The phrase, predictions of quantum mechanics

[hiddenvariable]

The phrase, "predictions of quantum mechanics"

Reading Anton Zeilinger's book, Dance of the Photons, I see the phrase, "the predictions of quantum mechanics". It is used in the sense that those predictions are confirmed in regard to a series of measurements of entangled particles. When I hear that, am I hearing that the outcomes of the measurements confirm that for entangled particles, the specific quantum state of entanglement was not determined until the quantum state of one of the entangled pair was measured? If so, then do "the predictions of QM" say that there is non-locality in nature, and therefore no hidden variables can produce the same results predicted by quantum mechanics?

I apologize in advance for using the ID "hiddenvariable" which implies I have made a determination in favor of that interpretation :(. I am a simple layman trying to sort out QM, and don't claim to have enough understanding to take any informed position on the matter of interpretation.

 

[UltrafastPED]

All experiments to date are in agreement "with the predictions of QM"; when tested, Bell's inequalities are violated, which shows that "local, hidden variable" theories are incorrect.

Here is a good explanation: http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm

 

[hiddenvariable]

All experiments to date are in agreement "with the predictions of QM"; when tested, Bell's inequalities are violated, which shows that "local, hidden variable" theories are incorrect.

Here is a good explanation: http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm

I'll take some time and go over that link in detail, and you have confirmed my take on the meaning of the phrase.

Is the following statement form my post correct?

... am I hearing that the outcomes of the measurements confirm that for entangled particles, the specific quantum state of entanglement was not determined until the quantum state of one of the entangled pair was measured?

 

[meBigGuy]

When I hear that, am I hearing that the outcomes of the measurements confirm that for entangled particles, the specific quantum state of entanglement was not determined until the quantum state of one of the entangled pair was measured?

That sentence is confusing for me. Specifically the phrase "the specific quantum state of entanglement was not determined..." If particles are entangled, say for spin, then measuring one of the pair gives you information that the other particle will have complementary spin. That is, the measurements of the entangled property of entangled particles will always correlate. That is different than what you are saying, I think.

 

[UltrafastPED]

Sounds correct to me.

 

[hiddenvariable]

That sentence is confusing for me. Specifically the phrase "the specific quantum state of entanglement was not determined..." If particles are entangled, say for spin, then measuring one of the pair gives you information that the other particle will have complementary spin. That is, the measurements will alway correlate.

Understood, they will always correlate, but the distinction I am trying to understand is, does the measurement of one of the pair have a random outcome, and that random outcome then determines the state of the other particle? Or was the outcome of the measurement of the first particle already established back when entanglement occurred, and by making that measurement, the quantum state of both entangled particles is revealed?

 

[meBigGuy]

The former. There is no preferred orientation for the measurement of the first particle, it will always be random, either up or down. After the first measurement the second particle will be the opposite. The math says it works that way, and experiments confirm. Violation of Bell's inequality says this is the case.

It is not like you have a quarter in one hand and a nickel in the other. It more like you have both a nickel and quarter in each hand, the first reveals one or the other randomly and the second will always reveal the other.

 

[naima]

Contextual hidden variables are not ruled out. Take the output of a measurement it IS a hidden variable!
you have no access to it until the end of the measurement. it obeys QM rules.
and as it belongs to the block universe you may consider that it is an element of reality.
You may think that for each measurement there is a hidden future result. randomness seems less mysterious.

 

[kith]

Understood, they will always correlate, but the distinction I am trying to understand is, does the measurement of one of the pair have a random outcome, and that random outcome then determines the state of the other particle? Or was the outcome of the measurement of the first particle already established back when entanglement occurred, and by making that measurement, the quantum state of both entangled particles is revealed?

Both are possible, it depends on your favourite interpretation. Your second question gives a definition of "realism" similar to Einstein. Bell has shown that if you assume realism, your interpretation can't be local which means that you have physical effects in your interpretation which propagate faster than light (but cannot be used to transmit information). The de Broglie-Bohm interpretation is of this type. The quasi-standard interpretation of the Copenhagen school is non-realistic.There, the outcomes are not predetermined.

The term "the predictions of QM" refers to all facts which can be derived from the formalism and confirmed in experiment. It does not refer to how you interpret these facts. As indicated above, there's no consensus on how to do so, but some intuitive interpretations are ruled out because they are only compatible with some facts and not with other ones. Einstein's search for a local realistic interpretation or underlying theory for example is based on very intuitive assumptions but contradicts the experimental facts from Bell test experiments.

