What is the mechanism behind Quantum Entanglement?

[CoolMint]

RUTA is insisting that the nobody understands quantum mechanics. Esp how it relates to the 'classical' world.
Vanhees71 is insisting that QT is fine and everybody understands quantum theory as it's almost a complete theory that makes the best predictions in the history of physics. Vanhees71 is saying that nobody understands reality and it's not even a duty of science to make reality comprehensible.
RUTA, you understand that Vanhees71 does not claim to understand how reality is, why it is the way it is? Right?
Because it seems you imply Vanhees71 is saying things he never intended to say. He flat out rejects discussion about philosophy. Not even once has he implied that he knows how and what reality is. Not even once.
Your philosophical musings seem to irk him because you seem to insist on having a Newtonian Universe which does not even exist. And it seems it never existed at all. He grapples with the same issues but from a wholly different perspective. I guess everybody wonders about entanglement... but here I wi side with Vanhees71. I worry about it all but from the POV of all reality. Entanglement is almost a minor issue given the failure of realism at the quantum scales.

 

[RUTA]

RUTA is insisting that the nobody understands quantum mechanics. Esp how it relates to the 'classical' world.
Vanhees71 is insisting that QT is fine and everybody understands quantum theory as it's almost a complete theory that makes the best predictions in the history of physics. Vanhees71 is saying that nobody understands reality and it's not even a duty of science to make reality comprehensible.
RUTA, you understand that Vanhees71 does not claim to understand how reality is, why it is the way it is? Right?
Because it seems you imply Vanhees71 is saying things he never intended to say. He flat out rejects discussion about philosophy. Not even once has he implied that he knows how and what reality is. Not even once.
Your philosophical musings seem to irk him because you seem to insist on having a Newtonian Universe which does not even exist. And it seems it never existed at all. He grapples with the same issues but from a wholly different perspective. I guess everybody wonders about entanglement... but here I wi side with Vanhees71. I worry about it all but from the POV of all reality. Entanglement is almost a minor issue given the failure of realism at the quantum scales.

If you reject philosophical discussion, this forum "Quantum Interpretations and Foundations" is not the place to be. It's all about philosophical perspectives on QM.

I never said I advocated a Newtonian Universe. Not even close. I advocate the relativity principle at the foundation of QM, just as it exists at the foundation of SR. Neither of those theories is Newtonian.

 

[vanhees71]

Your philosophical musings seem to irk him because you seem to insist on having a Newtonian Universe which does not even exist. And it seems it never existed at all. He grapples with the same issues but from a wholly different perspective. I guess everybody wonders about entanglement... but here I wi side with Vanhees71. I worry about it all but from the POV of all reality. Entanglement is almost a minor issue given the failure of realism at the quantum scales.

What irks me is when for some irrational "philosophical" reasons elementary observable facts, which don't need any vaguely defined interpretational notions, are denied. The claim that the conservation laws are "valid only on average" has been refuted by Bothe et al already about 100 years ago!

Otherwise it's clear that entanglement and particularly its experimental realization is intriguing, but it only seems "weird", because we are not used to quantum phenomena in everyday life. For me, scientific theories are descriptions of what can be objectively and quantitatively observed, and QT is very successful with that, including the correlations due to entanglement, and that's thus very well understood.

 

[bhobba]

And why this particular generalized probability theory? There are others besides QM.

That could be a fruitful line of research. If I was interested in research work (far too old now other than things that interest me from time to time) it could be something I could really get into.

Thanks
Bill

 

[bhobba]

So let me rephrase the question of "why these laws" into "why do we abduce these laws and not others".

When Feynman said, we guess them, everyone in the audience laughed. He then became stern and serious, saying that is how it is done. As to the why of certain guesses, I leave that to psychiatrists and psychologists, both legitimate scientific research areas. Symmetry is the one that enthrals me.

Thanks
Bill

 

[RUTA]

What irks me is when for some irrational "philosophical" reasons elementary observable facts, which don't need any vaguely defined interpretational notions, are denied. The claim that the conservation laws are "valid only on average" has been refuted by Bothe et al already about 100 years ago!

Otherwise it's clear that entanglement and particularly its experimental realization is intriguing, but it only seems "weird", because we are not used to quantum phenomena in everyday life. For me, scientific theories are descriptions of what can be objectively and quantitatively observed, and QT is very successful with that, including the correlations due to entanglement, and that's thus very well understood.

Let me try again, since this is directly relevant to the OP. "Average-only" conservation, which is a mathematical fact about Bell states, seems to be confusing vanhees71, so I'll go straight to the source of that fact, i.e., "average-only" projection aka Information Invariance & Continuity aka superposition aka spin aka the qubit aka ... . What I'm presenting next will probably not make any sense to those who haven't taken QM. That's good, it will make my point all the better. For those readers, just read the words and gloss right over the mathematics. No worries, I'll follow the Hilbert space formalism with a conceptual explanation that you can (probably) understand. That's the point of this exercise.

Suppose I make a measurement on a spin up state along the z axis. We might do that physically by sending a beam of silver atoms through a pair of Stern-Gerlach (SG) magnets aligned along what we call the z axis. Then we direct the atoms that are deflected upwards out of those SG magnets through another pair of SG magnets oriented at $\hat{b}$ making a an angle $\theta$ with respect to $\hat{z}$ (figure below). How does QM describe the outcomes of that measurement at $\hat{b}$?

The state being measured is $|\psi\rangle = |z+\rangle$ and there are two possible outcomes of our measurement that I will call +1 (deflected towards red pole of SG magnets) denoted by $|+\rangle$ and -1 (deflected towards green pole of SG magnets) denoted by $|-\rangle$. The Hilbert space formalism says the probability of getting the +1 outcome is $|\langle+|\psi\rangle|^2 = \cos^2{\left(\frac{\theta}{2}\right)}$ and the probability of getting the -1 outcome is $|\langle-|\psi\rangle|^2 = \sin^2{\left(\frac{\theta}{2}\right)}$ (Born rule). These are just the squares of the projection of $|\psi\rangle = |z+\rangle$ onto the two eigenvectors of our measurement operator $\sigma$ given by $\sigma = \hat{b}\cdot\vec{\sigma}=b_x\sigma_x + b_y\sigma_y + b_z\sigma_z$ where $\sigma_x$, $\sigma_y$, $\sigma_z$ are the Pauli matrices. The average is then given by the expectation value of $\sigma$ for $|\psi\rangle$, i.e.,

$\langle\sigma\rangle := \langle \psi| \sigma|\psi \rangle = \cos{(\theta)}$​

All of that is standard textbook QM. For physicists like vanhees71 this constitutes "understanding":

For me, scientific theories are descriptions of what can be objectively and quantitatively observed, and QT is very successful with that, including the correlations due to entanglement, and that's thus very well understood.

