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

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In summary, the EPRB experiment involves a local hidden variable and a uniform probability density at the source. The measurements are made at two places and the data is collected at the same point. However, the integration process seems to be influenced by the measurement angles, leading to the conclusion that the final correlation should be written as \int_{\Omega[ta,tb]}a(ta,v)b(tb,v)\rho_{end}(ta,tb,v). The measurement angles are not considered as variables in the integration process. In the analysis of Bell-CHSH, the measurement results for the operator CHSH are considered, leading to a potential measurement result of ab-ab'+a'b'+\-a'b.
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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] ?
 
  • #3
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.
 
  • #4
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 ?
 
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  • #5
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.
 

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

1. What is Bell's ansatz?

Bell's ansatz, also known as Bell's hypothesis or Bell's conjecture, is a fundamental assumption in quantum mechanics that states that the properties of a single particle cannot be fully described without taking into account the properties of other particles with which it may interact. This concept challenges the classical notion of local realism, which assumes that objects have well-defined properties independent of observation.

2. How does Bell's ansatz relate to knowledge?

Bell's ansatz has major implications for our understanding of knowledge and reality. It suggests that our knowledge of the world is limited by our ability to observe and measure it, and that there may be fundamental aspects of reality that are beyond our current understanding. It also raises questions about the role of consciousness in shaping our perceptions and the nature of reality.

3. Why is Bell's ansatz important in science?

Bell's ansatz has been a subject of much debate and research in the field of quantum mechanics. By challenging the traditional understanding of reality, it has led to significant advancements in our understanding of the fundamental principles of the universe. It has also opened up new avenues of exploration and has practical applications in fields such as quantum computing and cryptography.

4. How does Bell's ansatz impact our view of causality?

Bell's ansatz challenges the idea that events can only be caused by their immediate physical surroundings. It suggests that there may be hidden causal connections between particles that are not directly observable, and that these connections may play a role in shaping our reality. This concept has far-reaching implications for our understanding of causality and the nature of cause and effect.

5. What are the criticisms of Bell's ansatz?

There are several criticisms of Bell's ansatz, including the argument that it is not testable and therefore cannot be considered a scientific hypothesis. Some also argue that it is based on philosophical assumptions that may not be valid. Additionally, there are ongoing debates about the interpretation of the results of experiments testing Bell's ansatz, and whether they truly support or refute the concept.

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