Understanding particle spin and particle filters based on spin

[robinpike]

I would like to understand classical spin and quantum spin with regards to particle spin filters - I seem to be missing something fundamental on how they are used / work.

 

Starting with the classical understanding of spin, the set up is as follows...

A particle has an axis of spin along the vertical z-axis and it passes horizontally through a particle filter that only allows particles through with a vertical axis of spin, say to an accuracy of 5 degrees either side of the vertical. After passing through that filter, the particle goes through the same type of spin filter, but this time the filter is set at 45 degrees from the vertical z-axis (but the filter is still at right angles to the x-axis, which is the path of the particle).

I would expect the the particle with classical spin to fail to make it through the second filter. Is that correct?

Next take the quantum understanding of spin. If the same set up as above is used for a beam of quantum particles with a mixture of angles of spin and as yet un-measured axis of spin, what is the expected outcome?

- for the first vertical filter

- and then for filtered beam through the second filter

On the basis of the above, what is the first spin filter actually doing to a particle with quantum spin?

Thanks

Edited May 21, 2015 by robinpike

[swansont]

For photons this is polarization. For electrons it's spin. The effects are related, but the main difference is that the orthogonal spin states are up vs down (180º difference) while for photons it's nominally vertical vs horizontal (relative to your chosen axis), i.e. 90º difference, as we're used to.

 

Since photons act more like what we're used to, let's start there. If you have vertical (or horizontal) polarization and you send light through a polarizer at 45º, the light that makes it through is now polarized at 45º. The amount of light that makes it through a polarizer at an arbitrary angle is given by cos² (theta). So for 45º, that's 50%. The vertical light can be viewed as being equal parts 45 degree polarization and -45º polarization, and you reject half of it.

 

That's the concept of superposition that you have to understand. What you measure depends on how you measure it, and how you describe the state of the particle depends on how it's measured.

 

Unpolarized light sent through a vertical polarizer will give you vertically polarized light. if you then send it through a horizontal polarizer, you get no light going through. But if you out a 45º polarizer in between them, you get light: half the intensity after the 45º polarizer (as discussed above), and because the light is now polarized at 45º, going through the horizontal polarizer has the same exact effect, and you drop the light intensity by half again, (25%) and horizontally polarized.

 

For any individual photon, those intensities would be interpreted as probabilities.

 

If you grasp that, we can talk about spin.

[robinpike]

That is very clear to understand - thanks.

 

Your first point on the distinction between particle spin and photon polarization is a very good point to have made - discussions on Bell's inequalities quite often switch between referencing experiments with photons and experiments with particles, without highlighting that difference.

 

Yes please continue.

[swansont]

For the spin, the superposition is different, as I said. So when the detector is referred to (in the link in the Bell thread) as being at 0º, 45º or 90º being the "spin up" state is not the same as for photons, because electrons are not "up" vs "sideways", they are "up" vs "down". So they are saying that "up" at 0º passes all of the up electrons, a detector at 90º would pass half of them, rather than none, as would happen with photons. You would have to orient the detector at 180º (down) to exclude all of the up electrons.

 

So the analogous measurement is if you use half of the angle as for photons. That's mentioned further down the page. The detector at 45º for electrons gives the same result as 22.5º would for photons. cos^2(22.5) = 0.85

[robinpike]

Thanks, that is nice and clear as well.

 

So to state this completely when several filters are used in series, and the filters are at various angles to each other...

 

For the electrons that pass through the first filter (at 0 degrees), these can be considered as electrons with 'up' spin.

 

If these filtered electrons are then passed though a second filter:

 

• When the second filter is also at 0 degrees, then 100 % will go through.

• Whereas if the second filter is at 90 degrees, then only half of the filtered electrons would make it through.

• And if the second filter were to be at 180 degrees, then none of the filtered electrons would make it.

Edited May 22, 2015 by robinpike

[swansont]

 

Thanks, that is nice and clear as well.

 

So to state this completely when several filters are used in series, and the filters are at various angles to each other...

 

For the electrons that pass through the first filter (at 0 degrees), these can be considered as electrons with 'up' spin.

 

If these filtered electrons are then passed though a second filter:

 

• When the second filter is also at 0 degrees, then 100 % will go through.

