Insights Why the Quantum | A Response to Wheeler's 1986 Paper - Comments

[martinbn]

Of course classical mechanics is a limit of quantum mechanics. One can see this in the saddle point approximation to the path integral.

However, what you are not understanding and which Landau and Lifshitz state clearly, is that quantum mechanics cannot be formulated without "classical concepts" also in its assumptions. It is not possible to derive classical physics from "purely quantum" assumptions.

One can use different language to state this assumption, but they are all essentially equivalent - measurement has a different status than the interactions described in the Hamiltonian.

There is a difference between this and the statement that QT doesn't make any predictions without a cut.

 

[vanhees71]

I don't object to the choice. But after the observer has chosen the device (by whatever rule), there remains the pure quantum problem to show that the device actually produces on each reading the numbers that qualify as a measurement, in the sense that they satisfy Born's rule.

This is the measurement problem! It has nothing to do with the observer but is a purely quantum mechanical problem.

Ok, that's true. Of course, it's only possible for very simple cases in a strict way (like the famous analysis of tracks of charged particles in vapour chambers by Mott or the measurement of spin components in the Stern Geralach experiment).

 

[vanhees71]

So far so good...

No you cannot. There is no phenomenon as "state preparation" in nature. You (the observer) only do it in a lab, because you need that to match the ensemble with the esoteric Hilbert space, by using an ad-hoc Born rule. This ensemble exist only in your head. CM does not need any ad-hoc projection for observation, nor does nature (as per QM Schrodinger equation).You say much more then that. You made make hidden assumptions (often circular) and quite astonishing claim (like QM completeness). You say noticeably that there is no epistemological difference with CM.
But in CM you don't need to make measurement to "create" the value of any observable (out of probability or whatnot).

Of course we can handle electrons pretty well in accelerators and thus prepare, e.g., electrons with a pretty well determined energy and momentum to make all kinds of scattering experiments with them for decades. The ensemble doesn't exist only in my head, but it's realized with accelerators. That's why they aim at ever higher luminosities to "collect statistics as quickly as possible".

I don't claim the completeness of any physical theory we have so far. QM is incomplete because there is no satisfactory quantum description of the gravitational field yet. Indeed, I don't see any epistemological difference with CM. There's an ontological difference though.

 

[Boing3000]

Of course we can handle electrons pretty well in accelerators and thus prepare, e.g., electrons with a pretty well determined energy and momentum to make all kinds of scattering experiments with them for decades. The ensemble doesn't exist only in my head, but it's realized with accelerators. That's why they aim at ever higher luminosities to "collect statistics as quickly as possible".

Circular reasoning. You cannot prepare an electron in a pretty well defined state without measuring it first
The ensemble preparation is an laboratory artifact. You cannot, in the real world (or even based on QM phenomenology), propose an experiment to "ask/probe" an electron to find its companions in "an ensemble". This ensemble is not real. And the prediction are only more and more accurate with respect to the ensemble size.

Indeed, I don't see any epistemological difference with CM. There's an ontological difference though.

CM does not need an ad-hoc rule to connect the evolution formalism to the lab event. It does not need ensemble either. And CM don't treat measurement and interaction differently.

 

[zonde]

Because "ensemble" can not be defined in terms of QM, minimal QM is not a selfcontained model. It requires CM as a starting platform.

 

[stevendaryl]

But also #2 doesn't distinguish measurements from other interactions.

I think it definitely does.You measure a property and you get an eigenvalue $\lambda$ of the operator corresponding to the observable being measured. That means that the measuring device is in a specific state---the state of "having measured $\lambda$". But treating the device as a physical system and treating the measurement as a physical interaction leads to a different state--where the measuring device is not in a specific state, but is entangled with the system being measured. Those are two different situations in QM, and are described by different quantum-mechanical states and those states have theoretically different statistical properties, leading to different predictions for future states. The two possible quantum-mechanical states are different, with different (in theory) observable consequences. They can't both be correct.

