1. Blaylock - Williams College 4/17/15 Wringing John Bell vocabulary the EPR paradox Bell’s theorem Bell’s assumptions what does it mean? Guy Blaylock Williams College 4/17/15

2. Blaylock - Williams College 4/17/15 Characteristics of a Garden Variety Classical Scientific Theory locality – actions at one location do not immediately have any effect at a separate location. (counter) factual definiteness – any measurable quality of a physical system has a single well-defined value when it is measured (factual) or before it is measured (counterfactual). determinism – complete knowledge of the current state of a physical system is sufficient to determine the future state of the system.

3. Blaylock - Williams College 4/17/15 Characteristics of Orthodox QM Orthodox QM obeys none of these characteristics… When a wave function collapses, it collapses everywhere at once. (nonlocal) When a physical system is in a state of superposition, it is not in a single well-defined state. (indefinite) When a system collapses to a single final state among multiple possibilities of a superposition, it does so randomly. (indeterminate)

4. Blaylock - Williams College 4/17/15 EPR à la Bohm (almost) Consider a pair of photons produced with the same polarization. Measure the polarization of one. The polarization of the other must always turn out to be the same (in QM this is the “ twin state ” ). 1. atoms 2. downconverters 3. subatomic decays/annihilation There are several sources that do this: down conversion crystal polaroid filter

5. Blaylock - Williams College 4/17/15 Quantum Twin State QM explains the EPR experiment using the quantum twin state: Prior to measurement, the two-photon system is not in one definite state; it’s in a superposition of V 1 V 2 and H 1 H 2. When a measurement is made, both photon polarizations collapse, nonlocally. The final choice, V 1 V 2 or H 1 H 2, is determined randomly.

6. Blaylock - Williams College 4/17/15 EPR logic If one can determine certain parameters (such as polarizations in Bohm’s EPR) without interfering with the system, those parameters must be‘real’. If a theory is to be considered complete, it should predict all real parameters, including the polarizations in Bohm’s EPR experiment. QM does not predict the polarizations.  QM is not complete! One could determine the polarization of photon 2 simply by looking at photon 1, without disturbing photon 2. Similarly, one could determine the polarization of photon 1 without disturbing it.

7. Blaylock - Williams College 4/17/15 EPR caveat Original statement of EPR “ No reasonable definition of reality could be expected to permit this. ” “…one would not arrive at our conclusion if … [the values of the second system] depend upon the process of measurement carried out on the first system”

8. Blaylock - Williams College 4/17/15 newspapers Why can’t the photons just be generated with some definite polarization, like two newspapers sent to different places?

9. Blaylock - Williams College 4/17/15 Bell’s Theorem 1964 - John S. Bell publishes “ ON THE EINSTEIN PODOLSKY ROSEN PARADOX ” Physics 1 (1964) p.195-200. Reprinted in Speakable and Unspeakable in QM Exploring the correlations between different measurements leads to new constraints based on common sense (Bell inequalities). e.g. What if we measured polarizations at arbitrary angles  1,  2 ? QM makes predictions about the correlations of polarizations that are different from the predictions of ‘ common sense ’ theories!

10. Blaylock - Williams College 4/17/15 QM prediction What is the probability of getting the same measurement (i.e. both transmitted or both absorbed)? Prob( M 1 (  1 ) = M 2 (  2 ) ) = cos 2 (  2 -  1 ) What should we expect from Quantum Mechanics? down conversion crystal 11 22

11. Blaylock - Williams College 4/17/15 Amplitude filtering For a wave impinging on a filter at an arbitrary angle…     Acos(      A …the amplitude that passes through is Acos (      The probability that a photon passes through is cos 2 (     .

12. Blaylock - Williams College 4/17/15 Common Sense What should we expect from Common Sense? This is where Bell comes in.

13. Blaylock - Williams College 4/17/15 Arbitrary angle Prob( M 1 (  ) = M 2 (   ) ) = 0% coincidence For     between 0 and 90 o, the coincidence is between 100% and 0% In particular, let  be some angle such that Prob( M 1 (  ) = M 2 (  ) ) = 75% coincidence; mismatch 25% Prob( M 1 (  ) = M 2 (  ) ) is 100% coincidence A series of photon pairs will show a sequence of both being absorbed, or both transmitted, never one absorbed and one transmitted. F  :  F  :  ATTAATATATTTATAAAATATTAT ATTAATATATTTATAAAATATTAT

14. Blaylock - Williams College 4/17/15 AAAAATATTTTTATATTATATATT ATTTATATAATAATTATATATTTT Common Sense Prediction      avg mismatch 25% F  :  F  :        avg mismatch 25%  F  :  F  :       avg mismatch  50% F  :  F  :  Apply this “ common sense ” to several different cases: Bell ’ s Inequality ATTAATATATTTATAAAATATTAT ATTTATATAATAATTATATATTTT AAAAATATTTTTATATTATATATT ATTAATATATTTATAAAATATTAT

