist on a realistic interpretation of the quantum state and giving up the idea of a collapse.

The unitary time evolution occurs after the collapse. So neither collapse nor unitary time evolution are real.

 

[atyy]

So I would like to ask for explanation that does not relay on quantum collapse for this phenomena:
We have unpolarized beam of light. It goes trough two orthogonally oriented polarizers. Assuming idealized polarizers we detect no light after second polarizer. Then we insert third polarizer oriented at 45 degrees between the first two. Now we observe 1/8 of the intensity of original beam of light.

There is no collapse here. Collapse is needed when you make a sequence of measurements (ie. more than one measurement per setup). However, you have only described two different setups, each with a single measurement.

 

[tom.stoer]

The unitary time evolution occurs after the collapse. So neither collapse nor unitary time evolution are real.

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:-)

 

[zonde]

There is no collapse here. Collapse is needed when you make a sequence of measurements (ie. more than one measurement per setup). However, you have only described two different setups, each with a single measurement.

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?

 

[zonde]

The collapse happens at no specific point in space.

But decoherence is physical process that happens at specific limited span of time, right? So can you point out the "point" in time when decoherence happens? Does it happen when photon got past the polarizer or when it reaches detector?

 

[zonde]

If you measure an eigenvalue then you project the full state to the corresponding subspace. So the collapse happens in your mind when you readjust the information you have.

If physical situation out there changes with time and you reflect that change in time within your model using projection then projection represents some real dynamics. And while projection is done by you the changes of physical situation that are represented by projection are not done by you. Map is not the territory.

 

[tom.stoer]

But decoherence is physical process that happens at specific limited span of time, right? So can you point out the "point" in time when decoherence happens? Does it happen when photon got past the polarizer or when it reaches detector?

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

If physical situation out there changes with time and you reflect that change in time within your model using projection then projection represents some real dynamics.

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

From a realist perspective: the interaction of a quantum system with a measurement device (its atoms, electrons etc.) is a quantum mechanical process and therefore the dynamics must be compliant with unitary time evolution; b/c the collapse is non-unitary it violates the fundamental rule for any quantum mechanical process and cannot be "real".

The way out is that the collapse is only an apparent one, i.e. that the overall dynamics is unitary, compliant with quantum mechanics, but that due to decoherence it appears as collapse.

 

[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).