 

[hiddenvariable]

The former. There is no preferred orientation for the measurement of the first particle, it will always be random, either up or down. After the first measurement the second particle will be the opposite. The math says it works that way, and experiments confirm. Violation of Bell's inequality says this is the case.

Given those two states, either up or down, and given that it is unknown which of the two particles has which state, it seems logical to consider the first measurement to be a random choice between two possible states. And of course once the state of one particle is measured, the state of the other must be the other state. Is that what is meant by the first choice being random?

It is not like you have a quarter in one hand and a nickel in the other. It more like you have both a nickel and quarter in each hand, the first reveals one or the other randomly and the second will always reveal the other.

Are you referring to superposition of the two states? I take that to mean that we know we have two entangled particles, we know entanglement involves one being a quarter and one being a nickel, we don't know which is which until we measure the first one (that makes the first measurement random), and then after we measure the first particle's state we know the state of the other? Does that mean, according to the predictions of QM, that neither particle is in either state before we measure (the states are in superposition for both), and then when we measure the state of one, that measurement collapses the superposition of the second particle?

 

[hiddenvariable]

Both are possible, it depends on your favourite interpretation. Your second question gives a definition of "realism" similar to Einstein. Bell has shown that if you assume realism, your interpretation can't be local which means that you have physical effects in your interpretation which propagate faster than light (but cannot be used to transmit information). The de Broglie-Bohm interpretation is of this type. The quasi-standard interpretation of the Copenhagen school is non-realistic.There, the outcomes are not predetermined.

The term "the predictions of QM" refers to all facts which can be derived from the formalism and confirmed in experiment. It does not refer to how you interpret these facts. As indicated above, there's no consensus on how to do so, but some intuitive interpretations are ruled out because they are only compatible with some facts and not with other ones. Einstein's search for a local realistic interpretation or underlying theory for example is based on very intuitive assumptions but contradicts the experimental facts from Bell test experiments.

That description is consistent with what I get out of reading Zeilinger's "Dance of the Photons". Throughout the book, there are repeated statements like, "When one is measured, the state of the other is instantly influenced, no matter how far apart they are separated". The intuitive thinking is that each has its respective state like a pair of gloves, but which is right and which is left is undetermined until an observation is made, but that intuition seems to be exactly what the predictions of QM are arguing against.

 

[vanhees71]

Well, this is a flavor of the Copenhagen interpretation, where in addition to the minimal statistical interpretation a state collapse due to a measurement is postulated. In my opinion this is an unnecessary complication of the description of nature in terms of quantum theory since it is not necessary to apply the quantum-theoretical mathematical formalism to the real world and it explicitly violates Einstein causality. The minimal statistical interpretation serves its purpose as well as the collapse doctrine without its problems.

 

[hiddenvariable]

Well, this is a flavor of the Copenhagen interpretation, where in addition to the minimal statistical interpretation a state collapse due to a measurement is postulated. In my opinion this is an unnecessary complication of the description of nature in terms of quantum theory since it is not necessary to apply the quantum-theoretical mathematical formalism to the real world and it explicitly violates Einstein causality. The minimal statistical interpretation serves its purpose as well as the collapse doctrine without its problems.

If I understand you correctly, you refer to the minimal statistical interpretation which I take to mean doesn't invoke the collapse doctrine, plus the collapse doctrine when your refer to the flavor of the Copenhagen interpretation, i.e. the flavor of the Copenhagen interpretation is clearly non-local and instantaneous over distance, and precludes hidden variables? And if that is the case, you are acknowledging that there are interpretations that are more slanted to the statistical interpretation and less slanted toward the collapse doctrine?

 

[vanhees71]

I mean that the hypothesis of a state collapse as a physical process implies contradictions to Einstein causality given that the correlations predicted by quantum theory in terms of the entanglement of far distant particles or photons have been experimentally demonstrated with high accuracy. Assuming a state collapse as a physical process then implies that measuring some property at position A which is entangled with a property of an entangled subsystem at a far distant position B implies an instantaneous influence of the measurement at A on a physically measurable entity at position B, which clearly violates Einstein causality, according to which space-like separated events cannot be causally connected.

In the minimal statistical interpretation (also known as ensemble interpretation) the state describes our knowledge about the entire system due to a corresponding preparation process, and a local measurement at A simply changes our knowledge about the entire system. The state is not a physical entity but a description of our (statistical) knowledge about the entire system due to a preparation process. Thus when measuring some property at A simply leads to an adaption of the description of our knowledge but doesn't imply an instantaneous physical change at position B.

