High School Where does a quantum experiment *begin*?

[vanhees71]

Yes, gauge ghosts are just a tool, just a formal trick. But my point is that so is the collapse.

But what is a trick good for that only causes the theory to be contradicting itself?

 

[Demystifier]

But what is a trick good for that only causes the theory to be contradicting itself?

Suppose that before measurement the system is described by the state
$$|\psi>=c_1|\psi_1> + c_2|\psi_2>$$
where $|\psi_1>$ and $|\psi_2>$ are eigenstates of some observable $A$ that will be measured, with eigenvalues $a_1$ and $a_2$, respectively. Suppose that I perform a projective measurement of $A$ and that I find out that the result of measurement is $a_1$. Then it is a consequence of minimal ensemble interpretation that, after the measurement, I can make further statistical predictions by describing the system with a new state
$$|\psi_1>$$
In this sense, my acquire of knew knowledge induced a transition
$$|\psi> \rightarrow |\psi_1>$$
This transition is not a physical process in the measured system. (If this is a physical process at all, then it is only a process in my head, or a process at a peace of paper or computer screen, where I note changes about my current knowledge.)

For some reason this transition is called "collapse". Yes, the name can be misleading, but so can be the name "ghost".

And I don't see any contradiction. Moreover the trick is useful because it's simpler to make further predictions by using only $|\psi_1>$ instead of the full superposition $|\psi>$.

Moreover, if you insist on not using a collapse, then making predictions requires more effort, which leads to a risk of making wrong predictions. For instance, Ballentine in his book made a wrong prediction that quantum Zeno effect does not exist. In reality it does; it is measured. The effect can also be explained without collapse but then it's not so simple, which is why Ballentine made a mistake. The collapse makes it simpler, which is why it's useful.

 

[vanhees71]

So, you don't need a collapse either. What you describe is a preparation process by filtering a la von Neumann. Nowhere is there the slightest hint for a nonlocal interaction as invoked implicitly by the collapse interpretation. I don't see, why your description is more complicated than invoking the collapse. It's even more simple!

 

[Demystifier]

So, you don't need a collapse either. What you describe is a preparation process by filtering a la von Neumann. Nowhere is there the slightest hint for a nonlocal interaction as invoked implicitly by the collapse interpretation. I don't see, why your description is more complicated than invoking the collapse. It's even more simple!

I think you still don't get my point. There are two meanings of the word "collapse". One is a controversial interpretation, while another is a non-controversial tool. One requires a nonlocal interaction, while the other doesn't. One contradicts minimal ensemble interpretation, while the other can be derived from minimal ensemble interpretation. One talks about ontology, while the other talks about epistemology. And yet they are both called "collapse", which is the source of confusion (for instance, Ballentine failed to see the difference). I am invoking the latter type of collapse, and rejecting the former.

Another important point: By invoking only the non-controversial epistemic collapse, or even by not invoking any kind of collapse at all, one does not remove a need for non-locality. The Bell theorem proves that some kind of non-locality is unavoidable under much wider conditions.

 

[vanhees71]

There are no non-local interactions there are only long-range correlations! The former are incompatible the latter are compatible with local relativistic QFTs. So you should not simply say "non-locality" but clearly state what you mean (interactions vs. correlations). Same with collapse: If it's an ill-defined notion, don't use it!

 

[Demystifier]

There are no non-local interactions there are only long-range correlations!

In science (not only in quantum physics), correlations are what we observe. But we never observe interactions! Interactions are only a theoretical tool for explanation and prediction of correlations. (See also my new signature!) The measured correlations may be compatible with a theory of interactions, but we never measure interactions as such.

So, what do you mean by "there are no non-local interactions"? If you mean "they are not observed", then there are no any interactions, not only non-local ones. But if you mean "there is no theory of non-local interactions", then I say there are several such theories (Bohmian mechanics being one of them).

The former are incompatible the latter are compatible with local relativistic QFTs.