Now, I stuck the phrase "in theory" in there, because I think that the difference between an entangled macroscopic system and one that has a specific macroscopic properties may be undetectable in practice, but they are different states in QM. So you get different answers depending on whether you're treating the macroscopic system as a physical system following Schrodinger's equation or as a measuring device obeying the Born rule.

 

[stevendaryl]

But each individual system produces definite result (or appears to produce definite result). And either you have something to say about that, and then you participate in discussions about "collapse" and alternatives, or you keep agnostic position and do not say anything like "collapse is superfluous"/"collapse is required".

That's my feeling. A true minimalist interpretation, in the sense of making minimal assumptions, is not a denial of the collapse interpretation or the Many-Worlds Interpretation or the Bohmian interpretation, but should open to any of those possibilities. It should be silent on the question of what happens during a measurement.

 

[atyy]

Not again this wrong statement. You cannot admit at the same time that the classical behavior is derivable from QT and then claim that there is a cut. That's a contradictio in adjecto!

Which version of Landau and Lifshitz are you reading? Perhaps the German translation is different from the English one. There is a possibility the English version is biased towarda my views, since John Bell apparently had a role in it.

 

[martinbn]

Which version of Landau and Lifshitz are you reading? Perhaps the German translation is different from the English one. There is a possibility the English version is biased towarda my views, since John Bell apparently had a role in it.

The english translation of that section is faithfull to the original russian text.

 

[vanhees71]

Circular reasoning. You cannot prepare an electron in a pretty well defined state without measuring it first
The ensemble preparation is an laboratory artifact. You cannot, in the real world (or even based on QM phenomenology), propose an experiment to "ask/probe" an electron to find its companions in "an ensemble". This ensemble is not real. And the prediction are only more and more accurate with respect to the ensemble size.CM does not need an ad-hoc rule to connect the evolution formalism to the lab event. It does not need ensemble either. And CM don't treat measurement and interaction differently.

How do you come to these conclusions? We can prepare single electrons, even single photons, very well nowadays. And an ensemble can (among other ways to prepare them) consist of many repetitions of such single-quanta states. If this was not the case, we couldn't have ever checked that QT is describing things right in terms of the predicted probabilities.

Quantum mechanics doesn't treat measurement and interaction differently (I won't again repeat the obvious arguments I've stated several times in this thread again).

 

[Boing3000]

How do you come to these conclusions? We can prepare single electrons, even single photons, very well nowadays

The circularity of that claim is obvious.
But maybe that "preparation" is yet another kind of physical process I am not aware off, and described in your version of QM that is neither interaction nor measurement.

And an ensemble can (among other ways to prepare them) consist of many repetitions of such single-quanta states. If this was not the case, we couldn't have ever checked that QT is describing things right in terms of the predicted probabilities.

OK then how do you prepare an entangled pair of electron or photon that have probability 1 to be polarized at such angle along such axes...

 

[stevendaryl]

The circularity of that claim is obvious.
But maybe that "preparation" is yet another kind of physical process I am not aware off, and described in your version of QM that is neither interaction nor measurement.OK then how do you prepare an entangled pair of electron or photon that have probability 1 to be polarized at such angle along such axes...

I'm sort of in agreement with you that in QM, measurement and preparation seem very similar, but there are some circumstances where it is possible to get particles in a particular state without measuring them. For example, if you send electrons through a Stern-Gerlach device, the ones that are spin-up will go in one direction and the ones that are spin-down will go in another direction. Then if you perform an experiment on just one of the two streams, you can be assured that the electrons are in a specific spin state even though you didn't measure the spin.

 

[Boing3000]

I'm sort of in agreement with you that in QM, measurement and preparation seem very similar, but there are some circumstances where it is possible to get particles in a particular state without measuring them. For example, if you send electrons through a Stern-Gerlach device, the ones that are spin-up will go in one direction and the ones that are spin-down will go in another direction. Then if you perform an experiment on just one of the two streams, you can be assured that the electrons are in a specific spin state even though you didn't measure the spin.