However, if you who are not familiar with standard textbook QM, this quote by Chris Fuchs might resonant with you:

Associated with each system [in quantum mechanics] is a complex vector space. Vectors, tensor products, all of these things. Compare that to one of our other great physical theories, special relativity. One could make the statement of it in terms of some very crisp and clear physical principles: The speed of light is constant in all inertial frames, and the laws of physics are the same in all inertial frames. And it struck me that if we couldn’t take the structure of quantum theory and change it from this very overt mathematical speak—something that didn’t look to have much physical content at all, in a way that anyone could identify with some kind of physical principle—if we couldn’t turn that into something like this, then the debate would go on forever and ever. And it seemed like a worthwhile exercise to try to reduce the mathematical structure of quantum mechanics to some crisp physical statements.

That's what Gell-Mann, Feynman, and Mermin were talking about in their quotes I posted earlier. All of these people are very familiar with the textbook QM formalism, so what they mean by "understanding QM" goes beyond the mere formalism.

In response to this challenge by Fuchs, Hardy (and subsequently many others) are trying to "reconstruct" QM using principles rather than the pure math a la above. They chose principles from information theory while treating QM as a "general" probability theory. Luckily, we don't have to understand their reconstructions in detail, all we need is one part of what they discovered and we can understand that conceptually.

What they found originated with the first such "axiomatic reconstruction of QM based on information-theoretic principles" published by Hardy in 2001, Quantum Theory from Five Reasonable Axioms. What Hardy discovered was that by deleting one word ("continuous") from his fifth axiom, he would have classical probability theory instead of quantum probability theory. Thus, this quote from Koberinski and Mueller in an earlier post:

We suggest that (continuous) reversibility may be the postulate which comes closest to being a candidate for a glimpse on the genuinely physical kernel of ``quantum reality''. Even though Fuchs may want to set a higher threshold for a ``glimpse of quantum reality'', this postulate is quite surprising from the point of view of classical physics: when we have a discrete system that can be in a finite number of perfectly distinguishable alternatives, then one would classically expect that reversible evolution must be discrete too. For example, a single bit can only ever be flipped, which is a discrete indivisible operation. Not so in quantum theory: the state |0> of a qubit can be continuously-reversibly ``moved over'' to the state |1>. For people without knowledge of quantum theory (but of classical information theory), this may appear as surprising or ``paradoxical'' as Einstein's light postulate sounds to people without knowledge of relativity.

Now let me use what they discovered about "continuity", plus the relativity principle, to provide what Fuchs and others see as missing in the math above concerning spin measurements. Of course, there is more to QM, but I'm focusing here on the OP and vanhees71's confusion.

The classical probability theory we're comparing to quantum probability theory has to do with the "classical bit," which can be instantiated many ways physically, but for simplicity let's just look at two boxes and one ball. I have two measurement options, I can open box 1 or I can open box 2. I have two possible outcomes for each measurement, +1 meaning it contains a ball or -1 meaning it doesn't contain a ball. [Sometimes people use +1 and 0, as in the K-M quote, thinking of 1's and 0's for a computer, for example. I'll stick to +1 and -1 here for reasons that will be clear later.] Since the ball is in one of the two boxes, the probability that it is in box 1 plus the probability that it is in box 2 must equal 100%, i.e., $p_1 + p_2 = 1$. So, we can represent the probability space as a line connecting the fact that the ball is in box 2 ($p_2 = 1$) and the fact that the ball is in box 1 ($p_1 = 1$) (figure below).

The key feature of this probability pointed out by Hardy (and employed in many reconstructions since) is that there are only two actual measurements represented in the probability space for the classical bit depicted here, i.e., those along each axis. The points along the line connecting those two "pure states" are "mixtures", they don't actually represent a measurement because you can't open a box "between" boxes 1 and 2.

In contrast, the quantum version of a bit ("qubit") allows for pure states to be connected in continuous fashion by other pure states. Here is Brukner and Zeilinger's picture of the qubit for our QM formalism above:

As you can see, we are allowed to rotate our SG magnets for our $\sigma$ measurement of $|\psi\rangle$ and we have a measurement at every $\theta$ in continuous fashion, always obtaining one of two outcomes, +1 or -1. To relate this to typical QM terminology, this is superposition per the qubit representing spin. To relate this to the information-theoretic terminology, this is Information Invariance & Continuity per Brukner and Zeilinger:

The total information of one bit is invariant under a continuous change between different complete sets of mutually complementary measurements.

where the "mutually complementary spin measurements" here are the orthogonal set for each $\theta$ as shown in this figure

Now let's finish this conceptual understanding of Information Invariance & Continuity aka spin aka the qubit by looking at what makes the difference between the qubit and classical bit "weird." I'll characterize that "weird" empirical fact by "average-only" projection, justify it by the relativity principle, and we're done!

