Attempts to explain quantum entaglement

[povillsss]

So I tried googling it but unfortunately i haven't found anything, so I though i'll take my quarries here.

I would like to know, how scientists have tried to explain how quantum entanglement works.

Thanks for the answers. :)

 

[bhobba]

Its in its definition which, if you only read popularisations, you may not have seen.

Suppose you have two systems each of which can be in state |a> and state |b>. I system 1 is in state |a> and system 2 in state |b> this is written as |a>|b>. Conversely if system 1 is in state |b> and system 2 in state |a> this is written as |b>|a>. Now one of the fundamental principles of QM is the principle of superposition so that a state of the two systems is c1*|a>|b> + c2*|b>|a>. When that happens neither system is in a state - its entangled with the other system.

It comes about when systems interact and is responsible for decoherence which explains apparent collapse.

Thanks
Bill

 

[zonde]

I would like to know, how scientists have tried to explain how quantum entanglement works.

There are two ways how scientists have tried to explain entanglement:
- action at a distance;
- shared variables.

 

[povillsss]

So either i formulated my question wrongly or I don't fully understand what you guys are saying.

I know how quantum entanglement works, works. It's like I know that car moves because it's wheels are spinning but I want to know what makes them spin. I know that many scientists (well... at least the ones on TV) claim that we have no idea how 'spooky action at a distance' works and that it conflicts with relativity because 'nothing can travel faster than light', but I believe that there have been multiple attempts to explain it and i want to hear about these attempts

thanks.

 

[bhobba]

I know how quantum entanglement works, works. It's like I know that car moves because it's wheels are spinning but I want to know what makes them spin. I know that many scientists (well... at least the ones on TV) claim that we have no idea how 'spooky action at a distance' works and that it conflicts with relativity because 'nothing can travel faster than light', but I believe that there have been multiple attempts to explain it and i want to hear about these attempts

Here you face a problem because QM does not imply 'spooky action at a distance' - see exactly what bells theorem says:
http://en.wikipedia.org/wiki/Bell's_theorem

Of course those on TV won't tell you that

Now the question here regarding entanglement is why do we have it? Yes research has been done and we know much deeper why. But from what you wrote I don't think you will like it because it's not an answer in a common-sense classical way which most that ask that sort of thing want. But here it is anyway.

Research in quantum foundations has shown that its the most reasonable generalised probability theory that allows continuous transformations between pure states. In fact from some reasonable assumptions there are only two - ordinary probability theory and QM:
http://arxiv.org/pdf/quant-ph/0101012.pdf

When you think about it if you want to model physical systems you need states to have continuous transforms - if a system changes from one state to another state in one second it should reasonably go through another state in half a second.

The interesting thing is there is another thing that differentiates QM from probability theory - entanglement:
http://arxiv.org/pdf/0911.0695v1.pdf

So logically either continuous transformations or entanglement determines QM. So the deep reason for entanglement - we want continuous transformations between pure states.

But as you can see the answer is mathematical - not in terms of classical pictures. You may not like that - but its the way nature is - it doesn't have to oblige to how people want to view it.

Thanks
Bill

 

[zonde]

So either i formulated my question wrongly or I don't fully understand what you guys are saying.

I know how quantum entanglement works, works. It's like I know that car moves because it's wheels are spinning but I want to know what makes them spin. I know that many scientists (well... at least the ones on TV) claim that we have no idea how 'spooky action at a distance' works and that it conflicts with relativity because 'nothing can travel faster than light', but I believe that there have been multiple attempts to explain it and i want to hear about these attempts

thanks.

As I understand you want to hear about attempts to explain how 'spooky action at a distance' works, right?

Well, there is mathematically very simple and elegant theory - Newton's theory of gravity. It too works by 'instantaneous action at a distance'. It is now considered approximation of mathematically much more complex General relativity theory that works without 'instantaneous action at a distance'.
What I want to say is that it is generally considered undesirable to implement 'instantaneous action at a distance' in a theory. So there are attempts to explain entanglement without 'instantaneous action at a distance' but I doubt that there are recognized attempts to explain 'instantaneous action at a distance'.

 

[craigi]

So either i formulated my question wrongly or I don't fully understand what you guys are saying.

