Clarification of the postulates of QM

[atyy]

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!

vanhees71 is a secret many-worlder, since that is the interpretation in which the state is objective, and neither hidden variables nor collapse :)

In fact, it is because he thinks the state is objective that he objects to collapse. If the state were subjective or just FAPP, there would be no problems with collapse.

Of course, in a sense, if MWI works it is certainly the minimal interpretation!

 

[martinbn]

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

Not the way I see it. Collapse asumes that the state decribes the system and that before and after the measurement you have the same system but in a different state. But if the state describes the set of equivalently prepatered systems (not an individual one), then after the measurement you have a diffrent system, not the same with collapsed state. You may say that this is just words, but that's what interpretations are.

 

[atyy]

Not the way I see it. Collapse asumes that the state decribes the system and that before and after the measurement you have the same system but in a different state. But if the state describes the set of equivalently prepatered systems (not an individual one), then after the measurement you have a diffrent system, not the same with collapsed state. You may say that this is just words, but that's what interpretations are.

The point is that collapse allows you to calculate the conditional probability of the second measurement outcome conditioned on a sub-ensemble of outcomes from the the first measurement.

In calculating the conditional probability, you need the state of a sub-ensemble.

The collapse rule assigns the state of a sub-ensemble. So collapse is still needed within the ensemble interpretation.

 

[martinbn]

The point is that collapse allows you to calculate the conditional probability of the second measurement outcome conditioned on a sub-ensemble of outcomes from the the first measurement.

In calculating the conditional probability, you need the state of a sub-ensemble.

The collapse rule assigns the state of a sub-ensemble. So collapse is still needed within the ensemble interpretation.

I know all this, but my point is that what you call the second measurment of the sub-ensemble is in fact the first measurment of a new ensemble. Before the measurment you didn't have that ensemble i.e. you cannot talk about a sub-ensemble. So what allows me to calculate conditional probability is the preparation of a new ensemble.

 

[atyy]

I know all this, but my point is that what you call the second measurment of the sub-ensemble is in fact the first measurment of a new ensemble. Before the measurment you didn't have that ensemble i.e. you cannot talk about a sub-ensemble. So what allows me to calculate conditional probability is the preparation of a new ensemble.

Sure, collapse is a form of state preparation. The point of collapse is that it links measurement and state preparation. Without the collapse, you do not have that link.

 

[vanhees71]

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!

If you have a usual polarization filter and the detection of the particle doesn't destroy the corresponding spin state then of course A will associate the state represented by $|\sigma_z=1/2 \rangle$ with it. What else? I only say that this is an association of the state that Alice does to her particle and I don't think that anything instantaneous happens to Bob's particle, because this contradicts the dynamics of relativistic quantum fields, which by definition is microcausal, i.e., local field operators that represent observables commute at space-like distances and thus the local interaction of the particle with A's measurement apparatus doesn't change immediately B's particle in any way. That's math and not subject to any interpretational issue!

 

[ShayanJ]

If you have a usual polarization filter and the detection of the particle doesn't destroy the corresponding spin state then of course A will associate the state represented by $|\sigma_z=1/2 \rangle$ with it. What else? I only say that this is an association of the state that Alice does to her particle and I don't think that anything instantaneous happens to Bob's particle, because this contradicts the dynamics of relativistic quantum fields, which by definition is microcausal, i.e., local field operators that represent observables commute at space-like distances and thus the local interaction of the particle with A's measurement apparatus doesn't change immediately B's particle in any way. That's math and not subject to any interpretational issue!

But saying "this is an association of the state that Alice does to her particle", means you think the wave-function is subjective and only describes the observer's knowledge about the system!

 

[vanhees71]

Sure, what else should it describe?

 

[ShayanJ]

Sure, what else should it describe?

Its just that in post #68, you insisted that "the state is an objective description of the system".

 

[stevendaryl]

Sure, what else should it describe?

The wave function of an electron might describe facts about an electron, maybe?

 

[vanhees71]

Sure, it describes objective facts about the electron; objective facts the physicist knows due to the (equivalence class of) preparation procedures defining the state. I think, all this is a pretty empty debate about semantics, as usual in such discussions about "interpretation".

