Wednesday, December 06, 2006

Do EPR-Bohm experiments provide evidence for fuzzy quantum states?

The experimental data for EPR-Bohm experiments exclude hidden variable interpretations of quantum theory. What is less known that the experimental data for this kind of experiment (Phys. Rev. Lett. 81,23, p. 5039, 1998) indicates the possibility of an anomaly challenging quantum mechanics (I learned about this possibly anomaly from papers of Adenier and Khrennikov, see this and this. The obvious question is whether this anomaly might provide a test for the notion of fuzzy quantum logic inspired by the TGD based quantum measurement theory with finite measurement resolution.

The experimental situation involves emission of two photons from spin zero system so that photons have opposite spins. What is measured are polarizations of the two photons with respect to polarization axes which differ from standard choice of this axis by rotations around the axis of photon momentum characterized by angles α and β. The probabilities for observing polarizations (i,j), where i,j is taken Z2 valued variable for a convenience of notation are Pij(α,β), are predicted to be P00= P11=cos2(α-β)/2 and P01= P10= sin2(α-β)/2.

Consider now the discrepancies.

  • One has four identities Pi,i+Pi,i+1=Pi,i+ Pi+1,i=1/2 having interpretation in terms of probability conservation. Experimental data of the experiment reported in Phys. Rev. Lett. 81,23, p. 5039, 1998 are not completely consistent with this prediction and this is identified as a possible anomaly .

  • The QM prediction E(α,β)= ∑i (Pi,i-Pi,i+1)= cos(2(α-β) is not satisfied neither: the maxima for the magnitude of E are scaled down by a factor ≈ .9. This deviation is not discussed by Adenier and Khrennikov.

Both these findings raise the possibility that QM might not be consistent with the data. It turns out that fuzzy quantum logic predicted by TGD and implying that the predictions for the probabilities and correlation must be replaced by ensemble averages, can explain anomaly b) but not anomaly a). A "mundane" explanation for anomaly a) can be imagined.

For details see the chapter Was von Neumann Right After All? . See also the article TGD: an Overview.

3 Comments:

At 10:25 AM, Blogger Mahndisa S. Rigmaiden said...

12 07 06

Whoa Matti:
You left and came back with a vengeance! Now I must leave for a while but skimmed over this article. Very good points. Kea brought up MV logic and intuitionistic approaches to logic. If we constantly preach about the randomness in QM, but then don't apply this thought to measurement and assume that results of measurement are always a priori determinable, then we have some problems in interpretation. That is why the Bell tests and EPR paradox were always so bothersome.
Thus your approach is appreciated. I also have seen MV logic fall out of p-adic physics for some systems so let us see where these thoughts will take you. Thanks for continuing to post and have a nice rest of week.

 
At 7:03 PM, Blogger Matti Pitkanen said...

Dear Mahndiza,

the mathematical articulation of physical concepts like "quantum fluctuations", "long range quantum fluctuations", "quantum criticality", "measurement resolution", "momentum cutoff", etc., are examples of notions which are continually used but which have poorly defined mathematical content in the existing formalism of quantum theory.

To me this state of affairs suggests that something very essential is lacking from the mathematical structure of quantum theory and you can certainly guess my guess: Jones inclusions.

For instance, the notion of S-matrix with measurement resolution is really beautiful: transition probabilities for quantum S-matrix become commutating Hermitian operators and S-matrix in M/N has entire spectrum of of sets of transition probabilities corresponding to different contexts defined by the undetected degrees of freedom characterized by N.

Good Weekend,
Matti

 
At 11:17 AM, Blogger Mahndisa S. Rigmaiden said...

12 13 06

"For instance, the notion of S-matrix with measurement resolution is really beautiful: transition probabilities for quantum S-matrix become commutating Hermitian operators and S-matrix in M/N has entire spectrum of of sets of transition probabilities corresponding to different contexts defined by the undetected degrees of freedom characterized by N."

Matti:
I have been thinking about this statement for a long time now. Are you saying that the undetected degrees of freedom correspond to a hidden variable theory? Or are you saying that N characterizes these hidden dof?

 

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