Can Bell's Ansatz Explain the Correlation in the EPRB Experiment?

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Discussion Overview

The discussion centers on the applicability of Bell's Ansatz in explaining the correlations observed in the EPRB experiment. Participants explore the mathematical formulation of correlations, the role of local hidden variables, and implications of measurement outcomes in the context of quantum mechanics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes that the correlation in the EPRB experiment can be expressed as an integral involving measurement angles and a uniform probability density, suggesting that the integration process incorporates these angles.
  • Another participant emphasizes that while the measurement angles are fixed in the integration, they are embedded in the functions that generate outcomes, indicating a nuanced view of their role.
  • A different participant analyzes the CHSH inequality, discussing the implications of measurement outcomes on the wavefunction and how the results could vary based on the order of measurements, raising questions about the eigenstate properties after successive measurements.
  • Further, a participant adds that a negative result in the measurement could lead to specific outcomes for the measurement results, indicating a potential range of values based on the sign of the correlation.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of measurement angles and the implications of measurement order on outcomes. The discussion remains unresolved with multiple competing perspectives on the application of Bell's Ansatz.

Contextual Notes

There are limitations regarding the assumptions made about the uniformity of the probability density and the dependence on measurement angles, as well as the implications of measurement order on the wavefunction state, which are not fully resolved.

jk22
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considering the eprb experiment, the correlation is written in terms of local hidden variable :

The density of probability at the source is uniform it cannot depend on the measurement angles. Rho(v)

The measurement are made at the two places a(ta,v) b(tb,v)

The datas are the recollected at the same point.

In this last operation it is clear that the integration 'knows' about the measurement angles !

Hence the conclusion is that the correlation at the end should be written as [tex]\int_{\Omega[ta,tb]}a(ta,v)b(tb,v)\rho_{end}(ta,tb,v)[/tex] ?
 
jk22 said:
considering the eprb experiment, the correlation is written in terms of local hidden variable :

The density of probability at the source is uniform it cannot depend on the measurement angles. Rho(v)

The measurement are made at the two places a(ta,v) b(tb,v)

The datas are the recollected at the same point.

In this last operation it is clear that the integration 'knows' about the measurement angles !

Hence the conclusion is that the correlation at the end should be written as [tex]\int_{\Omega[ta,tb]}a(ta,v)b(tb,v)\rho_{end}(ta,tb,v)[/tex] ?
Strictly speaking, the measurement angles are not variables as far as the integration is concerned. They are embeded into the functions which generate the outcomes and are fixed.
 
To continue i had the following analysis of bell-chsh : we consider the measurement results of the operator chsh : AB-AB'+A'B'+A'B

Consdering first the a side we get result a for the forst term. Now the wavefunction is an eigenstate of A hence the measurement for the second term gives again a. The same reasoning applies for a'. Then i consider the b side and i got the following problem : after measuring the third term which gives b' i measure again with B but after measuring B' the wavefunction is not an eigen state of B hence the measurement result for chsh could be : ab-ab'+a'b'+\-a'b ?
 
Last edited:
Add: the later result if it is a minus sign would mean that we have for the measurement results (a+a')(b-b')=4,0 or -4 separately.
 

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