If we were to try to understand what is going on with our spin example above, we might suppose that the silver atoms are tiny magnetic dipoles being deflected by the SG magnetic field. If that is the case, we expect the amount of deflection to vary depending on how the atoms are oriented relative to the SG magnet field as they enter it. Here is a figure from Knight's intro physics text for that "classical" picture:

The problem with this picture is of course that we only ever get two deflections, i.e., up or down, relative to the SG magnets. Even when we chose a specific case $|\psi\rangle = |z+\rangle$ and measured at $\hat{b}$ we still always got +1 or -1, no fractions (again, look at qubit picture). What we expected per our classical model would be a fractional deflection along $\hat{b}$ like this:

But, guess what that projection equals ... $\cos{\theta}$ ... exactly what QM gives as the average of the +1 and -1 outcomes overall, $\langle \sigma \rangle$. And, if you start with this expectation for $\sigma$, you can derive the $\cos^2{\left(\frac{\theta}{2}\right)}$ and $\sin^2{\left(\frac{\theta}{2}\right)}$ probabilities by requiring additionally that the probabilities add to 1 (called "normalization"). Notice that since we can only ever get +1 or -1, no fractions, we cannot ever measure $\cos{\theta}$ directly. That is to say, the projected value can only obtain on average. This means the standard textbook formalism of QM for the spin qubit can be characterized as "average-only" projection. Thus, the probabilities of our Hilbert space mathematics can be understood to follow from "average-only" projection, which is an empirical fact.

Again, we haven't introduced any interpretations or opinions or proposals here. We're simply characterizing the QM formalism conceptually. And, "average-only" conservation is exactly the same, we just replace the counterfactual $\hat{b} = \hat{z}$ measurement outcome for Bob's single qubit experiment here with the counterfactual $\hat{b} = \hat{a}$ measurement outcome (required for conservation of spin angular momentum) for Bob when Alice measures at $\hat{a}$. In other words, "average-only" conservation for Bell state qubits results from "average-only" projection for single qubits. This is not an interpretation.

To conclude, as Weinberg pointed out, we are measuring Planck's constant h when we do our spin measurement. And, we are in different reference frames related by spatial rotations as we vary $\theta$ (per Brukner and Zeilinger). So, Information Invariance & Continuity entails everyone will measure the same value for h ($\pm$) regardless of their reference frame orientation relative to the source ("Planck postulate" -- an empirical fact equivalent to the light postulate of SR: everyone will measure the same value for c regardless of their reference frame motion relative to the source). Both are simply statements of empirical facts. Thus, everything presented to this point constitutes a collection of empirical and mathematical facts per standard textbook QM.

Finally, we give a principle account of the mathematical facts following from the empirical fact a la Einstein for SR. That is, we justify the "Planck postulate" by the relativity principle. Just as time dilation and length contraction follow mathematically from the light postulate which is justified by the relativity principle, the qubit probabilities (whence "average-only" conservation) follow mathematically from the Planck postulate which is justified by the relativity principle. This last step is indeed a proposal, but it's as solid as what Einstein did for SR :-)

 

[vanhees71]

When Feynman said, we guess them, everyone in the audience laughed. He then became stern and serious, saying that is how it is done. As to the why of certain guesses, I leave that to psychiatrists and psychologists, both legitimate scientific research areas. Symmetry is the one that enthrals me.

Thanks
Bill

I'd also say, that is as if you asked, how was a genius like Beethoven getting his ideas to compose his symphonies. As works of art, to discover physical theories to describe observed phenomena (as well as the invention of clever experiments to make the corresponding observations) is a creative act. You cannot explain, how Feynman came to his idea of the "space-time picture" of quantum mechanics (PhD thesis) and QED (Nobel prize).

 

[vanhees71]

Let me try again, since this is directly relevant to the OP. "Average-only" conservation, which is a mathematical fact about Bell states, seems to be confusing vanhees71, so I'll go straight to the source of that fact, i.e., "average-only" projection aka Information Invariance & Continuity aka superposition aka spin aka the qubit aka ... .

The statistics of measurements on Bell states consist of operations with single quantum systems (e.g., two entangled photons) event-by-event, and the conservation laws hold event by event. E.g., if you have a polarization-singlet two-photon state and you measure, e.g., the linear polarization of the two photons in the same direction you must always get opposite results, because the total angular momentum of the two-photon states is 0. Of course, to verify this, you must repeat the same experiment very often to gain sufficient statistics to meet your goal of statistical significance. That doesn't imply that the conservation laws hold only on average.

What I'm presenting next will probably not make any sense to those who haven't taken QM. That's good, it will make my point all the better. For those readers, just read the words and gloss right over the mathematics. No worries, I'll follow the Hilbert space formalism with a conceptual explanation that you can (probably) understand. That's the point of this exercise.

Suppose I make a measurement on a spin up state along the z axis. We might do that physically by sending a beam of silver atoms through a pair of Stern-Gerlach (SG) magnets aligned along what we call the z axis. Then we direct the atoms that are deflected upwards out of those SG magnets through another pair of SG magnets oriented at $\hat{b}$ making a an angle $\theta$ with respect to $\hat{z}$ (figure below). How does QM describe the outcomes of that measurement at $\hat{b}$?

View attachment 305358

The state being measured is $|\psi\rangle = |z+\rangle$ and there are two possible outcomes of our measurement that I will call +1 (deflected towards red pole of SG magnets) denoted by $|+\rangle$ and -1 (deflected towards green pole of SG magnets) denoted by $|-\rangle$. The Hilbert space formalism says the probability of getting the +1 outcome is $|\langle+|\psi\rangle|^2 = \cos^2{\left(\frac{\theta}{2}\right)}$ and the probability of getting the -1 outcome is $|\langle-|\psi\rangle|^2 = \sin^2{\left(\frac{\theta}{2}\right)}$ (Born rule). These are just the squares of the projection of $|\psi\rangle = |z+\rangle$ onto the two eigenvectors of our measurement operator $\sigma$ given by $\sigma = \hat{b}\cdot\vec{\sigma}=b_x\sigma_x + b_y\sigma_y + b_z\sigma_z$ where $\sigma_x$, $\sigma_y$, $\sigma_z$ are the Pauli matrices. The average is then given by the expectation value of $\sigma$ for $|\psi\rangle$, i.e.,

$\langle\sigma\rangle := \langle \psi| \sigma|\psi \rangle = \cos{(\theta)}$​

All of that is standard textbook QM. For physicists like vanhees71 this constitutes "understanding":

Indeed. What else do you need? That's all what has been ever observed in Stern-Gerlach experiments (including those much more accurate ones like using a Penning trap to measure the electron Lande g-factor to 12 (or more?) digits of accuracy.

