Bell's inequality and hidden variables

[grav]

Consider the following links describing a test of Bell's inequality involving the polarization of light.

http://en.wikipedia.org/wiki/Quantum...est_prediction

http://www.drchinese.com/David/Bell_..._Easy_Math.htm

http://www.optics.rochester.edu/work...pt253_lab1.pdf

An example would be when two polarizing filters are set to 90 degrees relative to each other and no light will get through, but if a third filter is set in between them at 45 degrees, suddenly some of the light gets through. If a plausible explanation using local variables were to be found which explains the mathematical results of such a polarization experiment, would that then defy Bell's theorem?

[RobA]

Actually, that wouldn't be an example.

Bells Inequality is concerned with Entanglement - that is, where you have two entangled spatially-separated particles and measure their complementary properties, then those measurements will always be found to be consistent (even when the measurements are performed further than light could possibly travel in the time between the measurements).

For example, two entangled electrons with indeterminate spin. When you measure them, you find one with Spin-Up and the other with Spin-Down.

For entanglement, you must by definition have more than one "thing" (pardon the blinding with science!), so a single beam of light doesn't qualify - although it's still a wonderful example of the counter-intuitive nature of light and QM.

The obvious answer to "why are the measurements consistent?" is "because the particles got those properties since they were entangled (eg. those electrons ALWAYS had those spins, but we just hadn't measured them)". This is the Hidden-Variables approach.
Bell's theorem provided a test to distinguish between Hidden-Variables and whether quantum properties (like Spin) really were determined at the time of measurement - and the result, when the tests were able to be performed some time later, completely invalidated hidden variables.

Personally, my favourite description of Bells inequality is here

[tusenfem]

Maybe it would be a good idea to first write down Bell's inequality (or at least how you understand it) before you start "discussing"?

[grav]

Actually, that wouldn't be an example.

Bells Inequality is concerned with Entanglement - that is, where you have two entangled spatially-separated particles and measure their complementary properties, then those measurements will always be found to be consistent (even when the measurements are performed further than light could possibly travel in the time between the measurements).

For example, two entangled electrons with indeterminate spin. When you measure them, you find one with Spin-Up and the other with Spin-Down.

For entanglement, you must by definition have more than one "thing" (pardon the blinding with science!), so a single beam of light doesn't qualify - although it's still a wonderful example of the counter-intuitive nature of light and QM.

The obvious answer to "why are the measurements consistent?" is "because the particles got those properties since they were entangled (eg. those electrons ALWAYS had those spins, but we just hadn't measured them)". This is the Hidden-Variables approach.
Bell's theorem provided a test to distinguish between Hidden-Variables and whether quantum properties (like Spin) really were determined at the time of measurement - and the result, when the tests were able to be performed some time later, completely invalidated hidden variables.

Personally, my favourite description of Bells inequality is here

Yes, spin up and spin down particles are the most common reference, but quantum mechanics considers that the polarization of particles can also be entangled in a similar way. When photons are polarized, they can be sent to a two way mirror and then be reflected or refracted through the glass. If they are reflected, then that flips the polarity and we now have two beams of photons with opposite polarization. If those two beams are then sent through polarization filters that are set at the same angle, then whatever intensity is not allowed through one filter should be allowed through the second, although generally 50/50. If another filter is set at a 45 degree angle in front of one of them, then that will change some part of the intensity that is allowed through, a percentage which correlates with the angle of the original polarization filter that is set there. Likewise, if it set in front of the other, it should also correlate with that one to the same degree. Here is a similar discussion that took place on BAUT, with a thought experiment described in post #20.

However, now that you mention it, the statistical result for an additional filter set at 45 degrees would not be .707 anyway, but I = Io (cos 0)^2 = Io / 2, which correlates with either of the original filters equally. So does that mean we can go ahead and cross light polarization off of our list of experimental evidence in support of Bell's inequality, then? It looks that way, thanks.

[macaw]

I = Io (cos 0)^2 = Io / 2,

You got your trigonometry wrong, you realize that?

[grav]

Maybe it would be a good idea to first write down Bell's inequality (or at least how you understand it) before you start "discussing"?

My interpretation is that there is no way to model the outcome of a particular experiment which operates on the principle of Bell's inequality through any physical attributes of the system, or local hidden variables, although there are still a few potential loopholes, one such being that information can somehow be transferred nonlocally between the particles, as with the many worlds interpretation.

[macaw]

An example would be when two polarizing filters are set to 90 degrees relative to each other and no light will get through, but if a third filter is set in between them at 45 degrees, suddenly some of the light gets through.

...and you know that the third filter makes light "get through" ?

[grav]

You got your trigonometry wrong, you realize that?

I am using Malus's law for a polarizing filter, applying it at 45 degrees which gives 1/2.

[grav]

...and you know that the third filter makes light "get through" ?

Right, that is part of the "quantum strangeness".

[macaw]

I am using Malus's law for a polarizing filter, applying it at 45 degrees which gives 1/2.