Yes, but QFT is only a theoretical tool. (My new signature again!) Another tool (say, an appropriate version of Bohmian mechanics) can have the same measurable predictions (correlations) as local relativistic QFT and yet involve non-local interactions.

So you should not simply say "non-locality" but clearly state what you mean (interactions vs. correlations).

Fine, I mean interactions.

Same with collapse: If it's an ill-defined notion, don't use it!

Fine, I think I well defined it in the post #32, and I often use it.

 

[vanhees71]

Let's forget about the "collapse". We'll never come to an agreement. I don't use it.

On the correlations vs. interactions. The interactions in usual relativistic local QFT (I don't discuss Bohmian mechanics, because I'm not aware of a working version for relativistic QFT). There, by construction, the interactions are local. So if you make an Aspect-Zeilinger like experiment with polarization-entangled photons the interaction of A's photon with her polarizer and photo detector are local, i.e., there is no faster-than-light propagating signal to B's polarizer+detector. Still A and B will find the 100% correlation of their photons' polarization although the single photons are maximally uncertain concerning their polarization (i.e., the polarization of each single photon is described by the statistical operator $\mathbb{1}/2$). These correlations are caused by the preparation of the biphoton in the polarization-entangled state and not due a faster-than-light influence of A's on B's experimental setup. For me, this is the only description that is compatible with the very foundation of relativistic local QFT, which particularly excludes nonlocal interaction by assumption/construction.

 

[Demystifier]

These correlations are caused by the preparation of the biphoton in the polarization-entangled state and not due a faster-than-light influence of A's on B's experimental setup.

I think you are missing the content of contextuality theorems for quantum mechanics. The theorems prove that QM is contextual, i.e. that measured results cannot be explained only by preparation. Instead, the experimental setups for final measurements also play a decisive rule. Even Ballentine discusses it in Secs. 20.6 and 20.7.

 

[atyy]

Thank you, this is what I was trying to articulate, the question of initial conditions. I was wondering if there is any difference in the prediction of the outcome (of, say, the double-slit experiment) if the quantum system we observe is modeled starting with pre-existing electrons flying towards the slits vs. starting with the process that heats up the filament and releases the electrons etc.

By prediction I mean things like how soon the interference pattern emerges, by some measure, or some other measurable outcomes. (And if I understand correctly, if we chose the initial conditions to be "electrons past either slit" such model wouldn't predict the interference pattern?)

It feels like the initial conditions are somehow the counterpart to the measurement, I'm trying to understand if it's true and relevant (and how, if it is).

Yes, there can be a difference - but there is never any observable difference, provided we include enough of the universe in the wave function.

 

[vanhees71]

Do you mean Kochen-Specker? Where do I contradict that? Of course, more importantly, where do you think relativistic QFT contradicts it?

 

[Demystifier]

Do you mean Kochen-Specker? Where do I contradict that?

Maybe I misunderstood you, but it seems to me that your sentence
"These correlations are caused by the preparation of the biphoton in the polarization-entangled state"
contradicts Kochen-Specker. According to Kochen-Specker, the preparation alone cannot be sufficient to cause correlations.

Of course, relativistic QFT does not contradict Kochen-Specker because relativistic QFT, in its minimal form, does not say what causes correlations. It only says that the correlations are there.

In fact, if one accepts minimal ensemble interpretation of QFT, then QFT says nothing about forces (either local or nonlocal) at all. Forces, by definition, happen between individual objects (particles, fields, etc), while minimal ensemble interpretation says nothing about individual objects. It only talks about (large) statistical ensembles.

 

[vanhees71]

What I meant is the most simple experiment, where I set A's and B's polarizers in perendicular directions with the biphoton in the state $|HV-VH \rangle$. Then you get 100% correlations (i.e., either both photons are registered or both are not, i.e., they are always perpendicularly polarized). Of course you get other correlations, particularly also ones that are violating Bell's inequality when measuring in other relative angles of the polarizers. Thus of course the correlations depend on which ones I measure, but were does this somehow violate Kochen-Specker (i.e., the noncontextuality of QT)?