However, if you who are not familiar with standard textbook QM, this quote by Chris Fuchs might resonant with you:

That's what Gell-Mann, Feynman, and Mermin were talking about in their quotes I posted earlier. All of these people are very familiar with the textbook QM formalism, so what they mean by "understanding QM" goes beyond the mere formalism.

What goes beyond the "mere formalism" and its application to real-world experiment is not subject to the objective natural sciences. An indication for that is that it seems impossible to clearly state, what "the problem" is.

In response to this challenge by Fuchs, Hardy (and subsequently many others) are trying to "reconstruct" QM using principles rather than the pure math a la above. They chose principles from information theory while treating QM as a "general" probability theory. Luckily, we don't have to understand their reconstructions in detail, all we need is one part of what they discovered and we can understand that conceptually.

Of course, an information theoretical approach to any kind of probabilistic description is an important aspect to understand the physics it describes. The claim that we "don't have to understand the reconstructions in detail" is another indication that here we leave the realm of exact science.

What they found originated with the first such "axiomatic reconstruction of QM based on information-theoretic principles" published by Hardy in 2001, Quantum Theory from Five Reasonable Axioms. What Hardy discovered was that by deleting one word ("continuous") from his fifth axiom, he would have classical probability theory instead of quantum probability theory. Thus, this quote from Koberinski and Mueller in an earlier post:

Now let me use what they discovered about "continuity", plus the relativity principle, to provide what Fuchs and others see as missing in the math above concerning spin measurements. Of course, there is more to QM, but I'm focusing here on the OP and vanhees71's confusion.

The classical probability theory we're comparing to quantum probability theory has to do with the "classical bit," which can be instantiated many ways physically, but for simplicity let's just look at two boxes and one ball. I have two measurement options, I can open box 1 or I can open box 2. I have two possible outcomes for each measurement, +1 meaning it contains a ball or -1 meaning it doesn't contain a ball. [Sometimes people use +1 and 0, as in the K-M quote, thinking of 1's and 0's for a computer, for example. I'll stick to +1 and -1 here for reasons that will be clear later.] Since the ball is in one of the two boxes, the probability that it is in box 1 plus the probability that it is in box 2 must equal 100%, i.e., $p_1 + p_2 = 1$. So, we can represent the probability space as a line connecting the fact that the ball is in box 2 ($p_2 = 1$) and the fact that the ball is in box 1 ($p_1 = 1$) (figure below).
View attachment 305366
The key feature of this probability pointed out by Hardy (and employed in many reconstructions since) is that there are only two actual measurements represented in the probability space for the classical bit depicted here, i.e., those along each axis. The points along the line connecting those two "pure states" are "mixtures", they don't actually represent a measurement because you can't open a box "between" boxes 1 and 2.

This I don't understand. It depends on the preparation of the system before measurement, which probabilities, $p_1$ and $p_2=1-p_1$ you'll find when repeating the experiment often enough to measure these probabilities at a given level of statistical significance. That's true for both "classical" and "quantum" probabilities.

In contrast, the quantum version of a bit ("qubit") allows for pure states to be connected in continuous fashion by other pure states. Here is Brukner and Zeilinger's picture of the qubit for our QM formalism above:

View attachment 305367
As you can see, we are allowed to rotate our SG magnets for our $\sigma$ measurement of $|\psi\rangle$ and we have a measurement at every $\theta$ in continuous fashion, always obtaining one of two outcomes, +1 or -1. To relate this to typical QM terminology, this is superposition per the qubit representing spin. To relate this to the information-theoretic terminology, this is Information Invariance & Continuity per Brukner and Zeilinger:
where the "mutually complementary spin measurements" here are the orthogonal set for each $\theta$ as shown in this figure

View attachment 305369Now let's finish this conceptual understanding of Information Invariance & Continuity aka spin aka the qubit by looking at what makes the difference between the qubit and classical bit "weird." I'll characterize that "weird" empirical fact by "average-only" projection, justify it by the relativity principle, and we're done!

What do you mean by "average-only projection"? If you measure the spin component in any arbitrary direction (by the way completely determined with two angles $(\vartheta,\varphi)$ indicating the unit vector determining that direction) precisely, you always find either a value $\hbar/2$ or $-\hbar/2$ in each event, independent of the (pure or mixed) state you prepared the particle's spin in. The probabilities are given by the statistical operator describing this state prepared before measurement.

If we were to try to understand what is going on with our spin example above, we might suppose that the silver atoms are tiny magnetic dipoles being deflected by the SG magnetic field. If that is the case, we expect the amount of deflection to vary depending on how the atoms are oriented relative to the SG magnet field as they enter it. Here is a figure from Knight's intro physics text for that "classical" picture:

View attachment 305370
The problem with this picture is of course that we only ever get two deflections, i.e., up or down, relative to the SG magnets. Even when we chose a specific case $|\psi\rangle = |z+\rangle$ and measured at $\hat{b}$ we still always got +1 or -1, no fractions (again, look at qubit picture). What we expected per our classical model would be a fractional deflection along $\hat{b}$ like this:

View attachment 305371

But, guess what that projection equals ... $\cos{\theta}$ ... exactly what QM gives as the average of the +1 and -1 outcomes overall, $\langle \sigma \rangle$. And, if you start with this expectation for $\sigma$, you can derive the $\cos^2{\left(\frac{\theta}{2}\right)}$ and $\sin^2{\left(\frac{\theta}{2}\right)}$ probabilities by requiring additionally that the probabilities add to 1 (called "normalization"). Notice that since we can only ever get +1 or -1, no fractions, we cannot ever measure $\cos{\theta}$ directly. That is to say, the projected value can only obtain on average. This means the standard textbook formalism of QM for the spin qubit can be characterized as "average-only" projection. Thus, the probabilities of our Hilbert space mathematics can be understood to follow from "average-only" projection, which is an empirical fact.

Of course, quantum theory provides different (probabilistic predictions than a classical model of the electron. It was Stern's very motivation to do this experiment. It was not even clear, what the prediction of the ("old" quantum theory!) was: Should one get two or three discrete lines (Bohr vs. Sommerfeld) or a continuum (classical physics).