You might be but last we all checked cos(0)=1. Your formula uses cos(0).

[macaw]

Right, that is part of the "quantum strangeness".

...and you read about this experiment where?
Would you care to describe the "experiment" in detail, so we could check its correctness?

[grav]

You might be but last we all checked cos(0)=1. Your formula uses cos(0).

We are placing another filter in front of the original at an angle of 45 degrees relative to the first, so that is the angle used for that.

[grav]

...and you read about this experiment where?
Would you care to describe the "experiment" in detail, so we could check its correctness?

There are links supplied in the OP, but here is also a very helpful applet where you can experiment for yourself with various settings of one, two, or three polarizing filters. Setting two filters at a 90 degree angle to each other allows none of the intensity of the light to pass, but setting a third between them at a 45 degree angle allows 1/8 of the intensity to pass.

[macaw]

There are links supplied in the OP, but here is also a very helpful applet where you can experiment for yourself with various settings of one, two, or three polarizing filters. Setting two filters at a 90 degree angle to each other allows none of the intensity of the light to pass, but setting a third between them at a 45 degree angle allows 1/8 of the intensity to pass.

Q1: So, what does the above have to do with quantum mechanics?
Q2: Can you explain the effect in your own words? Your own formulas?

[grav]

Q1: So, what does the above have to do with quantum mechanics?

It is considered a quantum effect, purely statistical, since it cannot so far be explained otherwise. Here is a link describing how it is determined through quantum mechanics.

Q2: Can youu explain the effect in your own words? Your own formulas?

Yes, I have a model which applies local physical attributes to what is taking place, which seems pretty simple in retrospect, but first, similarly to what tusenfem mentioned earlier, I am giving this thread a little time to try to get some kind of consensus about how directly an experiment such as this is tied to Bell's inequality before discussion takes place.

[macaw]

It is considered a quantum effect, purely statistical, since it cannot so far be explained otherwise. Here is a link describing how it is determined through quantum mechanics.

The question was asking you to explain the three filter effect using your own formulas. Can you do that?

Yes, I have a model which applies local physical attributes to what is taking place, which seems pretty simple in retrospect, but first, similarly to what tusenfem mentioned earlier, I am giving this thread a little time to try to get some kind of consensus about how directly an experiment such as this is tied to Bell's inequality before discussion takes place.

In the meanwhile, let's see your mathematical explanation as to why inserting the third filter makes the light go through.

[grav]

The question was asking you to explain the three filter effect using your own formulas. Can you do that?

In the meanwhile, let's see your mathematical explanation as to why inserting the third filter makes the light go through.

Yes I can, but my claim is that it demonstrates local physical attributes when Bell's inequality says otherwise. I will post my model later today, but if the consensus turns out to be that such an experiment is not representative of Bell's inequality after all, then I cannot claim that the model for the experiment defies it. Of course, that will also mean one less experiment out of three which is said to demonstrate Bell's inequality, leaving only the interference of light and the spin of entangled particles that I know of.

[macaw]

Yes I can, but my claim is that it demonstrates local physical attributes when Bell's inequality says otherwise. I will post my model later today, but if the consensus turns out to be that such an experiment is not representative of Bell's inequality after all, then I cannot claim that the model for the experiment defies it

You have been already told this in post #2, so why persist?
Besides, it isn't clear that you understand the basic experiment to begin with.

Q3: Why does the light go through when you insert the third filter between the first two? A couple of math formulas explain it.

Q4: Do you realize that there exist classical explanations (nothing to do with QM) for the experiment, so, it doesn't make any sense to connect this particular experiment to Bell's inequality?

[grav]

You have been already told this, so why persist?
Besides, it isn't clear that you understand the basic experiment to begin with.

Q3: Why does the light go through when you insert the third filter between the first two? A couple of math formulas explains it.

The experiment is not that difficult to understand, once one knows the basics. As far as the experiment applying to Bell's inequality, although the spin of entangled particles is a more common example, I also see the polarization experiment being referred to time and time again, as in the links of the OP and the discussion linked to in post #4, so it seems to be the general consensus that it does apply, although there also seems to be some disagreement according to RobA's reply.

[macaw]

The experiment is not that difficult to understand, once one knows the basics.

So,

Q5: Could you stop dodging and explain it? Two lines of math are sufficient in explaining it, so let's see them.

[grav]

So,

Q5: Could you stop dodging and explain it? Two lines of math are sufficient in explaining it, so let's see them.

As I have said, I'm waiting for a consensus. My claim is not so much that I have a model, but that if such a model can be presented, that it will defy Bell's theorem if the polarization experiment applies to that. But if the experiment is not considered to apply to Bell's inequality to begin with, then my original claim is null, although of course I will still present the model later on today. I have started a poll to help determine what that consensus is.

[macaw]

As I have said, I'm waiting for a consensus.

The consensus is that you are wrong.
Also, according to BAUT rules, you need to answer the challenges as they are posed to you.

[grav]

The consensus is that you are wrong.
Also, according to BAUT rules, you need to answer the challenges as they are posed to you.

