What is the mechanism behind Quantum Entanglement?

[vanhees71]

We state it, because you claim, against empirical facts, an "average-only validity" of the conservation laws. Also angular momentum is conserved event by event and not only on average, and indeed this false claim has nothing to do with any mystery of entanglement. In fact, often an entangled state results due to conservation laws, as in the original EPR gedanken experiment (for momentum) as well as in Bohm's version (for angular momentum).

 

[PeroK]

Charge and energy are conserved exactly (for each trial) in these experiments. Does that bear at all on the mystery of entanglement per the Bell states? No, so why state it when doing so leads precisely to confusing statements like this one? I think I'll stick to my presentation of the empirical and mathematical facts that define "average-only" projection and "average-only" conservation (for spin angular momentum in this case) and not introduce extraneous facts. Indeed, I'll make my Posts 113 and 129 an Insight so I can just link to that concise explanation and list of the relevant facts in the future.

Do you have experimental evidence of conservation of angular momentum being violated in a single experiment?

 

[RUTA]

We state it, because you claim, against empirical facts, an "average-only validity" of the conservation laws. Also angular momentum is conserved event by event and not only on average, and indeed this false claim has nothing to do with any mystery of entanglement. In fact, often an entangled state results due to conservation laws, as in the original EPR gedanken experiment (for momentum) as well as in Bohm's version (for angular momentum).

You're claiming the empirical and mathematical facts listed in Post 129 are false? If so, then you are denying standard textbook QM.

Here is the outline:
1. Some people find entanglement to be mysterious, despite the fact that the formalism of QM maps beautifully to the experiments and entanglement is being used to develop new technologies.
2. Entanglement is the key difference between quantum information processing and computing and its classical counterpart.
3. Quantum information theorists have reconstructed QM as a probability theory based on information-theoretic principles. In these reconstructions, they build the entirety of finite-dimensional QM from the indivisible fundamental unit of binary quantum information, i.e., the quantum bit (qubit).
4. The qubit differs from the classical bit for classical probability theory in one respect, i.e., continuous reversibility between pure states.
5. Facts 3 and 4 are summed up by Information Invariance & Continuity.
6. Therefore, the mystery of entanglement per quantum information theory ultimately resides in Information Invariance & Continuity. However, for those who are not practicing quantum information theorists, this is not a very transparent principle, so a physical example helps.
7. The qubit can be physically instantiated in any number of ways.
8. I (and Brukner, Zeilinger, Mueller, Dakic, etc.) find spin-1/2 particles to provide a nice visual example of the qubit (see figures in Post 113).
9. In that example, Information Invariance & Continuity manifests itself as "average-only" projection of spin angular momentum per the empirical and mathematical facts listed in Post 129. If you were using photons and polarizers instead, Information Invariance & Continuity manifests itself as "average-only" transmission through the polarizer (as explained in our published papers).
10. Extrapolating "average-only" projection to the corresponding Bell state, we have "average-only" conservation of spin angular momentum between different inertial reference frames related by spatial rotations in the plane of symmetry where the reference frames are those of the corresponding set of complementary spin measurements. These facts are listed in Post 129.
11. Facts 1-10 above are empirical and mathematical facts independent of interpretation.
Conclusion: The interpretation-independent "mechanism" responsible for entanglement and its "mysterious" (non-classical) behavior can be summed up most generally per information-theoretic reconstructions of QM by Information Invariance & Continuity. This is manifested in physical instantiations of Bell state entangled qubits as "average-only" conservation (as defined) of the relevant entangled property.

Everything you continue to request has already been posted, e.g., exact mathematical statements, example of state preparation, example of corresponding measurement, etc. Sorry if you still don't understand what has been presented, I can't think of any further simplifications. If anyone else sees how to make it simpler, please let me know!

 

[RUTA]

Do you have experimental evidence of conservation of angular momentum being violated in a single experiment?

See Post 155.

 

[RUTA]

I have to sign off now and get back to writing the Insight and book on what I've been presenting here. If anyone has any suggestions for how to make this presentation easier to understand, contact me directly via a Physics Forums Conversation.

 

[PeroK]

See Post 155.