I think it's pretty clear that A in our example knows something different than B, because she has done a "preparation procedure" with her particle by determining its spin component. Due to the $\sigma_z$-entangled state the two-particle system was prepared before, she knows also B's $\sigma_z$, but B doesn't know it, before he has measured it and just finds with 50% probability the one or the other outcome. So everything is consistent without any necessity to envoke "spooky action at a distance", which is indeed not implemented in the dynamics of the theory by construction, since we use a relativistic, local, microcausal QFT.

There'd be only a problem with this "interpretation" (which is just what the formalism, particularly Born's rule tells us, nothing else, and in this sense it's "minimal") if it would make a difference for B whether or note A measures her particle's $\sigma_z$ first or not, but it doesn't. So it's all consistent.

 

[stevendaryl]

Sure, it describes objective facts about the electron; objective facts the physicist knows due to the (equivalence class of) preparation procedures defining the state. I think, all this is a pretty empty debate about semantics, as usual in such discussions about "interpretation".

It's an empty debate because there is no real distinction between your position and those who believe that observation collapses the wave function.

What is a "preparation procedure"? Can you define it without invoking either the macroscopic/microscopic distinction, or the observer/observed distinction?

 

[stevendaryl]

So everything is consistent without any necessity to envoke "spooky action at a distance", which is indeed not implemented in the dynamics of the theory by construction, since we use a relativistic, local, microcausal QFT.

I don't see how the dynamics of QFT is relevant. There are two aspects to quantum theory: (1) Smooth evolution of the wave function (or smooth evolution of the field operators, in QFT), and (2) the Born interpretation of quantum amplitudes.

The issue is whether the combination is local, not whether the smooth evolution part is local.

 

[atyy]

Sure, it describes objective facts about the electron; objective facts the physicist knows due to the (equivalence class of) preparation procedures defining the state. I think, all this is a pretty empty debate about semantics, as usual in such discussions about "interpretation".

I think it's pretty clear that A in our example knows something different than B, because she has done a "preparation procedure" with her particle by determining its spin component. Due to the $\sigma_z$-entangled state the two-particle system was prepared before, she knows also B's $\sigma_z$, but B doesn't know it, before he has measured it and just finds with 50% probability the one or the other outcome. So everything is consistent without any necessity to envoke "spooky action at a distance", which is indeed not implemented in the dynamics of the theory by construction, since we use a relativistic, local, microcausal QFT.

There'd be only a problem with this "interpretation" (which is just what the formalism, particularly Born's rule tells us, nothing else, and in this sense it's "minimal") if it would make a difference for B whether or note A measures her particle's $\sigma_z$ first or not, but it doesn't. So it's all consistent.

But if collapse is a preparation, and the preparation prepares an objective state, then collapse would seem to be "objective" in your terminology.

 

[stevendaryl]

But if collapse is a preparation, and the preparation prepares an objective state, then collapse would seem to be "objective" in your terminology.

It occurs to me that there is (perhaps) a subtle distinction between measurement and preparation. For example, when you send a stream of electrons through a Stern-Gerlach device, those with spin-up are deflected one way and those with spin-down are deflected the other way. You haven't measured the spin of any electron, though.

Then you can send those electrons deflected in one direction to go on to a second Stern-Gerlach device, with a different orientation. Those electrons split into two groups, as well.

Eventually, you will (presumably) do a real measurement, by checking for the presence/absence of an electron. But all the selection prior to this doesn't involve measurement, and presumably doesn't collapse the wave function.

So I think that vanhees71 might be saying that it is possible to do experiments so that there is only one real measurement/observation, at the very end. So you don't need collapse (because you don't do any further experiments on the electron after the actual observation).

 

[atyy]

It occurs to me that there is (perhaps) a subtle distinction between measurement and preparation. For example, when you send a stream of electrons through a Stern-Gerlach device, those with spin-up are deflected one way and those with spin-down are deflected the other way. You haven't measured the spin of any electron, though.

Then you can send those electrons deflected in one direction to go on to a second Stern-Gerlach device, with a different orientation. Those electrons split into two groups, as well.

Eventually, you will (presumably) do a real measurement, by checking for the presence/absence of an electron. But all the selection prior to this doesn't involve measurement, and presumably doesn't collapse the wave function.

So I think that vanhees71 might be saying that it is possible to do experiments so that there is only one real measurement/observation, at the very end. So you don't need collapse (because you don't do any further experiments on the electron after the actual observation).

Not all preparations involve measurements, but some measurements are preparations.