Again, we haven't introduced any interpretations or opinions or proposals here. We're simply characterizing the QM formalism conceptually. And, "average-only" conservation is exactly the same, we just replace the counterfactual $\hat{b} = \hat{z}$ measurement outcome for Bob's single qubit experiment here with the counterfactual $\hat{b} = \hat{a}$ measurement outcome (required for conservation of spin angular momentum) for Bob when Alice measures at $\hat{a}$. In other words, "average-only" conservation for Bell state qubits results from "average-only" projection for single qubits. This is not an interpretation.

But you can check the conservation laws only for one component, because determining one component of the spin implies that any other component is indetermined, because components in different direction are incompatible observables. Also you can measure only one spin direction, i.e., you can only choose one direction by the magnetic field. You never measure two components of the spin in different directions on a single particle. This you can achieve only on an ensemble. If you test the conservation law for angular momentum you can do that event-by-event only when measuring the spins of the two particles in a single direction. Any other measurement gives random results with probabilities given by Born's rule, given the (pure or mixed) state the particles' spin is prepared in before measurement.

To conclude, as Weinberg pointed out, we are measuring Planck's constant h when we do our spin measurement. And, we are in different reference frames related by spatial rotations as we vary $\theta$ (per Brukner and Zeilinger). So, Information Invariance & Continuity entails everyone will measure the same value for h ($\pm$) regardless of their reference frame orientation relative to the source ("Planck postulate" -- an empirical fact equivalent to the light postulate of SR: everyone will measure the same value for c regardless of their reference frame motion relative to the source). Both are simply statements of empirical facts. Thus, everything presented to this point constitutes a collection of empirical and mathematical facts per standard textbook QM.

You are not in different reference frames. For that you'd have to use moving Stern-Gerlach magnets. Due to Galilei invariance the outcome of the measurements do not depend on the choice of the reference frame (defined, e.g., by the restframe of the magnets). The description of the same experiment in one frame is just a unitary transformation (given by the usual ray representation of the Gailei group for a particle with the given mass and spin). The same, of course, holds for Poincare invariance in the relativistic case (where however you have to be careful with the definition of "spin"; here you can only measure the total angular momentum of the electron, not the spin since the split into spin and orbital angular momentum is frame dependent).

Finally, we give a principle account of the mathematical facts following from the empirical fact a la Einstein for SR. That is, we justify the "Planck postulate" by the relativity principle. Just as time dilation and length contraction follow mathematically from the light postulate which is justified by the relativity principle, the qubit probabilities (whence "average-only" conservation) follow mathematically from the Planck postulate which is justified by the relativity principle. This last step is indeed a proposal, but it's as solid as what Einstein did for SR :-)

That there's one and only one frame-independent value for Planck's constant, $\hbar=h/(2 \pi)$, is implemented in the realization of either non-relativistic or relativistic QT. That has nothing to do with "average-only conservation", which claim contradicts all observations made so far.

 

[Fra]

I am guessing Karl Popper would be proud of you both I do understand but doesn't share the stance as optimal.

When Feynman said, we guess them, everyone in the audience laughed. He then became stern and serious, saying that is how it is done.

About laughing, the exact same thing happened to smolin as he held a talk SETI about the evolution of law and the principle of prescedence.



/Fredrik

 

[Fra]

I'd also say, that is as if you asked, how was a genius like Beethoven getting his ideas to compose his symphonies.

My comment on this comment is that I see it similar to those who in misinterpreted "observers knowledge" as something having to do with human brain or consciusness.

At human level, of course Feyman is right. And its not the job of physicists to model human intelligence. It is definitely not what anyone means.

But do we have to stop there, or are rhere further insights to get? This is where we disagree.

1) Observers knowledge is encoded in the physical observer side of the cut. Making it a relation or contextual. This has nothing todo with brains. I guess we agree here?

But in QM the observerside is always dominant and classical. We know how to explain interactions between classical objects but the background independent description of nonclassical systema is missing.

Is this satisfactory? Some of us say yes, but I say no.

/Fredrik

 

[Maarten Havinga]

I don't understand why this is a question of interpretation. We have mathematics to describe the mechanism and why it happens: the state of two entangled particles is one state. A particle's quanta are described by information that is simultaneously also information of the other particle. The mechanism creating entanglement is simply whenever the observed rules of quantum physics dictate that their states depend on the same events (history of quanta), is that right or not? If not, let me know - otherwise I fail to see the relevance of interpretations.

 

[Fra]

I fail to see the relevance of interpretations.

1) If one takes the view that we have an effective theory that is corroborated for certain domains, there isn't much to say about this. It is great and useful no matter how you interpret it. For some this is enough and we do not ask for more.

2) But some of us are obsessed with cravings for a unified theory or coherent understanding. We have now set of various theories whose parameters are on empirically determined, and they have also different constructing principles that are not obviously compatible while it seems reasonable to think that they will have some relation at different energy scales or observational scales, there is an urge for finding a coherent framework which is consistent when it comes to constructing principles. In this context, interpolating or extending theories naturally is interpretatation dependent.

3) Some other may also seek an pure interpretation without ambition to extend or reconstruct anything, for reasons such as casting a given theory to personal preferences.

I belong to the second group. An image is forming where other members here fall into other categories.

/Fredrik

 

[Maarten Havinga]

I belong to the second group

Me too. Only about how entanglement is created I thought it is quite much known, or am I wrong there?

 

[Maarten Havinga]

While I dislike the tone of "shut up and calculate", it is good to understand the mathematics well before arguing in interpretations or other less exact wordy definitions. For instance the poincare group being generated by the Lorentz transformations and translations is proof enough that special relativity gives no contradictions.

I don't know for sure if it applies here, but I thought it does.

 

[Lord Jestocost]

But some of us are obsessed with cravings for a unified theory or coherent understanding.

What's the obsession? The delusion of objectivity?

 

[vanhees71]

My comment on this comment is that I see it similar to those who in misinterpreted "observers knowledge" as something having to do with human brain or consciusness.

At human level, of course Feyman is right. And its not the job of physicists to model human intelligence. It is definitely not what anyone means.

But do we have to stop there, or are rhere further insights to get? This is where we disagree.

Of course not, but you should be aware that then you leave the solid ground of the natural sciences.

