Clarification of the postulates of QM

[vanhees71]

I mean QM. Ballentine rejects the collapse postulate, as does vanhees71 (see his post #23). In part, this is because Ballentine misunderstands Copenhagen, as bhbobba says. QM without the collapse postulate is wrong, possibly unless one uses many-worlds or Bohmian mechanics or consistent histories, but there is no sign that Ballentine or vanhees71 use any of these other interpretations.

Again, there's no necessity of the collapse postulate at all. It describes a very special preparation process, usually idealized, known as a "von Neumann filter measurement". You don't need the collapse posulate at all to make physics sense of quantum theory. You only need Born's Rule to define the meaning of states (represented by statistical operators). Copenhagen in Bohr's flavor is pretty close to the minimal interpretation. If you say "Copenhagen interpretation", it's never clear what's meant since there are as many sub-interpretations as believers in this "religion" ;-)).

I also don't need many worlds, Bohm etc. Why should I need these? I stick to physics, letting philosophy to the philosophers. Unobservable parallel universes and "trajectories" which are hard (if not impossible) to measure, are irrelevant for physics. For me the whole machinery of QT with the standard postulates are just descriptions of measurements. The "ontology" is purely operational, i.e., defined by hands-on real-world measurement/observation devices in the experimentalists setup. There's not less "ontology" in QT than in classical physics, where you have as abstract mathematical constructs like symplectic manifolds, pseudo-Riemannian space-time manifolds and the like. Nature couldn't care less about these abstract descriptions of our observations!

This fits a bit to Bohr's above quoted dictum, but I'd add that QT describes what we observe in Nature (at least up to now; who knows, whether there's some observation in the future contradicting it).

 

[bhobba]

Do you have any good quotes from the Founding Fathers or so which would support this view? Not that I have doubt about this - I would just like to have such quotes about the epistemic vs. ontic nature of the wave function, else I probably would have to search myself to find them.

I am pretty sure that Bohr etc were very careful to emphasize it wasn't real. I suspect it arose from people misinterpreting it eg it was the impression I got in some ancient texts I got from the library in my younger days.

Thanks
Bill

 

[Ilja]

"There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature..." Niels Bohr

Thanks. I have been able to identify the source as p.12 of Aage Petersen (1963: The Philosophy of Niels Bohr. Bulletin of the Atomic Scientists, XIX(7): 8–14, but unable to access this source, which seems hidden behind a paywall.

 

[stevendaryl]

Again, there's no necessity of the collapse postulate at all. It describes a very special preparation process, usually idealized, known as a "von Neumann filter measurement". You don't need the collapse posulate at all to make physics sense of quantum theory.

I think we've been over this several times, already, but it seems to me that in a sequence of measurements of different properties, to get the right the answer, you have to describe the statement between measurements using something like the collapse hypothesis. In spin-1/2 twin-pair EPR, the system being measured is initially in the state $\frac{1}{\sqrt{2}}(|U\rangle |D\rangle - |D\rangle |U\rangle)$. Alice measures her particle to have spin-up (along the z-axis). Then after her measurement, but before Bob's measurement, Bob's particle is in a state that is definitely spin-down along the z-axis. If you don't update the state of Bob's particle, you get the wrong answer.

An alternative is to not deal with states at all, but to deal with possible histories of measurements. There is a probability $\frac{1}{2}$ for the history in which Alice measures spin-up and Bob measures spin-down, and a probability of $\frac{1}{2}$ that Alice measures spin-up and Bob measures spin-down. But dealing with histories instead of states is not standard QM, so I disagree that such an approach is "minimal", in the sense of taking standard QM without collapse.

 

[martinbn]

I think we've been over this several times, already, but it seems to me that in a sequence of measurements of different properties, to get the right the answer, you have to describe the statement between measurements using something like the collapse hypothesis. In spin-1/2 twin-pair EPR, the system being measured is initially in the state $\frac{1}{\sqrt{2}}(|U\rangle |D\rangle - |D\rangle |U\rangle)$. Alice measures her particle to have spin-up (along the z-axis). Then after her measurement, but before Bob's measurement, Bob's particle is in a state that is definitely spin-down along the z-axis. If you don't update the state of Bob's particle, you get the wrong answer.