My understanding of what you say is that:

a) If you measure spin angular momentum about different axes, then the question of conservation is indeterminate - but conservation is not manifestly violated. And, indeed, the incompatibility of spin AM measurements about different axes precludes a comprehensive measurement of AM about all axes in any experiment. In that sense, three-dimensional spin AM in QM is fundamentally indeterminate. There is nothing special about Bell states in that respect.

b) You have manifestly conservation on average about all axes.

If that's correct, then saying you can't prove conservation of AM about the z-axis if you don't measure both particles about the z-axis is a hollow statement.

 

[vanhees71]

You're claiming the empirical and mathematical facts listed in Post 129 are false? If so, then you are denying standard textbook QM.

I don't know, what you want to say. So I can't say whether your claims are wrong or false. What for sure is wrong is the claim that the conservation laws wouldn't hold on an event-by-event basis.

Here is the outline:
1. Some people find entanglement to be mysterious, despite the fact that the formalism of QM maps beautifully to the experiments and entanglement is being used to develop new technologies.

This is irrelevant for physics.

2. Entanglement is the key difference between quantum information processing and computing and its classical counterpart.

Nobody denies this.

3. Quantum information theorists have reconstructed QM as a probability theory based on information-theoretic principles. In these reconstructions, they build the entirety of finite-dimensional QM from the indivisible fundamental unit of binary quantum information, i.e., the quantum bit (qubit).

This is no surprise either.

4. The qubit differs from the classical bit for classical probability theory in one respect, i.e., continuous reversibility between pure states.

Also agreed.

5. Facts 3 and 4 are summed up by Information Invariance & Continuity.

It's not clear to me, what you mean with that.

6. Therefore, the mystery of entanglement per quantum information theory ultimately resides in Information Invariance & Continuity. However, for those who are not practicing quantum information theorists, this is not a very transparent principle, so a physical example helps.
7. The qubit can be physically instantiated in any number of ways.
8. I (and Brukner, Zeilinger, Mueller, Dakic, etc.) find spin-1/2 particles to provide a nice visual example of the qubit (see figures in Post 113).

Sure.

9. In that example, Information Invariance & Continuity manifests itself as "average-only" projection of spin angular momentum per the empirical and mathematical facts listed in Post 129. If you were using photons and polarizers instead, Information Invariance & Continuity manifests itself as "average-only" transmission through the polarizer (as explained in our published papers).

Please finally define what you mean with "average-only projection" with clear mathematical statements. One cannot communicate without clear mathematical definitions.

10. Extrapolating "average-only" projection to the corresponding Bell state, we have "average-only" conservation of spin angular momentum between different inertial reference frames related by spatial rotations in the plane of symmetry where the reference frames are those of the corresponding set of complementary spin measurements. These facts are listed in Post 129.
11. Facts 1-10 above are empirical and mathematical facts independent of interpretation.
Conclusion: The interpretation-independent "mechanism" responsible for entanglement and its "mysterious" (non-classical) behavior can be summed up most generally per information-theoretic reconstructions of QM by Information Invariance & Continuity. This is manifested in physical instantiations of Bell state entangled qubits as "average-only" conservation (as defined) of the relevant entangled property.

You haven't made a clear mathematical statement. So it's impossible for me to understand the meaning for your text-only vague statements.

Everything you continue to request has already been posted, e.g., exact mathematical statements, example of state preparation, example of corresponding measurement, etc. Sorry if you still don't understand what has been presented, I can't think of any further simplifications. If anyone else sees how to make it simpler, please let me know!

You have not given a clear description of what you are talking about. This would mean:

(a) the system under consideration (one spin, many spins?)
(b) the state the system is prepared in ($\hat{\rho}=...$).
(c) which (spin?) observables are measured.
(d) what does "average-only validity of conservation laws" mean for you. In the standard meaning of this words it's clearly a wrong statement.
(e) what does "average-only projection" mean. It's not defined in the standard literature, and you haven't given a clear mahthemtal definition either.

 

[Maarten Havinga]

Averages are conserved indeed, and I understand how a measurement can appear to violate conservation laws in QM. However note that a measured state is in fact a partial state of a macroscopic measurement device entangled with one measured qubit. If the quantity in the measured qubit decreases by 1, could it be that the same quantity in the measurement device is increased by $1/n$ where n is the amount of that type of quantum information?