But didn't you just describe a measurement ? How can you say you didn't measure their spin ? Or are you saying you are no more interested by spin, but want to measure some other property (maybe loosely coupled with spin) ?

 

[Fra]

The ensemble doesn't exist only in my head, but it's realized with accelerators. That's why they aim at ever higher luminosities to "collect statistics as quickly as possible".

I agree this process is important, and this is where the probabilistic abstractions are attached to physics.

This requires two things to actually make sense:

- The timescale of the processes we observer must be "small" so that we can prepare, decode data, and repeat enough statistis fast on a relative timescale
- The experimental control requires the system of study to be small relative to the lab so that we can control its boundary.

This is certainly true for HEP where we can observe scattering on the boundary, but fails for cosmology (here a new paradigm for inference is needed! which one?)

If we can do this we have good foundation for the probabilistic predictions, as well as extracting timeless patterns that stay constant over trials (symmetries). This how the standard model of particle physics is designed. But if these premises fail, not only do "probability" loose its original meaning, we also loose the ability in inferring symmetries, either because its too much data and limiting processing power or because of insufficient data to with any reasonable accuracy make statistical statements.

/Fredrik

 

[stevendaryl]

But didn't you just describe a measurement ?

No. After sending an electron through a Stern-Gerlach device, I know that:

• If the electron went left, then it must have been spin-up
• If the electron went right, then it must have been spin-down

But I don't know which is the case, so I haven't actually measured the spin.

 

[Boing3000]

But I don't know which is the case, so I haven't actually measured the spin.

Do you mean someone else have chosen which stream (left or right, or apparatus angle) and that you just don't know on which one you are working on ?

 

[stevendaryl]

Do you mean someone else have chosen which stream (left or right, or apparatus angle) and that you just don't know on which one you are working on ?

Well, it depends on exactly what is done with the two streams. If I perform a measurement of the electrons that go through one of the streams and get some result, then I'm indirectly measuring which stream the electron went in (since only one of the streams is measured), and so that indirectly counts as a spin measurement. But the measurement occurs at the moment I measure something about the electron. The separation into streams did not constitute a measurement.

To see that the separation by itself is not a measurement, I could redirect both streams back together into a single stream, and then no measurement of spin would ever be performed.

So a preparation does not necessarily count as a measurement (although it can be a preliminary step in a measurement).

 

[Mentz114]

Well, it depends on exactly what is done with the two streams. If I perform a measurement of the electrons that go through one of the streams and get some result, then I'm indirectly measuring which stream the electron went in (since only one of the streams is measured), and so that indirectly counts as a spin measurement. But the measurement occurs at the moment I measure something about the electron. The separation into streams did not constitute a measurement.

To see that the separation by itself is not a measurement, I could redirect both streams back together into a single stream, and then no measurement of spin would ever be performed.

So a preparation does not necessarily count as a measurement (although it can be a preliminary step in a measurement).

If you recombine the beams you do not get a thermal state, but you may have had one before the projections (depending on your preparation !) .
All projective 'measurements' are preparations. Nothing has been measured and all information about the previous state is lost.

This is elementary stuff which most people choose to ignore.

 

[stevendaryl]

If you recombine the beams you do not get a thermal state, but you may have had one before the projections (depending on your preparation !) .
All projective 'measurements' are preparations. Nothing has been measured and all information about the previous state is lost.

I'm not sure what you mean. Suppose I do the following:

1. Start with a stream of electrons that are spin-up in the x-direction
2. Separate it into two streams by sending electrons that are spin-up in the z-direction to the left, and the ones that are spin-down in the z-direction to the right.
3. Now, I recombine the two beams into a single beam
4. Finally, I measure the spin of the combined beam in the x-direction

If step 2 were a measurement, then step 4 would yield spin-up or spin-down, with equal probability. If step 2 is not a measurement, then step 4 will only produce the result spin-up.