Why couldn't I say the following? Talking about before and after when the events a space-like is meaningless. So I will consider Alice's and Bob's measurement as one measurement (after all I have only one wave function) with possible outcomes (coming from the state you've written) "U and D" or "D and U" each with probability one half.

 

[stevendaryl]

Why couldn't I say the following? Talking about before and after when the events a space-like is meaningless. So I will consider Alice's and Bob's measurement as one measurement (after all I have only one wave function) with possible outcomes (coming from the state you've written) "U and D" or "D and U" each with probability one half.

Yes, I suppose you could consider Alice's and Bob's measurement as a single measurement, but in general, you might make a sequence of measurements that extend arbitrarily into the future: Do $M_1$ today, and $M_2$ tomorrow and $M_3$ the day after that, etc. If you don't update the state between measurements, you will get the wrong answer. If you want to treat the entire collection of measurements as a single, composite measurement (which I guess you can do), then to me, that's switching from a state-based formulation of quantum mechanics to a history-based formulation.

So I think I agree with atyy that "minimalist" quantum mechanics, which is state-based without collapse, is actually inconsistent. Something weird--many worlds, or consistent histories, or nonlocal effects or something--needs to be added above and beyond or instead of that minimalist QM.

 

[mfb]

Many worlds doesn't have to be added, it has to be removed manually if you don't want it.

 

[martinbn]

Yes, I suppose you could consider Alice's and Bob's measurement as a single measurement, but in general, you might make a sequence of measurements that extend arbitrarily into the future: Do $M_1$ today, and $M_2$ tomorrow and $M_3$ the day after that, etc. If you don't update the state between measurements, you will get the wrong answer. If you want to treat the entire collection of measurements as a single, composite measurement (which I guess you can do), then to me, that's switching from a state-based formulation of quantum mechanics to a history-based formulation.

Then for the second measurement you have a system (a new one, not the same) that is prepared by the first measurement in a new state. Say they measure U and D, then on the second day they are measuring the system that has been prepared in the state |U>|D>.

 

[martinbn]

So I think I agree with atyy that "minimalist" quantum mechanics, which is state-based without collapse, is actually inconsistent. Something weird--many worlds, or consistent histories, or nonlocal effects or something--needs to be added above and beyond or instead of that minimalist QM.

I would say that it is incomplete (I might be wrong), but I don't see why it would be inconsistent.

 

[stevendaryl]

I would say that it is incomplete (I might be wrong), but I don't see why it would be inconsistent.

It's inconsistent with experiment to not update the state after a measurement, if you're going to do followup measurements on the same system.

 

[stevendaryl]

Then for the second measurement you have a system (a new one, not the same) that is prepared by the first measurement in a new state. Say they measure U and D, then on the second day they are measuring the system that has been prepared in the state |U>|D>.

To say that measurement "prepares" the state is the same thing as collapse.

 

[vanhees71]

I think we've been over this several times, already, but it seems to me that in a sequence of measurements of different properties, to get the right the answer, you have to describe the statement between measurements using something like the collapse hypothesis. In spin-1/2 twin-pair EPR, the system being measured is initially in the state $\frac{1}{\sqrt{2}}(|U\rangle |D\rangle - |D\rangle |U\rangle)$. Alice measures her particle to have spin-up (along the z-axis). Then after her measurement, but before Bob's measurement, Bob's particle is in a state that is definitely spin-down along the z-axis. If you don't update the state of Bob's particle, you get the wrong answer.

No! That's only a claim, which is indistinguishable from the minimal interpretation. One must be a bit more precise. For Alice of course the situation changes and since she knows that she shares here photon with another one in the entangled pair, after her measurement she knows that Bob's particle will have for sure $\sigma_z=-1/2$, but nothing has instantaneously changed at Bob's particle. Nevertheless the minimal interpretation gets the correct answer about the measurement statistics.