 

[RUTA]

My understanding of what you say is that:

a) If you measure spin angular momentum about different axes, then the question of conservation is indeterminate - but conservation is not manifestly violated. And, indeed, the incompatibility of spin AM measurements about different axes precludes a comprehensive measurement of AM about all axes in any experiment. In that sense, three-dimensional spin AM in QM is fundamentally indeterminate. There is nothing special about Bell states in that respect.

b) You have manifestly conservation on average about all axes.

If that's correct, then saying you can't prove conservation of AM about the z-axis if you don't measure both particles about the z-axis is a hollow statement.

This reminds of me of something I meant to say. The key to understanding the mystery of entanglement as presented by EPR, Bell, and Mermin (and many others of course) is the assumption of counterfactual definiteness (CD) that seems to be necessary per the rotational symmetry of the Bell states giving exact conservation of spin AM in the same reference frame (aka when making the same spin measurements in the symmetry plane). However, if you assume CD when making different spin measurements, you get the Bell inequality which is violated by QM. The violation of CD is characterized in many ways, e.g., complementarity, non-Boolean algebra, non-commutativity, superposition, qubit structure, Information Invariance & Continuity, etc. We're adding one more way to characterize it, i.e., "average-only" projection/conservation as I described. Why bother adding yet another characterization? Because it leads immediately to a direct analogy with SR where NPRF has been long accepted as resolving the mysteries of time dilation and length contraction (see any intro physics textbook, for example).

If we had exact projection and conservation between different reference frames per CD, i.e., if we did measure $\cos{\theta}$ at $\hat{b}$ for $|\psi\rangle = |z+\rangle$ and Bob did measure $\cos{\theta}$ when Alice measured +1 for the Bell triplet state in the symmetry plane, then the $\hat{z}$ frame and Alice's frame would constitute "preferred frames" where you measure h while everyone else is measuring a fraction of h (like moving through the aether and getting some fraction of c for the speed of light).

I'll add that to the Insight, thnx.

 

[vanhees71]

Please make clear statements! Please define what you mean by "average-only" conservation. In the usual meaning of this word it's contradicting all empirical evidence. So you must mean something different.

The only thing I can clearly guess is that you discuss two spins $s=1/2$ in the singlet state,
$$|S=0,M=0 \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle-|-1/2,1/2 \rangle).$$
Angular-momentum conservation can now be discussed for the usual example of Bohm's version of EPR: The spin-singlet state is prepared by the decay of a spin-0-particle in its rest frame (and there's no merit in overcomplicating things by discussing this in another frame, where the particle moves, but if you want to, you can simply make a unitary transformation to such a frame; it won't change any conclusions of course). Then angular-momentum conservation in fact dictates the above singlet state, and this implies that the angular-momentum conservation is fulfilled event by event.

To empirically check angular-momentum distribution you must measure the spin of both particles in the same direction in each measurement, i.e., you measure first in a direction $\vec{n}_1$, and the prediction is that you get with probability 1/2 either $m_1=1/2$ and $m_2=-1/2$ or $m_1=-1/2$ and $m_2=+1/2$. The sum is always $M=1/2-1/2=0$, i.e., angular-momentum conservation for this component of the spin holds event by event. Now you repeat this for another direction $\vec{n}_2$, and again you find that the angular-momentum conservation holds event by event.

It doesn't make sense to try to confirm angular-momentum conservation by measuring the spin of particle 1 in one direction $\vec{n}_1$ and that of particle 2 in another direction $\vec{n}_2$, because then you never measure any total spin component. You cannot infer from such a measurement whether any component of the total spin is the same as before the mother particle's decay. To quote Peres: "Unperformed experiments have no results".

What's for me clear with all the confirmation of quantum theory against local HV theories is that observables only take predetermined values if the system is prepared in a corresponding state (an eigenstate of the corresponding self-adjoint operators of the measured observables). Thus of course "counteractual definiteness" is violated.

 

[jbergman]

I have to sign off now and get back to writing the Insight and book on what I've been presenting here. If anyone has any suggestions for how to make this presentation easier to understand, contact me directly via a Physics Forums Conversation.

I am sympathetic to what you are working on. It reminds me of some of the other work on unifying Probability and Quantum Probability as outlined in https://www.math.ucdavis.edu/~greg/intro-2005.pdf

One suggestion is to start with a more concise and mathematical presentation that could be more quickly digested by experts.