 

[Mentz114]

I'm not sure what you mean. Suppose I do the following:

1. Start with a stream of electrons that are spin-up in the x-direction
2. Separate it into two streams by sending electrons that are spin-up in the z-direction to the left, and the ones that are spin-down in the z-direction to the right.
3. Now, I recombine the two beams into a single beam
4. Finally, I measure the spin of the combined beam in the x-direction

If step 2 were a measurement, then step 4 would yield spin-up or spin-down, with equal probability. If step 2 is not a measurement, then step 4 will only produce the result spin-up.

If a coherent state is prepared before the splitting/recombination and coherence is maintained then there will be state reconstruction. In those circumstances the splitting is a 'reversible measurement' because it tells us nothing about the previous state - i.e. like having no 'which-path' information.

 

[stevendaryl]

If a coherent state is prepared before the splitting/recombination and coherence is maintained then there will be state reconstruction. In those circumstances the splitting is a 'reversible measurement' because it tells us nothing about the previous state.

I would call it "not a measurement" rather than "a reversible measurement".

 

[Mentz114]

I would call it "not a measurement" rather than "a reversible measurement".

The whole experiment amounts to prepaing the beam in +x state then measuiring in x and finding +x. The only measurement in this experiment is was the one where you prepared the initial beam. I stand by All projective 'measurements' are preparations. Nothing has been measured and all information about the previous state is lost.

 

[stevendaryl]

The whole experiment amounts to prepaing the beam in +x state then measuiring in x and finding +x. The only measurement in this experiment is was the one where you prepared the initial beam. I stand by All projective 'measurements' are preparations. Nothing has been measured and all information about the previous state is lost.

I don't know what you mean. I would have guessed that "information about the previous state" would cover "the electrons have spin-up in the x-direction". That information has not been lost.

Perhaps all measurements are preparations, but the issue is whether all preparations are measurements.

 

[Mentz114]

I don't know what you mean. I would have guessed that "information about the previous state" would cover "the electrons have spin-up in the x-direction". That information has not been lost.

In step 1 there is a measurement. You started with a thermal beam and separated out x+. That was a projection and the previous state is lost. Step 2 is not a measurement, nor is the final step a measurement because there was no projection, so nothing changed.

 

[stevendaryl]

In step 1 there is a measurement. You started with a thermal beam and separated out x+. That was a projection and the previous state is lost. Step 2 is not a measurement

Yes, I agree that it's not a measurement, but it is a preparation.

 

[Mentz114]

Yes, I agree that it's not a measurement, but it is a preparation.

Do you mean step 2 is a preparation but not a measurement ?

 

[stevendaryl]

Do you mean step 2 is a preparation but not a measurement ?

Yes, that's what I meant.

 

[Mentz114]

Yes, that's what I meant.

Whatever we call steps 2 and 3 we can ignore them and look at steps 1 and 4. The only actual projection ( which some people may call a collapse) happens in step 1. After that there is no further projection so no information is lost or gained. We prepared x+ and we've still got it.

It occurs that due to the idempotency of operators $\hat{S}_x\hat{S}_x|\phi\rangle=\hat{S}_x|\phi\rangle$

 

[Boing3000]

The separation into streams did not constitute a measurement.

OK do you call it an interaction ? but one that nobody "observe" ? The problem is that by you own setup, you are going to work on one of the stream only...

To see that the separation by itself is not a measurement

I am trying hard to follow your argumentation. Here I am still wondering how any preparation is different with "knowing/measuring/projecting" some state.

, I could redirect both streams back together into a single stream, and then no measurement of spin would ever be performed.

But a measurement has been made nonetheless. There is no way for someone not knowing/measuring (that is taking note of which electron when by which path) to assert/prove/measure that a measurement had not been made. Sure he cannot detect it, but it doesn't mean nobody can.
I someone else (aware of the result) come an got a much more accurate result (let's say 100% correct), it does not mean then QM is wrong. It means something did happen to each individual electron, no mater ones ignorance of it.
That thing is a measurement, not an interaction, because the projection is done by a classical apparatus which is the only thing able to set a particle into some eigenvalue. If the apparatus wasn't classical in the first place, you simply could not even set it in some orientation in the first place.
However that process take place, the only formulation of it is the Born rule, which may or may not be deduced in some way (but isn't currently).

