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פרושים של תורת הקוונטים בוהר :אסור לשאול איפה החלקיק בין המדידות Duality, Complementarity לנדאו :חייבים עולם הקלסי כדי להגדיר עולם קוונטי ספרי לימוד :משתנה – אופרטור ,משמאות גל רק לאנסמבל פון נוימן :הכל גל שמשתנה לפי שרדינגר אבל גם קורס במדידה בוהם :גל (בלי קריסה) הוא ,pilot waveהמציאות חלקיקים עולמות מרובים :הכל גל ,אין קריסה GRW-Pearleהכל גל ,יש קריסה ( )Flashes, Density Modal Interpretation Consistent Histories Quantum Logic Information Elements of Reality Counterfactuals Counterfactuals If it were that A then it would be that B If John were to jump out of the window of 10th floor, he would die. F If Nixon were to push the nuclear attack button, there would be a nuclear holocaust. True or False? B True or False in the CF world with A , closest to the actual world. Miracles Time Asymmetry “closest” is not well defined, Counterfactuals are vague F Counterfactuals in Physics If it were that A then it would be that B If it were that A was measured at time t then it would be that A=a True or False? B True or False in the CF world with A , closest to the actual world. SYSTEM No need for a miracle to have A In “closest” CF world the system has the same description at time t as in actual world “closest” is well defined, Counterfactuals are not vague Counterfactuals in Classical Physics If it were that A then it would be that B If it were that A was measured at time t then it would be that A=a True or False? B True or False in the CF world with A , closest to the actual world. SYSTEM No need for a miracle to have A In “closest” CF world the system has the same description at time t as in actual world “closest” is well defined, Counterfactuals are not vague Counterfactuals = conditionals Counterfactuals in Quantum Physics If it were that A then it would be that B If it were that A was measured at time t then it would be that A=a True or False? B True or False in the CF world with A , closest to the actual world. SYSTEM No need for a miracle to have A In “closest” CF world the system has the same description at time t as in actual world “closest” is well defined, Counterfactuals are not vague Counterfactuals = conditionals Counterfactuals in Quantum Physics If it were that only A was measured at time t then it would be that A=a If it were that only B was measured at time t then it would be that B=b Counterfactuals = counterfactual conditionals פורמליזם הדו וקטורי The two-state vector t P 1 t2 t t1 P 1 The two-state vector t P 1 t2 t P 1 t1 t2 t t1 P 1 ? t P 1 t t t t t t t The standard (one-state vector) description of a quantum system at time t H FREE 0 t t1 P 1 The standard (one-state vector) description of a quantum system at time t H FREE 0 t t1 The standard (one-state vector) description of a quantum system at time t H FREE 0 t t1 P' 1 =e i t t1 H FREE dt ' The standard (one-state vector) description of a quantum system at time t We assume: t t1 P 1 H FREE 0 The standard (one-state vector) description of a quantum system t x x 1 x x 1 z z 1 y y 1 (t ) The time reversal of t x x 1 x x 1 z z 1 y y 1 (t ) The backwards evolving quantum state x t x x The time reversal of x 1 (t ) (t ) x 1 The two-state vector x z z 1 z y y y 1 t2 t t1 P 1 ? t P 1 t2 t z t1 z 1 z 1 ? z t At time t: Prob( z ) 1 Prob( ) cos zˆ 2 2 ˆ Prob( z ) 1 Prob( ) ? z 1 t2 z t t1 ? z t z 1 t1 1 At time t: Prob( z ) 1 Prob( ) cos zˆ 2 2 ˆ Prob( z ) 1 Prob( ) 0 unknown t2 t z t1 z 1 t1 Prob( ) cos zˆ 2 2 z t At time t: Prob( z ) 1 z 1 ˆ known Prob( z ) 1 Prob( ) ?