 

[bhobba]

RUTA is insisting that the nobody understands quantum mechanics. Esp how it relates to the 'classical' world.

I know and understand Vanhees' view. But I don't think RUTA is saying nobody understands QM, except in the sense nobody understands anything. By this, I mean every theory, every single one, is based on assumptions that are simply accepted. In that sense, ultimate knowledge is unobtainable. Besides that, science rests on doubt - always, it must be somewhere in the back of your mind - this may be wrong. RUTA is saying that he believes there is a relativity principle similar to the POR (which says the laws of physics are the same in all inertial frames or frames traveling at constant velocity relative to an inertial frame). It is a beautiful principle of maximum symmetry in inertial frames. But that does not explain why it is true. Questions like that are rampant throughout science and always will be. My favourite area of science is how to formulate theories so that the assumptions are like the POR - beautiful and intuitive. But they are assumptions whose validity depends on experiments. That is the key:


And, of course, Brian Cox is right - we all should read Feynman. Caveat - not his Lectures on Physics except as a supplement to a more usual physics text or after, without going into why.

Thanks
Bill

 

[bhobba]

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

In many ways. One way often not mentioned is showing classical mechanics is a limiting case of QM. A common way is showing Feynman's path integral approach leads to the Principle Of Least Action. But a more sophisticated way is by the use of a process called coarse graining:
https://www.sciencenews.org/blog/context/gell-mann-hartle-spin-quantum-narrative-about-reality

Thanks
Bill

 

[Fra]

In many ways. One way often not mentioned is showing classical mechanics is a limiting case of QM. A common way is showing Feynman's path integral approach leads to the Principle Of Least Action. But a more sophisticated way is by the use of a process called coarse graining:
https://www.sciencenews.org/blog/context/gell-mann-hartle-spin-quantum-narrative-about-reality

Thanks
Bill

I am aware of that, but that is missing my point. I am not actually claiming that there IS a classical reality, on the contrary there is no evidence for any sharp Heisenberg cuts anywher in nature.

But if you look at the theory, to determine with certainty distributions, and process enough data to infer hamiltonians and distributions etc, IMHO at least, presumes conceptucally a SOLID reference frame for information processing and for a solid spacetime. And as this SOLID reference only exists approximately, but in the theory we use hard constraints to be eternal and timeless. This does not match to me.

If one only cares about the practical success this may seem esotheric, but if one looks at the structure of the theory, and how it's elements presumable map to nature, then QM is an effective theory at best, which means it is a potentia fallacy take the "truncated" wisdom from the effective theory and extrapolate to hold even when searching for unification (GUT as well as gravity).

/Fredrik

 

[Fra]

classical mechanics is a limiting case of QM.

Classical mechanics is not just Newtons "theory" is also represents that there is a place where information can be encoded (with certainty) and that can be SHARED among observers. Without this - we can not construct and conduct a quantum preparation an experiment and observers can't agree with certainty on distributions.

So what you say, IMO implies that not only CM but also QM is "emergent". IF you agree on that, then we agree. But I am searching for HOW QM emerges, and how that is described.

So to restate my point: What you describe, how QM works, is successful and explains CM in large limits, seems to represent what we see in nature, BUT I think theory of QM (with set hilbert spaces and god given hamiltonians) does not seem to describe the actual inferece we do.

/Fredrik

 

[Fra]

To make the point even clearer:

I am not actually claiming that there IS a classical reality, on the contrary there is no evidence for any sharp Heisenberg cuts anywher in nature.

This is also why the kind of "observers" that is required to construct QM, also does not exists. This is the core point.

Yes, it effectively works anyway. But when analysing the logical structure of the theory from inference, this is a problem for me at least.

/Fredrik

 

[bhobba]

Classical mechanics is not just Newtons "theory" is also represents that there is a place where information can be encoded (with certainty) and that can be SHARED among observers.

May I suggest you read Landau - Mechanics? It contains nothing about - information. It is, however, Classical Mechanics (non-relatvistic) based on the Principle Of Least Action, easily derivable from Feynman's Path Integral Formulation.

