1. 24 February 2010Modern Physics II Lecture 71 University of San Francisco Modern Physics for Frommies II The Universe of Schrödinger’s Cat Lecture 7

2. 24 February 2010Modern Physics II Lecture 72 Agenda Administrative Matters Superposition and Entanglement

3. 24 February 2010Modern Physics II Lecture 73 Standard Model of Particle Physics Bruce A. Schumm, Deep Down Things, The Breathtaking Beauty of Particle Physics, The Johns Hopkins University Press (2004) ISBN 0-8018-7971-X Administrative Matters Next Physics and Astronomy Colloquium This Wednesday, 24 February 2010 at 4 PM Professor Aparna Venkatesan, Department of Physics and Astronomy, University of San Francisco Topic: Stellar Archaeology: Tracking the Fossil Remains of the First Stars Refreshments at 3:30 PM Harney Science Center Room 127

4. 24 February 2010Modern Physics II Lecture 74 J. Robert Oppenheimer Lecture Monday, 1 March 2010, 5 - 6:30 PM Pauley Ballroom, MLK Student Union UC Berkeley Frank Wilczek, MIT Anticipating a New Golden Age

5. 24 February 2010Modern Physics II Lecture 75 Albert’s misgivings: One of the “fathers” or quantum theory. “God does not play dice” Chance has no place within the laws of nature. Believed QM to be correct in giving probabilities to results of experiments. We find it necessary to resort to probabilities due to our ignorance of a deeper theory describable by deterministic physics. 1927 Solvay Conference Einstein vs. Bohr Einstein proposes gedanken experiments refuting QM Bohr would reflect and clear up the matter in detail.

6. 24 February 2010Modern Physics II Lecture 76 The Einstein-Podolsky-Rosen (EPR) Paradox: Let’s consider a spin ½ particle in an l = 0 state Axis #1 Axis #2 mBmB > m B Classically it appears impossible to have a projection  m B on all axes. Quantum Mechanics and experiment say we always do.  z x y Restrict to x-z plane Projection onto vertical axis: m z Projection onto horizontal axis m x Projection onto downward vertical m (-z) Projection onto axis in x-z tilted by  m 

7. 24 February 2010Modern Physics II Lecture 77 The Stern-Gerlach experiment: If B is inhomogeneous there will be a net force as well as torque on the atom

8. 24 February 2010Modern Physics II Lecture 78 For l  0 the states should separate according to m l 2 lines seen instead of the expected 3 (or 2l+1 = odd) Haven’t seen the whole picture yet.

9. 24 February 2010Modern Physics II Lecture 79 An instrument stock room full of Stern-Gerlach Analyzers + - m z = +m B m z = -m B Vertical Orient the analyzer horizontally rather than vertically and the sort is m x =  m B Orient at 7º to the vertical and the sort is m 7º =  m B

10. 24 February 2010Modern Physics II Lecture 710 Repeated Measurement Experiments Exp.1: Measurement of m z and m z + - Exp.Exp. - ignore all none m z = + m B at first analysis and at second

11. 24 February 2010Modern Physics II Lecture 711 Exp. 2: Measurement of m z and m (-z) + - + - ignore all none m z = + m B at first analysis m (-z) = -m B at second analysis

12. 24 February 2010Modern Physics II Lecture 712 Exp. 3: Measurement of m z then m x and then m z again + - - + + - ignore A B C m z = + m B from analysis at A m x = + m B from analysis at B What happens at analysis at C? Good if naïve guess: Atom has m z = + m B from A and m x = + m B from B, so C should have same result as Exp. 1. All leave on + path. ?? Not so, if you do the experiment, some leave by + path and others by -.

13. 24 February 2010Modern Physics II Lecture 713 When atom enters B it has a definite value of m z = + m B by virtue of its analysis at A. When it leaves B it does not because it may leave C by either path. In fact if we repeat the experiment many times there is equal probability of  exits from C. In quantum mechanics, an atom with a value for m x does not have a value for m z. If it did… z x m z = + m B m x = + m B Quantum mechanics says m 45º =  m B All projections must be  m B. The assumption that an atom leaving B has the same m z as it did when entering is bad.

14. 24 February 2010Modern Physics II Lecture 714 Summarizing so far: An atom with a definite value of m z doesn’t have a definite value of m x. All that can be said is that when m x is measured, there is a probability of ½ of finding + m B and ½ of finding – m B. There are other possibilities. For example: “Measurement disturbs classical system” An atom with a definite value of m z also has a definite value of m x, but the measurement of m z disturbs the value of m x in an unpredictable way. “Complex atom” An atom with a definite value of m z also has a definite value of m x, but this value changes so rapidly that no one can figure out what that value is.