I know how quantum entanglement works, works. It's like I know that car moves because it's wheels are spinning but I want to know what makes them spin. I know that many scientists (well... at least the ones on TV) claim that we have no idea how 'spooky action at a distance' works and that it conflicts with relativity because 'nothing can travel faster than light', but I believe that there have been multiple attempts to explain it and i want to hear about these attempts

thanks.

Try the following links:

http://en.wikipedia.org/wiki/Hidden_variable_theory
http://en.wikipedia.org/wiki/De_Broglie–Bohm_theory
http://en.wikipedia.org/wiki/Superdeterminism
http://przyrbwn.icm.edu.pl/APP/PDF/125/a125z5p07.pdf (Read the editor's note at the end for further clarification)

It's not an exhaustive list, but I think they're what you're looking for.

 

[naima]

Action at a distance in entanglement is an attempt to introduce a distance where nothing needs it. Of course Bob and Alice make their measurements at different places but they also are in rooms with different temperatures. Would you then speak of an action at a distance along the axis of temperatures?
Entanglement needs nor temperature nor distance.

 

[vanhees71]

There's a very simple answer to the question in the OP: Quantum theory is how entanglement is defined and explained. There's nothing else to add, at least not according to contemporary knowledge of physics. Physics, of course, is not complete, as long as there's not one consistent theory describing (note that physics never explains nature but describes her as precisely as possible) all observable reproducible objective phenomena in nature.

So far, we have two fundamental theories, describing all known phenomena: The one is the mathematical description of space and time, the General Theory of Relativity, which has its centennary this year, and the other other quantum theory, which describes the so far understood part of the matter in terms of elementary particles. Fortunately this latter realm is describable using the Special Theory of Relativity as a space-time model, i.e., neglecting the very weak gravitational interaction. To formulate a quantum (field) theory with a general relativistic space-time model is quite difficult and not fully understood in all its details. What's a totally open question is whether there exists a consistent mathematical description of quantum gravitation. The reason is that it is very hard to find observable quantum effects of the gravitational interaction.

However, entanglement is a ubiquitous phenomenon and described to a very high accuracy in accordance with all high-precision experiments in terms of standard relativistic quantum field theory, and it is very important to note that there is non action at a distance whatsoever involved with it. This is so even by construction! In the so far successful realizations of relativistic quantum theory, one assumes from the very beginning that all interactions are local, and as a consequence there cannot be an action at a distance. An action in some region cannot causally affect another phenomenon at a distant region instantaneously, but it needs at least the time light would need to travel from the first place to the second. That's the "cosmic speed limit" inherent in the theory of relativity and thus by construction also for local relativistic quantum field theories. This type of models is very successful in describing the matter surrounding us in terms of quarks, leptons, the Higgs boson and socalled gauge fields, the Standard Model of Elementary Particle Physics.

Although there are no actions at a distance, you can create composite systems whose "parts" are correlated over very long distances. This is one aspect of entanglement. It is quite difficult to keep this entanglement for some time to enable such long-distance correlations, because it can be prepared only for microscopic objects, and such objects are very easily affected by interactions with anything in the "environment". That's why most experiments demonstrating this very fascinating long-distance correlations are done with photons, which can be created in entangled pairs (biphotons) and these can be kept entangled quite successfully nowadays.

A biphoton is created by shooting a laser into a birefringent crystal by a process called "parametric downconversion". Very simplified one can say, a photon out of the laser field is split into two lower-energetic photons in such a way that their polarizations are entangled. These photons then run "back to back" (again spoken in a very simplified way), and if you wait long enough, they are located at far distances, but they still need a finite time since they travel with a finite speed through a vacuum, the speed of light. Now, the entanglement of their polarization is still preserved.

