Particles from a thermal source

[A. Neumaier]

In the following, I want to consider both photons in a sharply focussed, monochromatic beam of light (''type P'') and electrons in an electron beam (''type E'') on the same footing. In the following, X is either P or E. If we only concentrate on the internal degrees of freedom, both kinds of particles can be described as a 2-level system, with a 2-dimensional Hilbert space.

Consider a stationary thermal source that emits particles of type X in a sharply focussed, monochromatic beam. Due to the thermal nature of the source, one has to use statistical mechanics to model its statistical behavior. Thus a ##2\times 2## density matrix ##\rho## gives a complete account of the statistics of the ensemble of particles emitted by the source. The density matrix is Hermitian and positive semidefinite of trace 1, such that ##\langle A\rangle=\mbox{tr} \rho A## gives the mean response of a particle received in a detector measuring ##A##. In our particular case, the density matrix is given by ##\rho=\pmatrix{0.5 & 0\cr 0 &0.5}## since the thermal setting implies that no transversal direction is preferred. We say that the beam is unpolarized. (For the electron, see spin polarization.)

By passing the beam through various equipment (filters) we may prepare modified states. I am considering only perfect filters that project to a 1-dimensional subspace in direction of a normalized state vector ##\phi##, which is adjustable by the experimenter. Such a filter can be realized for photons (type X=P) by a polarizer, and for electrons (X=E) by deflecting the beam by a magnet and passing the two resulting daughter beams through a slit that absorbs the electrons in one of the daughter beams.

If we denote by ##P=\phi\phi^*## the associated orthogonal projector, the effect on the filtering is that particles pass the filter with a probability of ##\langle P\rangle=\mbox{tr} \rho P =\phi^*\rho\phi##, and the density matrix of the ensemble of particles that passed the beam is ##P=\phi\phi^*##. This corresponds to a pure state, and implies that the modified beam is completely polarized, with polarization (if X=P) resp. spin direction (if X=E) determined by the filter setting.

The above is the shut-up-and-calculate description of the experiment. It only refers to macroscopic objects and to properties that can be directly checked by statistical measurements. The latter consist of counting sufficiently many detection events of a particle counter placed after the filter, using enough filter vectors ##\phi## to be able to determine the density matrix of an arbitrary beam.

I'd like to know what some interpretations of quantum mechanics assert about states and observables of individual particles and about which properties they are silent,

• (a) direcly after emission,
  
• (b) directly after having passed the filter,
  
• (c) directly after having been measured.

In particular, I invite the currently most outspoken proponents on PF of three interpretations (minimal ensemble, @vanhees71; Copenhagen, @atyy; Bohmian, @Demystifier) to state their views about individual particles regarding the above experimental setting.

 

[vanhees71]

Well, I've the most simple task, because you've already answered it for me in your question! I only strongly disagree in principle with the claim that you can ignore the space-time part of the quantum fields, but for this matter-of-principle discussion it's enough.

So you say, you have a thermal source, which means you are in thermal equilibrium. That implies that the statistical operator to use is the one of maximum von Neumann entropy (because that's the definition of "thermal source" in this theory context). The Hilbert space is then simply the unitary space in 2 dimensions. That means in both cases your density matrix is indeed ##\hat{\rho}=1/2 \mathbb{1}_2## (to write it in my private notation, which I find pretty clear).

Now let ##|a \rangle## be the normalized eigenbasis of the polarization/spin in the measured direction. Then
$$P(a)=\langle a|\hat{\rho}|a \rangle=\mathrm{Tr} (\hat{\rho} |a \rangle \langle a|)$$
is the probability to measure the polarization/spin to take the value ##a##.

There's no other content in the formalism of quantum theory. That's all you can say about the system given the state it is prepared in. The claim that it is in this state can only be proven by measuring a complete set of compatible observables of a (sufficiently large) ensemble.

 

[A. Neumaier]

your density matrix is indeed ##\hat{\rho}=1/2 \mathbb{1}_2## (to write it in my private notation, which I find pretty clear).