The only thing one knows for the experiment as a whole that the two particles have been prepared in the spin-singlet state $|\psi \rangle=\sqrt{0.5} (|1/2,-1/2 \rangle-|-1/2,1/2 \rangle)$ and that Alice and Bob have their SG apparatus directed in $z$ direction. Then you can ask for the probabilities that they find the four possibilities of outcomes $(\sigma_1,\sigma_2)$ with $\sigma_j \in \{-1/2,+1/2 \}$. The four matrix elements obviously are
$$\langle 1/2,1/2 | \psi \rangle=\langle -1/2,-1/2|\psi \rangle=0, \quad \langle 1/2,-1/2 | \psi \rangle=-\langle -1/2,1/2|\psi \rangle=1/\sqrt{2},$$
i.e., you find with probility 1/2 either $(1/2,-1/2)$ or $(-1/2,1/2)$ but never $(1/2,1/2)$ or $(-1/2,-1/2)$. That's just described by the initially prepared state. There's no need to change the state of B's particle due to A's measurement (*).

Of course from the point of view of A also everything is consistent. If A measures $\sigma_z$ of her particle, she'll find with probability 1/2 that $\sigma_z=+1/2$ and then knows that Bob will with certainty find $\sigma_z=-1/2$, because there's no other possibility left. The outcome is the same as above, i.e., they measure $(1/2,-1/2)$ with probability 1/2 (and $(-1/2,1/2)$ also with probability 1/2), while it's not possible to find the same $\sigma_z$ for both particles.

So at the place of A you can invoke the "collapse hypothesis", but it's just about A's knowledge. Nothing happened instantaneously at B's place. The collapse is not "real". You don't make a mistake to apply it as a statement of A's knowledge about B's particle after having measured her particle's $\sigma_z$, but it doesn't change anything concerning the outcome of the measurement and the statement about the physical meaning of the initially prepared spin-entangled two-particle state. So you can as well also forget about the collapse.

(*) Remark: The single-particle states of the two particles in the spin-entangled two-particle state is described by the reduced states, which are both
$$\hat{\rho}_A=\hat{\rho}_B = \frac{1}{2} \mathbb{1}.$$
For A and B they just find maximally unpolarized particles.

An alternative is to not deal with states at all, but to deal with possible histories of measurements. There is a probability $\frac{1}{2}$ for the history in which Alice measures spin-up and Bob measures spin-down, and a probability of $\frac{1}{2}$ that Alice measures spin-up and Bob measures spin-down. But dealing with histories instead of states is not standard QM, so I disagree that such an approach is "minimal", in the sense of taking standard QM without collapse.

Well, that's why I deal with the state, and nothing else. Envoking the collapse in the above very weak (not to say trivial sense) is more like this "history approach".

 

[vanhees71]

To say that measurement "prepares" the state is the same thing as collapse.

Well, then you can call putting a beam dump at all partial beams of a Stern-Gerlach apparatus except one with a definite spin component in direction of the B-field is a "collapse". Maybe, that's nice for some reason, but all you do in reality is to filter out all "unwanted" states by letting the particles in these unwanted states hit a wall ;-)), and (more importantly) you don't do anything non-local. The particle hit's a wall and gets locally absorbed in this wall. That's it, no spooky action at a distance I can make out here.

 

[stevendaryl]

No! That's only a claim, which is indistinguishable from the minimal interpretation. One must be a bit more precise. For Alice of course the situation changes and since she knows that she shares here photon with another one in the entangled pair, after her measurement she knows that Bob's particle will have for sure $\sigma_z=-1/2$, but nothing has instantaneously changed at Bob's particle.

I don't see how that makes any sense. Before Alice's measurement, Bob's particle was not in the state of having definite spin-down in the z-direction. After Alice's measurement, Bob's particle is in the state of having definite spin-down in the z-direction. That seems like an instantaneous change, to me.

Of course, you can say that it's only a change of Alice's knowledge, but that only makes sense if you assume that Bob's particle was in the spin-down state before her measurement, and she only learned about it through her measurement. That would seem to be contradicted by Bell's inequality.

