Thank you. The Aspect experiment is of importance to quantum computing. Nonlocality is an essential part of entanglement, so it seems. But, this may come as a shock, Aspect's experiment is statistically flawed. Bear with me please.
The x is angle(a,b) in [0,2π).
The, a, is Alice's instrument parameter vector. The, b, is Bob's instrument parameter vector.
The angle is measured in the plane orthogonal to the A-S-B axis. This “orthogonal to the A-S-B in the plane variation of x" is sufficient variation for understanding the statistics of the experiment. It is also physically valid.
Note furthermore that the experiment is embedded in classical probability theory. E.g. the law of large numbers to estimate the probability space behind the Bell correlation formula.
Aspect then requires:
1. cos(x)= P(x,=) - P(x,≠)
1a. P(x,=)=N(x,=)/N
1b. P(x,≠)=N(x,≠)/N
1c. N(x,=)=N(x,+,+)+N(x,-,-)
1d. N(x,≠)=N(x,+,-)+N(x,-,+)
1e. N=N(x,=)+N(x,≠)
2. cos(x)=1-2sin²(x/2), x in [0,2π)
3. P(x,=)+P(x,≠)=1
4. P(x,≠)=sin²(x/2), x in [0,2π)
The left-hand in 4. is a data probability (estimate) determined by nature. The right-hand isn't a probability function. It isn't monotone non-descending for x in [0,2π).
5. For x in [0,2π), the alleged associated probability density is f(x)=(1/2)sin(x).
5a. This alleged probability density is derived from 4. via f(x)=dF(x)/dx. But observe, f(x)=(1/2)sin(x), x in [0,2π), isn't a probability density. It isn't positive definite for x in [0,2π).
5b. This f(x) results in negative probabilities and other violations of Kolmogorov axioms.
Thank you. The Aspect experiment is of importance to quantum computing. Nonlocality is an essential part of entanglement, so it seems. But, this may come as a shock, Aspect's experiment is statistically flawed. Bear with me please.
The x is angle(a,b) in [0,2π).
The, a, is Alice's instrument parameter vector. The, b, is Bob's instrument parameter vector.
The angle is measured in the plane orthogonal to the A-S-B axis. This “orthogonal to the A-S-B in the plane variation of x" is sufficient variation for understanding the statistics of the experiment. It is also physically valid.
Note furthermore that the experiment is embedded in classical probability theory. E.g. the law of large numbers to estimate the probability space behind the Bell correlation formula.
Aspect then requires:
1. cos(x)= P(x,=) - P(x,≠)
1a. P(x,=)=N(x,=)/N
1b. P(x,≠)=N(x,≠)/N
1c. N(x,=)=N(x,+,+)+N(x,-,-)
1d. N(x,≠)=N(x,+,-)+N(x,-,+)
1e. N=N(x,=)+N(x,≠)
2. cos(x)=1-2sin²(x/2), x in [0,2π)
3. P(x,=)+P(x,≠)=1
4. P(x,≠)=sin²(x/2), x in [0,2π)
The left-hand in 4. is a data probability (estimate) determined by nature. The right-hand isn't a probability function. It isn't monotone non-descending for x in [0,2π).
5. For x in [0,2π), the alleged associated probability density is f(x)=(1/2)sin(x).
5a. This alleged probability density is derived from 4. via f(x)=dF(x)/dx. But observe, f(x)=(1/2)sin(x), x in [0,2π), isn't a probability density. It isn't positive definite for x in [0,2π).
5b. This f(x) results in negative probabilities and other violations of Kolmogorov axioms.
No data exists that can meet the requirement.