So a preparation does not necessarily count as a measurement (although it can be a preliminary step in a measurement).

Even with your second example in post #269, step 2 is a also a measurement (in another bases, but nonetheless). Why should it change step 4 ? But it does change the wavefunction (of this basis, and maybe in other, but then QM would predict it anyway).

Can you try to give another example where no classical apparatus is used to "prepare" a state ? I kind of think it is impossible given the very definition of quanta.

 

[Mentz114]

[..]
But a measurement has been made nonetheless. There is no way for someone not knowing/measuring (that is taking note of which electron when by which path) to assert/prove/measure that a measurement had not been made. Sure he cannot detect it, but it doesn't mean nobody can.
I someone else (aware of the result) come an got a much more accurate result (let's say 100% correct), it does not mean then QM is wrong. It means something did happen to each individual electron, no mater ones ignorance of it.
[..]

The experiment that @stevendaryl described has been analysed in terms of projection operators here in post#5
https://www.physicsforums.com/threads/spin-state-recombination.927182/

 

[stevendaryl]

But a measurement has been made nonetheless. There is no way for someone not knowing/measuring (that is taking note of which electron when by which path) to assert/prove/measure that a measurement had not been made. Sure he cannot detect it, but it doesn't mean nobody can.

No, it's not a measurement until someone detects it. The definition of "measurement" is that you have measured some quantity when you have made a persistent record of its value (or something that maps to its value). If that hasn't happened, then a measurement hasn't been made.

In deflecting an electron to the left or to the right, what you've done is set up a correlation between two different properties of the electron: its position (left or right) and its spin (up or down). Every interaction sets up a correlation of that type, but not every interaction is a measurement.

That thing is a measurement, not an interaction, because the projection is done by a classical apparatus which is the only thing able to set a particle into some eigenvalue. If the apparatus wasn't classical in the first place, you simply could not even set it in some orientation in the first place.
However that process take place, the only formulation of it is the Born rule, which may or may not be deduced in some way (but isn't currently).

No, not all interactions with a macroscopic/classical apparatus result in a measurement. Only irreversible interactions---interactions that leave the apparatus in a persistent state that records the value being measured.

Even with your second example in post #269, step 2 is a also a measurement (in another bases, but nonetheless).

Not by the definition of "measurement" that I'm using. By what definition is it a measurement? It doesn't collapse the wavefunction.

 

[kith]

Not by the definition of "measurement" that I'm using. By what definition is it a measurement? It doesn't collapse the wavefunction.

And yet it is the most prominent example where projected wavefunctions are actually used in practise.

I don't disagree with your terminology but this is something about the measurement problem which I find peculiar. The collapse postulate is only needed for sequential measurements (because only there, we can check the state after a measurement). Textbook examples of sequential measurements mostly involve multiple Stern Gerlach devices or multiple polarizers. After each device, the new state vector is calculated by a projection. But usually, the only actual measurement is provided by a single screen at the end. So in these cases, collapse arguably is just a convenient way to simplify calculations.

I think that a lot of discussions about the measurement problem would gain considerable clarity if people tried to focus on distinguishing these two classes of experiments:
1) Real sequential measurements where outcomes are obtained at each device.
2) Sequential preparations, where state vectors are projected for convenience because nobody cares about what happens inside the devices.

It turns out that there aren't many experiments of type 1 if by "outcome" we mean things which are actually reported by the experimenters. If people agree about the classification of typical experiments, the focus of the discussion can be narrowed. If they don't, the discussion is probably shifted from an issue which is specific to QM to the broader issue of irreversibility first.

 

[Boing3000]

If people agree about the classification of typical experiments, the focus of the discussion can be narrowed.

