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- Thread starter Nick V
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In summary, the collapse of the wave function of the electron in the double slit experiment is not solely based on the act of observation, but can also be influenced by the physical interactions of the instrument used to measure the electron. This is supported by the delayed choice experiment. The term "collapse" is not used in a precise statement of quantum mechanics, and different interpretations such as the Bohmian or Many-Worlds approach may provide alternative explanations.

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Nick V said:

QM says that the probability of the electron landing at a particular point on the screen is affected by any interactions (for example, with the slits, or with measuring devices behind the slits) it has on the way to the screen. There's nothing special about the subset of interactions that (for historical reasons) we call "observations"; if the interaction is such that we could in principle know which path the electron took, the effect of the interaction will be to eliminate the interference pattern.

That's pretty much a "no" answer to your first question and a "yes" to the second... but you should note that the word "collapse" does not appear in a precise statement of exactly what QM does and doesn't tell us.

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Nugatory said:but you should note that the word "collapse" does not appear in a precise statement of exactly what QM does and doesn't tell us.

Are you allowing a Bohmian or Many-Worlds interpretation in this statement? The standard Copenhagen-style interpretation does include a mathematically precise statement that corresponds to what is colloquially called collapse, or more formally called state reduction or the conditional state or the a posteriori state.

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atyy said:Are you allowing a Bohmian or Many-Worlds interpretation in this statement? The standard Copenhagen-style interpretation does include a mathematically precise statement that corresponds to what is colloquially called collapse, or more formally called state reduction or the conditional state or the a posteriori state.

That's a fair criticism, and I wouldn't even have made the comment if OP had said "state reduction" or similar.

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Nugatory said:That's a fair criticism, and I wouldn't even have made the comment if OP had said "state reduction" or similar.

Well it's good to agree (I think) on the physics. I have come to realize that "collapse" is a loaded term, where Copenhagenists like me routinely mean "state reduction", while others think of something far more colourful.

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When we consider ALL the possible states we have a deterministic function, even if we don't know in advance what is the state of the system?

If we could know the state of the system and its evolution's equations, then we can write down deterministic equations with only those states? Without using probabilistic ones?

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afcsimoes said:

When we consider ALL the possible states we have a deterministic function, even if we don't know in advance what is the state of the system?

If we could know the state of the system and its evolution's equations, then we can write down deterministic equations with only those states? Without using probabilistic ones?

In the orthodox Copenhagen interpretation, time evolution is deterministic between measurements, and random at the instant of a measurement. Although this approach is consistent with all data to date, there problem with this approach is that the theory does not say when a measurement is made, which is something that the user of the theory must put in from outside.

This problem is solved in the Bohmian interpretation. In Bohmian mechanics, time evolution is determinstic, while the randomness lies in the initial conditions. However, there is not a unique Bohmian dynamics, and there is also no consensus yet about whether a Bohmian view is possible for all aspects of the standard model of particle physics.

A third approach called Many-Worlds is possibly completely deterministic. In this approach, all measurement outcomes occur. However, it is not yet known if this approach is correct in all details.

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I think my question before is a little unclear but let me edit it...Nugatory said:QM says that the probability of the electron landing at a particular point on the screen is affected by any interactions (for example, with the slits, or with measuring devices behind the slits) it has on the way to the screen. There's nothing special about the subset of interactions that (for historical reasons) we call "observations"; if the interaction is such that we could in principle know which path the electron took, the effect of the interaction will be to eliminate the interference pattern.

That's pretty much a "no" answer to your first question and a "yes" to the second... but you should note that the word "collapse" does not appear in a precise statement of exactly what QM does and doesn't tell us.

When the electrons go through the double slit they create a wave like pattern. However, when there is a tracker to measure the electrons, they create a double band particle pattern. Could it be that the instrument used to measure the electrons is physically interacting with them causing them to collapse the wave like pattern, or is it just the act of observing that causes them to collapse the wave like pattern into a particle like pattern?

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Nick V said:I think my question before is a little unclear but let me edit it...

