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

[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.

 

[vanhees71]

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.

For sure not. If I absorb a photon to detect it, this photon is gone. It's not prepared in anything but it's simply not there anymore. Almost all measurements we can do with quantum systems are not preparations. That's another very simple argument why the idea of state collapse in some flavors of Copenhagen is flawed and not relevant for real-world experiments in the lab anyway.

 

[Boing3000]

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.

0 along which axis ? Otherwise said, is it possible to prepare pion by measuring their spin along some angle, and will it affect the prediction you can make on the spin of the e/p pair ?
Likewise, is putting a polarizer on the incident photon before the crystal, modifying the setup in any measurable way ?

A related question, is that in both cases what is the mathematical relationship for the spin conservation ? I mean the spin must change, because the axis of travel split in two (and thus differ by some angle)

 

[vanhees71]

If you prepare a spin in $s=0$ the components $\vec{n} \cdot \vec{\sigma}$ are determined to be 0 for any direction $\vec{n}$. It's the most simple example that sometimes in fact you can prepare special states where incompatible observables are all determined at once.

 

[atyy]

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

Section 9.5 of the 1998 edition which purports to show the quantum state is not subject to any state reduction

 

[vanhees71]

Well, and what's in your opinion wrong with this section?

I must say, you have indeed a point here, since no spin component is measured at points B and C, and thus even if I assume a collapse in measurements I don't expect any to occur here.

 

[stevendaryl]

If you prepare a spin in $s=0$ the components $\vec{n} \cdot \vec{\sigma}$ are determined to be 0 for any direction $\vec{n}$. It's the most simple example that sometimes in fact you can prepare special states where incompatible observables are all determined at once.

Well, you could say that the notion of "compatible" is state-dependent. For spin, for example, we have:

$[S_i, S_j] = i \varepsilon_{ijk} S_k$

If compatible means that the commutator is zero, then $S_i$ and $S_j$ are compatible when all components of spin are zero.

 

[kith]

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".

Step 3 is different because there's also the screen which allows the experimenter to make an observation.

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

If you have only a single electron and use a Stern Gerlach apparatus to put it in a superposition of flying to the right with spin up and flying to the left with spin down you cannot say anything definite about its spin. So you shouldn't call this a measurement. Yet if you perform a measurement located somewhere to the right of the SG apparatus, you know that if the electron arrives there, it definitely has spin up. This is why it is sensible to call this a preparation for this measurement.

 

[martinbn]

Section 9.5 of the 1998 edition which purports to show the quantum state is not subject to any state reduction

I don't see how that supports what you claimed earlier! There is nothing erroneous in that section, and he doesn't say anything aboutCopenhagen.

 

[atyy]

I don't see how that supports what you claimed earlier! There is nothing erroneous in that section, and he doesn't say anything aboutCopenhagen.

So you claim.

 

[atyy]

Well, and what's in your opinion wrong with this section?

I must say, you have indeed a point here, since no spin component is measured at points B and C, and thus even if I assume a collapse in measurements I don't expect any to occur here.

Yes, what you said is what is wrong about that section.

 

[kith]

So you shouldn't call this a measurement.

Actually, I did use the term like this myself in the past. My usage of the term "measurement" has considerably evolved over the time and now I think that the best way to speak of it is simply the everyday language: a measurement is the action of a person to obtain knowledge about a part of the world. A necessary condition for a device to act as a measurement device is that said person can read out the measurement outcome. This leads to certain requirements about the physical interaction between the device and the system of interest.

I don't like the equation of measurement with state reduction or terminology like "a measurement has occurred". State reduction neither fully captures what happens in a measurement (it leaves out the outcome) nor is it exclusively used for measurements (it's also used for convenience in situations where the observer doesn't obtain any knowledge).

 

[kith]

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.

I agree that he strawmans Copenhagen. But to be fair, I don't know any textbook which carefully distinguishes situations without intermediate outcomes from real sequential measurements off the top of my head.

 

[atyy]

I agree that he strawmans Copenhagen. But to be fair, I don't know any textbook which carefully distinguishes situations without intermediate outcomes from real sequential measurements off the top of my head.

Landau and Lifshitz does. They are careful to say that a measurement produces an irreversible macroscopic mark, which is nowadays often called a "definite outcome" following Schlosshauer's influential review.

Edit: I just looked again at LL, and I see that even they do not state it that clearly as an "irreversible macroscopic mark", though they do state the peculiar status of measurements in QM." LL was the book in which first understood the meaning of the QM formalism given in other books, so perhaps I tend to remember them too fondly.

 

[martinbn]

So you claim.

What he shows there is that in this case there cannot be a state reduction. Exactly as described by stevendarryl. Do you disagree with that?

 

[vanhees71]

Well, you could say that the notion of "compatible" is state-dependent. For spin, for example, we have:

$[S_i, S_j] = i \varepsilon_{ijk} S_k$

If compatible means that the commutator is zero, then $S_i$ and $S_j$ are compatible when all components of spin are zero.

Usually one defines observables as compatible only when their representing operators commute, i.e., when there exists a complete set of orthonormalized simultaneous eigenvectors.