I find it confusing. Could you please explain? Ah, from the latex I see that you mean half the identity matrix of size 2. But MathJax converts it to something incomprehensible...

 

[vanhees71]

I don't understand. It's just a convenient notation. It's ##\mathbb{1}_2## is the identity operator in 2D complex vector space.

 

[A. Neumaier]

I don't understand. It's just a convenient notation. It's ##\mathbb{1}_2## is the identity operator in 2D complex vector space.

Next time you'd do some extra formatting. ##\frac12 \cdot{\bf 1}_2## reads much better than ##1/2\mathbb{1}_2##.

 

[vanhees71]

I don't know, why black-board fonts don't work. Sorry for the confusion.

 

[A. Neumaier]

There's no other content in the formalism of quantum theory.

So you no longer want to assert anything about the state of the individual particles in the ensemble, as in another recent thread (can't find the precise post anymore)?

 

[vanhees71]

Of course, still the physical definition of state must be operative. The formalized way to express this is to say that a state is defined by a preparation procedure (or more precisely an equivalence class of preparation procedures). An operation precedure of course must refer to a single system, and you have to demand that you can repeat this procedure arbitrarily often in the same way to prepare as large an ensemble of independently (i.e., uncorrelatedly) prepared systems.

"Preparation" can be very simple. E.g., to define the equilibrium state of the various ensembles (microcanonical, canonical, grand canonical) you simply have to take a (closed, to a heat bath coupled, and to a heat-particle bath coupled) system and wait long enough until the system becomes stationary in the appropriate macroscopic observables. Other preparations can be quite complicated and subtle, e.g., to prepare a single-photon state you need, e.g., a laser and parametric-down-conversion material like certain birefringent crystals.

What I was referring to is the pure meaning of the various notions of the formalism. Of course you have to fill the words "the system is prepared in a state described by the Stat. Op. ##\hat{\rho}##" and "measuring an observable ##O##, represented by a self-adjoint operator ##\hat{O}##" with physical meaning. As in classical physics, I leave this to the experimentalists. As a theorist I can just take it for granted that a clever enough experimentalist can define a preparation procedure for the state and a measuring device to measure the observable(s) in question.

The meaning of "state" is purely probabilistic and given by the Born rule, which implies FAPP that the state refers to ensembles only since probabilities can be determined only on a large ensemble. Thus the claim that the system is prepared in a state described by ##\hat{\rho}## must verify at least the probabilities for a complete set of compatible observables. A detailed discussion about how to completely determine a state through measurements is given in Ballentines textbook.

 

[A. Neumaier]

So you no longer want to assert anything about the state of the individual particles

the claim that the system is prepared in a state described by ##\hat{\rho}## must verify at least the probabilities for a complete set of compatible observables. An operation precedure of course must refer to a single system.

In the present case, the preparation procedure is completely describe by saying that the source is stationary and thermal, so that the state is ##\frac12 \cdot{\bf 1}_2##. This can be checked independent of the particular source [you can buy a black box source with the properties claimed, and check them in this way] by measuring (in random, sufficiently long time intervals) the detection rate with the filter in four arbitrary random (or appropriately chosen) directions [so that their projectors form a complete system of Hermitian operators] and verifying that within the statistical error, the detection rates agree. No reference to the single system is necessary in this preparation and calibration procedure.

 

[Demystifier]

In particular, I invite the currently most outspoken proponents on PF of three interpretations (minimal ensemble, @vanhees71; Copenhagen, @atyy; Bohmian, @Demystifier) to state their views about individual particles regarding the above experimental setting.

Can you be more specific why are you interested in the Bohmian interpretation in this particular case? Do you suspect that there might be some particular problem with the Bohmian interpretation in this case?

 

[A. Neumaier]

Can you be more specific why are you interested in the Bohmian interpretation in this particular case?

The motivation for starting this thread came from reading an old paper by U. Fano, Description of states in quantum mechanics by density matrix and operator techniques, Reviews of Modern Physics 29 (1957), 74.