1) Observers knowledge is encoded in the physical observer side of the cut. Making it a relation or contextual. This has nothing todo with brains. I guess we agree here?

Of course not. QM in its minimal interpretation describes what's objectively observed. It has nothing to do with the workings of the human brain.

But in QM the observerside is always dominant and classical. We know how to explain interactions between classical objects but the background independent description of nonclassical systema is missing.

It's not clear what you mean by "classical". Classical physics is an approximation of QT valid for coarse-grained descriptions of "macroscopic observables" with a limited range of applicability. It is a good approximation if the averages over many microscopic observables that constitute the macroscopic observables and their changes are large compared to the quantum (or thermal) fluctuations of these quantities.

Is this satisfactory? Some of us say yes, but I say no.

/Fredrik

What do you mean by "background independent description"? QT describes all there is to be described, as far as we know today.

 

[PeterDonis]

"Average-only" conservation, which is a mathematical fact about Bell states

More precisely, it's a "mathematical fact" if you ignore the interaction between the measured systems and the measuring devices. Once you include that interaction, it's obvious that conserved quantities--energy, momentum, angular momentum--can be exchanged between the measured systems and the measuring devices, so there is no reason to expect exact conservation of those quantities if you only look at the measured systems. In other words, the measured systems, by themselves, do not constitute an isolated, closed system, so you should not expect them to exactly obey conservation laws. This does not mean conservation laws only hold "on average" for quantum systems; it just means that, as always, conservation laws only hold for isolated, closed systems that don't interact with anything else.

 

[Fra]

Of course not, but you should be aware that then you leave the solid ground of the natural sciences.

I see myself in the domain of "hypothesis generation", which is the fuzzy but nevertheless a part of the scientific process, but it is not a coincidence that it's the part of the scientific process that some people (like Popper) wanted to play down.

What do you mean by "background independent description"? QT describes all there is to be described, as far as we know today.

QT rests on backgrounds in several ways ways, first in the way that is emphasised by Bohr and manifested by the Heisenberg cut. This is part of the "classical world" making up the observer, including it's encoding capacity (storing pointer variables etc) and processing power.

The other way is the one meant in GR/QG, that QFT is constructed relative to a classical spacetime. It corresponds at best to the equivalence class of the SR-observers, sitting at an asymptotic distance from the interactions they describe. This makes up for a weird relation between QFT and gravity that isn't easily dismissed. Even without a lot of engineering problems, it's a severe issue for anyone that focuses on the coherence of the explanations. It is not even clear that "gravity" should be "quantized" as per the same procedure as other fields.

So how we can use QM inference model (that presumes classical reality and classical spacetime to be defined), to infer what it assumes? What QM explains, is rather bits and pieces in the classical world, such as stability of atoms etc.

/Fredrik

 

[vanhees71]

There is no cut between a classical and a quantum world within QT, and there's no empirical evidence for one to exist in nature. This is, however, under investigation, i.e., there are experiments going on testing the (im)possibility to demonstrate "quantum behavior" of ever larger objects.

 

[Fra]

What's the obsession? The delusion of objectivity?

Can't speak for others that confess to cat 2 think, but I have no desire whatsoever to restore objectivity if that is what you mean. For me objectivity is effectively emergent among interacting systems and not fundamental, and I am fine with this.

To describe my obsession is in detail will be off topic and off limits, but I analyse the structure of physical interactions from the view of intrinsic inference (from a hypothetical inside general observer) rather than human inferences which are closely tied to the classical macroscopic world and classical apparatous. The reason for this is that I have come to my own opinion that this the core of many other open problems. Solve this, and lots of other things will be solved too. In the end of all this, there is the step of falsficiation or corroboratation. But all me "interpretations". But it's what "drives" the interpretational discussions from my side.

Without this, I would probably also prefer some sort of minimal interpretation, but the minimal interpretation gives me no sense of "direction" for modification.

/Fredrik

 

[Fra]

There is no cut between a classical and a quantum world within QT, and there's no empirical evidence for one to exist in nature.

When you make a preparation of a source and detectors etc, and data acquisiton devices, and computers that log all the data of virtual event counters, it's treated classically right? From that you compute distributions etc.

Without that SOLID support to make preparation and log massive amounts of data, how would you corroborate QM in the first place?

/Fredrik

 

[RUTA]

The statistics of measurements on Bell states consist of operations with single quantum systems (e.g., two entangled photons) event-by-event, and the conservation laws hold event by event. E.g., if you have a polarization-singlet two-photon state and you measure, e.g., the linear polarization of the two photons in the same direction you must always get opposite results, because the total angular momentum of the two-photon states is 0. Of course, to verify this, you must repeat the same experiment very often to gain sufficient statistics to meet your goal of statistical significance. That doesn't imply that the conservation laws hold only on average.

You're still missing the point entirely. Let's continue with what I said about "average-only" projection because it is exactly the same point, but with just one particle. Set your particular "constructive" account aside. [Random components of some hidden, underlying vector? And you always get +/- 1 for these random components? Weird.] You can have whatever view of the unseen underlying situation you like, it's absolutely irrelevant and won't affect what I'm saying at all because all I'm referring to are mathematical and empirical facts about spin.

Indeed. What else do you need? That's all what has been ever observed in Stern-Gerlach experiments (including those much more accurate ones like using a Penning trap to measure the electron Lande g-factor to 12 (or more?) digits of accuracy.

Again, this is your particular personal response to the situation. There are physicists who are/were not satisfied with the formalism and experiments alone, e.g., Gell-Mann, Feynman, Mermin, Bell, Einstein, etc. People with the mindset of this latter group participate in forums like this one to share ideas on how to satisfy their need for understanding.

What goes beyond the "mere formalism" and its application to real-world experiment is not subject to the objective natural sciences. An indication for that is that it seems impossible to clearly state, what "the problem" is.

Despite reading many posts and papers on the questions researchers in foundations are trying to answer, you still don't "get it." As I said before, I infer from this history that you are unlikely to ever get it. But, let's continue here and see if you can at least understand "average-only" projection whence "average-only" conservation, even if you don't appreciate why anyone would bother to characterize the mathematical and empirical facts this way.