If Alice knows for certain what Bob's measurement result will be, then that sure seems to be a fact about Bob's situation. How could it not be? Either that fact was true before her measurement, or it became true during her measurement. You can avoid that conclusion by denying that there is such a thing as "states", there is only possible histories, but that's not the minimal interpretation.

 

[vanhees71]

Before A's measurement the system has been prepared in the given state. That's all. Since A knows this she updates her knowledge about B's measurement (no matter whether he measures before or after her). That happens locally at her place in her brain, but nothing happens instantaneously to B's particle. As I said countless times before, the 100% correlation between A's and B's outcomes of measurements is due to the state preparation not due to a mutual influence of A's and B's measurements. Great effort has been put into the "loop-hole free" setup of these measurements to demonstrate precisely this! This particular loophole is excluded by making sure that the measurement events (registrations of particles) at A's and B's place are truly space-like separated. Is there any reason for doubts that these experimental setups are somehow flawed, and the loop hole is still there? Do you think that there are still hidden correlations built up by faster-than-light influence of the apparati at the far distant places? Well, then you can never close that loophole, but I'd invoke Occam's razor here to say that it's the most simple explanation.

 

[stevendaryl]

Well, then you can call putting a beam dump at all partial beams of a Stern-Gerlach apparatus except one with a definite spin component in direction of the B-field is a "collapse".

You're saying if I believe X, then I have to believe Y. Well, I believe X and I don't believe Y. So there.

The collapse hypothesis is simply the rule that if I have a system in state $\psi$ and I perform a measurement $M_1$ and get result $r_1$, then afterwards, the appropriate state to use for subsequent measurements is $\Pi_{M_1, r_1} \psi$, the result of projecting $\psi$ onto the subspace of those wave functions that are eigenstates of $M_1$ with eigenvalue $r_1$. Nothing is changed by calling the measurement a "preparation" instead of a "measurement". That seems like a completely ridiculous argument. You're using the collapse hypothesis at the same time you're denying it.

 

[stevendaryl]

Before A's measurement the system has been prepared in the given state. That's all. Since A knows this she updates her knowledge about B's measurement (no matter whether he measures before or after her). That happens locally at her place in her brain, but nothing happens instantaneously to B's particle. As I said countless times before, the 100% correlation between A's and B's outcomes of measurements is due to the state preparation not due to a mutual influence of A's and B's measurements. Great effort has been put into the "loop-hole free" setup of these measurements to demonstrate precisely this! This particular loophole is excluded by making sure that the measurement events (registrations of particles) at A's and B's place are truly space-like separated. Is there any reason for doubts that these experimental setups are somehow flawed, and the loop hole is still there? Do you think that there are still hidden correlations built up by faster-than-light influence of the apparati at the far distant places? Well, then you can never close that loophole, but I'd invoke Occam's razor here to say that it's the most simple explanation.

It seems to me that there is no substantial difference between your way of interpreting QM and the way that uses Von Neumann collapse. You just don't like to use that word.

 

[vanhees71]

You're saying if I believe X, then I have to believe Y. Well, I believe X and I don't believe Y. So there.

The collapse hypothesis is simply the rule that if I have a system in state $\psi$ and I perform a measurement $M_1$ and get result $r_1$, then afterwards, the appropriate state to use for subsequent measurements is $\Pi_{M_1, r_1} \psi$, the result of projecting $\psi$ onto the subspace of those wave functions that are eigenstates of $M_1$ with eigenvalue $r_1$. Nothing is changed by calling the measurement a "preparation" instead of a "measurement". That seems like a completely ridiculous argument. You're using the collapse hypothesis at the same time you're denying it.

Well, in the above example your rule is obviously not true, because either the particle runs further without much happening to it or it's absorbed by a wall. In the latter case it's far from the state predicted to be assiciated with it by your collapse hypothesis.

It's also clear that measuring something is not necessary also preparing the measured object. E.g., usually a photon gets absorbed by the detector, and it's not prepared for further experiments.

