# Aren't Entanglement & Uncertainty mutually exclusive?

1. Sep 15, 2009

### mjcguest

Please bear with me on this one; this is a plea for understanding rather than a "the theory doesn't work" post! I'll keep the question simple... and hope the answers are equally as simple!!

In my naive "understanding" of entanglement, I can not refute an alternative explanation that
- two particles have their particular symetical/complementaty characteristics defined at a point when they are entangled
- when you observe them at a distance, it's therefore no surprise that they remain paired without any need for superluminal / tachyonic / (or whatever!) communication between them

This would seem a more plausible explanation than spooky action at a distance. What am I missing?

Thanks
Matt

2. Sep 15, 2009

### kote

There is no possible explanation using finite three-dimensional local variables that can explain the predictions of QM (and observed correlations). To put it another way, if you're measuring the spin of two entangled electrons, there is no possible definition of spin as a property of electrons that can explain the results of experiments, no matter how the spin of two particles interact with each other during entanglement.

We observe correlations that are simply not possible if spin is a property of electrons unless there is nonlocal signaling. It's all tied to http://plato.stanford.edu/entries/bell-theorem/" [Broken].

Hope that helps!

Last edited by a moderator: May 4, 2017
3. Sep 15, 2009

### tiny-tim

Hi Matt!

You're missing the whole Schrödinger's cat thing …

until we observer the cat, it is neither alive nor dead, and similarly until we observe the spin (say) of one electron, it is neither up nor down …

(and observing the spin in, say the x-direction, stops us from also observing it in the y-direction)

but, if they are entangled, we can tell the spin of electron A (in any direction!) without ever observing it … we only have to observe electron B.

4. Sep 15, 2009

### mjcguest

I've read all the laymen shrodinger, bell type books I can get my hands on; it's just that as soon as I get to entanglement... the "natural" explanations seems so much more compelling! Maybe that's the biggest mistake - looking for an explanation that feels right!

5. Sep 15, 2009

### alxm

Well, did you read about 'hidden variable theories'? Because when you say the properties are defined when they become entangled, unless I've misread you - what you're proposing is exactly that. A local hidden variable. They have values, we just don't know what they are until they're measured.

That's indeed the easy answer, the intuitive answer, and I'm pretty sure most would agree it would've been the answer we'd have preferred, had we had a choice in the matter!

But.. the result of these Bell-test experiments has only proven that it's simply not the case...

6. Sep 15, 2009

### DrChinese

The issue is that the math doesn't work with your hypothesis. Look at the correlation rate for 120 degrees, which QM predicts as 25% due to entanglement. Your idea would require the correlation rate to be 33%, but of course QM is actually correct.

Yours is a good idea. It was good enough for Einstein, who believed as you. Unfortunately, he did not live to read Bell's paper which would easily have convinced him (at least in my opinion). For more info on this, check out:

Bell's Theorem with Easy Math

7. Sep 15, 2009

### mjcguest

8. Sep 16, 2009

### zonde

I found visualization method used in this paper very useful even if there are no creditable solutions for entanglement nonlocality in this paper:
http://arxiv.org/abs/quant-ph/9611037v3" [Broken]

Using this visualization one can easily test that there could not be any local realistic solution if fair sampling assumption is considered to be true.

Last edited by a moderator: May 4, 2017
9. Sep 16, 2009

### DrChinese

This is a completely inappropriate reference on Bell.

First, it is attacking Bell, not explaining Bell. The OP needs to understand WHY the math does not work in his example. Second, it is wrong and is not generally accepted science.

I understand that the idea for for visualization, but Mermin's approach is pretty easy. Discussing fair sampling before understanding Bell is the wrong order, in my opinion. Fair sampling is an experimental issue, more than theoretical.

Last edited by a moderator: May 4, 2017
10. Sep 16, 2009

### zonde

To understand WHY the math does not work in this case visualization was perfect tool for me. So maybe it could be perfect tool for some other newcomer.

Fair sampling is an experimental issue, more than theoretical in most cases. But if we talk about possibility of very serious systematic error that can be included in theory without even noticing it then this is not experimental issue.

11. Sep 16, 2009

### kote

I agree. I would not recommend starting with this paper. The visualization it offers is incorrect. It is an interesting read once you understand all the basic issues and how it fits in to the history of things, but it is entirely misleading if taken anywhere close to face value.