• Whereas if the second filter is at 90 degrees, then only half of the filtered electrons would make it through.

• And if the second filter were to be at 180 degrees, then none of the filtered electrons would make it.

 

 

Yes.

 

Once you have measured the state of the particle, it has that orientation. In another measurement basis (another angle), you have a combination of states.

[Strange]

This may be a slight diversion, but it might help to tie things together a bit...

 

Whereas if the second filter is at 90 degrees, then only half of the filtered electrons would make it through.

 

And the probability of a particular electron (or photon) getting through is related to the cosine of the angle between the first and second filter (cosine squared, actually).

 

In the classical view of light (as a continuous waveform) this means that the amplitude of the light getting through also depends on the cosine² of the angle. (You may have seen a previous thread in speculations where a poster started from this fact and thought he had shown that Bell's inequality was wrong/irrelevant - but because he started with the result he wanted to demonstrate this was just an example of the fallacy of begging the question.)

[robinpike]

 

 

 

I have put into a table the probabilities of photons with known polarization angles (to the vertical) when they go through three detectors A, B and C at their 0, 120 and 240 angle settings (table as below). Also included in the table is the probability of photon pairs at those known polarization angles going through one of the detectors each, when their detectors are not at the same angle as each other.

 

What I haven't figured out is how to go from these values to the "++" and "--" pairings (A+, B+, C+, A-, B-, C-) that are used in the table from Dr Chinese's web site (table as above).

 

What does Dr Chinese mean when he says that a measurement at one detector agrees with the measurement at one of the others?

 

For example, this being marked as "A+" and "B+" in the table.

Edited May 25, 2015 by robinpike

[imatfaal]

++ is transmission at both filters, -- is no transmission at both, and -+ , +- is transmission at one and not the other.

So without checking your maths - Dr. Chinese's table (which is based on hidden variables) says that we must get agreement at least 33% of the time. I haven't looked at your table in depth (and something does seems wrong) but you are producing in the 2nd,3rd,4th columns from the right analogous coincidence of measurement data that Dr.Chinese did (ie A transmits and B transmits, AC.., BC..). But from your table the transmission rates are far far lower than predicted by Dr.Chinese's table - that is as it should be; cos squared is the result of QM investigations and produces a rate of transmission that is outside the bounds set by Bell's Inequality - well done.

[robinpike]

Imatfaal, thanks for explaining the meaning of the "++" agreement and the "--" agreement.

 

In my table, I only calculated the probability of both detectors letting the paired photons through: the "++" agreement.

 

I haven't included the probability of both detectors stopping the paired photons: the "--" agreement.

 

I will update the table and see what the new values come out to.

[robinpike]

I've been having at look at the table for the three detector settings and (if I've got this right) it would seem that the analysis needs only two detectors, set at an angle of 120 degrees to each other.

 

I'm taking it that the cosine squared probabilities of a photon making it through a detector at various angles is from experiment? Say by passing photons through a vertical polarizing filter first and then passing those photons - now of known polarization - through a second filter, setting the second filter at the various angles.

 

So the experiment can be performed for coupled photons i.e. with opposite spins / polarization but of an unknown, random angle, with one photon going left to the vertical 'A' polarizing filter and the other going right to the 120 degree 'B' polarizing filter (which say is slightly further away from the photon source).

 

 

If the photon pairs are taken as being quantum coupled, then...

 

When a left photon reaches the vertical 'A' polarizing filter, if it makes it through the filter - which 50% of them will - it is then of known polarization (vertical). This causes the paired quantum coupled photon to 'collapse its wave function' to the vertical polarization too - which on reaching the 120 degree 'B' filter, the photon has a 25% chance of making it though the filter.

 

Whereas if the photon pairs are taken as being classically coupled, then...

 

The left photon behaves the same as above for the quantum left photon - that is 50% of them will make it through the 'A' polarizing filter - which is then of known polarization (vertical). But this time the paired classical photon remains with its original orientation, and on reaching the 120 degree 'B' filter, has various chances of making it through the filter - listed in column G.