 

[stevendaryl]

It seems to me that there is no substantial difference between your way of interpreting QM and the way that uses Von Neumann collapse. You just don't like to use that word.

As I said, before Alice's measurement, Bob's particle is not in a state of having a definite value for spin in the z-direction. Afterwards, it is in the state of having a definite value for spin in the z-direction. How can you say that's not a change in the state of Bob's particle? The only way (it seems to me) is to deny that there is such a thing as "the state of Bob's particle".

 

[stevendaryl]

Well, in the above example your rule is obviously not true, because either the particle runs further without much happening to it or it's absorbed by a wall. In the latter case it's far from the state predicted to be assiciated with it by your collapse hypothesis.

Yes, measurement processes typically are destructive, so further measurements are impossible. But you can salvage that by considering composite systems:

$|\Psi\rangle = \sum_{\alpha j} C_{\alpha j} |\phi_\alpha\rangle |\chi_\beta\rangle$

A destructive measurement of a property of one subsystem would still allow followup measurements to be performed on the other subsystem.

 

[vanhees71]

For Bob his particle is always described by the state $\hat{\rho}_B=1/2 \mathbb{1}$. He just has a beam of unpolarized particles. This finding is unchanged no matter whether A made her measurement before B made his measurement or not.

 

[stevendaryl]

For Bob his particle is always described by the state $\hat{\rho}_B=1/2 \mathbb{1}$. He just has a beam of unpolarized particles. This finding is unchanged no matter whether A made her measurement before B made his measurement or not.

But Alice knows better. If she has measured her particle to have spin-up in the z-direction, then she knows for sure that Bob will measure spin-down in the z-direction. So Bob's description of his particle using $\hat{\rho}_B=1/2 \mathbb{1}$ is not the most accurate, for predicting Bob's future measurements.

 

[vanhees71]

It is. Why should it not be accurate? You can of course find the correlations described by the entangled state by comparing A's and B's measurement protocols with precise enough time stamps of their particle registrations (and provided the particles come well-separated enough to the detectors, so that you precisely know which two measurement events at A's and B's place belong to precisely the same entangled particle pair).

 

[stevendaryl]

It is. Why should it not be accurate?

Because, that density matrix is consistent with either result for Bob's measurement of spin along the z-axis, while Alice knows that he can only get spin-down along the z-axis.

 

[vanhees71]

But that doesn't make the assignment of the state $\hat{\rho}_B$ invalid. It still describes Bob's knowledge about the spin state of his particle correctly, no matter what Alice knows about what he will find. Of course, if A tells him what she has measured, B also knows what he will measure, but A can send her message only with at most the speed of light to B. Thus no instantaneous "collapse" happens from B's point of view but just information provided by A separately from the system measured, but I think we just turn in the usual circles here :-(.

 

[stevendaryl]

But that doesn't make the assignment of the state $\hat{\rho}_B$ invalid.

It's a perfectly valid description of Bob's knowledge about his particle, but it's not an accurate description of the particle itself. Saying it's spin-down in the z-direction is more accurate.

 

[ShayanJ]

But that doesn't make the assignment of the state $\hat{\rho}_B$ invalid. It still describes Bob's knowledge about the spin state of his particle correctly, no matter what Alice knows about what he will find. Of course, if A tells him what she has measured, B also knows what he will measure, but A can send her message only with at most the speed of light to B. Thus no instantaneous "collapse" happens from B's point of view but just information provided by A separately from the system measured, but I think we just turn in the usual circles here :-(.

Let me see if I get it right. You're saying that in B's view, the state of his particle is $\rho_B= \frac 1 2 \hat 1$ no matter before or after A's measurement. But in A's view, the state of B's particle is $\rho_B=\frac 1 2 \hat 1$ before A's measurement and either $|S_z;+ \rangle$ or $|S_z; - \rangle$(depending on A's result) after A's measurement. But this means there is a collapse, its just subjective!(Which also means you think the state vector only describes the observer's knowledge about the system, and not anything objective.)