The whole treatment of quantum-mechanical problems in terms of density matrices can thereby reflect the features of physical phenomena more directly and in closer correspondence to macroscopic methods than is otherwise possible.

(''thereby'' refers to that the density matrix is well handled by operator techniques.)

The particular setting described is just the simplest nontrivial case where density matrices appear. (Fano also considers a number of more complex examples, among them - in 1957, long before Bell! - coincidence polarization measurements on thermal entangled photon pairs from positron annihilation.) That the setting is not described by a pure state gives all interpretations an extra twist with respect to the relation between the single system and the ensemble. I think it is an excellent example for comparing interpretations without yet having to deal with more sophisticated instances of quantum weirdness.

Do you suspect that there might be some particular problem with the Bohmian interpretation in this case?

Possibly yes since position seems to be irrelevant in the above setting - it is not even represented in the state, which factors with respect to all variables except for polarization/spin. But in the Bohmian interpretation, position plays a distinguished role. Thus I wonder to which extent the interpretation is different for electrons (where a position operator exists) and for photons (where it doesn't exist). Also I haven't studied the Bohmian take on mixtures, so I'd learn something new. (In this thread, I don't want to be aggressively critical, and will only ask questions that help clarifying the claims.)

 

[vanhees71]

In the present case, the preparation procedure is completely describe by saying that the source is stationary and thermal, so that the state is ##\frac12 \cdot{\bf 1}_2##. This can be checked independent of the particular source [you can buy a black box source with the properties claimed, and check them in this way] by measuring (in random, sufficiently long time intervals) the detection rate with the filter in four arbitrary random (or appropriately chosen) directions [so that their projectors form a complete system of Hermitian operators] and verifying that within the statistical error, the detection rates agree. No reference to the single system is necessary in this preparation and calibration procedure.

I disagree. You have to assume that a specific preparation of your black box leads to a well determined state. In this case it's an equilibrium state and you can verify this as you said on an ensemble. If you don't assume this, the state definition doesn't make physics sense in any interpretation!

A nice example are ultrarelativistic heavy-ion collisions. The claim is that the particle abundancies follow that of a (grand-)canonical ensemble. This is verified by measuring particle abundancies in a lot of single collisions and average over them. Then you can check the particle ratios by fitting to a grand canonical ensemble leading to a temperature, baryo-chemical potential, and volume of the fireball at chemical freeze-out. This works amazingly well, and thus one concludes that the fireball chemically freeze out close to the pseudocritical temperature for the confinement-deconfinement cross over transition as calculated from lattice QCD. At the LHC the baryo-chemical potenial is very small.

 

[A. Neumaier]

You have to assume that a specific preparation of your black box leads to a well determined state. In this case it's an equilibrium state and you can verify this as you said on an ensemble.

Suppose that the instruction sheet asserts that, after switching on the source, setting the intensity to a given level, and waiting for 5 minutes, it will produce thermal particles at this rate. The manufacturer may have needed to make assumptions to model his source design to ensure that it works as described.

But users don't need any assumptions: They can check by proceeding according to the instructions, and test the resulting output beam according to the recipe given in my post #9. If it works as predicted the users can be confident that the source produces a stream of thermal particles as claimed; if not they can complain in the shop where they bought the source. Or they correct the description given in the instruction sheet by noting the state reconstructed from the measurements, and its deviations from stationarity, thus calibrating the source behavior. No reference to any property of the particles is needed to verify any claim about the state of a particular preparation of a sufficiently stationary source, only references to control settings and to detection events. Indeed, this is the reason why the minimal interpretation works!

This also holds for your more complex example, and for anything done in the labs.

 

[Demystifier]

Possibly yes since position seems to be irrelevant in the above setting - it is not even represented in the state, which factors with respect to all variables except for polarization/spin. But in the Bohmian interpretation, position plays a distinguished role.

The reason why Bohmian interpretation works for measurement of any observable is the fact that any measurement eventually reduces to an observation of a position. For example, in the Stern-Gerlach "measurement of spin", what you really observe is the position of the detector which "clicks".