15. 24 February 2010Modern Physics II Lecture 715 The EPR argument shows that these “other interpretations are untenable. Locality: Clearly something happening at point A can influence what happens at point B. e.g. Sinking of USS Maine in Havana Harbor leads President McKinley, in Washington DC, to declare war on Spain. Effect occurs some after the cause. It takes time for the news to travel.. No instantaneous communication. This method of influence is said to be local. Special relativity: No causal agent can travel faster than a light signal

16. 24 February 2010Modern Physics II Lecture 716 Distant Measurements: + - + - source Source produces back to back pair of atoms with net spin zero. Each atom is detected by its own vertical S-G analyzer. At each analyzer, the (  ) probability is ½. If right hand is (+) then left hand is (-) and vice-versa. This is true regardless of relative proximity to source and true for any common analyzer orientation

17. 24 February 2010Modern Physics II Lecture 717 Suppose the left analyzer is five miles from the source and the right is five miles plus one inch from the source. If the left atom leaves its analyzer through the (+) exit then we know the right atom will have m z = - m B. But, the right atom itself has not been measured. It is impossible for the right atom, 10 miles away, to have been mechanically disturbed by the measurement of the left atom. The “measurement disturbs” alternative interpretation must be discarded.

18. 24 February 2010Modern Physics II Lecture 718 At first glance there appears to be instantaneous communication between the atoms. When the atoms are launched it can not be predicted whether the right atom will leave the + or the – exit of its analyzer. But, the instant the left atom leaves the + exit of its analyzer it is known that the right atom (now 10 miles away) will leave its analyzer via the – exit. The real question is “who knows the right atom will leave via -?” A person next to the left analyzer knows it immediately but will have to convey this information to a person next to the right analyzer via some slower than light mechanism. “Spooky action at a distance”? Spooky yes, but no violation of special relativity.

19. 24 February 2010Modern Physics II Lecture 719 Random Distant Measurements: source R G A B C Tilting S-G analyzers in 120º orientations A, B and C (+) exit = red light, (-) exit = green light If analyzers have same orientation, experiment is same as previous one. Different colors always flash. Relax the orientation constraint and let the left detector be closer to the source and let its orientation be A.

20. 24 February 2010Modern Physics II Lecture 720 source R G A B C Tilting S-G analyzers in 120º orientations A, B and C (+) exit = red light, (-) exit = green light Left detector flashes green  right atom has m z = + m B Right detector flashes red with a probability of ½. See next slide Conclusion: If orientations are the same, flashes are different always. If orientations are ignored, flashes are different with probability ½. This is, in fact, what is observed.

21. 24 February 2010Modern Physics II Lecture 721 Probability ½ argument

22. 24 February 2010Modern Physics II Lecture 722 Prediction of Local Determinism: Each atom leaves source with an “instruction set” saying which lamp flashes for each orientation setting e.g Orientation Color ARed B CGreen Atom leaves through which the exit towards which its spin arrow most closely points. Paired atoms have opposite instruction sets, e.g. GRG and RGR

23. 24 February 2010Modern Physics II Lecture 723 Suppose the instruction sets are RRG and GGR OrientationDetectors flash AARG: different BBRG: different CCGR: different ABRG: different BARG: different BCRR: same CBGG: same ACRR: same CAGG: same Probability of different color flashes is 5/9

24. 24 February 2010Modern Physics II Lecture 724 The above holds for any instruction set Now we know the probability of different color flashes for any given instruction set. We want to find the probability of different color flashes period. To do this we need to know what sort of atoms the source produces. RRR-GGG pairs only  probability = 1 RRG-GGR pairs only  probability = 5/9 If it does each of the above half the time the probability is half way between 5/9 and 1. I do know that the source can only produce 8 types of atoms. See below.

25. 24 February 2010Modern Physics II Lecture 725 Kind of atom going left Probability of different color flashes RRR1 GGG1 RRG5/95/9 RGR5/95/9 GRR5/95/9 RGG5/95/9 GRG5/95/9 GGR5/95/9 So, in any instruction set scheme, the detectors will flash different colors with a probability between 5/9 and 1.

26. 24 February 2010Modern Physics II Lecture 726 Experimentally, the detectors flash different colors with probability ½. The assumption of local determinism has produced a conclusion which is violated in the real world and hence must be wrong. Probability is not just the easiest way out of the conundrum of projection, it is the only way out.