 

[vanhees71]

I don't see how the dynamics of QFT is relevant. There are two aspects to quantum theory: (1) Smooth evolution of the wave function (or smooth evolution of the field operators, in QFT), and (2) the Born interpretation of quantum amplitudes.

The issue is whether the combination is local, not whether the smooth evolution part is local.

Well, if you only consider non-relativistic QT, there's no problem with a collapse concerning causality. You an assume an instantaneous action at a distance without any problem, and then there's no debate to begin with, i.e., you can use collapse arguments without contradictions.

The final sentence doesn't make sense to me. What do you mean by "local" here. Of course, in relativistic QFT by construction all interactions are local in space and time (you write down a Lagrangian with field operators multiplied at the same space-time point only). What's in some sense "non-local" in QT is related to our debate and entanglement, but that I'd not call "non-local" but long-range correlations between parts of a quantum system. One must not misunderstand long-range correlations with non-local interactions at a distance!

 

[stevendaryl]

Not all preparations involve measurements, but some measurements are preparations.

Yes. The tricky thing about applying the collapse hypothesis is that it's rare that you can do nothing more than measure an observable. To measure the position of an electron, you might have the electron collide with a photographic plate and see where the dot is. But that's a destructive measurement. The electron is gone afterward (absorbed by the photographic material).

That's what's special about entangled systems: You can perform a destructive measurement on one subsystem and that counts as a non-destructive measurement of the other subsystem.

 

[vanhees71]

Yes, and this is the truly interesting feature. One thing you can do nowadays, which sounds trivial first, is that you can prepare heralded single photons, i.e., a true single-photon Fock state by creating an entangled photon pair by parametric downconversion and measure one of the photons (the "trigger photon"), and then you now with certainty that you also have another photon (the "idler photon"), even with a specific polarization when the trigger photon's polarization state was determined by the measurement (putting a usual polarizer or other "optical elements" like quarter-wave plates before the detector). As usual, here you have preparation by filtering, i.e., you consider only a subensemble of many prepared photons selecting the wanted ones by a measurement. The point here is that you sort out the photons you want by this preparation procedure, but the measurement of the idler is not the cause of the idlers state, but the cause is that in the very beginning the two photons were prepared in the entangled two-photon state via parametric downconversion, and then you just sort out what's unwanted!

 

[atyy]

Well, if you only consider non-relativistic QT, there's no problem with a collapse concerning causality. You an assume an instantaneous action at a distance without any problem, and then there's no debate to begin with, i.e., you can use collapse arguments without contradictions.

The final sentence doesn't make sense to me. What do you mean by "local" here. Of course, in relativistic QFT by construction all interactions are local in space and time (you write down a Lagrangian with field operators multiplied at the same space-time point only). What's in some sense "non-local" in QT is related to our debate and entanglement, but that I'd not call "non-local" but long-range correlations between parts of a quantum system. One must not misunderstand long-range correlations with non-local interactions at a distance!

But the interesting point is that there is no problem with collapse in relativistic QFT.

If you think there is a problem, then you are using the wrong definition of causality.

 

[stevendaryl]

The final sentence doesn't make sense to me. What do you mean by "local" here. Of course, in relativistic QFT by construction all interactions are local in space and time (you write down a Lagrangian with field operators multiplied at the same space-time point only).

And that has nothing to do with the reason that people suspect that QM is nonlocal. So it's a distraction to bring it up.

What's in some sense "non-local" in QT is related to our debate and entanglement, but that I'd not call "non-local" but long-range correlations between parts of a quantum system. One must not misunderstand long-range correlations with non-local interactions at a distance!

I would say that because QT has nonlocal correlations that do not reduce to local interactions on local variables, QT is inherently a nonlocal theory.

 

[vanhees71]

But the interesting point is that there is no problem with collapse in relativistic QFT.

If you think there is a problem, then you are using the wrong definition of causality.

No, there's no problem in relativistic QFT, as I stress all the time. It's only a problem if you assume a litteral collapse, where instaneously Bob's particle is affected by Alice's measurement. In the "minimal interpretation" there's no such assumption and thus no such problem.

 

[stevendaryl]

No, there's no problem in relativistic QFT, as I stress all the time. It's only a problem if you assume a litteral collapse, where instaneously Bob's particle is affected by Alice's measurement. In the "minimal interpretation" there's no such assumption and thus no such problem.