When the electrons go through the double slit they create a wave like pattern. However, when there is a tracker to measure the electrons, they create a double band particle pattern. Could it be that the instrument used to measure the electrons is physically interacting with them causing them to collapse the wave like pattern, or is it just the act of observing that causes them to collapse the wave like pattern into a particle like pattern?

It is the interaction. But do remember that it is impossible to observe without interacting: all observations are interactions, but not all interactions are observations.

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afcsimoes said:When we consider ALL the possible states we have a deterministic function

Can you expand on what you mean because I can't follow it.

Its simple really. The state encodes within it the probabilities of the outcomes of observations. It evolves deterministically, but what it represents doesn't change.

Thanks

Bill

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Ok, but does the delay choice experiment play any partNugatory said:It is the interaction. But do remember that it is impossible to observe without interacting: all observations are interactions, but not all interactions are observations.

Sorry if this is a stupid question.

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See the explanation here:

https://www.physicsforums.com/threa...xperiment-affects-result.785711/#post-4935759

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vanhees71 said:

I guess we have discussed this many times, and I do not accept that the minimal interpretation does not have collapse or state reduction.

State reduction is undoubtedly part of the minimal interpretation, and is also known as the conditional state or the a posterior state. This is found in almost all standard textbooks, from Dirac, Landau & Lifshitz, Nieslen and Chuang, Weinberg, Sakurai & Napolitano, Shankar etc, and there really should be no controversy here.

Where there could be some controversy is whether the state reduction can be derived from unitary evolution and the Born rule alone. As far as I understand, it cannot, and requires an additional assumption. The main reason is that the Born rule only gives probabilities for a single time, whereas the conditional probability requires a rule for the joint probability of observations at different times. For spacelike observations, the Lorentz invariance can be used in place of the state reduction postulate, but the Lorentz invariance and spacelike separation is still an additional postulate.

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maline said:

The Ensemble interpretation is fully compatible with a number of different interpretations that say more about what going on so to speak eg Primary State Diffusion, Bohmian Mechanics, Nelson Stochastics, Many Worlds, and GRW collapse theory. The reason is its a minimalist interpretation making as few assumptions as possible - basically the assumption it makes is a frequentest interpretation of probability rather than a Baysian one which would lead to something like Copenhagen - it's what people mean when they say shut up and calculate - they mean an interpretation with very minimalist assumptions. Some have collapse and some do not. For definiteness I will pick Bohmian Mechanics. It does not have collapse - particles have well defined momentum, position etc at all times. What happens is when an observation is made decoherence occurs and you end up with the standard mixed state. However since it has definite properties the mixed state is a proper one and no collapse occurred. The ensemble interpretation is ambivalent to how the mixed state after decoherence becomes a proper mixed state - it simply assumes it is - somehow. That somehow may or may not involve collapse.

To understand the issue of proper and improper mixed states see the following:

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Thanks

Bill

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bhobba said:The Ensemble interpretation is fully compatible with a number of different interpretations that say more about what going on so to speak eg Primary State Diffusion, Bohmian Mechanics, Nelson Stochastics, Many Worlds, and GRW collapse theory. The reason is its a minimalist interpretation making as few assumptions as possible - basically the assumption it makes is a frequentest interpretation of probability rather than a Baysian one which would lead to something like Copenhagen - it's what people mean when they say shut up and calculate - they mean an interpretation with very minimalist assumptions. Some have collapse and some do not. For definiteness I will pick Bohmian Mechanics. It does not have collapse - particles have well defined momentum, position etc at all times. What happens is when an observation is made decoherence occurs and you end up with the standard mixed state. However since it has definite properties the mixed state is a proper one and no collapse occurred. The ensemble interpretation is ambivalent to how the mixed state after decoherence becomes a proper mixed state - it simply assumes it is - somehow. That somehow may or may not involve collapse.

To understand the issue of proper and improper mixed states see the following:

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

As far as I can tell, and as I have said many times, I don't disagree at all and I believe this is a correct Ensemble Interpretation. Although there are some difference in terminology, I cannot tell if it differs in any way in content from my default interpretation, which I usually call "Copenhagen" or "Copenhagen-style". When I say "collapse" I simply mean exactly what bhobba says by "The ensemble interpretation is ambivalent to how the mixed state after decoherence becomes a proper mixed state - it simply assumes it is - somehow."

