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

[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.

 

[vanhees71]

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.

But in this case he is wrong. A measurement means that you have let the system interact with an apparatus with outcomes for pointers that are in one-to-one correspondence with the value of the measured observable (I don't talk about incomplete measurements here; that's another interesting story of quite recent research on what measurement means in quantum theory), but this is not the case in the neutron interferometer experiment described in Ballentines book.

 

[vanhees71]

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?

Ballentine indeed does show that in his setup there's no state reduction. The only problem with this argument is that even a proponent of the collapse hyposis wouldn't claim that a state reduction has happened since in this setup the spin components at points B and C are not measured.

 

[zonde]

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.

I have no suggestion about "correct" terminology, however I see no contradiction between the idea that SG apparatus changes the spin state of particle and the fact that two beams can be recombined in a way that restores original spin state.
In order to observe interference we have to preserve relative phase between spin modes and have to make it matter by recombining beams. And interference is responsible for restoration of the original spin state.
If relative phase plays no role in later manipulations we of course can drop spatially separate part of the beam from description by projection.
Production of measurement record necessarily destroys any relative phase relationship as in this process the system interacts with one or more particles which are necessarily removed from experimental setup and do not participate in any later manipulations. But then it has little to do with spin or any other property of the particle (except position of course as we place detectors at certain spot).

 

[Boing3000]

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

OK the screen is a different apparatus. There is only one screen, and it is after step4. I recognize that. The screen interact with the position observable.

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.

Of course, if there is not "spacial/position" screening... and there is only one electron...

So you shouldn't call this a measurement.

OK fine, I'll not call it a measurement, even though every single one of the electron are known to have been prepared/picked up from the left beam. Which seem to me to be identical to having put a screen with a hole only on the left path.

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.

But what I cannot got trough my thick skull (or sick, go figure), is how that differs in any shape of form from the very definition of "measurement".

Listen I found some resource with similar setup that seems to be analysed in detail. I'll read it ten time over and eventually get back to you.

Thank you

 

[vanhees71]

I have no suggestion about "correct" terminology, however I see no contradiction between the idea that SG apparatus changes the spin state of particle and the fact that two beams can be recombined in a way that restores original spin state.
In order to observe interference we have to preserve relative phase between spin modes and have to make it matter by recombining beams. And interference is responsible for restoration of the original spin state.
If relative phase plays no role in later manipulations we of course can drop spatially separate part of the beam from description by projection.
Production of measurement record necessarily destroys any relative phase relationship as in this process the system interacts with one or more particles which are necessarily removed from experimental setup and do not participate in any later manipulations. But then it has little to do with spin or any other property of the particle (except position of course as we place detectors at certain spot).

An SG apparatus without a screen to detect the two partial beams of the silver atom can, however, be seen as a preparation procedure for definite spin states, i.e., you get an entanglement between position and spin component in direction of the magnetic field (with theoretically arbitrary accuracy), i.e., an atom at one of the clearly distinguished places of the two partial beams has a determined spin component $\pm \hbar/2$. The wave function (a Weyl spinor) is
$$\Psi(x)=\psi_+(x) |\hbar/2 \rangle + \psi_{-}(x) |-\hbar/2 \rangle,$$
where the $\psi_{\pm}$ have (FAPP) no overlap.

At this point, however, the spin component has not yet been measured, i.e., to know the spin component of a single atom that run through the magnet you have to register at which position it ends up at a screen or something equivalent. Only then you have done a measurement, and this measurement will distroy the relative phase between the two partial beams, which occur in the superposition written above for $\Psi$. After such a measurement a "recombination" of the two partial beams in the sense Ballentine writes in his book is not possible anymore. This is due to the decoherence that necessarily occurs through the interaction of the atom with the measurement apparatus.

 

[kith]

But in this case he is wrong.

I don't dispute this. I just don't have access to the book right now and can't comment on the specifics of where I think he went wrong.

 

[kith]

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.

But what I cannot got trough my thick skull (or sick, go figure), is how that differs in any shape of form from the very definition of "measurement".

Because of "if the electron arrives there". You don't know if it will arrive to the right or to the left. Only after the measurement to the right has been performed do you know that it arrived there.

 

[Boing3000]

Because of "if the electron arrives there". You don't know if it will arrive to the right or to the left. Only after the measurement to the right has been performed do you know that it arrived there.

But the preparation consist of taking only the electron from the left path ! Every electron used after that first "preparating" "Left of Stern Gerlach" is one of those... There is no uncertainty there, isn't it ? What am I missing that is so obvious for you physicists ?

 

[Mentz114]

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

Ballentine is not confusing me - atyy is !

 

[vanhees71]

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

Me neither. There's nothing incorrect on pages 5, 6 in Ballentine's book, where he discusses an SG experiment with neutrons. Also there, however, he doesn't measure the spin components before recombining the "partial beams", i.e., there's no decoherence and that's why the recombination leads back to the original state.