Well, I don't see any difference between a literal and nonliteral collapse unless you have a clear idea of the separation between what is real and what is subjective. To say that there are no nonlocal influences is to say that no change of a physical quantity here can affect a physical quantity at a spacelike separation. But what properties are physical, in quantum theory? Copenhagen says that only macroscopic properties are real, or only observed properties are real. But that requires a distinction between macroscopic/microscopic or between observer/observed which isn't made clear in the theory.

 

[atyy]

No, there's no problem in relativistic QFT, as I stress all the time. It's only a problem if you assume a litteral collapse, where instaneously Bob's particle is affected by Alice's measurement. In the "minimal interpretation" there's no such assumption and thus no such problem.

1) But if there is no difference in predictions between a literal and a non-literal collapse, why would one who holds to a minimal interpretation object to a literal collapse?

2) Why do you object to the collapse in Cohen-Tannoudji, Diu and Laloe's book? As far as I can tell, they are agnostic as to whether collapse is literal. (In fact, I have never heard of a collapse as literal, except from people who object to it.)

 

[vanhees71]

1) Well, if you take the state as a physical entity and claim that when A measures $\sigma_z$ instantaneously the state collapses, this is a real instaneous effect in the entire universe. This contradicts the very construction of local microcausal QFT. I don't see, why I should buy a self-contradictory postulate, which in fact I never need to describe observations using Q(F)T.

2) I'm a bit surprised, how inaccurate these authors (Nobel laureat included) state the fundamental postulates. I guess, they are pretty uninterested in "interpretation" and rather present the applications of the theory to observable phenomena, and this they do very well. So I don't say that it's a bad book, but, e.g., the formulation that if the system is prepared in state $|\psi \rangle$ the probability to find the system in state $|\phi \rangle$ is $|\langle \phi|\psi \rangle|^2$ is misleading. It made me crazy when I learned QT from another book (I don't remember which one it was), because I couldn't get how in this formulation anything can be independent of the picture of time evolution chosen, and that should be true, because how you choose the picture is quite arbitrary. The resolution is, of course, easy if you put it in the right way: If the system is prepared in the state $|\psi \rangle$ (more precisely the state is reprsented by $|\psi \rangle \langle \psi|$ or equivalently by the corresponding ray, which is another glitch in the chapter on the postulates), then the probability to measure the value $a$ of an observable $A$ is given by $P(a)=\sum_{\beta} |\langle a,\beta|\psi \rangle|^2$, where $|a,\beta \rangle$ is the orthonormal basis of the subspace $\mathrm{Eig}(\hat{A},a)$ (modulo the possibility of continuous spectral values, where you have an integral instead of the sum).

 

[atyy]

1) Well, if you take the state as a physical entity and claim that when A measures $\sigma_z$ instantaneously the state collapses, this is a real instaneous effect in the entire universe. This contradicts the very construction of local microcausal QFT. I don't see, why I should buy a self-contradictory postulate, which in fact I never need to describe observations using Q(F)T.

The local microcausal construction is used for the Hamiltonian, which determines the unitary evolution between measurements. The collapse occurs at a measurement. There is no contradiction.

2) I'm a bit surprised, how inaccurate these authors (Nobel laureat included) state the fundamental postulates. I guess, they are pretty uninterested in "interpretation" and rather present the applications of the theory to observable phenomena, and this they do very well. So I don't say that it's a bad book, but, e.g., the formulation that if the system is prepared in state $|\psi \rangle$ the probability to find the system in state $|\phi \rangle$ is $|\langle \phi|\psi \rangle|^2$ is misleading. It made me crazy when I learned QT from another book (I don't remember which one it was), because I couldn't get how in this formulation anything can be independent of the picture of time evolution chosen, and that should be true, because how you choose the picture is quite arbitrary. The resolution is, of course, easy if you put it in the right way: If the system is prepared in the state $|\psi \rangle$ (more precisely the state is reprsented by $|\psi \rangle \langle \psi|$ or equivalently by the corresponding ray, which is another glitch in the chapter on the postulates), then the probability to measure the value $a$ of an observable $A$ is given by $P(a)=\sum_{\beta} |\langle a,\beta|\psi \rangle|^2$, where $|a,\beta \rangle$ is the orthonormal basis of the subspace $\mathrm{Eig}(\hat{A},a)$ (modulo the possibility of continuous spectral values, where you have an integral instead of the sum).

But the Cohen-Tannoudji formulation on their p220 of volume 1 looks exactly the same as what you wrote (ie. one has to specify the measurement observable), except that they add that after the measurement, the state of the system is different from before the measurement.

