by Joy Christian » Fri Aug 07, 2015 1:17 am
Let me reproduce here the essential part of the code in the above simulation:
http://rpubs.com/jjc/84238. The measurement functions
}$)
= +/-1 of Alice and
}$)
= +/-1 of Bob generated in the simulation are exactly the local functions demanded by Bell in his 1964 paper, and the correlations are then calculated using the coincidence counts in the same manner as done in the actual experiments. The displayed plots put to rest any lingering doubt that there might be somehow some uncounted "0 outcomes" in the simulation. But in the
3-sphere there are no "0 outcomes", as is evident from Eq. (B10) of
this paper consolidating the analytical model:
- Code: Select all
A = +sign(g(a,e,s)) # Alice's measurement results A(a, e, s) = +/-1 # Here g(u,v,s) is a metric on S^3, reducing to the usual g on R^3
B = -sign(g(b,e,s)) # Bob's measurement results B(b, e, s) = -/+1 # A(a, L) = +/-1 and B(b, L) = +/-1 are exactly as defined by Bell
Cuu = length((A*B)[A > 0 & B > 0]) # Coincidence count of (+,+) events
Cdd = length((A*B)[A < 0 & B < 0]) # Coincidence count of (-,-) events
Cud = length((A*B)[A > 0 & B < 0]) # Coincidence count of (+,-) events
Cdu = length((A*B)[A < 0 & B > 0]) # Coincidence count of (-,+) events
corrs[i,j] = (Cuu + Cdd - Cud - Cdu) / (Cuu + Cdd + Cud + Cdu) # = -a.b
# There are no "0 outcomes" within S^3: Cou = Cod = Cuo = Cdo = Coo = 0
CoB = length(A[g(a,e,s) & A == 0]) # Number of A = 0 events within S^3 (regardless of B events) = 0
CAo = length(B[g(b,e,s) & B == 0]) # Number of B = 0 events within S^3 (regardless of A events) = 0
Joy Christian 
Let me reproduce here the essential part of the code in the above simulation: http://rpubs.com/jjc/84238. The measurement functions [tex]${A(a, \lambda)}$[/tex] = +/-1 of Alice and [tex]${B(b, \lambda)}$[/tex] = +/-1 of Bob generated in the simulation are exactly the local functions demanded by Bell in his 1964 paper, and the correlations are then calculated using the coincidence counts in the same manner as done in the actual experiments. The displayed plots put to rest any lingering doubt that there might be somehow some uncounted "0 outcomes" in the simulation. But in the [url=http://arxiv.org/abs/1405.2355]3-sphere[/url] there are no "0 outcomes", as is evident from Eq. (B10) of [url=http://arxiv.org/abs/1501.03393]this paper[/url] consolidating the analytical model:
[code]
A = +sign(g(a,e,s)) # Alice's measurement results A(a, e, s) = +/-1 # Here g(u,v,s) is a metric on S^3, reducing to the usual g on R^3
B = -sign(g(b,e,s)) # Bob's measurement results B(b, e, s) = -/+1 # A(a, L) = +/-1 and B(b, L) = +/-1 are exactly as defined by Bell
Cuu = length((A*B)[A > 0 & B > 0]) # Coincidence count of (+,+) events
Cdd = length((A*B)[A < 0 & B < 0]) # Coincidence count of (-,-) events
Cud = length((A*B)[A > 0 & B < 0]) # Coincidence count of (+,-) events
Cdu = length((A*B)[A < 0 & B > 0]) # Coincidence count of (-,+) events
corrs[i,j] = (Cuu + Cdd - Cud - Cdu) / (Cuu + Cdd + Cud + Cdu) # = -a.b
# There are no "0 outcomes" within S^3: Cou = Cod = Cuo = Cdo = Coo = 0
CoB = length(A[g(a,e,s) & A == 0]) # Number of A = 0 events within S^3 (regardless of B events) = 0
CAo = length(B[g(b,e,s) & B == 0]) # Number of B = 0 events within S^3 (regardless of A events) = 0
[/code]
[url=http://libertesphilosophica.info/blog/]Joy Christian[/url] :)