The mind-boggling consequence of such a biphoton state is now the following: According to quantum theory, when measuring the polarization of each of these photons at far-distant places (usually named A and B for the names Alice and Bob of observers doing the experiment), you'll find absolutely random polarizations. You cannot predict which polarization (horizontal or vertical using a correspondingly directed polarization filter) you'll observe, but quantum theory tells you that with 50% probability A and B find a h-polarized photon and with 50% a v-polarized photon. However, the photon polarizations are entangled, as long as during their way from the source to Alice's and Bob's detectors they are no disturbed in any way, and this preparation of entangled polarization implies that the outcomes of Alice's and Bob's measurements are 100% correlated! If Alice measures a h-polarized photon, Bob with certainty finds a v-polarized photon. It doesn't matter who measures her or his photon first, which shows that it is not the Alice's measurement that can affect Bob's result and vice versa (at least if you believe in causality according to the relativistic space-time description), but that it is the preparation in the very beginning that causes this 100% correlation of totally random single-photon polarizations.

Now, there was an objection against this "minimal statistical interpretation" of quantum theory, mostly brought forward, because many scientists have had (and some have still today) objections against a probabilistic world view. What if nature is deterministic, and the single-photon polarizations only appear random, because we don't know some "hidden parameters"? At the first glance, this could well be true, and for some time the physicists thought that you cannot easily distinguish such a deterministic hidden local variable model from the intrinsically probabilistic quantum behavior. Then John Bell showed in the 1960ies that this is not true! At least if you assume that the deterministic theory is also local (i.e., that there are no actions at a distance), you can derive an inequality about the probabilities to measure certain polarizations that are violated when the quantum theoretical prediction is used (in this case Alice and Bob must put their polarization filters in certain non-collinear and non-perpendicular angles). This violation of Bell's inequality has been demonstrated with an overwhelming accuracy. In fact, it's among the most accurate tests of a theory done in physics so far!

Although you still cannot exclude the possibility that one day somebody finds a non-local deterministic theory describing all observed phenomena as well as quantum theory, but so far to my knowledge nobody has found one, and at the same time quantum theory works very well, so that there's no reason to find such an alternative theory.

 

[Matta Tanning]

Entanglement is the name we give to nature's violation of Bell's inequalities. Bell's inequalities are derived from the consideration of a local universe. Quantum mechanics predicted this violation and it was verified in the http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.47.460 experiment in 1981.

To understand what this means, the best person in the whole world to learn from is Bell. One paper I love is La Nouvelle Cuisine written in 1990.

Explanations of entanglement I have known:

1. Quantum mechanics allows for superluminal influence (i.e. it breaks Bell inequalities) but does not allow superluminal signalling with its conscious operators. So no explanation required because relativity doesn't mind. Bell assaults this at the end of La Nouvelle Cuisine.
   
2. The universe is superdeterministic so the universe ensured that Aspect and his mates at the other end of the apparatus did precisely the right experiments on the right day of the week having eaten a good breakfast to come out with the results that looked nonlocal. Nothing nonlocal was going on, fate is playing with us.
3. EPR = ER. I don't understand this too well. My best guess is entanglement equals wormholes.
   
4. de Broglie Bohm. A nonlocal formulation of quantum mechanics. Boom goes relativistic causal structure.
   
5. Bell's theorem is based on some assumptions: a certain amount of free will, relativistic causal structure and classical logic. Quantum Measure Theory is an attempt to fuzzify the universe a bit so that Bell's theorem no longer holds. Entanglement is not real, we live in a local universe, the violation of Bell's theorem is actually a violation of classical logic, rather than relativistic causal structure.

A very good clarification of Bell can be found in Norsen's 2011 paper: J.S. Bell's concept of local causality.

 

[Nugatory]

A very good clarification of Bell can be found in Norsen's 2011 paper: J.S. Bell's concept of local causality.

Look for posts by member ttn: https://www.physicsforums.com/members/ttn.16261/

 

[vanhees71]

Again: According to standard relativistic quantum theory, which is realized as local microcausal quantum field theory, there is no action at a distance and no superluminal signal propagation whatsoever. This is excluded by construction, i.e., microcausality!

Entanglement describes quantum correlations, which can refer to parts of a composite system that are detected at far-distant local experiments. This does in no way imply the possibility of superluminal signal propagation (information transfer). Also this is inherent in the construction of relativistic QT as a local microcausal quantum field theory, because these properties are sufficient for the validity of the linked-cluster theorem. See S. Weinberg, Quantum Theory of Fields, vol. 1.

