Oddly a comment on the post below contains a link to a post on quantum measurement paradoxes. Oddly Lepp at Cornell does not seem to have permalinks so here is a google search which shows that Google considers Neil Bates the web's leading expert on "quantum measurement paradox"

That reminds me of this from my archives, except for the fact that the commenter tyranogenius AKA Neil Bates seems to know what he is talking about.

I wrote

Another locally realistic violation of Bell?s inequality ?

On December 9 2003 I was thinking about the EPR experiment. I am actually thinking about the

experiment as proposed by E P and R, not the experiment as performed. There are

four basic but very weird points to remember in order to understand the proposed

experiment. One is that electrons spin around sort of like little globes but that the

absolute value of the angular momentum is always hbar/2 no matter from which

direction you look at them. This is not like, say, the earth which spins around the

North-South axis so the angular momentum is less if you look down another axis.

The second strange fact is that you can?t measure the angular momentum of one

single electron around two different axis (one version of the Heisenberg

principal). This can be understood as measuring around one axis changes the spin

around another axis. This makes sense in terms of comprehensible things like

macroscopic magnets because the way to measure spin is with a magnet and a

magnet does change spin. The third strange fact is that sometimes you know that

the spin of two electrons around any axis is opposite. This is true if the two

electrons are in what is called a singlet state. This means that even if you can?t

know which way (clockwise or counterclockwise) each electron is spinning

around both the North South axis and the East West axis you can know that the

two are spinning in opposite directions around each axis. The fourth strange fact

is that, according to quantum mechanics the correlation between ?spin is

clockwise around the North South axis? and ?Spin is clockwise around the North-

East South-West axis? is greater than one !!! that is the probability both are

clockwise is greater than the probability that the spin around the North South axis

is clockwise and the spin around the other axis is whatever and unmeasured. I

won?t be able to explain this so that it makes sense. It is clearly crazy. It is also an

experimental result not just a theory. I am sure I will never understand this, so I

can?t explain it. Trying to grasp this fact, and it appears to be a fact (see below) is

like trying to pound a square peg into a round hole.

Now the point of EPR is that Heisenberg shmeizenberg you can use the singlet

state fact to test the quantum mechanical correlation greater than one by

measuring the spin around N-S of one of the electrons and the Spin NE-SW of the

other. They were very sure that the experimental result would disprove quantum

mechanics. After some decades the experiment was finally performed (with light

not electrons) and quantum mechanics was confirmed. I gave up.

Then I heard about the work of Luigi Accardi and Massimo Regoli. They have an

argument that you can reconcile the experimental result with a locally realistic

theory (one that makes sense as correlations are less than or equal to one) if the

singlet state is a statement about measuring spin around one magic axis (NS say).

The quantum craziness comes from treating electron 2 is counterclockwise around

NS as equivalent to electron 1 is clockwise around NS AND electron 2 is

counterclockwise around NE-SW as equivalent to electron 1 is clockwise around

NE-SW. What if the singlet state had to do only with the N-S axis ?

An objection is that the singlet state fact has been tested for many directions and

always works.

I have a slightly modified version of the Accardi Regoli story (which is probably

in one of their working papers which I haven?t read). Here the experiment is we

have electrons that were in the signlet state flying out of a source each one

through an electromagnet which can be oriented NS or NE-SW. If both

electromagnets are oriented the same way, the spins are opposite. If the

experimenter moves the electromagnets so they are not oriented the same way, the

electrons see this and don?t act like singlet state electrons at all anymore. This

means that the EPR experiment result is not equivalent to a correlation greater

than one.

OK so the little electrons are spying on the experimenter. There are two things.

Which way does he point the electromagnets and are both turned on (measuring)

or not. If they are oriented on the same axis then the measurement of electrons

going through magnet 1 does not depend on whether magnet two is turned on and

the measurement of electrons going through magnet 2 is always opposite. If they

are oriented in different directions, then the measurement of electrons going

through magnet 1 depends on whether magnet two is turned on. This is an effect

of an event which took place a long time ago (by flying electron terms) so there is

nothing impossible about it.

## 1 comment:

Thanks for the nod to my "new quantum measurement paradox." It really wasn't about the EPR, which involves connections between separated particles and their properties. My point was that repeated interactions of a single particle with something could reveal properties not normally considered accessible. In the case I originally posted, a photon of arbitrary polarization state passes through many half-wave plates. Each pass builds up a little bit of shift in the expectation value of the spin of the plate, depending on the amount of circular polarization in that photon. When we sum up the spins in all the plates, we can find the amount of circular polarization of the photon - on a range between fully positive and fully negative spin (for example, a linear polarized photon should produce no spin.)

That is considered impossible according to standard theory. (Compare with "weak measurements.") In my newer versions, I have the photon go through the same plate many times instead of the photon going through many plates one time each.

tyrannogenius

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