12. Sep 16, 2009

### ThomasT

Your "naive understanding" of entanglement is in line with the basic strategies of experiments designed to produce quantum entanglement. There is a common torque imparted to separated groups of particles, or at least two particles (disturbances) have interacted or had a common origin (eg., they were emitted from the same atom at the same time).

It's assumed (at least tacitly) that the entanglement (the shared or common characteristics produced via common or direct interaction) is produced via local transmissions. Modelling this realistically presents some, maybe insurmountable, formal problems. There are at least a few threads here at PF that have discussed this at length.

Instantaneous action at a distance isn't an explanation. It's a physical impossibility. While FTL proposals seem more plausible, they're not supported by any empirical evidence.

13. Sep 16, 2009

### zonde

You are wrong. Visualization just repeats Bell math giving it all in one simple picture.
This visualization leads exactly to the same results as Bell theorem. The bands she introduce later of course are not from Bell.

14. Sep 16, 2009

### kote

If complementary properties are basic properties that exist persistently in particles, faster than light signaling is required. This has been proven empirically countless times. FTL can only be denied if you deny that spin, for example, is a basic property, or that electrons with spin have a persistent existence. If electrons have persistent existence, FTL is the only explanation.

You're right in that one can always deny that experiments are evidence for anything in particular. That's the problem with science. There are always assumptions that can be denied.

You won't find empirical evidence that supports any other theory more strongly than it supports FTL though. It's empirically as good and as real an explanation as any we have.

I should mention though that FTL is not part of any version of the Copenhagen Interpretation. Bohr denied the persistence of basic properties.

Last edited: Sep 16, 2009
15. Sep 16, 2009

### ThomasT

Nobody can definitively affirm or deny the persistent existence of spinning electrons. Anyway, I don't think of particles and particle properties as constituting what is fundamental in Nature. They're byproducts of the dynamics, which is/are fundamental.

Qm is, in its application, a step up and away from what's fundamental in Nature (imho).

Quantum entanglement has to do with a presumed relationship between two or more particles (quantum disturbances) due to direct interaction (eg., collision with each other), indirect interaction (eg., the imparting of a common torque from a common source while separated), or creation from the same source at the same time (eg., simultaneous emission by the same atom).

Exactly where, when, and how the entanglement relationship is produced is unknown. The mainstream assumption is that it's due to local transmissions/interactions such as in the examples given above.

I don't think "it's empirically as good and as real an explanation as any we have." It stems from a misinterpretation of the meaning of violations of Bell inequalities.

The faulty assumption is statistical, or outcome, independence which is manifested in the factorizable (separable) representation of locality, which representation also includes parameter independence. The principle of locality is compatible with the statistical dependence of entanglement experiments.

Hence experimental violations of Bell inequalities can be used as entanglement witnesses but not as evidence for nonlocality or FTL propagations.

16. Sep 16, 2009

### kote

This last statement is equally impossible to affirm or deny, which is why the empirical evidence is just as good for FTL as anything else. It's similar to the empirical evidence being the same for epicycles and heliocentric motion. If we decide on an interpretation of QM it will be because we've come up with a more fundamental theory or because we make an empirically arbitrary choice between heliocentricity and epicycles.
So you're in the fair sampling camp? I don't think I've seen a combination of "it's fair sampling" and "persistent particles are not basic" before. Maybe I'm misunderstanding you though.

17. Sep 16, 2009

### ThomasT

Physical evidence of luminal and subluminal propagation is all around us. There is, afaik, no physical evidence of superluminal transmissions. In the absence of some sort of evidence to the contrary, then the most reasonable assumption seems to me to be that Nature is exclusively local.

Afaik, the empirical evidence isn't the same for epicycles and heliocentric, eliptical motion.

The assumption is that the Bell test correlations are solely due to local interactions/transmissions. There's no physical evidence that contradicts this assumption.

Wrt the OP, I think that there's no particular reason to abandon the classical, visualizable idea of the nature of quantum entanglement. It has to do with a relationship between entangled quantum disturbances that, presumably, exists before filtration and detection.