 

[Demystifier]

What I meant is the most simple experiment, where I set A's and B's polarizers in perendicular directions with the biphoton in the state $|HV-VH \rangle$. Then you get 100% correlations (i.e., either both photons are registered or both are not, i.e., they are always perpendicularly polarized). Of course you get other correlations, particularly also ones that are violating Bell's inequality when measuring in other relative angles of the polarizers. Thus of course the correlations depend on which ones I measure, but were does this somehow violate Kochen-Specker (i.e., the noncontextuality of QT)?

With such a minimal formulation, you don't violate Kochen-Specker. Nor you contradict any other established fact, which is why the minimal ensemble interpretation (MEI) is so good. And so powerful.

Nevertheless, it's not perfect. In a sense, MEI works as a black box, and that's not what physicists want. Physicists like to think in terms of causes, forces, single physical systems, properties existing even when they are not measured, etc. But MEI does not provide any of such things. That's why there is no real physicist who uses only MEI and nothing but MEI. In reality, the way physicists think is always a mixture (often incoherent mixture) of MEI and something beyond MEI.

 

[atyy]

Quite simply, MEI as vanhees71 understands it does not work.

MEI has collapse. Only with collapse is it a proper black box.

 

[vanhees71]

There is no collapse as a physical process in MEI.

 

[atyy]

There is no collapse as a physical process in MEI.

There is no unitary evolution as a physical process in MEI.

 

[Demystifier]

You are both right, because
There are no physical processes at all in MEI.
This is so because statistical ensemble is not a physical object. It is, well, see my signature.

 

[vanhees71]

Well, a statistical ensemble is used all the time in HEP and nuclear physics. All the results from all accelerators in the history of this field till the newest toy, LHC@CERN have prepared "ensembles" many kinds of collision experiments (pp, pA, AA, eP, eA, $\mathrm{e}^+ \mathrm{e}^-$,...) and then use a lot of statistical analyses to measure cross sections of all kinds. The experimental test of all kinds of quantum-theoretical models (including the Standard Model) for such collisions make directly use of such "ensembles", i.e., of repetitions of equally prepared experiments all the time, and often you even hear the experimentalists lament: "We need more statistics!" which means nothing else than "We need larger ensembles!". It's true that in theory it's a "thinking tool" (invented by the pioneers of statistical mechanics, quite a while before the discovery of quantum theory!), but it's also present in the hands-on experiments in the labs around the world!

 

[atyy]

Well, a statistical ensemble is used all the time in HEP and nuclear physics. All the results from all accelerators in the history of this field till the newest toy, LHC@CERN have prepared "ensembles" many kinds of collision experiments (pp, pA, AA, eP, eA, $\mathrm{e}^+ \mathrm{e}^-$,...) and then use a lot of statistical analyses to measure cross sections of all kinds. The experimental test of all kinds of quantum-theoretical models (including the Standard Model) for such collisions make directly use of such "ensembles", i.e., of repetitions of equally prepared experiments all the time, and often you even hear the experimentalists lament: "We need more statistics!" which means nothing else than "We need larger ensembles!". It's true that in theory it's a "thinking tool" (invented by the pioneers of statistical mechanics, quite a while before the discovery of quantum theory!), but it's also present in the hands-on experiments in the labs around the world!

That's not the point. The point is you should not object to collapse unless you also object to unitary evolution.

 

[vanhees71]

This I don't understand. The unitary evolution (I guess you mean the dynamics) is part of the mathematical formalism of QT and as well experimentally confirmed as anything about QT. You cannot take unitary time evolution of states (statistical operators) and observables (representing operators) from QT without giving up QT as a whole, while the collapse postulate is contradicting the very foundations of physics and is not needed.

The point of controversy in the "interpretation question" is also not so much the dynamics but rather the interpretation of the states themselves, which in the standard theory is just Born's Law (no collapse necessary), i.e., the usual probabilistic content of the state. There is, however, nothing which makes a collapse postulate necessary. You just state that QT predicts probabilities for measurement given the preparation of the measured system (and preparation can be very crude, e.g., you describe a gas by the usual thermodynamical quantities like temperature, volume of the container, and density of conserved charges), which allows the association of a statistical operator to the system.