And yes, if they only care about applications of the theory to observable phenomena, then they are agnostic as to whether the wave function and collapse are real or not. Isn't that the minimal interpretation?

 

[vanhees71]

The measurement is due to interaction of the measured system with a measurement apparatus. I also never bought the argument that this is something different than the interactions described by quantum theory. This doesn't make sense either! On the one hand we have to use quantum theory, driven by observations that tell us that the classical theory is only an approximation. So to claim a measurement doesn't follow the laws of QT is not very satisfactory, and I don't see, why one should use this assumption nowadays, where we have understood much better the emergence of classical behavior of macroscopic systems from quantum theory than the "founding fathers" of QT could have known in the beginning. The interaction of a particle with a detector follows the rules of quantum theory and thus is described as a local interaction between the measured system.

I don't want to bash the textbook by Cohen-Tanoudji et al, but I think you should get the postulates as precise as possible, because this helps tremendously to study the subject.

 

[ShayanJ]

The measurement is due to interaction of the measured system with a measurement apparatus. I also never bought the argument that this is something different than the interactions described by quantum theory. This doesn't make sense either! On the one hand we have to use quantum theory, driven by observations that tell us that the classical theory is only an approximation. So to claim a measurement doesn't follow the laws of QT is not very satisfactory, and I don't see, why one should use this assumption nowadays, where we have understood much better the emergence of classical behavior of macroscopic systems from quantum theory than the "founding fathers" of QT could have known in the beginning. The interaction of a particle with a detector follows the rules of quantum theory and thus is described as a local interaction between the measured system.

If you're talking about quantum decoherence, then what you've described in this thread till now, is in contradiction with it.
You say that a measurement doesn't change the wave-function at all, i.e. there is no collapse.
But when collapse is assumed, its assumed as a blackbox. No one says it has to come from somewhere else than the Schrodinger equation, its just assumed and the possibility of explaining it is left open. And decoherence has been able to explain it partially. So decoherence has been able to explain something(partially), that you've always denied. How can you consider it as a support for your arguments? Because it actually rules out what you suggest!

 

[vanhees71]

No, I don't say that measurements change the wave function (or better the state, because we discuss relativistic QT here, and there is no consistent descriptions of it by wave functions a la Schrödinger). I only say that the change of the state is due to quantum dynamics and not an instantaneous action at a distance leading to some collapse thing that is somehow outside of the general dynamical laws of QT. The emergence of classical behavior of macroscopic systems, among them measurement apparati, is quite well understood nowadys within quantum many-body theory, but this is just relativistic local microcausal QFT. So there are only local interactions, no actions at a distance by construction. So this cannot rule out what I suggest!

 

[AlexCaledin]

In the relativistic QFT, instead of "instantaneous action at a distance",

"it is impossible to keep a particle from traveling faster than light"

https://en.wikipedia.org/wiki/Path_integral_formulation#Quantum_field_theory

 

[bhobba]

"it is impossible to keep a particle from traveling faster than light"

That one must use such in the path integral does not imply any particles are actually traveling FTL.

Thanks
Bill

 

[AlexCaledin]

That ... does not imply any particles are actually traveling F[aster ]T[han ]L[ight]...

Quite right - because actual traveling always consists of acts of observing the particle (observable drops or bubbles or something else)...

 

[vanhees71]

How do you come to this conclusion? Massive particles are traveling with speeds less than the speed of light.

 

[stevendaryl]

The measurement is due to interaction of the measured system with a measurement apparatus. I also never bought the argument that this is something different than the interactions described by quantum theory. This doesn't make sense either!

I agree, that's why the standard Copenhagen interpretation of QM is unsatisfying to me. It seems to rely on either a classical/quantum split, or a macroscopic/microscopic split, or an observer/observed split. In any of those types of split, you're distinguishing systems that should (in my opinion) be treated the same--they're just quantum systems.

But to me, the Born rule is the source of this, not just collapse. You can't formulate the Born rule without mentioning one of these splits.

 

[vanhees71]

Why do you need one of the splits to formulate Born's rule? It just gives the physical meaning to quantum states. You just prepare your system and measure the observable you like to observe, and then the quantum state you've prepared tells you the probabilities to find values of this observable. With a large enough ensemble you can check whether the prediction is correct. That's it. I don't need more to make sense out of quantum theory. Where do you need the split?