 

[atyy]

Now, there was an objection against this "minimal statistical interpretation" of quantum theory, mostly brought forward, because many scientists have had (and some have still today) objections against a probabilistic world view. What if nature is deterministic, and the single-photon polarizations only appear random, because we don't know some "hidden parameters"? At the first glance, this could well be true, and for some time the physicists thought that you cannot easily distinguish such a deterministic hidden local variable model from the intrinsically probabilistic quantum behavior. Then John Bell showed in the 1960ies that this is not true! At least if you assume that the deterministic theory is also local (i.e., that there are no actions at a distance), you can derive an inequality about the probabilities to measure certain polarizations that are violated when the quantum theoretical prediction is used (in this case Alice and Bob must put their polarization filters in certain non-collinear and non-perpendicular angles). This violation of Bell's inequality has been demonstrated with an overwhelming accuracy. In fact, it's among the most accurate tests of a theory done in physics so far!

That is not the "objection". The idea is that the minimal statistical interpretation requires an observer, and we have trouble including the observer in the purely quantum part of the system. So if we believe the observer is also described by laws of physics, then quantum mechanics is incomplete, unless something like MWI works. The objection is not randomness per se, but rather than there are two rules of evolution - one deterministic and one random, and an observer is needed to decide when each rule is applied.

 

[vanhees71]

What do you mean by "observer"? If you consider measurement apparati as "observers", I agree that one needs them to define the meaning of natural science to begin with. That's not specifically quantum theoretical. To be able to do physics in the modern sense you need to define observables in terms of a description how to measure them. This is true already for classical mechanics, where you need operational descriptions of how to measure time, position, velocity, mass, force, etc.

Why this argument implies that quantum theory is less complete than classical deterministic world models thus is not very convincing for me. BTW I don't believe that any so far established model is "complete", and I don't think that you can make quantum theory a "complete" one (whatever "complete" means) by just finding other interpretations. Why makes MWI (for me pure esoterics without any scientific implications going beyond the minimal interpretation) quantum theory more "complete" than it already is within the minimal interpretation, which latter is the only interpretation you need to apply quantum theory to real-world experiments?

 

[atyy]

What do you mean by "observer"? If you consider measurement apparati as "observers", I agree that one needs them to define the meaning of natural science to begin with. That's not specifically quantum theoretical. To be able to do physics in the modern sense you need to define observables in terms of a description how to measure them. This is true already for classical mechanics, where you need operational descriptions of how to measure time, position, velocity, mass, force, etc.

Why this argument implies that quantum theory is less complete than classical deterministic world models thus is not very convincing for me. BTW I don't believe that any so far established model is "complete", and I don't think that you can make quantum theory a "complete" one (whatever "complete" means) by just finding other interpretations. Why makes MWI (for me pure esoterics without any scientific implications going beyond the minimal interpretation) quantum theory more "complete" than it already is within the minimal interpretation, which latter is the only interpretation you need to apply quantum theory to real-world experiments?

In classical mechanics, you can set the initial conditions and then the time evolution occurs.

In quantum mechanics, there is deterministic unitary evolution and random collapse when a measurement occurs. So there are 2 rules for time evolution. When does which occur? That requires an external observer, something not required in classical physics.

One could argue that the system is open. However, that means that we have trouble saying quantum mechanics is a theory of the whole universe, since in what sense is the universe "open"? So the observer has a special status in quantum mechanics in any minimal interpretation.

 

[craigi]

What do you mean by "observer"? If you consider measurement apparati as "observers", I agree that one needs them to define the meaning of natural science to begin with. That's not specifically quantum theoretical. To be able to do physics in the modern sense you need to define observables in terms of a description how to measure them. This is true already for classical mechanics, where you need operational descriptions of how to measure time, position, velocity, mass, force, etc.

Why this argument implies that quantum theory is less complete than classical deterministic world models thus is not very convincing for me. BTW I don't believe that any so far established model is "complete", and I don't think that you can make quantum theory a "complete" one (whatever "complete" means) by just finding other interpretations. Why makes MWI (for me pure esoterics without any scientific implications going beyond the minimal interpretation) quantum theory more "complete" than it already is within the minimal interpretation, which latter is the only interpretation you need to apply quantum theory to real-world experiments?