From this point of view, if you introduce a collapse into QT, you have to introduce it for the probabilities in classical statistical physics too. E.g., take a dice (thought of as a classical system) and you just say that the indeterminism of the outcome of throughing it comes from the unknown initial conditions, there will always be a clear and not a somehow "smeared" outcome. Nobody would come to the idea of a "collapse", i.e., it just turns up with a specific result, and throughing many times leads to an experimental test of the prediction of any theoretical probability. You can also envoke some theory behind how to postulate such probabilities like information theory a la Shannon and say that as long as you don't know anything about the dice you say each outcome will have a probability of 1/6 (maximum-entropy probability). Then you can do the experiment and confirm or refute the estimate of the probabilities with some confidence level given the experimental outcomes of your measured ensemble.

Where is the difference to QT? The only difference is that, according to the minimal interpretation, the observables that are not determined by the preparation, are "really random", i.e., they have indeed no determined value and not only because we don't know them. Then a lot of philosophical mumbling is done about, how it can be that one has a clear outcome of any proper measurement of such observables. My point is that this is due to the construction of the measurement device, which works with very good precision as a classical system, and classicality can be explained satisfactorily by quantum statistics and coarse graining. It's just the usual quantum theoretical dynamics ("unitary evolution") of this interaction, and this interaction is (according to the best QT we have, which is relativistic local QFT) local and thus there cannot be an instantaneous influence of a measurement at a position A to another far-distant measurement at position B, but that's what's postulated when "envoking" a collapse.

It's simply wrong to claim that there is "action at a distance" in the usual Aspect-like experiments. The interactions of the photons with the polarization measurement device (say a polarizer with a photodetector behind it) are local as any interaction described by QED. The only thing is the adaption of the probabilities when measuring the polarization by the experimenter taking notice of the result. Of course, the association of probabilities to a given situation depends on what's known. Say A finds her photon to be H-polarized. Then she knows that the entangled other photon of the pair measured by B will be V polarized. So after her measurement she associate 100% probability for B's photon to be V polarized, while B doesn't know that yet because he still just knows that his photon is unpolarized, i.e., he associate 50% probability for finding V.

You can also put this in the language of ensembles. A can sort out the photon pairs that are H-polarized. This will be an ensemble about half as large as the full ensemble. For this partial ensemble she knows that B's photon will be V-polarized. It's not very surprising that certain partial ensembles have a different probability than the full ensemble.

No matter how you look at it, within the minimal interpretation, A's knowledge about B's photon is due to the preparation of the photon pair as a polarization-entangled pair at the very beginning and not due to her measurement. You can also play this game with other setups of the polarization filters at A and B. Then of course, you don't have 100% correlation any more, if the relative angle between the polarizer orientations are not an integer multiple of $\pi/2$. Of course, the probabilities depend on what's measured, and there is no contradiction of assumptions of the minimal interpretation with Kochen-Specker. How could it? The Kochen-Specker theorem is a consequence of the formalism of QT and thus not dependent on which interpretation of this standard formalism you use.

 

[atyy]

This I don't understand. The unitary evolution (I guess you mean the dynamics) is part of the mathematical formalism of QT and as well experimentally confirmed as anything about QT. You cannot take unitary time evolution of states (statistical operators) and observables (representing operators) from QT without giving up QT as a whole, while the collapse postulate is contradicting the very foundations of physics and is not needed.

No, in fact the collapse is also part of the mathematical formalism of QT and is needed for mathematical consistency of QT.

The collapse is consistent with the very foundations of relativistic QT.

 

[vanhees71]

Ok, so what's for you the collapse? The collapse I learned in my QM1 lecture means, applied to the Aspect-type experiment with polarization-entangled photons, that at the moment A measured her photon's polarization to be H this measurement affects B's photon to get its polarization to be determined as V. This contradicts clearly the locality of interactions, which is the very foundation of relativistic QFT (or QED in this case).