Thus I wonder to which extent the interpretation is different for electrons (where a position operator exists) and for photons (where it doesn't exist).

There is no much difference in practice, as long as the macroscopic detector is made of atoms. You don't observe the position of the photon, you observe the position of some macroscopic pointer made of atoms.

But still, in a Bohmian interpretation you may want to calculate the photon trajectories, even if you don't observe them. Unfortunately, photons are relativistic and there is no unique relativistic Bohmian mechanics. In the simplest version one introduces a preferred Lorentz frame, which, among other things, allows you to define a Lorentz non-invariant photon position-operator. This means that the interpretation will depend on the choice of the preferred frame, but it can be shown that measurable predictions do not depend on it.

Also I haven't studied the Bohmian take on mixtures, so I'd learn something new.

Bohmian mechanics always takes a view that the full closed system is in a pure state, even if an open subsystem is in a mixed state.

(In this thread, I don't want to be aggressively critical, and will only ask questions that help clarifying the claims.)

Good!

 

[A. Neumaier]

Bohmian mechanics always takes a view that the full closed system is in a pure state, even if a open subsystem is in a mixed state.

Ok. So what are the properties that Bohmian mechanics claims in my setting about the state or the polarization/spin of the single particles (rather than the full closed system), at the points (a), (b), (c) of post #1?

 

[Demystifier]

Ok. So what are the properties that Bohmian mechanics claims in my setting about the state or the polarization/spin of the single particles (rather than the full closed system), at the points (a), (b), (c) of post #1?

It claims the following:
- At each point, the particle has a well defined position and velocity. Yet, in the absence of full information about the full closed system, this position and velocity cannot be precisely calculated.
- The particle does not have polarization/spin at any point. Polarization/spin is a property of the wave function, not of the particle.

 

[vanhees71]

Suppose that the instruction sheet asserts that, after switching the source on, setting the intensity to a given level, and waiting for 5 minutes, it will produce thermal particles at this rate. The manufacturer may have needed to make assumptions to model his source design to ensure that it works as described.

But users don't need any assumptions: They can check by proceeding according to the instructions, and test the resulting output beam according to the recipe given in my post #9. If it works as predicted the users can be confident that the source produces a stream of thermal particles as claimed; if not they can complain in the shop where they bought the source. Or they correct the description given in the instruction sheet by noting the state reconstructed from the measurements, and its deviations from stationarity, thus calibrating the source behavior. No reference to any property of the particles is needed to verify any claim about the state of a particular preparation of a sufficiently stationary source, only references to control settings and to detection events. Indeed, this is the reason why the minimal interpretation works!

This also holds for your more complex example, and for anything done in the labs.

Sure, but the point is that you claim that the state is not associated to a single system but only to the ensemble, but that's a contractio in adjecto, because if the state is not associated to the single systems that make up an ensemble, it can also not be assiciated to this ensemble as a whole, because by definition the preparation of the single systems making up the ensemble must be independent.

 

[A. Neumaier]

Sure, but the point is that you claim that the state is not associated to a single system but only to the ensemble, but that's a contractio in adjecto, because if the state is not associated to the single systems that make up an ensemble, it can also not be associated to this ensemble as a whole, because by definition the preparation of the single systems making up the ensemble must be independent.

Well, I actually associate the state to the beam; talking about particles and ensembles in addition to the beam was just a concession to tradition. To phrase it without this concession:

We prepare the stationary light beam or electron beam (i.e., whatever leaves the source under discussion), observe sufficiently many macroscopic detection events in dependence on the filter setting, calculate from it the appropriate statistics, compare it with the shut-up-and-calculate predictions, and find agreement with each other within the statistical uncertainty. Thus all physics is preserved!

This is much more minimal than what you like to call the minimal interpretation! Neither the ensemble nor the particles, nor any independence assumption plays any role in the experimental setting or its analysis, except to color the intuitive picture. By Ockham's razor, one can eliminate them completely from the language, without impairing the shut-up-and-calculate part and the comparison with the detection statistics!