 

[stevendaryl]

It's a perfectly valid description of Bob's knowledge about his particle, but it's not an accurate description of the particle itself. Saying it's spin-down in the z-direction is more accurate.

Let me give an analogy. If Bob is handed a deck of 52 cards, and he's asked to describe his probability of getting an ace of spades if he selects one at random, he might say: My chances are 1.9%

But if beforehand, Alice swapped the ace of spades for a Joker, then she knows that Bob has 0% chance of picking the ace of spades.

Bob's prediction was as accurate as he could possibly be, given his knowledge, but Alice's prediction is more accurate.

 

[vanhees71]

Sure, you can have such subjective ideas, but it has nothing to do with the physics of the two particles measured by A and B. I can as well say that for me the state of the German lottery drawing machine instantaneously collapses every Saturday as soon as the numbers are drawn, but that happens for me only if I take notice of the outcome of the experiment. It doesn't do anything on what's going on at the drawing of the actual numbers.

 

[ShayanJ]

Sure, you can have such subjective ideas, but it has nothing to do with the physics of the two particles measured by A and B. I can as well say that for me the state of the German lottery drawing machine instantaneously collapses every Saturday as soon as the numbers are drawn, but that happens for me only if I take notice of the outcome of the experiment. It doesn't do anything on what's going on at the drawing of the actual numbers.

But this inevitably means that you consider the state vector to be a subjective concept only describing the observer's knowledge about the system! This doesn't seem to be minimalistic in that one may ask "what's actually going on down there?", unless by minimalistic, you mean just not asking such questions.

Also, you're a proponent of the ensemble interpretation, so you shouldn't be able to talk about experiments not involving an ensemble. But now you're talking about a single pair of particles!

 

[vanhees71]

Let me give an analogy. If Bob is handed a deck of 52 cards, and he's asked to describe his probability of getting an ace of spades if he selects one at random, he might say: My chances are 1.9%

But if beforehand, Alice swapped the ace of spades for a Joker, then she knows that Bob has 0% chance of picking the ace of spades.

Bob's prediction was as accurate as he could possibly be, given his knowledge, but Alice's prediction is more accurate.

Well, sure. But what does this tell us about the QT example we are discussing? Of course, you'll put different probability distributions on the same situation if you have different knowledge about the system. That's very trivial, but in this case A and B have precisely the same knowledge, namely that each of them measure the spin of one of two spin-entangled particles. So the only thing both know is that each of them just has an unpolarized particle. Only bringing both measurements together in a way that you can compare what was measured for each of the particles prepared in the entangled two-particle state reveals the correlation implied by the entanglement. Of course, you can check it only with some significance at a large enough ensemble of so prepared two-particle states.

 

[stevendaryl]

Well, sure. But what does this tell us about the QT example we are discussing?

It seems perfectly analogous. Bob thinks he has a 50/50 chance of getting spin-up or spin-down, but Alice knows that he has 0% of getting spin-up.

 

[vanhees71]

But this inevitably means that you consider the state vector to be a subjective concept only describing the observer's knowledge about the system! This doesn't seem to be minimalistic in that one may ask "what's actually going on down there?", unless by minimalistic, you mean just not asking such questions.

Also, you're a proponent of the ensemble interpretation, so you shouldn't be able to talk about a experiments not involving an ensemble. But now you're talking about a single pair of particles!

No. The state is an objective description of the system, which is prepared in this state. Of course, any probabilistic statement can be checked only at an ensemble.

 

[vanhees71]

It seems perfectly analogous. Bob thinks he has a 50/50 chance of getting spin-up or spin-down, but Alice knows that he has 0% of getting spin-up.

So?

 

[ShayanJ]

No. The state is an objective description of the system, which is prepared in this state. Of course, any probabilistic statement can be checked only at an ensemble.

So before A's measurement, her spin is in the state $\frac 1 2 \hat 1$. Then she measures her spin and gets the result +, so she knows that her spin is pointing upward. But she's actually wrong and her measurement is meaningless because her spin is still in the state $\frac 1 2 \hat 1$ and not $|S_z;+\rangle$? This doesn't make sense!