# Attempts to explain quantum entaglement

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1. Apr 17, 2015

### 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.

2. Apr 17, 2015

### Staff: Mentor

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

3. Apr 18, 2015

### zonde

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

4. Apr 18, 2015

### 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.

5. Apr 18, 2015

### Staff: Mentor

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 wont 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

6. Apr 19, 2015

### zonde

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'.

7. Apr 19, 2015

### craigi

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.

8. Apr 19, 2015

### 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.

9. Apr 19, 2015

### 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.

Last edited: Apr 20, 2015
10. Apr 22, 2015

### 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 [Broken] 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.

Last edited by a moderator: May 7, 2017
11. Apr 22, 2015

### Staff: Mentor

12. Apr 22, 2015

### 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.

13. Apr 22, 2015

### atyy

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.

14. Apr 22, 2015

### 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?

15. Apr 22, 2015

### atyy

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.

16. Apr 22, 2015

### craigi

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.

Last edited: Apr 22, 2015
17. Apr 22, 2015

### Staff: Mentor

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.

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

Last edited: Apr 22, 2015
18. Apr 22, 2015

### Staff: Mentor

No. One can define QM rigorously as, for example, the following details:

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

Last edited by a moderator: May 7, 2017
19. Apr 23, 2015

### vanhees71

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?

20. Apr 23, 2015

### vanhees71

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).