So what is clear in bhobba's post is that there has to be something beyond unitary evolution and the Born rule in order to calculate the joint probability for sequential measurements. This clarity is lacking in Ballentine making his interpretation dubious at best, and as far as I can tell it is rejected by vanhees71.

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atyy said:This clarity is lacking in Ballentine making his interpretation dubious at best, and as far as I can tell it is rejected by vanhees71.

I strongly disagree - but I will let Vanhees speak to his position.

Thanks

Bill

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bhobba said:To understand the issue of proper and improper mixed states see the following:

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

As I said above, I agree with bhobba on physics, and at worst we only disagree on the interpretation of Ballentine. The linked article by Hansen is excellent, and as far as I can tell, I agree with it. Let me present Hansen's argument in a more mathematical way to make it clear that we have equations to discuss, and that the difference between proper and improper mixtures is not some vague interpretive thing.

First let's just assume unitary evolution and the Born rule, and no (the following are equivalent) collapse or state reduction or change from improper to proper mixtures. We have a quantum system and quantum ancilla. They start to interact at time=0, and finish interacting at time=t via unitary evolution. At time t, an observable A is measured on the ancilla and an observable B is measured on the system. Decoherence does not alter the picture for this argument, as it only restricts which observables A we can measure in a practical way. Since A and B are commuting observables that are measured at the same time, the Born rule gives P(A,B), and we can define the reduced density operator of the system by tracing over the ancilla, and we can define the conditional state or a posteriori state of the system using Bayes's rule. As long as we only calculate things derivable from P(A,B), the conditional state can be derived from unitary evolution and the Born rule alone, since it just amounts to writing Bayes's rule applied to P(A,B) in a different way. (See eg. http://arxiv.org/abs/0810.3536, Eq 6.7, 6.8 and Section 6.2.3.)

But if we use the conditional state or a posteriori state to calculate P(B,C), where C is a measurement on the system at a later time t+dt, then we are using the conditional state in a way that goes beyond applying Bayes's rule to P(A,B), and amounts to a postulate beyond unitary evolution and the Born rule, and this is collapse or state reduction or a change from an improper to proper mixture.

There is also very interesting discussion of the issue by Ozawa in http://arxiv.org/abs/quant-ph/9706027 and http://arxiv.org/abs/quant-ph/9711006. But I reference those papers only to note that as late as 1997, he writes that the consensus is that "partial trace does not derive state reduction", which is the same issue that bhobba brings up about improper and proper mixtures. Other texts that explicitly consider the issue and agree with bhobba are Haag https://www.amazon.com/dp/3540610499/?tag=pfamazon01-20 (1996, p301) and Haroche and Raimond https://www.amazon.com/dp/0198509146/?tag=pfamazon01-20 (2006, p82).

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A good example is quantum optics. The quantum opticians on the one hand deal with single photons (or other many-photon Fock states like the entangled biphotons from parametric down conversion) and on the other with macroscopic optical devices as known from classical optics. The latter are usually described classically, e.g., birefringent crystals used for parametric down conversion via an index of refraction (linear response) and some non-linear "susceptibilities". The same holds for phase shifters, lenses, polarizers, beam splitters,... I don't think that a fully microscopic description exists and is possible in practice. Of course, it's fully sufficient to describe the measured effects, which are among the most fascinating and important findings about fundamental quantum physics made in recent decades!

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maline said:

Just to be clear, I don't agree that in what is usually called a minimal interpretation that one can do without state reduction. Bhobba's "minimal interpretation" (I agree with bhobba, I put "minimal interpretation" in quotes just to clarify that his terminology is different from mine) explicitly mentions approaches like hidden variables or many-worlds as a possibility so that one can do without postulating state reduction, so that state reduction can be derived. However, there is no consensus that any of these can reproduce the standard quantum mechanical predictions for all known quantum mechanical predictions with state reduction or a change from an improper to proper mixture simply postulated as a phenomenological rule. What vanhees71 seems to be saying is we don't have to postulate hidden variables, many worlds, or state reduction or a change from an improper to proper mixture - that is strange. Certainly from unitary evolution and the Born rule alone, we can at least partly derive state reduction as a consistency requirement for measurements at spacelike separation - so state reduction is needed and standard in what is usually called a minimal interpretation.