 

[hiddenvariable]

Vanhees71, that is helpful. Interestingly, it is beginning to fall into place with what Zeilinger is writing in "Dance ...". He does point out that the Copenhagen Interpretation most succinctly expresses the considerations, given of the specifics of the particular experimental settings.

If I am beginning to sort it out, our knowledge depends on what we measure, and those measurements, given the predictions of QM, are subject to change as additional measurements are made or changes are made to the experimental settings? The phrase "predictions of QM" does not really mean that one interpretation of what is happening, whether locally or non locally, is proven by the measurements, but if you are comparing results to Bell's inequalities, measurements can falsify them?

 

[DrChinese]

That description is consistent with what I get out of reading Zeilinger's "Dance of the Photons". Throughout the book, there are repeated statements like, "When one is measured, the state of the other is instantly influenced, no matter how far apart they are separated". The intuitive thinking is that each has its respective state like a pair of gloves, but which is right and which is left is undetermined until an observation is made, but that intuition seems to be exactly what the predictions of QM are arguing against.

Yes and no. Here are a couple of comments:

1. When one is measured...: It could be either one being measured first. The results are the same. Time ordering is not significant and there is no theoretical test which can lead you to believe the first causes the second and not vice versa.

2. It is not quite like a set of gloves, because that implies that both were determined before any measurements were made. Bell's Theorem shows us that either that idea is false, or there are non-local influences from one glove to the other (or both).

 

[meBigGuy]

Does that mean, according to the predictions of QM, that neither particle is in either state before we measure (the states are in superposition for both), and then when we measure the state of one, that measurement collapses the superposition of the second particle?

No. When you measure the first particle, the second is merely no longer entangled. Not entangled does not mean there is no superposition. Don't mix up entanglement and superposition, or connect them in such a way. The second particle still behaves in a QM way the same as any particle prepared with spin in a certain direction. Collapsing (if you want to think of it that way) of the second particle happens when it is eventually measured. Measuring the first does not measure the second. Measuring the first merely tells you how the second will behave if you measure it in the same direction as the first. It still behaves in a probabalistic way consistent with any particle with known spin.

 

[lightarrow]

No. When you measure the first particle, the second is merely no longer entangled. Not entangled does not mean there is no superposition. Don't mix up entanglement and superposition, or connect them in such a way. The second particle still behaves in a QM way the same as any particle prepared with spin in a certain direction. Collapsing (if you want to think of it that way) of the second particle happens when it is eventually measured. Measuring the first does not measure the second. Measuring the first merely tells you how the second will behave if you measure it in the same direction as the first. It still behaves in a probabalistic way consistent with any particle with known spin.

And this is the QM description. But given what vanhees71 writes about our knowledge of the system, shouldn't we consider the possibility that the QM description is not perfect and say that, indeed, the state of the second particle does vary after the first is measured?
(Don't want to be another Einstein-against-Bohr).

--
lightarrow

 

[StevieTNZ]

Technically entanglement never ends between the two particles when one is 'measured'. When you 'measure' one, it merely gets entangled with the apparatus used to measure it.

 

[meBigGuy]

I agree, but isn't it true that if you limit the system to a simple two particle system where the first is measured and then the second is measured, the second particle will behave just as if it were no longer entangled with the first. (deliberately avoiding entanglement swapping,etc)

 

[naima]

particles are entangled when the Schmidt decomposition contains more than one term. Bell states contains two terms. After measurement one of the terms is chosen and the Schmidt decomposition is reduced to one of the terms. There is no more entanglement.

 

[ZapperZ]

Technically entanglement never ends between the two particles when one is 'measured'. When you 'measure' one, it merely gets entangled with the apparatus used to measure it.

But the apparatus has a huge degree of freedom and the clear signature of the entanglement is lost. That is why we no longer can observe clear quantum signatures anymore.

BTW, this is already clearly described in a paper a while back:

https://www.physicsforums.com/showpost.php?p=1498616&postcount=55

Zz.

 

[DrChinese]

I agree, but isn't it true that if you limit the system to a simple two particle system where the first is measured and then the second is measured, the second particle will behave just as if it were no longer entangled with the first. (deliberately avoiding entanglement swapping,etc)

That is correct. No one actually knows when entanglement physically ends.