 

[vanhees71]

If you take the electron beam as a whole, you are right. Then you take the entire ensemble as one preparation. I don't see any difference between your and my interpretation then. It's just semantics.

The independence assumption is crucial. There is a difference between an ensemble of equally prepared single systems, which is by definition prepared such that there are no correlations between the single preparations, and preparing one big many-body system, which may contain correlations. The latter represents a different state than the single particle state you like to investigate with your preparation of an ensemble for this single-particle state. This is part of any proper definition of statistics for empirically checking probabilistic assertions (within the frequentist interpretation of probabilities).

This is the whole point of some of the loopholes in Bell experiments. E.g., sometimes the experimenters want to demonstrate the correlations in entangled far-distant entities and exclude the possibility that any classical (perhaps non-local) information can cause the corresponding correlations in randomly choosing what to measure (e.g., the direction of a polarization measurement on a photon) very close before detection, so that there's no signal between the measurements at the far distant places possible (provided that relatistic causality holds true). This, however, is not so simple, because you cannot exclude the possibility that the "random-number generators" (which can be quantum systems themselves) used to make the "random choice" of the measured observable are somehow correlated (although it's very unlikely).

 

[A. Neumaier]

There is a difference between an ensemble of equally prepared single systems, which is by definition prepared such that there are no correlations between the single preparations, and preparing one big many-body system,

Of course, since these are described by different states. Thus given the complete state, the degree of independence is encoded in it and needs no additional specification. Thus it seems we have reached complete agreement?

 

[vanhees71]

I guess so :-).

 

[A. Neumaier]

I am still hoping for atyy or someone else to address what the Copenhagen interpretation says in the context of my post #1.
In particular, since pure states play a distinguished role in the Copenhagen interpretation, I'd like to know whether each individual particle is in a pure state after leaving the source? How is this state assigned or tested?

1) The ensemble interpretation when done correctly is not different from Copenhagen where probability is given a frequentist interpretation, hence there is no difference (except terminology, where one would use terms like "sub-ensemble" instead of assigning a state to an individual system).

2) In all forms of Copenhagen, where there is only a single measurement (instead of a sequence of measurements), wave function collapse is not needed.

Is the filter a measurement in the sense of your version of the Copenhagen interpretation? If so, what does your version of the Copenhagen interpretation assert about state and properties of the single particle in the three cases (a), (b), (c)? If not, what happens to the state of a particle when passing the filter?

 

[Demystifier]

I am still hoping for atyy or someone else to address what the Copenhagen interpretation says in the context of my post #1.
In particular, since pure states play a distinguished role in the Copenhagen interpretation, I'd like to know whether each individual particle is in a pure state after leaving the source? How is this state assigned or tested?

Is the filter a measurement in the sense of your version of the Copenhagen interpretation? If so, what does your version of the Copenhagen interpretation assert about state and properties of the single particle in the three cases (a), (b), (c)? If not, what happens to the state of a particle when passing the filter?

I think you should be more specific about what exactly do you mean by "Copenhagen interpretation" (CI), as there are several very different versions of it
https://www.physicsforums.com/threads/there-is-no-copenhagen-interpretation-of-qm.332269/
and answers to your questions may be different in different versions of CI.

 

[vanhees71]

I am still hoping for atyy or someone else to address what the Copenhagen interpretation says in the context of my post #1.
In particular, since pure states play a distinguished role in the Copenhagen interpretation, I'd like to know whether each individual particle is in a pure state after leaving the source? How is this state assigned or tested?

Please, define what you mean by "Copenhagen Interpretation". The whole trouble with interpretation starts in Copenhagen and Bohr's habit to mumble about philosophy rather than physics. If you want to have QT presented as weird as possible, read his papers ;-)). Try to understand, what "complementarity" means and in which way it helps to describe nature. That's Bohr's key idea concerning the interpretation problem, but for me it's not clear, what this idea is good for. Fortunately, from the very beginning there were the great no-nonsense physicists in the early days, boiling down QT to a great mathematical tool to describe an amazingly comprehensive part of nature (today, the only great problem left to be solved is a consistent description of gravity in terms of QT): Born, Dirac, Sommerfeld, Pauli to mention just a view.