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Further I don't understand, what you mean by "part of a wave function" (I prefer to call what we discuss about the quantum state, because there are interesting things, where there is no wave-function description as for relativistic QT and photons particularly)? If I have an electron, described by a wave function (which makes sense in the non-relativistic approximation), I either detect it or not. In the latter case, I cannot say anything (not even, whether there was an electron at all). If I detect it and measure some of its observables, I just determine a fact that was either determined before through the state preparation or it was not, and then it's the outcome of a random experiment. The probabilities for the outcomes are predicted by the wave function describing the state, my electron was prepared in at the time of the measurement, and I can check this prediction in the usual way by repeating the preparation and measurement procedures independently for a many times and evaluate the findings with the usual mathematical tools of statistics. That's all. Nothing collapses. Or what collapses, if they draw the numbers of the weekly lottery?

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That seems to be very accurate!

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Feeble Wonk said:

vanhees71 said:That seems to be very accurate!

That is not accurate at all. The question is a mathematical statement. Collapse is the statement that after a measurement, we can use a classical measurement outcome to label a subensemble. In Ballentine, this is equation 9.28 and the statement preceding that this is the state of the sub-ensemble that is labelled by the previous measurement outcome. Ballentine does not call that state reduction, but that is only a matter of terminology since other people do call it state reduction or collapse. So yes, Ballentine does have collapse. So the question is can that be derived from unitary evolution and the Born rule alone?

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Your position would seem to be the ultimate in the "shut up and calculate" school of thought regarding quantum physics. Does that mean that you believe it is impossible to interpret the findings of QT with regard to what it implies about the fundamental nature of physical existence? Or is it simply your preference on how to approach the subject.vanhees71 said:That seems to be very accurate!

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Feeble Wonk said:Your position would seem to be the ultimate in the "shut up and calculate" school of thought regarding quantum physics.

Let's be clear the difference between vanhees71 and me is not "shut up and calculate". In fact in a sense my view is more shut up and calculate. If one shuts up and calculates, there is absolutely nothing wrong with collapse or state reduction.

I am simply defending traditional shut up and calculate :)

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The question is a physical statement. What Ballentine describes with his Eq. (9.28) is the Statistical operator after a von Neumann "filter measurement", which I'd consider a state-preparation procedure. For those who don't have available this excellent textbook, here's the statementatyy said:That is not accurate at all. The question is a mathematical statement. Collapse is the statement that after a measurement, we can use a classical measurement outcome to label a subensemble. In Ballentine, this is equation 9.28 and the statement preceding that this is the state of the sub-ensemble that is labelled by the previous measurement outcome. Ballentine does not call that state reduction, but that is only a matter of terminology since other people do call it state reduction or collapse. So yes, Ballentine does have collapse. So the question is can that be derived from unitary evolution and the Born rule alone?

Suppose an ensemble of a quantum mechanical system is prepared such that it is discribed by the statistical operator ##\hat{\rho}##. Then a measurement of an observable ##R##. He takes an observable with a continuous spectrum. Let ##|r,\beta \rangle## denote the generalized eigenvectors, normalized to a ##\delta## distribution and ##\beta## labeling a possible degeneracy, which I take as a discrete set (you can also have a continuous set, but that doesn't change much). Then he considers a state-preparation procedure which filters out all systems out of the ensemble for which ##R## takes a value in an interval ##\Delta_a##. The remaining sub-ensemble is then described by a new statistical operator, which is constructed as follows: We first define the projection operator

$$\hat{M}_R(\Delta_a)=\int_{\Delta_a} \mathrm{d} r \sum_{\beta} |r,\beta \rangle \langle r,\beta|$$

and then define

$$\hat{\rho}'=\frac{1}{Z} \hat{M}_R(\Delta_a) \hat{\rho} \hat{M}_R(\Delta_a), \quad Z=\mathrm{Tr} \left [\hat{M}_R(\Delta_a) \hat{\rho} \hat{M}_R(\Delta_a)

\right]$$

as the statistical operator of the corresponding sub-ensemble.