My ATM at this point is that if local physical attributes can be modelled for the light polarization experiment, then that defies Bell's inequality. I asked the question about it being directly tied to Bell's inequality in Q&A but got no response, so RobA's and yours are the only ones I've received so far. However, if that particular experiment is not considered to apply to Bell's theorem to begin with, then I can no longer claim that. If that turns out to be the case, then the status of my current ATM will necessarily change and I will simply present the model for light polarization later as is and take it from there.

[tusenfem]

My interpretation is that there is no way to model the outcome of a particular experiment which operates on the principle of Bell's inequality through any physical attributes of the system, or local hidden variables, although there are still a few potential loopholes, one such being that information can somehow be transferred nonlocally between the particles, as with the many worlds interpretation.

That is not a description of Bell's inequality, you cannot use Bell's ineq. to explain Bell's ineq. You have not explained anything here, least of all if you indeed understand BI.

ETA: IMHO this is a very good place discussing Bell's theorem and the "inequalities."

[macaw]

My ATM at this point is that if local physical attributes can be modelled for the light polarization experiment, then that defies Bell's inequality. I asked the question about it being directly tied to Bell's inequality in Q&A but got no response, so RobA's and yours are the only ones I've received so far. However, if that particular experiment is not considered to apply to Bell's theorem to begin with, then I can no longer claim that.

There is no if, it cannot. So, can you provide the explanation for the experiment, this is the fourth time you are being asked.

[Tobin Dax]

You might be but last we all checked cos(0)=1. Your formula uses cos(0).

Come on, macaw. grav, here's a theta for you: θ. Copy and paste it.

[tusenfem]

My ATM at this point is that if local physical attributes can be modelled for the light polarization experiment, then that defies Bell's inequality. I asked the question about it being directly tied to Bell's inequality in Q&A but got no response, so RobA's and yours are the only ones I've received so far. However, if that particular experiment is not considered to apply to Bell's theorem to begin with, then I can no longer claim that. If that turns out to be the case, then the status of my current ATM will necessarily change and I will simply present the model for light polarization later as is and take it from there.

The problem that you are having here is that you try to combine a macroscopic and a microscopic process here and that always brings trouble.

In the polarization filters you find that if you use the macroscopic, i.e. wave theory of light, with non-polarized light of intensity I₀ and let is pass through the polarization filter you end up with half the intensity, which is linearly polarized at intensity I₀/2.

Now place the second polarization filter perpendicular to the first one, and naturally nothing gets trough.

Now place a third filter between the two at 45 deg to the first. Then a simple drawing will show you that what gets through the first one is I₀/2 * cos*(45) = 0.707*I₀/2. Now note that this not only reduced the intensity of the light but also ROTATES the plane of polarization of the light.

Then at the last filter the same happens as at the middle one and we get again a reduction by a factor of 0.707, and again a rotation of the polarization plane of 45 degrees and you have an intensity of 0.5*I₀/2.

This works really best if you make a simple drawing.

Now if you start working with photons, then you run into a problem, because that photon will have a polarization in a certain direction and it either gets through a filter or not. And there we run into the main problem. Naturally, then you will now have to go into the quantum mechanical description of the photons and their eigenstates, which is easier read in the page that I linked to. However, naturally the quantum mechanical result in the end has to come up with the same simple result as the wave description is giving.

[grav]

That is not a description of Bell's inequality, you cannot use Bell's ineq. to explain Bell's ineq. You have not explained anything here, least of all if you indeed understand BI.

ETA: IMHO this is a very good place discussing Bell's theorem and the "inequalities."

Yes, but that's the thing. Most systems rely upon cause and effect through local demonstratable physical attributes, so it is difficult to say precisely which systems should have no such local variables, and it cannot ever be demonstrated to be such in any way as far as I know, since one cannot prove a negative. All we can do is to say that according to Bell's theorem, such a system could or should potentially exist, but since only cause and effect can ever be demonstrated, there is no way to tell what proportion of experiments should follow Bell's inequality and so a local physical cause never be found and which ones just aren't known yet but eventually will be, so the number that actually follow Bell's theorem could just as easily be zero. Overall, we can really only just point to some experiment that seems to defy explanation in terms of such local variables and say that Bell's inequality probably then applies to that experiment, and that becomes the consensus. That is, unless or until a local cause is ever found, and then it never really applied to that experiment in the first place.

[macaw]

Come on, macaw. grav, here's a theta for you: θ. Copy and paste it.

No prompting, please :-)

[grav]

There is no if, it cannot.

Although Bell's inequality was originally intended to apply to the spin of entangled particles, the links below show that most experiments to date which test Bell's inequality have actually been performed using the polarization of light. The polarization angles of 0, 22.5, 45, 67.5, and 90 degrees are even referred to as the Bell test angles.

http://en.wikipedia.org/wiki/Bell_test_experiments

http://en.wikipedia.org/wiki/CHSH_inequality

http://freespace.virgin.net/ch.thomp...ssumptions.htm