Then for quite a while any interperational issue was rejected from the physics discussion. On the one hand that was for a good reason: Instead of getting stuck in unsolvable metaphysical and philosophical issues, which are quite irrelevant for physics itself, people concentrated on the application of quantum theory to real-world problems and the understanding of empirical facts.

On the other hand, for many people QT had (and oviously for some still has) unsatisfactory open issues concerning its interpretation, and with Bell's reformulation of a rather metaphysical and hitherto untestable assumptions (like in the famous EPR paper; read Bohr's response to it as an example for a completely incomprehensible text of the Copenhagen gang) to a physics prediction of any local deterministic (hidden-variable) theory testable against the predictions of quantum theory. All experiments so far, including all kinds of high-precision Bell tests with entangled photons, atoms, confirm the predictions of quantum theory. Nowhere is anything else needed than the standard postulates, including Born's rule, to describe the outcome of these measurements. So any Copenhagen esoterics beyond the minimal interpretation is totally unnecessary. Taking out the collapse hypothesis from the Copenhagen interpretation, you are pretty close at the minimal interpretation. In my opinion, there is not the slightest evidence for the reality of any collapse-like dynamics whatsoever!

 

[A. Neumaier]

I think you should be more specific about what exactly do you mean by "Copenhagen interpretation" (CI), as there are several very different versions of it
https://www.physicsforums.com/threads/there-is-no-copenhagen-interpretation-of-qm.332269/
and answers to your questions may be different in different versions of CI.

Please, define what you mean by "Copenhagen Interpretation".

For the purpose of this experiment (where the systems prepared are single particles], a Copenhagen interpretation is one that assigns a state vector to each single particle, and declares this state vector to be the complete description of its properties. (In general, replace ''particle'' by ''observed system''.)

If here on PF there are proponents of different versions of the Copenhagen interpretation, or of versions that do not conform to my description of it, they are welcome to state their different points of view if they differ in the analysis of the particular experimental setting in post #1.

 

[Demystifier]

For me, a Copenhagen interpretation is one that assigns a state vector to each single particle, and declares this state vector to be the complete description of its properties.

A state vector can be assigned to each single particle only after the measurement, not before the measurement. There is no variant of Copenhagen interpretation which assigns a state vector to each of the entangled photons before measurement. With that being said, the definition of the Copenhagen interpretation is still not unique.

 

[vanhees71]

For me, a Copenhagen interpretation is one that assigns a state vector to each single particle, and declares this state vector to be the complete description of its properties.

If here on PF there are proponents of different versions of the Copenhagen interpretation, or of versions that do not conform to my description of it, they are welcome to state their different points of view if they differ in the analysis of the particular experimental setting in post #1.

Well if so defined, then I'm a proponent of Copenhagen ;-)). For me Copenhagen is more or less defined as Bohr's point of view, and that's part of the problem, because it's very hard to know, what Bohr really thought because of his notorious "unsharp" writing style. Anyway, as far as I understand, it's not too far from the minimal interpretation with two important additions:

(a) State collapse: If an observable is measured accurately (and it is assumed that an observable can be measured accurately, because otherwise it's not an observable at all), then the state of the system instantaneously collapses into an eigenstate of the observable with the measured eigenvalue. This collapse is not described by any dynamical law and it's particularly outside of the dynamical laws of quantum theory.

The problem with this assumption is twofold: (i) it contradicts relativistic causality. An instantaneous collapse means the instantaneous change of the state in the entire universe due to a local measurement on a system. Particularly the correlations between entangled far-distant systems are instantaneously destroyed, which is a clear violation to the relativistic causality structure. (ii) it isn't true for very many sorts of measurements. E.g., a photon absorbed by a polarization foil is afterwards not in an eigenstate of the corresponding polarization but it's gone. The state of the system after the measurement, in my opinion, must be the subject of careful analysis of the individual measurement procedure. Almost always it is completely irrelevant FAPP anyway ;-).