That would be great indeed. But I am more inclined to think people will prefer to inject meaning instead. The setup #269 seems pretty clear. There are 3 identical Stern-Gerlach "apparatus". Yet the step1 is call a "preparer" the step2 a "interaction/useless" the step3 a "measurer".
I cannot fathom why on Earth preparing +X is not a measurement to +X. Nor have I obtained any example of a preparation that is not a measure. But OK if the terminology requires that identical apparatus working identically (and perfectly exchangeable in the setup) are designated by different word if a start and at end, then OK, I'll do it.
Likewise the step2 is an identical process. But because the angle is different, somewhat some experimenter can decide that "it does not collapse the wave function". My understanding was that it did not bother him to take note and modify its expectation with the projection (because, say, it is a case where it wouldn't change expectation in X anyway).
But my point is that a measurement did occur, and it can be measured at 4 (but in Z). No willing to do that do not destroy or retroactively nullify the apparatus (it is there, whatever you take note or not).
I am not even sure that @stevendaryl is not thinking that the human-mind/or consciousness/or maybe a piece of paper, only constitute a measurement (doing physical projection to eigenvalue).

If they don't, the discussion is probably shifted from an issue which is specific to QM to the broader issue of irreversibility first.

Maybe it is what I don't get to get out of this conundrum. Do step 3 actually totally reverse the step2, in the sense that not even data collected after step2 modify some expectation at step4 even in Z?
Or do you mean special measurement that destroy the state (photon absorption, anti-electron anhihilation) making it irreversible ?

 

[stevendaryl]

I cannot fathom why on Earth preparing +X is not a measurement to +X.

Why on Earth would it be a measurement? Isn't it part of the definition of "measurement" that afterward, you know the value of whatever was being measured?

Nor have I obtained any example of a preparation that is not a measure.

Yes, you have. Sending spin-up electrons to the left and sending spin-down electrons to the right is a preparation, but not a measurement.

 

[stevendaryl]

But my point is that a measurement did occur, and it can be measured at 4 (but in Z). No willing to do that do not destroy or retroactively nullify the apparatus (it is there, whatever you take note or not).

I really don't understand why you want to call it a measurement when spin-up electrons are sent to the left and spin-down electrons are sent to the right. But I can accommodate whatever terminology you want. What point are you wanting to make about measurements?

The significance of measurement in QM (or at least, the usual, informal interpretation) is that:

1. A measurement produces a result, and the result is an eigenvalue of the operator corresponding to the observable being measured.
2. The probability of the various results is given by the square of the amplitudes for the corresponding elements of the superposition.
3. (Some people include this, and some don't) After the measurement, the system being measured is treated as if it is now in an eigenstate of the operator.

These three points don't apply to a non-destructive preparation procedure. So lumping all preparation procedures in with measurements seems to be mixing up things that are fundamentally unalike.

 

[Boing3000]

Why on Earth would it be a measurement? Isn't it part of the definition of "measurement" that afterward, you know the value of whatever was being measured?

Is this a joke ? Preparing +X means you know they are +X, if not, what would be the point of "preparation"

Yes, you have. Sending spin-up electrons to the left and sending spin-down electrons to the right is a preparation, but not a measurement.

I see, i see

 

[stevendaryl]

Is this a joke ? Preparing +X means you know they are +X, if not, what would be the point of "preparation"

If you arrange for spin-up electrons to be sent to the left and spin-down electrons to be sent to the right, you still don't know whether the electron is spin-up or spin-down. Not until you detect the electron on the right, or on the left. Until you do that, you don't have a measurement.

I really don't understand what you're saying.

What is the point of such a preparation? It's not an end in itself, it's a PREPARATION for some further experiment. You send the spin-up electrons one direction toward an experimental setup. You send the spin-down electrons another direction toward a different setup. In the analysis of the first experiment, you can assume that any electrons that you find will be spin-up, because only the spin-up electrons are sent there. But until you find the electron, you haven't measured the spin.