Nevertheless, Ballentine is among the best QM textbooks I know of.

Concerning the question of interpretation, Weinberg's book "Lectures on Quantum Mechanics" is even better although I don't agree with his conclusion that there's something unsolved concerning QM and measurements. What's unsolved is the lack of a consistent quantum description of the gravitational field, but it's not measurement within standard QM and QFT, where the great success of QT describing the empirical findings shows that in fact there's no problem from the point of view of physics. Maybe there's a puzzle for philosophers about reality and such things, but that's philosophy, not physics.

 

[kith]

But the preparation consist of taking only the electron from the left path ! Every electron used after that first "preparating" "Left of Stern Gerlach" is one of those... There is no certainty there, isn't it ? What am I missing that is so obvious for you physicists ?

I don't understand what you mean. Let me introduce one more step: after the interaction of the electron with the SG apparatus we have a superposition of a state where it flies to the left with spin up and a state where it flies to the right with spin down. If you put a screen as a measurement device to right, you either get a blob or you don't. Getting a blob corresponds to the electron traveling to the right with spin down, not getting a blob corresponds to the electron traveling to the left with spin up. So only after looking for the presence of the blob, the observer can say anything definite about the spin.

 

[stevendaryl]

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).

That's true. For the purposes of the interpretation of quantum mechanics, I think what's important is not measurement, specifically, but interactions that cause a microscopic quantity to become correlated with the results of an irreversible macroscopic change. Such interactions are not actually measurements, because we might not actually learn anything from them.

For modeling purposes, one of these examples of interactions leading to decoherence and macroscopic entanglement can often be thought of as a measurement followed by forgetting the result of the measurement. That sounds like that combination should be the same as doing nothing, but it isn't, in combination with the Born rules.

 

[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!

OK, let's try this again, since we seem to agree on the error in section 9.5 of Ballentine's book. Here is LL stating explicitly that classical concepts are needed in the formulation of QM postulates, and that it is also true that classical mechanics is a limit of quantum mechanics. Here are some relevant quotes from p2-3 of the English translation.

"A more general theory can usually be formulated in a logically complete manner, independent of a less general theory which forms a limiting case of it. ... It is in principle impossible, however, to formulate the basic concepts of quantum mechanics without using classical mechanics."

"By measurement, in quantum mechanics, we understand any process of interaction between classical and quantum objects ..."

"Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation."

 

[kith]

Landau and Lifshitz does. They are careful to say that a measurement produces an irreversible macroscopic mark, [...]

By "carefully distinguish" I mean a tangible discussion of both types of situations: an experiment, where the observer actually gets multiple outcomes and an experiment, where state reduction is used for convenience because certain parts of the state aren't relevant for future measurements. And ideally also how one can modify an experiment such that it falls into the other class.

which is nowadays often called a "definite outcome" following Schlosshauer's influential review.

What passage exactly do you have in mind? In his 2004 paper, he talks about the possibility of "subjective definiteness" so his notion of "definite outcome" seems to be more general to me.

In any case, I think that the word "outcome" should be avoided if one doesn't speak about the perception of a person. It is loaded language which blurrs the boundary between what is independent of the observer and what isnt.

 

[atyy]

By "carefully distinguish" I mean a tangible discussion of both types of situations: an experiment, where the observer actually gets multiple outcomes and an experiment, where state reduction is used for convenience because certain parts of the state aren't relevant for future measurements. And ideally also how one can modify an experiment such that it falls into the other class.

Yes, I've never seen that explicitly discussed in a textbook. I think I realized it sometime after reading LL (which is the first book from which I understood quantum mechanics because of its explicit mention of the classical measuring apparatus), and not just the formal postulates. It also helped by explicitly seeing how this is played out in the indirect measurements formalism with a quantum ancilla, and showing that the reduced density matrix is the same as that after a projective measurement in which information about the result is not retained. However, I still did not know it in every specific situation. For example, I did not know about the unitary description of a polarizer until @Cthugha pointed it out to me here on PF many years after I had already learned QM.

What passage exactly do you have in mind? In his 2005 paper, he talks about the possibility of "subjective definiteness" so his notion of "definite outcome" seems to be more general to me.

Nothing so specific, just his general term "definite outcome", eg. https://arxiv.org/abs/quant-ph/0312059 has a whole section II.B headed "The problem of definite outcomes".

BTW, I realized my memory of LL was faulty, and even they do not state the idea of an "irreversible macroscopic outcome" so clearly. It must be something I picked up with their help.

The concept of irreversibility is mentioned more clearly in Haag's 1996 "Local Quantum Physics" on p304: "In Bohr's discussion the time asymmetry appears as obvious. For instance: "The irreversible amplification effects on which the registration of the existence of atomic objects depends reminds us of the essential irreversibility inherent in the very concept of observation" [Bohr 58]."