Entanglement HELP: A Heuristic Explination Needed

[Glenns]

Entanglement HELP!

I can't find a decent, heuristic explanation for entanglement anywhere. Wikipedia is both pedantic and pretentious on the subject.
Can someone on this message board with a good, solid understanding of entanglement please give a heuristic, non-mathematical explanation? I know it has to do with HTZ, whic is a special experiment, but the only source I could find (pdf on the internet) was all but incomprehensible.
HELP!

 

[Tac-Tics]

I'll explain it as best I can with precision hand-waving.

We're talking about states. A state is a generic term for something we can measure. Position, energy, momentum, spin... even macroscopic things, like color or intelligence. Even though we don't see quantum effects, we can still pretend, because it makes it more amusing for me. In this hand-waving example, we're going to use dodgeballs. Dodgeballs come in two classic colors: blue and red.

We take one ball. The classical states it can be in are |Blue> and |Red>. Whenever we look at it, its color is one of those colors. But when we aren't looking at it, it can do cool quantum mechanical things. I can be in a superposition of states. That is, it can be in any state "A |Blue> + B |Red>" where A and B are (complex) numbers. When we look at the ball, though, that complex state reduces to a classical one, and we see either a |Blue> ball or a |Red> ball (governed by the squares of the lengths of A and B in the quantum state).

So a ball in a superposition of states acts like a probabilistic ball. As soon as we look at it, it becomes |Blue> or |Red>. That's really not the amazing part. The coolness comes in when we have two or more balls.

Are looking at two balls, each ball can either be |Blue> or |Red>. There are four possible classical states: |Blue-Blue>, |Blue-Red>, |Red-Blue>, and |Red-Red>. When we look at the balls, we always find the pair in one of these states. But when we're not looking at them, they can be in funny superposition states. One interesting state is called the Bell state: $$1 / \sqrt{2}$$(|Blue-Blue> + |Red-Red>).

Take a pair of balls in the Bell state. When we look at them, the state of the system collapses (with equal probability) to either |Blue-Blue> or |Red-Red>. The balls are always the same color, but which color is chosen randomly. If these two balls are put into the Bell state, and then taken to opposite ends of the playground without looking at them, we don't know what color either is, but we know when we eventually get curious and look, the color of the ball on the other side of the playground will be the same.

This is a big deal for classical physicists and the thing that drove a lot of scientists crazy in the 1920s while simultaneously providing them with a good source of research. The fate of the two dodgeballs is intertwined. You cannot treat them as two balls with a 50% chance of being Blue or Red, because their color is correlated. In a sense, you can't treat them as two balls; you must treat them as a single pair of balls.

Einstein and friends really badly wanted to show that quantum mechanics *could* treat the balls as a having their own individual identities, but later John Bell came up with an experiment that disproved this (the details of which I don't know and won't explain here).

But I hope that gives you at least a little idea what the heck people are talking about!

 

[Dragonfall]

Entanglement is like knowing that $$a\oplus b=0$$, but (1) you can at best make a statistical guess about a and b and (2) knowing either reveals what the other is.

 

[ourben]

This is what I always understood entanglement to mean... and this is exactly why I don't get it.

How do we know the state isn't already determined? Is that something we discovered by adding further polarisers to the experiment?

I wish there was a garden shed way of witnessing this proof.

 

[DrChinese]

This is what I always understood entanglement to mean... and this is exactly why I don't get it.

How do we know the state isn't already determined? Is that something we discovered by adding further polarisers to the experiment?

I wish there was a garden shed way of witnessing this proof.

To understand why the result is not predetermined, you need to look at Bell's Theorem. Unfortunately, there is math to follow - which is easy - but that is the proof.

I have a very simple proof of Bell's Theorem on the following page:

Bell's Theorem with Easy Math

The upshot is that Bell discovered that predetermination involves an implied assumption, and that assumption is incompatible with the predictions of Quantum Mechanics. If there is predetermination, then the choice of measurement setting should not affect the results. On the other hand, the results DO appear to be affected by the subsequent choice of measurement settings. Therefore, the results are NOT predetermined.

 

[ThomasT]

I can't find a decent, heuristic explanation for entanglement anywhere.

That's because there isn't one.

Can someone on this message board with a good, solid understanding of entanglement please give a heuristic, non-mathematical explanation?

Again, there isn't, afaik, a qualitative, non-mathematical description of what quantum entanglement is in the physical world that, presumably, underlies experimental instrumental behavior.

Many have tried in vain to understand quantum entanglement in the way that you would like to, however, the quantum theory itself seems to say that such an understanding is impossible.

A heuristic approach has been useful (and sometimes almost necessary in the beginning phases) in the development of some physical models (eg., Schroedinger's ideas on quantum entanglement, Einstein's ideas on light quanta, etc.). However, the current understanding of quantum entanglement is strictly technical and mathematical. And, the point of departure for this understanding is the experimental preparation and behavior of materials and instruments, not some apprehension of the underlying causes of that behavior. Afaik, all attempts to develop such an apprehension, which would manifest itself as a rather useful heuristic, are so far either incoherent or untestable.