(b) Quantum-classical cut: It is assumed that there is a quantum and a classical realm of validity. Particularly measurement apparati are working according to classical physics, as stressed by Bohr repeatedly.

The problem with this is that there's no way to say, how this "cut" is defined. Often it is claimed that it is simply the size of macroscopic objects, but that's contradicting the more an more refined possibilities to demonstrate quantum behavior on pretty large objects, e.g., C60 molecules ("buckyballs") can be used to demonstrate coherence effects in typical double-slit/grating experiments, even with partial and total destruction of interference due to decoherence through the emission of soft photons, depending on the temperature of the molecules (Zeilinger et al, if needed, I can try to find the citation) or entanglement of phonon states in macroscopic diamonds, recently discussed in this forum. It also contradicts the postulate cited by Arnold above that the state vector (imho not only for single particles but for any single- or many-particle system) is the most complete description of the system possible, and I think this is part of any interpretation of quantum theory, including Bohr's.

Of course, the claim that a physical theory is "complete" is always quite an empty statement, because it is true as long as no observations contradict it. So far there's no contradiction to QT (in the minimal interpretation) and thus we don't know, in which sense it might become "incomplete". IMHO any physical theory is incomplete, and QT for sure too, because there's no satisfactory QT-compatible description of gravity yet.

 

[A. Neumaier]

In my opinion, there is not the slightest evidence for the reality of any collapse-like dynamics whatsoever!

What do you make of the following papers?

http://arxiv.org/abs/1009.2969
R Vijay, DH Slichter, I Siddiqi 2011
Observation of quantum jumps in a superconducting artificial atom

http://arxiv.org/abs/1310.8529
A Delteil et al. 2014
Observation of quantum jumps of a single quantum dot spin using submicrosecond single-shot optical readout

http://arxiv.org/abs/1110.0069
HM Wiseman, JM Gambetta 2012
Are dynamical quantum jumps detector dependent?

http://www.physi.uni-heidelberg.de/~schmiedm/seminar/QuPhys2001/QuJumps/nagourney.pdf
W Nagourney, J Sandberg, H Dehmelt 1986
Shelved optical electron amplifier: Observation of quantum jumps

http://www.nature.com/nature/journal/v446/n7133/full/nature05589.html
S Gleyzes et al. - Nature 2007
Quantum jumps of light recording the birth and death of a photon in a cavity

http://www.nature.com/nature/journal/v373/n6510/abs/373132a0.html
T Basche et al. - Nature 1995
Direct spectroscopic observation of quantum jumps of a single molecule

 

[A. Neumaier]

A state vector can be assigned to each single particle only after the measurement, not before the measurement. There is no variant of Copenhagen interpretation which assigns a state vector to each of the entangled photons before measurement.

My experiment doesn't involve entangled photons - just single photons. For a composite system, one must of course replace in my definition of the Copenhagen interpretation ''particle'' by ''observed system''. Also, I defined ''a copenhagen interpretation'', not ''the Copenhagen interpretation'', leaving room for variations.

 

[vanhees71]

Wow, I've to read a lot over the weekend :-). Perhaps you can help with this effort: Is there anywhere in those papers a clear contradiction to the dynamics of quantum theory, i.e., can any of these groups, claiming to observe quantum jumps (in my opinion a clear contradiction to the basic principles of quantum theory, because there's nothing jumping at all in the dynamical equations of QT, which are all (operator valued) differential equations) or "a collapse" prove with certainty that standard quantum dynamics (including the interaction of the system with the used measurement devices!) is invalid? If so, I wonder that they didn't declare the invalidity of quantum theory, which would be a pretty certain ticket to Stockholm!