Of course, an information theoretical approach to any kind of probabilistic description is an important aspect to understand the physics it describes. The claim that we "don't have to understand the reconstructions in detail" is another indication that here we leave the realm of exact science.

The details I'm leaving out are those not relevant to my point. Those included are "exact science."

This I don't understand. It depends on the preparation of the system before measurement, which probabilities, $p_1$ and $p_2=1-p_1$ you'll find when repeating the experiment often enough to measure these probabilities at a given level of statistical significance. That's true for both "classical" and "quantum" probabilities.

I'm just stating a fact about the classical bit to contrast its difference with the qubit, i.e., "continuity." As the reconstructions show, classical probability theory and quantum probability theory only differ in this one respect -- reversible transformations between pure states are continuous for the qubit while they are discrete for the classical bit. That's the "Continuity" part of Information Invariance & Continuity.

What do you mean by "average-only projection"? If you measure the spin component in any arbitrary direction (by the way completely determined with two angles $(\vartheta,\varphi)$ indicating the unit vector determining that direction) precisely, you always find either a value $\hbar/2$ or $-\hbar/2$ in each event, independent of the (pure or mixed) state you prepared the particle's spin in. The probabilities are given by the statistical operator describing this state prepared before measurement.

Keep reading, I explain what is meant by "average-only" projection using the mathematical and empirical facts later in the post.

Of course, quantum theory provides different (probabilistic predictions than a classical model of the electron. It was Stern's very motivation to do this experiment. It was not even clear, what the prediction of the ("old" quantum theory!) was: Should one get two or three discrete lines (Bohr vs. Sommerfeld) or a continuum (classical physics).

Yes, here's an interesting historical account.

But you can check the conservation laws only for one component, because determining one component of the spin implies that any other component is indetermined, because components in different direction are incompatible observables. Also you can measure only one spin direction, i.e., you can only choose one direction by the magnetic field. You never measure two components of the spin in different directions on a single particle. This you can achieve only on an ensemble. If you test the conservation law for angular momentum you can do that event-by-event only when measuring the spins of the two particles in a single direction. Any other measurement gives random results with probabilities given by Born's rule, given the (pure or mixed) state the particles' spin is prepared in before measurement.

In order to understand what is meant by "average-only" projection, you have to stick to the following facts, (which hold regardless of the underlying ontology you are imagining might be responsible for them):

1. When $\hat{b} = \hat{z}$, you always get +1.
2. When $\hat{b}$ makes an angle $\theta$ with respect to $\hat{z}$, you get +1 with a frequency of $\cos^2{\left(\frac{\theta}{2}\right)}$ and you get -1 with a frequency of $\sin^2{\left(\frac{\theta}{2}\right)}$. These average to $\cos{\theta}$. You never measure anything other than +1 or -1.
3. $\cos{\theta}$ is the projection of +1 along $\hat{b}$.

This collection of facts is what is meant by "average-only" projection. As you see, it is a statement of mathematical and empirical facts associated with spin. The classical constructive model (Knight figure) says we should get $\cos{\theta}$ every time, but in actuality we only get $\cos{\theta}$ on average. As you can (hopefully) see, "average-only" projection is not a matter of opinion or interpretation.

You are not in different reference frames. For that you'd have to use moving Stern-Gerlach magnets. Due to Galilei invariance the outcome of the measurements do not depend on the choice of the reference frame (defined, e.g., by the restframe of the magnets). The description of the same experiment in one frame is just a unitary transformation (given by the usual ray representation of the Gailei group for a particle with the given mass and spin). The same, of course, holds for Poincare invariance in the relativistic case (where however you have to be careful with the definition of "spin"; here you can only measure the total angular momentum of the electron, not the spin since the split into spin and orbital angular momentum is frame dependent).

That there's one and only one frame-independent value for Planck's constant, $\hbar=h/(2 \pi)$, is implemented in the realization of either non-relativistic or relativistic QT. That has nothing to do with "average-only conservation", which claim contradicts all observations made so far.

Different inertial reference frames are related by boosts (as you state), but they are also related by spatial rotations. The reference frame of the complementary spin measurements associated with $\hat{b}$ is indeed spatially rotated with respect to the reference frame of the complementary spin measurements associated with $\hat{z}$ (per Brukner and Zeilinger). Again, no interpretation here.

The relativity principle aka no preferred reference frame (NPRF) says we should measure the same value for fundamental constants of Nature like c (light postulate) and h (call this the "Planck postulate"), regardless of our inertial reference frame. Since we are in fact measuring h here (per Weinberg), then NPRF says we have to get (+\-) h for all $\hat{b}$. So, we can justify the fact that we have "average-only" projection rather than direct projection by the Planck postulate, which follows from NPRF. This justification is a "principle" account, so it is not threatened by any "constructive" account (like your "random components" model).

Here are the facts for "average-only" conservation (triplet states):
1. When $\hat{b} = \hat{a}$, Alice and Bob always get the same result, i.e., they both get +1 or they both get -1. This fact holds everywhere in the plane of symmetry. This is the rotational invariance for conservation of spin angular momentum.
2. When $\hat{b}$ makes an angle $\theta$ with respect to $\hat{a}$ (in the plane of symmetry), Bob gets +1 with a frequency of $\cos^2{\left(\frac{\theta}{2}\right)}$ and he gets -1 with a frequency of $\sin^2{\left(\frac{\theta}{2}\right)}$ corresponding to Alice's +1 outcome. These average to $\cos{\theta}$. Similarly for Alice's -1 outcome, Bob's +1 and -1 results average to $-\cos{\theta}$. Alice and Bob never measure anything other than +1 or -1.
3. $\pm\cos{\theta}$ is the projection of $\pm 1$ along $\hat{b}$ in accord with conservation of spin angular momentum in Fact 1, i.e., had Bob measured at $\hat{b} = \hat{a}$, he would have gotten the same $\pm 1$ outcome that Alice did, as demanded by conservation of spin angular momentum.
4. The situation is entirely symmetric under the interchange of Alice and Bob.

This is what is meant by "average-only" conservation. As you can (hopefully) see, it is not a matter of interpretation or opinion. It is standard textbook QM for the Bell states.