Complete theory is a rigorously defined term in mathematical logic.
http://en.wikipedia.org/wiki/Complete_theory

It was in this sense that Einstein considered Quantum Theory incomplete. Specifically, he believed that the wavefunction could not be the complete description of a system. In the MWI, the wavefunction is universal. It describes everything, the system under observation, observers and observation devices.

 

[bhobba]

Entanglement is the name we give to nature's violation of Bell's inequalities.

Its a lot wider that that. Bells inequality is simply the consequence of entanglement as found in so called Bell states. Although if you read popularisations its easy to get that view.

Its what I said before. Suppose you have two systems each of which can be in state |a> and state |b>. I system 1 is in state |a> and system 2 in state |b> this is written as |a>|b>. Conversely if system 1 is in state |b> and system 2 in state |a> this is written as |b>|a>. Now one of the fundamental principles of QM is the principle of superposition so that a state of the two systems is c1*|a>|b> + c2*|b>|a>. When that happens neither system is in a state - its entangled with the other system.

Explanations of entanglement I have known

There is no explanation - its a fundamental property of quantum systems implied by the principle of superposition. I gave some links previously that examines why that's the case (its to do with the requirement of continuous transformations between pure states). But basically there is no explanation.

Thanks
Bill

 

[bhobba]

It was in this sense that Einstein considered Quantum Theory incomplete

No. One can define QM rigorously as, for example, the following details:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

The sense Einstein meant it is that is was an approximation to a more complete theory that removed the issues he saw with QM in a similar way QM removed some issues with classical mechanics such as applying thermodynamics to Blackbody radiation. He may be correct - we simply do not now.

Thanks
Bill

 

[vanhees71]

In classical mechanics, you can set the initial conditions and then the time evolution occurs.

In quantum mechanics, there is deterministic unitary evolution and random collapse when a measurement occurs. So there are 2 rules for time evolution. When does which occur? That requires an external observer, something not required in classical physics.

One could argue that the system is open. However, that means that we have trouble saying quantum mechanics is a theory of the whole universe, since in what sense is the universe "open"? So the observer has a special status in quantum mechanics in any minimal interpretation.

In quantum mechanics I can set the initial conditions ("preparation") and there's causal evolution of the state. There's no collapse as a physical process. It's just the interaction of the system with the macroscopic measurement apparatus, which is described in a (semi-)classical approximation (coarse-graining). This changes the state of the measured system (often in such a way that it is destroyed and cannot be used anymore for further investigations; the other extreme is a von-Neumann-filter measurement, which can be considered a possible preparation procedure).

There is no physical theory for the universe as a whole. You cannot even define, how to test such a theory, because you cannot repeat the "experiment" in "preparing" ever new universes. So why should I, as a physicist, bother about such a "theory" at all?

 

[vanhees71]

Complete theory is a rigorously defined term in mathematical logic.
http://en.wikipedia.org/wiki/Complete_theory

It was in this sense that Einstein considered Quantum Theory incomplete. Specifically, he believed that the wavefunction could not be the complete description of a system. In the MWI, the wavefunction is universal. It describes everything, the system under observation, observers and observation devices.

This is a mathematical definition without much relevance for what Einstein (EPR) and Bohr in his answer were after in their debate about the "completeness" of quantum theory. To the contrary this is a (still ongoing) debate about the physical interpretation of the mathematical formalism, which latter is not much to debate about, because it's just the theory of unbound operators on Hilbert space.

This is, unfortunately, true only for non-relativistic QT. Today, there's no realistic completely defined mathematical consistent QFT, applicable to the real world. Nevertheless the perturbative definition of the Standard Model is the most successful physical theory ever. It's so successful that this becomes a problem since one knows that it is not a complete description of matter and it also has intrinsic problems like the hierarchy problem etc. Unfortunately, there's no clear hint, where it fails and thus there's no clear idea how to extend the Standard Model to a more comprehensive model, perhaps also including possible candidates for Dark Matter. The experimental proof for the existence of, e.g., SUSY-particles is a much bigger challenge than the finding of the Higgs (unfortunately it seems to be really THE Higgs of the SM with the minimal Higgs doublet).