 

[Boing3000]

If you arrange for spin-up electrons to be sent to the left and spin-down electrons to be sent to the right, you still don't know whether the electron is spin-up or spin-down. Not until you detect the electron on the right, or on the left. Until you do that, you don't have a measurement.

I thought the preparation consist exactly to keep the right beam (by filtering it with a Stern Gerlach in X).

How do you preparation electron in a +X state ?

 

[stevendaryl]

I thought the preparation consist exactly to keep the right beam (by filtering it with a Stern Gerlach in X).

How do you preparation electron in a +X state ?

I think I've said the same answer many times now. I don't have any idea why you want more.

If you send the spin-up electrons to the left, and sent the spin-down electrons to the right, then you know that any electrons you find on the left will be spin-up. That doesn't mean that you have detected any electrons at all, so it doesn't mean that you have measured anything at all.

When you detect an electron on the left, at that moment you will (indirectly) be measuring the spin state. But not until then. The measurement does not happen when the electrons are sent one way or the other, but later.

You keep wanting to say that the splitting into two beams is a measurement, even though it has none of the properties of a measurement. It doesn't collapse the wave function. It doesn't result in my knowing the spin. It doesn't produce a probabilistic outcome according to the Born rule. Nothing about measurements apply. But you still want to call it a measurement?

 

[Mentz114]

[..]
The collapse postulate is only needed for sequential measurements (because only there, we can check the state after a measurement). Textbook examples of sequential measurements mostly involve multiple Stern Gerlach devices or multiple polarizers. After each device, the new state vector is calculated by a projection. But usually, the only actual measurement is provided by a single screen at the end. So in these cases, collapse arguably is just a convenient way to simplify calculations.
[..]
It turns out that there aren't many experiments of type 1 if by "outcome" we mean things which are actually reported by the experimenters. If people agree about the classification of typical experiments, the focus of the discussion can be narrowed. If they don't, the discussion is probably shifted from an issue which is specific to QM to the broader issue of irreversibility first.

In all cases I know we used a macroscopic variable which becomes correlated to the quantum state to make a calculation.

In cavity QED expriments with Rydberg atoms a detector can find the excited state |e> by applying a potential just strong enough to cause ionization and send the state to |g>. This is a projection operator but (again) in order to make a decision we use something that is correlated with the state (ionization) to get a measurement. Is there collapse in this case ?

Irreversibility is key - for example the splitting in step 2 is reversible until either beam is decohered for instance by being interrupted.

 

[Boing3000]

But you still want to call it a measurement?

Thanks for the conversation, it has been very enlightening.

 

[stevendaryl]

Irreversibility is key - for example the splitting in step 2 is irreversible until either beam is decohered by being interrupted for instance.

Do you mean "reversible" instead of "Irreversible"?

 

[Mentz114]

Do you mean "reversible" instead of "Irreversible"?

Sorry, I lost control of my fingers. Now corrected, thanks.

 

[atyy]

No, it's not a measurement until someone detects it. The definition of "measurement" is that you have measured some quantity when you have made a persistent record of its value (or something that maps to its value). If that hasn't happened, then a measurement hasn't been made.

In deflecting an electron to the left or to the right, what you've done is set up a correlation between two different properties of the electron: its position (left or right) and its spin (up or down). Every interaction sets up a correlation of that type, but not every interaction is a measurement.
No, not all interactions with a macroscopic/classical apparatus result in a measurement. Only irreversible interactions---interactions that leave the apparatus in a persistent state that records the value being measured.
Not by the definition of "measurement" that I'm using. By what definition is it a measurement? It doesn't collapse the wavefunction.

And yet it is the most prominent example where projected wavefunctions are actually used in practise.

I don't disagree with your terminology but this is something about the measurement problem which I find peculiar. The collapse postulate is only needed for sequential measurements (because only there, we can check the state after a measurement). Textbook examples of sequential measurements mostly involve multiple Stern Gerlach devices or multiple polarizers. After each device, the new state vector is calculated by a projection. But usually, the only actual measurement is provided by a single screen at the end. So in these cases, collapse arguably is just a convenient way to simplify calculations.