 

[RUTA]

More precisely, it's a "mathematical fact" if you ignore the interaction between the measured systems and the measuring devices. Once you include that interaction, it's obvious that conserved quantities--energy, momentum, angular momentum--can be exchanged between the measured systems and the measuring devices, so there is no reason to expect exact conservation of those quantities if you only look at the measured systems. In other words, the measured systems, by themselves, do not constitute an isolated, closed system, so you should not expect them to exactly obey conservation laws. This does not mean conservation laws only hold "on average" for quantum systems; it just means that, as always, conservation laws only hold for isolated, closed systems that don't interact with anything else.

No such qualifier is needed, see Post #129.

 

[PeterDonis]

No such qualifier is needed, see Post #129.

I see a lot of detail in post #129 about the mathematical calculations that underlie what you mean by "average only conservation" (which I didn't need, I already understand the math), but I don't see anything that addresses the physical point I made.

 

[RUTA]

I see a lot of detail in post #129 about the mathematical calculations that underlie what you mean by "average only conservation" (which I didn't need, I already understand the math), but I don't see anything that addresses the physical point I made.

If you understand what I said “average-only” conservation means in that post, then you should understand that the physical details of your post are irrelevant.

 

[PeterDonis]

If you understand what I said “average-only” conservation means in that post, then you should understand that the physical details of your post are irrelevant.

Even if you think I "should" understand this, i don't.

 

[RUTA]

Even if you think I "should" understand this, i don't.

Sorry, let me try again. The facts defining “average-only” conservation as listed in Post 129 do not depend on the physical facts in your post. Worse, your physical facts confuse what is meant by “average-only” conservation” as defined by my listed facts.

 

[*now*]

I am guessing Karl Popper would be proud of you both I do understand but doesn't share the stance as optimal.

About laughing, the exact same thing happened to smolin as he held a talk SETI about the evolution of law and the principle of prescedence….

There was an interesting debate held on that sort of topic recently but I think it is behind a paywall, “Is the universe fundamentally predictable or unpredictable? Does the degree to which the future remains unknown reflect our own cognitive limitations, or the fundamentally open structure of reality?… a remarkable panel comprising of Lee Smolin, Francesca Vidotto and John Vervaeke debated these questions during an IAI Live event, streamed in real time from the Institute of Art and Ideas in London. The universe, the panelists agreed, is a place of constant change and surprise, and its future remains fundamentally open.“ In the talk Fra posted Anaximander was mentioned, and this is also interesting I think-

 

[hutchphd]

If you understand what I said “average-only” conservation means in that post, then you should understand that the physical details of your post are irrelevant.

So the result "average only conservation" is to give a new name to completely settled and understood Quantum Practice?
Why is this to be desired? ( And why choose that name?)

.

 

[gentzen]

So the result "average only conservation" is to give a new name to completely settled and understood Quantum Practice?
Why is this to be desired? ( And why choose that name?)

You could ask a similar question to @vanhess71, when he keeps insisting that the word "locality" really means "microcausality principle". He complains that people keep using the word "locality" with its well established meaning instead, and even dare to doubt that QFT + the minimal statistical interpretation satisfy locality. For him, it is an established mathematical fact that QFT satisfies locality, because it satisfies the "microcausality principle" after all.

P.S.: To be honest, Demystifier's recent thread (which already got closed) trying to refute vanhees71's locality claims seemed pointless to me, because it seems pretty clear to me that in the end, it is just a disagreement about the proper use of words.

 

[RUTA]

So the result "average only conservation" is to give a new name to completely settled and understood Quantum Practice?

Yes! Did you see that immediately? Or was there something in my later posts that made that clear to you? I’m writing a book for the general reader on this so I’d like to know how best to say it.

Why is this to be desired? ( And why choose that name?)

It’s a way to distinguish quantum behavior from classical expectations. In that sense it provides the “mechanism” for the “mystery” of Bell state entanglement. For Unnikrishnan who first pointed this out for the singlet state it resolved the mystery too. Since the weirdness (violation of classical expectations) of the phenomenon resides in average-only conservation and since conservation principles are widely accepted as explanatory in physics, average-only conservation both identifies the mystery and solves it.

Most in foundations want average-only conservation explained though. NPRF + h is a principle way to do that.

 

[PeterDonis]

The facts defining “average-only” conservation as listed in Post 129 do not depend on the physical facts in your post.

I didn't say they did. Of course they don't.

Worse, your physical facts confuse what is meant by “average-only” conservation” as defined by my listed facts.

No, they don't "confuse what is meant", they just make explicit something you didn't, namely, that "average-only conservation" as you define it is perfectly consistent with exact conservation for each individual event, because each individual event involves more than just the quantum systems being measured, so those systems are not isolated. So "average-only conservation" is not any kind of alternative to exact conservation for each individual event. It's just using different words to describe a particular aspect of these types of measurements.

If you are not claiming that "average-only conservation" as you define it rules out exact conservation for each individual event, then there is no issue. But @vanhees71, at least, appears to think that you are claiming that "average-only conservation" rules out exact conservation for each individual event; that's why he keeps arguing, correctly, that exact conservation can hold for each individual event. If you are not claiming that average-only conservation rules out exact conservation for each individual event, it would probably be a good idea to clarify that point.

 

[PeterDonis]

It’s a way to distinguish quantum behavior from classical expectations.

This appears to require that average-only conservation does rule out exact conservation for each individual event. Is that your intent?

 

[hutchphd]

This appears to require that average-only conservation does rule out exact conservation for each individual event. Is that your intent?

And please carefully define what you mean by an "event". The particles that "appear" in a particular perturbation expansion are entirely chimerical until measured otherwise.

 

[PeterDonis]

And please carefully define what you mean by an "event".

I was using "event" to mean something like "a single run of an experiment that involves spin measurements on each of an entangled pair of particles".

The particles that "appear" in a particular perturbation expansion are entirely chimerical

I don't think this is relevant to the kinds of experiments being discussed in this thread; they involve quantum systems that are unproblematically "particles", in entangled pairs produced by sources that are well understood, and using spin measurements that are well understood.