The current techno/math understanding (and the Wikipedia article seems to be an ok exposition of it) is neither pretentious nor unnecessarily pedantic. It's the culmination of the better part of a century's worth of theoretical and experimental research on the subject. And, it's the only way in which quantum entanglement is understood.

Below is a link to a thread in which I try to approach a heuristic understanding of quantum entanglement, and in which one of the PF Mentors, vanesch, effectively argues against my feeble attempt(s).
https://www.physicsforums.com/showthread.php?t=250187

So, don't lose any sleep over not having a qualitative understanding of the deep nature of quantum entanglement. Nobody does.

 

[ourben]

To understand why the result is not predetermined, you need to look at Bell's Theorem. Unfortunately, there is math to follow - which is easy - but that is the proof.

I have a very simple proof of Bell's Theorem on the following page:

Bell's Theorem with Easy Math

The upshot is that Bell discovered that predetermination involves an implied assumption, and that assumption is incompatible with the predictions of Quantum Mechanics. If there is predetermination, then the choice of measurement setting should not affect the results. On the other hand, the results DO appear to be affected by the subsequent choice of measurement settings. Therefore, the results are NOT predetermined.

Thank you DrChinese,

I'm going to have to witness a practical experiment before it will sink in though. Not that what that link said doesn't make sense, but I need to see it happen. On a side note, why does that page say the moon doesn't exist when nobody is looking? Or was that a joke?

 

[RandallB]

On a side note, why does that page say the moon doesn't exist when nobody is looking? Or was that a joke?

No Joke
It speaks directly to how the Copenhagen (Bohr) Interpretation of QM conflicted with the Einstein view of a realistic reality.

A good way to illustrate the issue is simple SINGLE SLIT experiment. (Don’t even need to use two slits or some fancy entanglement demonstration.)
By sending individual particles through a narrow single slit; a screen at some distance will show a dispersion pattern of particle hits.
Common sense (Einstein) says that as each particle departs the slit it obviously has assumed a direction (Based on whatever apparently random function) and once established it follows that determinate direction.
Note: this view allows for a random function to set the determinate direction with no requirement for a identifiable predetermined detection to be preset in any way – Einstein was not advocating what most refer to a “determinism”. Just that the direction was set upon leaving the slit – and yes that does pre-determine the area on the screen where it will hit; that is a determinate parameter of the particle after leaving the slit. Knowing what that path is cannot be determined prior to the particle reaching the slit is a matter of measurement uncertainty the random changes in how the two (Particle & Slit) for so many variables involved are just a part of that measurement uncertainty.

Copenhagen takes a different view:
that reality involves more than a measurement uncertainty but a fundamental uncertainty that can be mathematically defined.
And part of defining it depends on only using what is observed as being “real”.
Thus, since there is nothing to be observed until the particles actually hit the screen their reality is spread across the entire screen in a HUP function and not until the screen reduces that HUP function to a detection is the location on the screen determined. No here is the important part for Copenhagen – it does not say that when it set that location on the screen you may draw a line back to the slit and declare that as the path the photon took. Until the detection of the photon it had no path just the HUP probability distribution across the range of the screen. A function that of course cannot exist if anything should disturb the function like detecting the particle somewhere between the slit and the screen.
With no defined path back to the slit, there is no way to tell which slit was used if there happened to be two slits. Only the HUP function defined by there being two or more slits available.

So if HUP says things are only where we see them, when we see them there. The Moon could be anywhere when it is not measured though some observation and is only really there for sure when we see that it is there. Einstein complained that the moon is there if we look at it or not; just as the photon must follow some path to the screen even if it cannot be measured.

So the counter to the Moon complaint: if there is a determinate path for a photon then when using two slits why not just show what that path must be for one or some of them indicating which slit was used.
I assume you are familiar with attempts to show “Which Way”.

Likewise entanglement Polarization experiments are just more sophisticated attempts to do the same thing. Give realistic views a chance to explain phenomena that unrealistic (Non-Local) views can.

So far it hasn’t worked out so good for realistic interpretations attempting to support the Einstein view that the Moon is for sure there if we don’t see it.

 

[Bible Thumper]

I was thinking that the equation (or system of equations) was actually created around a perceived uncertainty. Later on, this equation proved to be applicable to all areas of quantum phenomena in it's accuracy of prediction. Thus, the assumption that quantum phenomena is uncertain was born.

It could be that the photon leaving the slit is deterministic; it's just that our mathematical framework (framework that was built around uncertainty) works fine in predicting where that photon will land on the screen, provided we jettison any idea of determinism.