This is just a definition what you call preparation through an idealized von Neumann filter measurement. An example, where you can describe this entirely with quantum theory is the Stern-Gerlach experiment. In this example there's then no collapse but just the ignorance of all particles with the spin component not in the desired state. The "collapse" in the Copenhagen doctrine is nothing but the choice of the subensemble by the experimenter through filtering out all undesired complementary subensembles. There's no spooky non-quantum action-at-a-distance magic called "collapse"!

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vanhees71 said:The question is a physical statement. What Ballentine describes with his Eq. (9.28) is the Statistical operator after a von Neumann "filter measurement", which I'd consider a state-preparation procedure. For those who don't have available this excellent textbook, here's the statement

Suppose an ensemble of a quantum mechanical system is prepared such that it is discribed by the statistical operator ##\hat{\rho}##. Then a measurement of an observable ##R##. He takes an observable with a continuous spectrum. Let ##|r,\beta \rangle## denote the generalized eigenvectors, normalized to a ##\delta## distribution and ##\beta## labeling a possible degeneracy, which I take as a discrete set (you can also have a continuous set, but that doesn't change much). Then he considers a state-preparation procedure which filters out all systems out of the ensemble for which ##R## takes a value in an interval ##\Delta_a##. The remaining sub-ensemble is then described by a new statistical operator, which is constructed as follows: We first define the projection operator

$$\hat{M}_R(\Delta_a)=\int_{\Delta_a} \mathrm{d} r \sum_{\beta} |r,\beta \rangle \langle r,\beta|$$

and then define

$$\hat{\rho}'=\frac{1}{Z} \hat{M}_R(\Delta_a) \hat{\rho} \hat{M}_R(\Delta_a), \quad Z=\mathrm{Tr} \left [\hat{M}_R(\Delta_a) \hat{\rho} \hat{M}_R(\Delta_a)

\right]$$

as the statistical operator of the corresponding sub-ensemble.

This is just a definition what you call preparation through an idealized von Neumann filter measurement. An example, where you can describe this entirely with quantum theory is the Stern-Gerlach experiment. In this example there's then no collapse but just the ignorance of all particles with the spin component not in the desired state. The "collapse" in the Copenhagen doctrine is nothing but the choice of the subensemble by the experimenter through filtering out all undesired complementary subensembles. There's no spooky non-quantum action-at-a-distance magic called "collapse"!

The reason that this is not preparation only is that it is preparation based on the outcome of the preceding measurement. The new quantum state is prepared based on the previous outcome that ##R## takes a value in an interval ##\Delta_a##, so it is a conditional preparation, and is a conditional state. By saying that the new state is prepared by conditioning on the preceding outcome, one has in effect generalized the Born rule for the preceding outcome to the new state.

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atyy, my interest in this debate has receded a bit but in our recent discussion of the double slit you linked to a nice computer simulation which seems relevant to me.

A gaussian wave packet hits the double slit. There, a part of the wave packet is transmitted and propagated to the screen and a part is reflected. The reflected part never hits the screen. So for a position measurement at the screen, we get the same probabilities for two different states: (a) the superposition of the transmitted and the reflected part of the wave packet and (b) the transmitted part of the wave packet alone.

Would you say that QM needs a postulate for the case that we chose description (b) for calculations because we don't want to calculate things which aren't relevant for the measurement outcome?

A gaussian wave packet hits the double slit. There, a part of the wave packet is transmitted and propagated to the screen and a part is reflected. The reflected part never hits the screen. So for a position measurement at the screen, we get the same probabilities for two different states: (a) the superposition of the transmitted and the reflected part of the wave packet and (b) the transmitted part of the wave packet alone.

Would you say that QM needs a postulate for the case that we chose description (b) for calculations because we don't want to calculate things which aren't relevant for the measurement outcome?

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