Proof that no non-local variable can exist ?

  • Context: Graduate 
  • Thread starter Thread starter jk22
  • Start date Start date
  • Tags Tags
    Proof Variable
Click For Summary

Discussion Overview

The discussion revolves around the existence of non-local variables in quantum mechanics, particularly in relation to measurement outcomes derived from the Bell operator. Participants explore the implications of measurement processes and the nature of addition in quantum experiments.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant suggests that if non-local variables existed, the measurement outcomes would differ from those predicted by quantum mechanics, specifically referencing the Bell operator's outcomes.
  • Another participant argues that measuring the sum of two variables is not equivalent to measuring each variable separately and then adding the results, referencing a historical mistake by von Neumann.
  • A participant questions whether the addition of results is part of the measurement process, suggesting that it is performed by a computer and thus may not affect the measurement of individual variables.
  • Another participant reiterates the idea that any interaction with the system to extract a value will disturb the system, affecting subsequent measurements.
  • A participant raises a question about whether the preparation of experiments changes based on the measurement approach, particularly in relation to the expected outcomes of different measurement setups.
  • One participant confirms that the addition of results can be considered separate from the measurement process.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between measurement processes and the existence of non-local variables. There is no consensus on the implications of measurement methods or the nature of addition in this context.

Contextual Notes

Participants reference specific mathematical properties of operators and measurement outcomes, indicating a need for clarity on assumptions regarding operator eigenvalues and the nature of measurements in quantum mechanics.

jk22
Messages
732
Reaction score
25
Suppose we consider the measurement of [tex]A\otimes B-A\otimes B'+A'\otimes B+A'\otimes B'[/tex]at angles 0, 45, 90, 135 degrees.

If there exist a non-local variable that determine the result of the pair of result, then one gets for result of measurement [tex]0, 4, -4[/tex]

Whereas in quantum mechanics, the total Bell operator is [tex]\frac{1}{\sqrt{2}}\left(\begin{array}{cc} 2 &0&0&2\\0&-2&2&0\\0&2&-2&0\\2&0&0&2\end{array}\right)[/tex] which has as possible measurement outcomes : [tex]0, 2\sqrt{2},-2\sqrt{2}[/tex] which are not the same as the one given by a nonlocal variable since the eigenvalue of a sum of operator is not equal to the sum of the eigenvalues.

Since the measurement outcomes are not the same, does this indicates that there can be no non-local variable can exist ?
 
Physics news on Phys.org
I think you are doing the same mistake von Neumann have done a long time ago. Measuring A+B is not the same as measuring A, measuring B, and then adding results.
 
Can we say that the addition is not part of the measurement process, since it's made by a computer, so that we really measure and add +1 and -1 in an experiment ? I made another mistake, it's that the eigevalues of the sum of operators is the sum of the eigenvalues if both operator are diagonal.
 
Last edited:
jk22 said:
Can we say that the addition is not part of the measurement process, since it's made by a computer, so that we really measure and add +1 and -1 in an experiment ?

If anything (computer, human, animal, vegetable, or mineral) interacts with the system in a way that extracts a value of A, that's a measurement of A and it will disturb the system in such a way that (the distribution of subsequent) measurements of B will be affected.
 
Ok.
But does the way we prepare an experiment change : if we measure AB we set the experimental apparatus to give 1 or -1 as result, whereas if we measure AB-AB'+A'B+A'B' at the given angle we should set the experimental apparatus to give -2sqrt(2) as result ? Or does the experimental apparatus in some way know we measure the sum ? In the case of the Bell operator the singlet state is an eigenstate and is not degenerate, so it's not an average, we know the result with certainty.
 
jk22 said:
Can we say that the addition is not part of the measurement process, since it's made by a computer
Yes we can.
 

Similar threads

Graduate Can anyone give me the details of creating a cat state in Circuit QED?
  • · Replies 16 ·
Replies
16
Views
4K
Graduate Another proof that local realism does not work
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Can local conservation be verified experimentally?
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Does there exist a super-quantum correlation in mixed-state formalism
  • · Replies 3 ·
Replies
3
Views
1K
High School Quantum entanglement and hidden variables
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Can a State with Nonmeasurable Local Properties be Described by Quantum Rules?
  • · Replies 2 ·
Replies
2
Views
900
Graduate Conditional time evolution entropy and the experimenter?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How to numerically diagonalize a Hamiltonian in a subspace?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate John Bell 1964 toy model for spin
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Does there exist a proof for these conjectures?
  • · Replies 2 ·
Replies
2
Views
2K