15. Blaylock - Williams College 4/17/15 QM for 30/60 o For         QM says the coincidence should be: cos 2 (30 o + 30 o ) = cos 2 (60 o ) = 25% mismatch = 75%, certainly not less than 50% QM disagrees! For  = 30 o, coincidence is 75%, mismatch 25% (Remember cos 2 (30 o ) = 0.75)

16. Blaylock - Williams College 4/17/15 Experiment vindicates QM 1972 -- John Clauser (Berkeley) performs a Bell measurement using mercury vapor atoms that produce twin state photons. QM wins but the experiment does not rule out slower than light speed interactions. 1982 -- Alain Aspect performs an experiment with extremely fast acousto-optical switches to demonstrate faster-than-light effects. 1997 -- Nicolas Gisin uses Swiss telecom network optical fiber and a downconverter to demonstrate quantum effects over a distance of 7 miles. …and many more.

17. Blaylock - Williams College 4/17/15 AAAAATATTTTTATATTATATATT ATTTATATAATAATTATATATTTT Why is Bell ’ s inequality violated?      avg mismatch 25% F  :  F  :        avg mismatch 25%  F  :  F  :       avg mismatch  50% F  :  F  :  Why is Bell’s inequality violated? ATTAATATATTTATAAAATATTAT ATTTATATAATAATTATATATTTT AAAAATATTTTTATATTATATATT ATTAATATATTTATAAAATATTAT Assume that rotating F 2 from    to    does not affect what happens at F 1. locality!

18. Blaylock - Williams College 4/17/15 … the other assumption 1.The two photons always yield the same polarization. easily verified by experiment 2.There exists an angle , such that mismatch = 25%. easily verified by experiment 3.The mismatch for      is the same as for      (i.e. rotational symmetry) easily verified by experiment 4.The mismatch rate between  and  is still 25% even when we don’t make the measurement for  Counterfactual definiteness (CFD). QM says there is more than one possibility for each measurement. The  sequence that disagrees with  by 25% is not the same as the  sequence that disagrees with  by 25%.

19. Blaylock - Williams College 4/17/15 Common Sense Prediction      avg mismatch 25% F  :  F  :        avg mismatch 25%  F  :  F  :  ATTAATATATTTATAAAATATTAT ATTTATATAATAATTATATATTTT AAAAATATTTTTATATTATATATT ATTAATATATTTATAAAATATTAT In QM the two sequences for    and    don’t need to be the same!

20. Blaylock - Williams College 4/17/15 Conclusions The universe is nonlocal or non-CFD, or both. There are interpretations of QM that follow each. Whatever you decide, the world is

21. Blaylock - Williams College 4/17/15 underlying realities Orthodox/Copenhagen - (Bohr, Heisenberg) non-CFD, non-deterministic & non-local Bohm’s interpretation - (Bell, Bohm, deBroglie) definite, deterministic & non-local Pilot waves direct the particles non-locally. Many Worlds - (DeWitt, Everett) local, deterministic & indefinite No collapse; every possibility exists as a part of the superposition. Agnostic - (many contemporary scientists) Who knows, who cares. Makes no sense to ask what is going on outside of observation.

22. Blaylock - Williams College 4/17/15 More on Definiteness CFD might seem to imply‘realism’. This is probably what EPR were trying to say with their ‘elements of reality’. The reverse is not true. Realism does not imply CFD. If one considered a photon wave function (which may be a superposition) to be real, it still would not imply a definite polarization. Definiteness does not imply determinism. The definite characteristic could evolve randomly. BTW, if a theory is local it must also be deterministic. (deduce from EPR expt.)

23. Blaylock - Williams College 4/17/15

24. History of the Worlds 1957 Hugh Everett writes a thesis on the “relative state” interpretation of QM [Hugh Everett III, “ Relative State ’ Formulation of Quantum Mechanics ”, Rev. Mod. Phys. 29, 454-462 (1957)] The essence of Everett ’ s many worlds interpretation is the same as orthodox QM except that collapse does not happen. Superpositions persist. Bryce DeWitt popularizes, embellishes and somewhat misrepresents the concept in the “many worlds” interpretation [Bryce S. DeWitt, “Quantum mechanics and Reality”, Physics Today 23, 30-35. (1970)] “… every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth in myriads of copies of itself. ”

25. Blaylock - Williams College 4/17/15 A wave that moves only in a plane is called plane-polarized or linearly polarized. polarizing filters A vertical filter allows a vertically polarized wave to pass, … but blocks a horizontally polarized wave,… and let ’ s the vertical part of a 45 o wave through. vertically polarized

26. Blaylock - Williams College 4/17/15 polarized photons Think of photon polarization as a binary quantity. A polarizer provides a way of measuring it. For light waves, the plane of oscillation defines the polarization. A photon ’ s polarization is determined by whether it does or does not pass through a polarizing filter. A photon that passes through a vertical filter is “ vertically polarized ”. …but it will not make it through a horizontal filter. It will pass through any number of other vertical filters.

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