I think that a lot of discussions about the measurement problem would gain considerable clarity if people tried to focus on distinguishing these two classes of experiments:
1) Real sequential measurements where outcomes are obtained at each device.
2) Sequential preparations, where state vectors are projected for convenience because nobody cares about what happens inside the devices.

It turns out that there aren't many experiments of type 1 if by "outcome" we mean things which are actually reported by the experimenters. If people agree about the classification of typical experiments, the focus of the discussion can be narrowed. If they don't, the discussion is probably shifted from an issue which is specific to QM to the broader issue of irreversibility first.

This is indeed one of the errors in Ballentine - he claims that Copenhagen must treat this as a collapse even when no definite outcome is obtained.

 

[Mentz114]

This is indeed one of the errors in Ballentine - he claims that Copenhagen must treat this as a collapse even when no definite outcome is obtained.

Even so, on page 5 Ballentine describes exactly the same recombination setup for neutrons. It is confusing because here he cannot mean that the split is irreversible, surely ?

 

[atyy]

Even so, on page 5 Ballentine describes exactly the same recombination setup for neutrons. It is confusing because here he cannot mean that the split is irreversible, surely ?

I'll let someone else answer. For me, Ballentine is in such sustained and fundamental error, I ignore his writings on many topics.

 

[martinbn]

Even so, on page 5 Ballentine describes exactly the same recombination setup for neutrons. It is confusing because here he cannot mean that the split is irreversible, surely ?

I don't see anything confusing or incorrect on page 5, 6. What do you mean exactly?

 

[martinbn]

This is indeed one of the errors in Ballentine - he claims that Copenhagen must treat this as a collapse even when no definite outcome is obtained.

The book is over 600 pages, can you be more specific with the citation.

 

[vanhees71]

The circularity of that claim is obvious.
But maybe that "preparation" is yet another kind of physical process I am not aware off, and described in your version of QM that is neither interaction nor measurement.OK then how do you prepare an entangled pair of electron or photon that have probability 1 to be polarized at such angle along such axes...

I've no clue what you want me to prepare. It seems self-contradictory to me what you want me to prepare.

A polarization-entangled pair of photons nowadays is easily prepared by using parametric down conversion using certain kinds of birefringent crystals and a laser:

https://en.wikipedia.org/wiki/Quantum_entanglement
https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

To make a spin-entangled electron-positron pair one way is to use a neutral pion which (however rarely) can decay into a single electron-positron pair with total spin 0. The single electron in the pair is of course not polarized in a certain direction, but for any direction you may measure the spin component you get 50% +1/2 and 50% -1/2. The single-electron spin is in the state $\hat{\rho}=\hat{1}/2$, i.e., the spin component in any direction is maximally uncertain (i.e., in the state of maximum entropy).

 

[vanhees71]

I'm sort of in agreement with you that in QM, measurement and preparation seem very similar, but there are some circumstances where it is possible to get particles in a particular state without measuring them. For example, if you send electrons through a Stern-Gerlach device, the ones that are spin-up will go in one direction and the ones that are spin-down will go in another direction. Then if you perform an experiment on just one of the two streams, you can be assured that the electrons are in a specific spin state even though you didn't measure the spin.

In fact you have to clearly distinguish preparation (which defines states in an operational sense) and measurements. E.g., the uncertainty principle clearly says that it is not possible to prepare an electron to have determined two spin components in different directions. Nevertheless, no matter in which pure of mixed state the electron might be prepared in you can measure accurately any spin component you like. Often you read wrong statements about these ideas, because people don't precisely distinguish the subtle difference between state preparation and measurement.

Indeed what you describe concerning the SG experiment by filtering out one partial beam is a preparation procedure for the spin component of the particle, i.e., you prepare the particle with a determined spin component in the direction of the magnetic field of the SG apparatus. Then you can measure the spin component in any direction you like.