As I have said, we cannot directly interact with the QM world. We know about it from its interactions with the classical world of everyday experience or increasingly from strange phenomena here in the everyday world that can only be explained by QM. Now pinning what the everyday world is, is a deep philosophical issue and, by the forum rules, not on topic here. For our purpose, a world out there that we experience is taken as a given. Since everything is quantum, how such a world is a limiting case of a theory that assumes it in the first place is a deep issue. The surprising thing is that significant progress, such as using coarse-grained histories, decoherence etc, has allowed significant progress to be made - although problems remain. If you would like more detail, may I suggest a modern interpretation like Consistent Histories that delves into such issues:

https://quantum.phys.cmu.edu/CHS/histories.html

This is not an endorsement of Consistent Histories except that it is an interesting interpretation many call - Copenhagen done right. I have laid my cards on the table regarding interpretations far too many times to repeat it here. It is a reasonable starting point to answer the questions you seem interested in.

Thanks
Bill

 

[bhobba]

This is also why the kind of "observers" that is required to construct QM, also does not exists. This is the core point.

QM can be formulated in a way that does not require observers. However, it is a good place to start viewing QM as a generalised probability theory, although, strictly speaking, even that view does not require observers. It would require a deep sojourn into the philosophy of probability, again not on topic here. If it worries you look at probability as the Kolmogorov axioms and Generalised Probability Theory as a generalisation of those axioms. Applying an axiomatic mathematical system is also a deep but philosophical issue. Like Euclidian Geometry, we simply use intuitive ideas such as a point has position and no size and a line length but no breadth. Of course, such don't exist but are useful abstractions in applications. It is similar to the inertial frames of SR.

Thanks
Bill

 

[vanhees71]

May I suggest you read Landau - Mechanics? It contains nothing about - information. It is, however, Classical Mechanics (non-relatvistic) based on the Principle Of Least Action, easily derivable from Feynman's Path Integral Formulation.

As I have said, we cannot directly interact with the QM world.

How do you come to that conclusion? To the contrary, with more and more advanced technology we are more and more able to observe the "quantum world" (as if there were any other world than the "quantum world"). To handle generic quantum system nowadays becomes more and more applied, and more and more universities of applied sciences develop curricula for the development of "quantum technology".

 

[CoolMint]

We do not have direct sensory interaction with the quantum world as for example the Planck constant is very small to make any useful difference or contribution. If the quantum world exist as such between measurements. In that sense, we are probing indirectly, as you need classical-like machinery, usually bigger than а kitchen table which is already classical.
Maybe bhobba had this in mind by 'direct' experience of the quantum world.

 

[Morbert]

Obligatory Consistent Histories take: We probe the quantum world by identifying properties which are 'ambivalent' (having both a classical and a quantum description, e.g. the collective degrees of freedom of some measurement apparatus), and using quantum theory to establish a logical relation between these ambivalent properties and the quantum properties we are interested in probing. I.e. Not so much a Heisenberg cut, but a 'Heisenberg overlap'

 

[gentzen]

Classical mechanics is not just Newtons "theory" is also represents that there is a place where information can be encoded (with certainty) and that can be SHARED among observers.

May I suggest you read Landau - Mechanics? It contains nothing about - information.

A different suggestion (SCNR): Fra, your views seem to be sufficiently evolved and detailed that it would make sense to write them down in a more coherent form than just as comments on other peoples questions and answers. Maybe as an FQXi essay, maybe as a paper of some form, maybe as a series of blog post, or... I am not suggesting that you should link your PF account to those "external activities" and give away more of your identity than you want. But I do suggest that you should do some activity in that direction. Otherwise you risk kidding yourself with respect to your views and their impact.

 

[physika]

When Alice and Bob make measurements in different reference frames, Alice(Bob) says Bob(Alice) must average his(her) data according to her(his) partition of the data in order to conserve spin angular momentum. All of this follows from the exact conservation of spin angular momentum responsible for the Bell state with its rotational symmetry to begin with. As long as Alice and Bob are making measurements in the same reference frame (same orientation relative to source) their outcomes will be exactly in accord with conservation of spin angular momentum. And, not surprisingly, that can be easily accounted for via local realism. The “weirdness” of entanglement occurs for measurements in different reference frames. That’s where the relative “average-only” conservation holds

a sort of statistical consistency?