This accuracy of the equation may give the appearance of quantum uncertainty, but behind the apparent statistical behavior of the photon lies a truly classical way of explaining why the photon lands on the screen from the slit where it does. Under current theory, the photon lands where it does because there's a superposition. But it's our mathematics that tells us there's the superposition, when in fact, the equation was built on and created by experimental results in the first place.

Experiment gave way to the equation (Heisenberg's uncertainty relation and others); the equation gave way to explaining things in a statistical way (that a wavefunction 'collapses' when observed, sum over histories, etc.).

Quantum theory (and its related mathematics) can't be contested because it agrees so well with experiment. But it was experiment that created quantum theory and its equations in the first place. By contesting and questioning quantum theory, you are questioning the mathematics behind quantum theory. And when you are questioning the mathematics behind quantum theory, you are questioning the evidence that gave birth to those equations. Again, by contesting and questioning quantum theory, you are questioning the mathematics behind quantum theory. When you are questioning the equations behind quantum theory, you are questioning the evidence that gave birth to those equations, ad infinitum.

 

[Bible Thumper]

I edited that last post of mine a cajillion times, so if it's not clear, let me know...

 

[DrChinese]

On a side note, why does that page say the moon doesn't exist when nobody is looking? Or was that a joke?

It's just a saying, not meant literally. No one is saying that the moon itself does not exist when no one is looking, or that a particle itself does not exist.

What is serious is the question of whether particle observable ATTRIBUTES have simultaneous reality. That is the fundamental question being posed. When someone says that realism must be jettisoned, they mean that there are NOT simultaneously real particle attributes. This position is fully compatible with the facts.

Einstein, on the other hand, was both a realist AND a skeptic of "spooky action at a distance". This position no longer has accepted scientific merit.

 

[DrChinese]

I was thinking that the equation (or system of equations) was actually created around a perceived uncertainty. Later on, this equation proved to be applicable to all areas of quantum phenomena in it's accuracy of prediction. Thus, the assumption that quantum phenomena is uncertain was born...

This is not an accurate summary. The uncertainty principle was designed to match the facts, not the other way around. Once created, it has proven itself useful in all manner of predictions.

There are plenty of experiments in which the uncertainty principle has been shown to be accurate in which there is no apparent uncertainty in the measuring apparatus itself. Bell tests - i.e. on photon polarization - are an example. These results clearly cannot be explained classically; many have tried but Bell's Theorem is just too powerful.

Your reasoning is essentially circular, because anyone could take a different approach to the mathematics if it would lead to a useful alternative theory. But that has not yet been presented. On the other hand, Quantum Theory is useful.

 

[RandallB]

I was thinking that the equation (or system of equations) was actually created around a perceived uncertainty. Later on, this equation proved to be applicable to all areas of quantum …..

NO
as I read the history the issue of Measurement Uncertainty was a growing problem and “equations” to resolve that were not what grew into QM.
HUP was proposed as a key to understanding a new way of looking at the issue. Bohr helped move the idea to a new view of reality (Copenhagen) that needed QM equations. So Measurement Uncertainty did not build QM directly; QM was a new view (that built equations based on observations) that solved or accounted for the paradox of Measurement Uncertainty.
The issue is – does QM give a complete as possible accounting of reality. (the ‘as possible’ part comes directly from Bohr and is important)

It could be that the photon leaving the slit is deterministic; it's just that our mathematical framework (framework that was built around uncertainty) works fine in predicting where that photon will land on the screen, provided we jettison any idea of determinism.

Personally, I dislike the term “deterministic” here, better to say the photon leaving the slit has acquired determinate parameters including a LHV to express the Einstein view. Not that it is technically wrong at all, but using it will inevitably have some assume determinism is involved and even Einstein had trouble getting people to stop saying he believed in determinism.

This accuracy of the equation may give the appearance of quantum uncertainty, but behind the apparent statistical behavior of the photon lies a truly classical way of explaining why the photon lands on the screen from the slit where it does. Under current theory, the photon lands where it does because there's a superposition.

The problem here is the blind statement:
“behind the apparent statistical behavior of the photon lies a truly classical way of explaining why the photon lands on the screen from the slit where it does”

There is no such established fact. Where is that way of explaining the behavior of an individual photon? Classical explanations are based on observations too. And observations of Light, not individual photons both for Mauls Law of polarization and inference patterns becoming imbedded in the dispersion pattern of a double slit.

Although I personal have the same preference as Einstein for realism, against “action at a distance”, and that there is a more complete “Local” explanation; no one can make your statement that there is such an explanation until that explanation is presented.

Also, there is no evidence presented by QM proponents that a “Local” solution cannot be made for the double slit, only that no one has done so successfully. But the Bell Theorem & Experiments make a negative proof argument against a HV Local solution. So if there is a non QM way to explain it – the EPR Polarization correlations is the one to give an explanation for if any claim to being better than the QM explanation is to be considered.

Just do not claim there is an explanation without giving it.