 

So the probability of when a coupled pair of photons make it through both the 'A' filter and the 'B' filter, is different for quantum couple photons (12.5% i.e. 12.5% = 1/4 of 50%) to classical coupled photons (18.9%) - for the 120 degree setting.

 

And this difference can be measured by experiment.

 

So first point, before moving on to applying Bell's Inequalities, is the above simplification correct?

Edited May 27, 2015 by robinpike

[robinpike]

My understanding of how this experiment works doesn't seem to be right?

 

If the percentage of the right photons passing through filter B was really effected by the left photons passing through filter A, then this could easily be shown by counting the photons passing through filter B WITHOUT filter A present for the left photons, and then without changing the rate of the photons, counting them through filter B when the left photons have filter A present.

 

If the act of measuring the random polarization of the left photons meant that the orientation of the right photons became biased towards the orientation of the A filter, then the above would cause a different number of the right photons to be counted in each situation.

 

So what is it that I have misunderstood?

[imatfaal]

But the point of Bell and EPR is not to show that something strange is happening - we know that, everyone agreed that. EPR claimed that all could be explained by the addition of local hidden variables which do not violate causality, or locality, or speed of light (ie Einsteins spooky action at a distance). Bells Inequality showed that there was an experimental test that would distinguish between local hidden variables and quantum superposition

 

I really would recommend you stop trying to put your own gloss on the theory and methods of experimentation and get settled on completely understanding one explanation.

[robinpike]

Okay, let's forget my attempt to understand the experiments and go back to EPR, before Bell's Inequality Theorem.

 

Einstein, Podolsky and Rosen - information from Wikipedia...

 

It was known from experiments that the outcome of an experiment sometimes cannot be uniquely predicted. An example of such indeterminacy can be seen when a beam of light is incident on a half-silvered mirror. One half of the beam will reflect, and the other will pass. If the intensity of the beam is reduced until only one photon is in transit at any time, whether that photon will reflect or transmit cannot be predicted quantum mechanically.

The routine explanation of this effect was, at that time, provided by Heisenberg's uncertainty principle. Physical quantities come in pairs called conjugate quantities. Examples of such conjugate pairs are position and momentum of a particle and components of spin measured around different axes. When one quantity was measured, and became determined, the conjugated quantity became indeterminate. Heisenberg explained this as a disturbance caused by measurement.

The EPR paper, written in 1935, was intended to illustrate that this explanation is inadequate. It considered two entangled particles, referred to as A and B, and pointed out that measuring a quantity of a particle A will cause the conjugated quantity of particle B to become undetermined, even if there was no contact, no classical disturbance. The basic idea was that the quantum states of two particles in a system cannot always be decomposed from the joint state of the two.

Heisenberg's principle was an attempt to provide a classical explanation of a quantum effect sometimes called non-locality. According to EPR there were two possible explanations. Either there was some interaction between the particles, even though they were separated, or the information about the outcome of all possible measurements was already present in both particles.

The EPR authors preferred the second explanation according to which that information was encoded in some 'hidden parameters'. The first explanation, that an effect propagated instantly, across a distance, is in conflict with the theory of relativity. They then concluded that quantum mechanics was incomplete since, in its formalism, there was no room for such hidden parameters.

Violations of the conclusions of Bell's theorem are generally understood to have demonstrated that the hypotheses of Bell's theorem, also assumed by Einstein, Podolsky and Rosen, do not apply in our world.^[2] Most physicists who have examined the issue concur that experiments, such as those of Alain Aspect and his group, have confirmed that physical probabilities, as predicted by quantum theory, do exhibit the phenomena of Bell-inequality violations that are considered to invalidate EPR's preferred "local hidden-variables" type of explanation for the correlations to which EPR first drew attention.

============================================================================

So without applying Bell's Inequality Theorem, do both the classical explanation and the quantum mechanical explanation predict the same outcome in experiments that measure the polarization of 'entangled' photon pairs?

If there is a difference between the two predictions, then what is that difference?

[imatfaal]

These experiments are investigating unmistakeably quantum mechanical effects. The inequality is a purely mathematical system. Bell realised that the inequality could be applied to experiments which advocates of local hidden variables said required these prearranged variables and which most physicists said showed quantum superposition ie the experiment Dr Chinese talked about with photon polorization being measured in two different planes or electon spin being measured. Classically these experiments don't really mean anything.