 

[Fra]

May I suggest you read Landau - Mechanics? It contains nothing about - information. It is, however, Classical Mechanics (non-relatvistic) based on the Principle Of Least Action, easily derivable from Feynman's Path Integral Formulation.

Thanks for the suggestion, I haven't read that book, but if it's point is to start with some principle of least action, given a lagrangian or hamiltonian I can't see how that will solve any of the deeper questions?

https://quantum.phys.cmu.edu/CHS/histories.html

This is not an endorsement of Consistent Histories except that it is an interesting interpretation many call - Copenhagen done right.

I'm sure it's interesting but I am not a fan of that interpretation.

/Fredrik

 

[Fra]

QM can be formulated in a way that does not require observers.

Yes, this is what many even wants to do. Ie. solve the measurement problem by REMOVING the observer.
This is the opposite strategy of what I suggest.

I take here a more qbist stance, that the agent is CENTRAL. Doing away with this, is throwing the baby out with the bathwater.

When I wrote that the observers that are needed to construct QM "does not exist", I didn't mean that the observers are not important or a problem, just that the idealisation of the "observer" that supports the theory, also defines it. Instead of doing away with the observers, I suggest only that we realized that an observer is more than merely a spacetime frame of reference?

However, it is a good place to start viewing QM as a generalised probability theory, although, strictly speaking, even that view does not require observers.

I do view it a bit like "generalised probability" as well, but I think we see it in different ways and will most certainly not agree. The "generalised probability" is what I call "inference", and it's more than just probability one fixed states spaces so I think inference is a better name. In this generalisation the "observer" is the subsystem that detects, postprocesses and encodes the "observations". (I.e the agent).

It would require a deep sojourn into the philosophy of probability, again not on topic here

Indeed, the boots are already in the mud.

/Fredrik

 

[Fra]

A different suggestion (SCNR): Fra, your views seem to be sufficiently evolved and detailed that it would make sense to write them down in a more coherent form than just as comments on other peoples questions and answers. Maybe as an FQXi essay, maybe as a paper of some form, maybe as a series of blog post, or... I am not suggesting that you should link your PF account to those "external activities" and give away more of your identity than you want. But I do suggest that you should do some activity in that direction. Otherwise you risk kidding yourself with respect to your views and their impact.

Thanks for your concern! But I have no illusions of anything here. I've been struggling with this for 25 years by now, and the a priori chance of working this out is of course nil. I decided long ago to not officially publish and vauge ideas anywhere, but have the ambition to work the theory out and publish something iff it solves some of the major the problems. Before then, no one will care about this no more than I care about string theory. Whoever has an idea, bears the responsibility to realize it. All else along the way are informal discussions for me that is often interesting for several reasons.

/Fredrik

 

[bhobba]

How do you come to that conclusion? To the contrary, with more and more advanced technology we are more and more able to observe the "quantum world" (as if there were any other world than the "quantum world"). To handle generic quantum system nowadays becomes more and more applied, and more and more universities of applied sciences develop curricula for the development of "quantum technology".

I think at the moment, direct observation of the quantum world, such as the scanning tunnelling microscope, requires the use of a macro object. But I take your point - technology is progressing rapidly, and such may (perhaps even likely) not hold in the future. So I stand corrected. It is a leftover from the early days of QM and is only an intuitive starting point to a theory based on observables. Even then, there are several QM formulations, all equivalent, some of which do not require observation:
http://math.bu.edu/people/mak/papers/Styer Am J Phys 2002.pdf

So I retract my statement, except as a starting point to a deeper understanding of QM.

Thanks
Bill

 

[Fra]

How do you come to that conclusion? To the contrary, with more and more advanced technology we are more and more able to observe the "quantum world"

This is what I consider to be the meaning of the indirect contact. Ie. The increasing amount of complexity of both preparation and postprocessing of large amounts of information for the image to emerge is what creates a sort of distance in the inference chain. But yes technology makes us reach further.

/Fredrik

 

[vanhees71]

Sure, without measurement devices and other technology there'd not be much of physics and the other natural sciences as we know it today!

 

[CoolMint]

It is just impossible to go much below several nm of scale as the familiar building blocks of matter turn to quantumness(unpredictability). Sure, single atoms can still be manipulated but on a very different set of terms. I'd love to be able to dive in that Sea of unpredictability.