السلام عليكم و رحمة الله
كنت أقرأ اليوم فى النظرية الكمية و لفت انتباهى ما قام به Von Neumann و غيره من محاولة تفسير الظواهر الكمية Interpretation باستخدام منطق يُسمى المنطق الكمى أو #Quantum Logic
و يقوم هذا المنطق على رفض بعض مسلمات المنطق المعروف ب Propositional Logic فمثلاً قانون التوزيع:
A and ( B or C)= (A and B )or (A and C) ------Distribution Law
لا يصح فى عالم ميكانيكا الكم
فكان السؤال الذى دار بخلدى هو : ما هى المسلمات البديهية فى المنطق و ما هى المتغيرات التى قد تكون قابلة للتغيير
فحين قرأت المثال المذكور فى الويكيبديا اقتنعت به و معنى هذا أنه مطابق للمنطق
و نظراً لخلط الكثير بين الثابت و المتغير فى المنطق مما يؤدى الى التشكيك بأى استدلال عقلى فأرجو من الأخوة الكرام توضيح الثابت و المتغير فى علم المنطق
ما يخص علم المنطق الكمى على الرابط التالى
الجزء المهم:
In quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of quantum theory into account. This research area and its name originated in the 1936 paper by Garrett Birkhoff and John von Neumann, who were attempting to reconcile the apparent inconsistency of classical boolean logic with the facts concerning the measurement of complementary variables in quantum mechanics, such as position and momentum.
Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and non-associative many-valued (MV) logic[1][2][3][4][5].
Quantum logic has some properties which clearly distinguish it from classical logic, most notably, the failure of the distributive law of propositional logic:
p and (q or r) = (p and q) or (p and r),
where the symbols p, q and r are propositional variables. To illustrate why the distributive law fails, consider a particle moving on a line and let
p = "the particle is moving to the right"
q = "the particle is in the interval [-1,1]"
r = "the particle is not in the interval [-1,1]"
then the proposition "q or r" is true, so
p and (q or r) = p
On the other hand, the propositions "p and q" and "p and r" are both false, since they assert tighter restrictions on simultaneous values of position and momentum than is allowed by the uncertainty principle. So,
(p and q) or (p and r) = false
Thus the distributive law fails.
كنت أقرأ اليوم فى النظرية الكمية و لفت انتباهى ما قام به Von Neumann و غيره من محاولة تفسير الظواهر الكمية Interpretation باستخدام منطق يُسمى المنطق الكمى أو #Quantum Logic
و يقوم هذا المنطق على رفض بعض مسلمات المنطق المعروف ب Propositional Logic فمثلاً قانون التوزيع:
A and ( B or C)= (A and B )or (A and C) ------Distribution Law
لا يصح فى عالم ميكانيكا الكم
فكان السؤال الذى دار بخلدى هو : ما هى المسلمات البديهية فى المنطق و ما هى المتغيرات التى قد تكون قابلة للتغيير
فحين قرأت المثال المذكور فى الويكيبديا اقتنعت به و معنى هذا أنه مطابق للمنطق
و نظراً لخلط الكثير بين الثابت و المتغير فى المنطق مما يؤدى الى التشكيك بأى استدلال عقلى فأرجو من الأخوة الكرام توضيح الثابت و المتغير فى علم المنطق
ما يخص علم المنطق الكمى على الرابط التالى
الجزء المهم:
In quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of quantum theory into account. This research area and its name originated in the 1936 paper by Garrett Birkhoff and John von Neumann, who were attempting to reconcile the apparent inconsistency of classical boolean logic with the facts concerning the measurement of complementary variables in quantum mechanics, such as position and momentum.
Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and non-associative many-valued (MV) logic[1][2][3][4][5].
Quantum logic has some properties which clearly distinguish it from classical logic, most notably, the failure of the distributive law of propositional logic:
p and (q or r) = (p and q) or (p and r),
where the symbols p, q and r are propositional variables. To illustrate why the distributive law fails, consider a particle moving on a line and let
p = "the particle is moving to the right"
q = "the particle is in the interval [-1,1]"
r = "the particle is not in the interval [-1,1]"
then the proposition "q or r" is true, so
p and (q or r) = p
On the other hand, the propositions "p and q" and "p and r" are both false, since they assert tighter restrictions on simultaneous values of position and momentum than is allowed by the uncertainty principle. So,
(p and q) or (p and r) = false
Thus the distributive law fails.
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