 

[Demystifier]

I am still hoping for atyy or someone else to address what the Copenhagen interpretation says in the context of my post #1.
In particular, since pure states play a distinguished role in the Copenhagen interpretation, I'd like to know whether each individual particle is in a pure state after leaving the source? How is this state assigned or tested?

Is the filter a measurement in the sense of your version of the Copenhagen interpretation? If so, what does your version of the Copenhagen interpretation assert about state and properties of the single particle in the three cases (a), (b), (c)? If not, what happens to the state of a particle when passing the filter?

The only version of Copenhagen which answers "what happens" type of questions is the collapse interpretation. So here I will use this version (vanhees71, please don't read it!).

Still, we have two different versions. In one version, collapse happens only when a conscious observer observes. In another version, collapse happens whenever interaction with a macroscopic apparatus takes place. For definiteness, I will use the latter version.

So here is what happens according to this version of CI:
(a) At the moment of emission, wave function collapses into a state with a definite spin in some random direction.
(b) At the filter the wave function is either destroyed (which can also be thought of as a kind of collapse) or collapses into a state with a definite spin in the direction defined by the filter.
(c) At the measurement the wave function is destroyed (provided that it was not already destroyed at the filter) and the measuring apparatus collapses into a state of a definite outcome of spin measurement.

 

[A. Neumaier]

Wow, I've to read a lot over the weekend :-). Perhaps you can help with this effort: Is there anywhere in those papers a clear contradiction to the dynamics of quantum theory, i.e., can any of these groups, claiming to observe quantum jumps (in my opinion a clear contradiction to the basic principles of quantum theory, because there's nothing jumping at all in the dynamical equations of QT, which are all (operator valued) differential equations) or "a collapse" prove with certainty that standard quantum dynamics (including the interaction of the system with the used measurement devices!) is invalid? If so, I wonder that they didn't declare the invalidity of quantum theory, which would be a pretty certain ticket to Stockholm!

Of course the quantum jumps are due to the interaction with the measurement device, consistent with the collapse, which only happens when passing an instrument. In every interpretation, no interaction with the environment means nothing that can be measured by an observer sitting in the environment, hence unitary evolution. But if one considers the interaction with the environment and traces out its influence in a dynamical way one ends up (in the Markov approximation) with an approximate dynamics that is stochastic and dissipative and gives, under the appropriate conditions, rise to directly observable quantum jumps.

Thus there is no contradiction to shut-up-and-calculate (which leaves a lot of freedom how to relate the calculations to experiment), and everything is consistent with QM as I understand it. But since everyone has a slighly different personal understanding, and since everyone adds to the outspoken assumptions extra ad hoc twists whenever needed to interpret shut-up-and-calculate in an actual experimental settings, I do not dare to speak for everyone. You need to make up your own mind.

 

[A. Neumaier]

So here is what happens according to this version of CI:
(a) At the moment of emission, wave function collapses into a state with a definite spin in some random direction.
(b) At the filter the wave function is either destroyed (which can also be thought of as a kind of collapse) or collapses into a state with a definite spin in the direction defined by the filter.
(c) At the measurement the wave function is destroyed (provided that it was not already destroyed at the filter) and the measuring apparatus collapses into a state of a definite outcome of spin measurement.

Thanks. Can you please clarify a detail in (b)? When happens one or the other of your description? Randomly with probability ##\langle P\rangle=\mbox{tr} \rho P =\phi^*\rho\phi##?

 

[Demystifier]

Thanks. Can you please clarify a detail in (b)? When happens one or the other of your description? Randomly with probability ##\langle P\rangle=\mbox{tr} \rho P =\phi^*\rho\phi##?

Yes, of course.

EDIT: When I was talking about destruction, I assumed that the particles were photons. Now I have noted that you asked about electrons. Electrons are not destroyed, but absorbed without destruction. The rest is the same.

 

[A. Neumaier]

Yes, of course.

This cannot be quite correct since the particle no longer knows that it was prepared in a mixed state since it collapsed already to some pure state ##\psi##. According to Born's rule, the probability should depend only on ##\psi## but the observed statistics should still be that predicted by the mixed state...