If it's just the knowledge of A about B's photon's polarization due to the knowledge of the photon pair being prepared in the polarization-entangled state, that's of course just the statistical interpretation, but I'd not call this collapse, because collapse usually has the above "action-at-a-distance" meaning.

 

[Demystifier]

If it's just the knowledge of A about B's photon's polarization due to the knowledge of the photon pair being prepared in the polarization-entangled state, that's of course just the statistical interpretation, but I'd not call this collapse, because collapse usually has the above "action-at-a-distance" meaning.

But people still call this collapse. As I emphasized in one of previous posts, people use the word "collapse" for two different things.

Anyway, if you don't like to call this "collapse", how would you call it? Can we agree on some common name for that? How about "quantum-state update"?

 

[vanhees71]

I don't call it anything at all. Nobody calls it somehow in usual situations where probability and statistics is applied. So why should one give it an imprecise name leading to confusion?

 

[atyy]

Ok, so what's for you the collapse? The collapse I learned in my QM1 lecture means, applied to the Aspect-type experiment with polarization-entangled photons, that at the moment A measured her photon's polarization to be H this measurement affects B's photon to get its polarization to be determined as V. This contradicts clearly the locality of interactions, which is the very foundation of relativistic QFT (or QED in this case).

If it's just the knowledge of A about B's photon's polarization due to the knowledge of the photon pair being prepared in the polarization-entangled state, that's of course just the statistical interpretation, but I'd not call this collapse, because collapse usually has the above "action-at-a-distance" meaning.

There are two problems:

(1) Collapse is an update of the knowledge. In the standard interpretation, one is agnostic as to whether collapse is "physical" or not - the wave function itself is not a necessarily physical, so unitary evolution and collapse are also not necessarily physical. Unless I state otherwise, I use the standard interpretation - so it is you that is bringing in the "collapse is physical" interpretation, not me.

(2) Your reason for rejecting collapse as physical is wrong - no local physical theory is compatible with quantum mechanics.

 

[vanhees71]

Ad (1): The abstract quantum theoretical elements are all "not physical" in the sense that they are a description of phenomena, but that's semantics, because it's true for any mathematical theory, including classical mechanics. A point paricle is not a 6-tupel of real numbers (phase-space coordinates) in Newtonian mechanics either!

Ad (2): Local relativistic QFT, as formulated in any good textbook on the subject is by construction compatible with quantum theory (of course not with Schrödinger-like wave mechanics, which doesn't make sense for relativistically interacting particles), and it defines precisely what's meant by "local interaction": Interactions are described by Lagrangians that are polynomials of the fields and their derivatives; local observables commute for arguments at space-like distances. This implies causality and unitarity of the S-matrix, and thus is a sufficient (not necessarily necessary) condition for a relativistic QT.

 

[ShayanJ]

the wave function itself is not a necessarily physical

If wave-function is not physical and only represents our knowledge about the system, then Schrodinger equation describes the evolution of our knowledge. So, to describe the the evolution of our knowledge, we need the Hamiltonian of the system? Really? This...doesn't seem right!

 

[ddd123]

I haven't been able to find a QFT calculation of the EPR type gedanken experiment. Has it been done?

 

[Demystifier]

If wave-function is not physical and only represents our knowledge about the system, then Schrodinger equation describes the evolution of our knowledge. So, to describe the the evolution of our knowledge, we need the Hamiltonian of the system? Really? This...doesn't seem right!

Why not? Even classical mechanics can be formulated/interpreted such that Hamiltonian only describes the evolution of our knowledge. See e.g.
http://arxiv.org/abs/quant-ph/0505143

 

[Demystifier]

I don't call it anything at all. Nobody calls it somehow in usual situations where probability and statistics is applied. So why should one give it an imprecise name leading to confusion?

Well, when some concept is often used, I like to use a name for it. Names are also thinking tools (I like my new signature) which simplify thinking.

If, in some future discussion, I mention that "observation induces an update of quantum state", will you understand what I am talking about? Or will you object that this is wrong/misleading?