 

To re-iterate Bell's Inequality and the experiments which test it do not seek to distinguish classical effect from quantum mechanical effects. They seek to distinguish between local hidden variables and non-local quantum superposition of states.

[swansont]

So without applying Bell's Inequality Theorem, do both the classical explanation and the quantum mechanical explanation predict the same outcome in experiments that measure the polarization of 'entangled' photon pairs?

If there is a difference between the two predictions, then what is that difference?

 

It depends on what you mean by classical. Let's say we have an entangled pair of photons such that they have orthogonal polarizations. In fact, we have a large number of them identically prepared, so we measure intensities rather than probabilities. In the QM view, the individual states are not determined until we measure. If by classical you mean they are determined before the measurement, but still orthogonal, then yes, the QM result is different.

 

In QM if we measure one set of photons with a polarizer at 0º, we know the other set is at 90º. The classical view would then have to be that the photons had those polarizations all along. But QM says if we measure the light with the analyzer at +45º, we know the other beam is at -45º. But we will only see that half the time if the photons are "really" 0º and 90º. If we do individual photons, we will get counts from one polarizer but not the other, half the time.

[robinpike]

I’m still struggling with some of this. To summarise what I think I understand so far…

 

Polarizers, whether absorbing or beam splitters, are not 100% efficient. But that can be taken into account and an absorbing polarizer can be considered as filtering out 50% of a beam of photons with random orientations.

 

For ‘photon pairs’ going through a pair of absorbing filters (one filter either side of the source), individual photons - on average - will make it through the filters 50% of the time. This is regardless as to the orientation of the filters to the beam of photons, and regardless as to the orientation of the filters relative to each other.

 

This average behaviour applies to both classical and QM interpretations.

 

The difference between classical and QM arises when individual pairs of photons are considered - and the two filters are orientated at an angle to each other, with certain angles giving the greatest discrepancy between classical and QM predictions as to whether both of the paired photons make it through the filters, or not.

 

When a photon’s polarization is not aligned to the filter, there is a statistical probability of whether that photon makes it through the filter, or not, based on the angle between the photon’s polarization and the filter.

 

And that statistical behaviour complicates the analysis.

 

(I’m assuming that is why Bell’s Inequality is required, rather than being able to use the direct percentage of photon pairs that get through the filters at those angles?)

 

When Alain Aspect performed this type of experiment with the filters several kilometres apart, the results were no different to when the filters were just a few metres apart.

 

This seems to suggest that the mechanism IS classical – for a classical explanation is not affected by the distance between the filters. (If the filters were at opposite ends of the universe, it would be of no consequence to a classical mechanism.)

 

I am wondering if there are any assumptions not mentioned, as to how a photon makes it through a polarizing filter, which could have an impact on the analysis (and conclusions with Bell’s Inequalities).

 

For example, as well as the photon’s angle of polarization to the filter, what other local variable could be involved that decides whether a photon makes it through a filter or not?

 

Does that probability involve the particular position that the photon arrives at the atom lattice on the surface of the filter, which in essence is a random local variable?

Edited June 9, 2015 by robinpike

[robinpike]

I am beginning to understand this better now - having gone through lots of different web sites discussing this type of experiment.

 

One thing I didn't realise before, and keeping the discussion to the entangled photon experiments, is that when the photons are orthogonally correlated and the filters are also at right angles to themselves... then the detectors ALWAYS register either both photons of the pair making it though the filters, or both photons of the pair not making it through the filters.

 

This result on its own seems to defy a classical explanation, since with a classical polarization, each photon pair will be at a random angle to the filters (not perfectly aligned to the filters) and so for some angles sometimes one of the photon pair would make it through while its partner does not.

 

Here is a link to a pdf document discussing the above written by Alain Aspect...

 

http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf

 

Since the reason for my posts on this subject is to understand whether a classical explanation could be at all feasible, have I got the above experimental outcome correct?

Edited June 15, 2015 by robinpike

[swansont]

Yes. The result is not classical; the particles do not have a particular spin or polarization while in transit. It's the correlation that is preserved.