18. Sep 16, 2009

### kote

We can debate which assumptions should be made, and no experiment will decide those issues, but we can't have a classical, local, and visualizable theory... not if you mean visualizable in the way Bohr did when he used it extensively.

If you want classical locality you have to ditch visualizability - the idea that we can visualize (understand) the causal processes. This is exactly what Bohr proposes we do, but it's a step that has to be made if you want to keep classical local reality.

19. Sep 16, 2009

### jambaugh

Pardon me for disagreeing. Bell theorem violation in entangled pairs does not imply non-local signaling. Entanglement is simply a priori strong quantum correlation of two systems. This correlation is obtained at the cost of knowing anything about the actual "state" of each individual particle in an entangled pair.

It is true that we cannot due to Bell inequality violation describe the pair in the classical sense of local objective properties. But this doesn't imply non-local signaling. Rather we must invoke non-local signaling in order to recover a "classical" local description and still violate Bell's inequality.

Let's take the example of a pair of totally anti-correlated electrons created at the origin. To keep things simple lets confine them to channels running along the z-axis and ignore x and y components of momentum and position.

The total momentum and spin and center of mass is zero. Now we are in a quandary as to how to label these two electrons. All we have to distinguish them is values for observables. We may consider for example the z-component of momentum and speak of the rising electron vs the descending electron. Or we may consider the z-component of spin and speak of the up electron and the down electron, or we may consider some other component of spin and e.g. refer to the spin x+ and spin x - electron.

In each of these cases we are factoring the two electron system into distinct pairs in a non-mutually consistent way. The spin z+ electron will be in a superposition of x spins.
These different factorizations show that we are not talking about local reality, not about reality at all as such. You must abandon the "state of reality" concept when dealing with quantum systems. This would be necessary if non-local effects were present anyway since any prior observed state could be changed by some future act, i.e. future acts could change the past and any concept of "reality" goes right out the window. But we can abandon classical "reality" and still keep local causality.

Back to the OP's question and the implied question in the title. Does entanglement violate Heisenberg's Uncertainty Principle?

Lets use the z-component of momentum as our labels A = rising electron and B = descending electron.

Now the question is, how does measuring say the z-component of spin for the A electron and the x-component of spin for the B electron not violate HUP?
Since spin components in the different cardinal directions do not commute HUP says we cannot know (=measure) the component of spin in say both the z and x directions.

Lets say we measured the z-component of spin for the A electron and let's say it's spin up. This means we know the z-component we would measure for the B electron if we choose to measure it. So far no HUP violation. Now we choose what to measure...

Case 1: We choose to measure the z-component of spin for the B electron and sure enough it is spin down. No HUP violation there!

Case 2: We choose to measure the x-component of spin for the B electron... just prior to measuring it we don't have a clue what the value will be so no HUP violation yet.
Once we make the measurement (and let's say we got a neg. value) then we loose information about subsequent z-component measurements and HUP is still in force.

Critical to this preservation of HUP is that by virtue of the two particles being entangled, all specific information about either part of the two particles must be unknown. It is actually another application of HUP. The observable for the pair which defines them as anti-correlated does not commute with any of the single particle observables whose values have been so correlated.

You cannot go back and apply HUP conterfactually by saying "well we know the z-component of electron A was +, and now we know if we had gone back and instead measured the x component it would have been + as well." This is a true statement but HUP does not apply because by going back and changing the assumption about what you actually did you also go back and change the assumption that you know what the z-component is. In QM you only know what you measure and Heisenberg's uncertainty principle only applies to measurements not counterfactual hypotheses.

In short, "what we know" about a quantum system depends on "what we do" (measure). Changing assumptions about "what was done" changes "what was known". It's a subtle question of logic you must pay attention to when working with thought experiments vs. actual experiments.

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20. Sep 16, 2009

### kote

Notice that I qualified my statement about nonlocality being implied. I'm not sure what you're disagreeing with, but I can't see anything you've said that contradicts anything I've said . If electrons have persistent reality and the property of spin then nonlocal signaling is the only explanation (along with some other modifications).

Not many interpretations choose nonlocality, but it is a metaphysical interpretive choice. You just have to make sure your assumptions are consistent. David Bohm's interpretation tells one such story with real persistent electrons and spins and nonlocal signaling between electrons.

Of course I'm just using electrons as an example in all of this.