 

[atyy]

There is no physical theory for the universe as a whole. You cannot even define, how to test such a theory, because you cannot repeat the "experiment" in "preparing" ever new universes. So why should I, as a physicist, bother about such a "theory" at all?

There are two separate issues:
(1) Do we need an ensemble to test a theory? (2) Is there a theory of the whole universe?

(1) Do we need an ensemble to test a theory? I think we don't, even with the minimal interpretation of quantum mechanics, otherwise the wonderful calculation of Mukhanov and Chibisov will not make any sense. Here, we only have repeated observations, which collapse the observed universe repeatedly, with which to test their theory. In order to test their theory, we have to somehow assume that we are typical.

(2) Is there a theory of the whole universe? A theory is necessarily something that humans can imagine. The main reason for thinking there is one is that we believe that the observer is also described by laws of physics. The main reason for thinking there may not be one is that such a "theory" may not be something humans can imagine. Traditionally, physics does not know where the limit of human comprehension lies, and works on the first assumption. Classical general relativity is a theory of the whole universe. Furthermore it is a theory which is used in quantum mechanics, because with the positive cosmological constant, the background on which quantum mechanics is done is a curved classical spacetime.

 

[vanhees71]

Which calculation by Mukhanov and Chibisov? I'm pretty impressed about my power to collapse the entire observable universe by observing it ;-)).

There's a theory about the whole universe, but it's not testable and thus not a physical theory in the usual sense. It's a delicate question, whether you consider cosmology a science. The only thing we can say is that the assumptions underlying the Cosmological Standard Model are consistent with all our observations so far (CMBR anisotropies/polarization, redshift-distance relations of supernovae,?).

Usually we don't do relativistic QFT in an GR background. It's not an easy issue to define even such a theory with a classical background space-time, although it's feasible. On the other hand, are there any testable predictions of such a theory?

 

[atyy]

Which calculation by Mukhanov and Chibisov? I'm pretty impressed about my power to collapse the entire observable universe by observing it ;-)).

The one about quantum fluctuations in the context of inflation producing large scale structure.

There's a theory about the whole universe, but it's not testable and thus not a physical theory in the usual sense. It's a delicate question, whether you consider cosmology a science. The only thing we can say is that the assumptions underlying the Cosmological Standard Model are consistent with all our observations so far (CMBR anisotropies/polarization, redshift-distance relations of supernovae,?).

Usually we don't do relativistic QFT in an GR background. It's not an easy issue to define even such a theory with a classical background space-time, although it's feasible. On the other hand, are there any testable predictions of such a theory?

Well, since the cosmological constant is positive, we have to assume the standard model of particle physics is really on a curved spacetime - or can we still consider perturbations about flat spacetime?

 

[vanhees71]

True, but for all experiments with accelerators on Earth, the corresponding corrections to the usual Minkowski-space QFT is tiny.

 

[atyy]

True, but for all experiments with accelerators on Earth, the corresponding corrections to the usual Minkowski-space QFT is tiny.

Yes, it's more a matter of principle, so we can say quantum mechanics accounts for all current observations. When I say that I usually take QFT on curved spacetime, include the standard model of particle physics, and include quantum Einstein-gravity, all taken as low energy effective theories.

The missing terms there are dark matter and neutrino mass, but they are not very severe, since we think we will know how to add those when the observations come into constrain the theory.

It isn't ok to define a theory perturbatively, even in the Wilsonian framework, since at least the high energy theory must have non-perturbative definition. So I usually take QED to be non-perturbatively defined via a lattice with small but finite spacing, and large but finite volume. But I don't know what the non-perturbative definition when chiral fermions interacting with non-Abelian gauge fields are - currently there is no known lattice solution - is there any other way to define the standard model non-perturbatively?

 

[atyy]

Which calculation I'm pretty impressed about my power to collapse the entire observable universe by observing it ;-)).

Oh, of course you only collapse the wave function of the entire observable universe :) Whether that is the same as collapsing the entire observable universe is a matter of intepretation.

 

[povillsss]

Wow, guys, Thanks for all the answers.

I really appreciate them :)